{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":59034,"title":"Compute the maximum length of a contaminant plume in groundwater","description":"Problem statement \r\nWrite a function to compute the maximum length of a contaminant plume for steady, one-dimensional transport in groundwater. The leaking source has a constant concentration of , and the end of the plume for each contaminant is taken to be where the concentration equals some limit (e.g., the U.S. Environmental Protection Agency’s maximum contaminant level, or MCL). Assume the aquifer to be infinite and initially clean. Relevant properties of the confined aquifer are the hydraulic conductivity , the magnitude of the head gradient , effective porosity , bulk density , and soil organic fraction . Along with the MCLs, the properties of the contaminants provided to the function are the half life  and the octanol-water partition coefficient .\r\nCompute the longitudinal dispersion coefficient as , where  is the average linear velocity and  is the longitudinal dispersivity. The variable aL will be specified as either a number or ‘X\u0026E’. In the latter case, compute the longitudinal dispersivity with the empirical formula of Xu \u0026 Eckstein (1995):\r\n\r\nwhere  is in meters if the flow length  is in meters. Take the flow length to be the length of the plume—that is, guess a plume length, compute the new plume, and repeat until the plume length stops changing.\r\nBackground\r\nContaminants in groundwater are subject to advection, retardation, dispersion, and degradation. If the transport is assumed to be one-dimensional, then the variation of the concentration  of the contaminant in time  and spatial coordinate  can be computed with\r\n\r\nThe four terms represent the effects of unsteadiness, advection, dispersion, and degradation, where . Retardation is included in the retardation coefficient . The maximum length occurs when all processes have had sufficient time to operate—that is, in steady state. In that case, the first term can be ignored, and the equation becomes a second-order linear ordinary differential equation with constant coefficients, which can be solved with the boundary conditions  and . ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 605.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 302.95px; transform-origin: 407px 302.95px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.95px 8px; transform-origin: 64.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 151px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 75.5px; text-align: left; transform-origin: 384px 75.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 350.983px 8px; transform-origin: 350.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the maximum length of a contaminant plume for steady, one-dimensional transport in groundwater. The leaking source has a constant concentration of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"18\" height=\"20\" alt=\"C0\" style=\"width: 18px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.525px 8px; transform-origin: 157.525px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the end of the plume for each contaminant is taken to be where the concentration equals some limit (e.g., the U.S. Environmental Protection Agency’s \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003emaximum contaminant level\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 325.967px 8px; transform-origin: 325.967px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, or MCL). Assume the aquifer to be infinite and initially clean. Relevant properties of the confined aquifer are the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.358px 8px; transform-origin: 114.358px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the magnitude of the head gradient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"49.5\" height=\"18.5\" alt=\"|dh/dx|\" style=\"width: 49.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.2083px 8px; transform-origin: 58.2083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, effective porosity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"20\" alt=\"ne\" style=\"width: 15px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7833px 8px; transform-origin: 42.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, bulk density \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"rhob\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.125px 8px; transform-origin: 29.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and soil organic fraction \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17.5\" height=\"20\" alt=\"phio\" style=\"width: 17.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 302.217px 8px; transform-origin: 302.217px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Along with the MCLs, the properties of the contaminants provided to the function are the half life \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"26.5\" height=\"20\" alt=\"T_1/2\" style=\"width: 26.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the octanol-water partition coefficient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"22.5\" height=\"20\" alt=\"Koc\" style=\"width: 22.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32.5px; text-align: left; transform-origin: 384px 32.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 155.875px 8px; transform-origin: 155.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute the longitudinal dispersion coefficient as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"65.5\" height=\"20\" alt=\"DL = aLvL\" style=\"width: 65.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.8917px 8px; transform-origin: 24.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"123.5\" height=\"20\" alt=\"vL = (K/ne)|dh/dx|\" style=\"width: 123.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 105.808px 8px; transform-origin: 105.808px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the average linear velocity and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17\" height=\"20\" alt=\"aL\" style=\"width: 17px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 136.417px 8px; transform-origin: 136.417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the longitudinal dispersivity. The variable \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eaL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 121.367px 8px; transform-origin: 121.367px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be specified as either a number or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.25px 8px; transform-origin: 19.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e‘X\u0026amp;E’\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.275px 8px; transform-origin: 88.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. In the latter case, compute the longitudinal dispersivity with the empirical formula of Xu \u0026amp; Eckstein (1995):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARUAAAAqCAYAAACdtc8uAAAMQ0lEQVR4Xu2dW+i+2RTHZ+5JuCJRuKARyjGimUmmRJJySvqHHC4kTabhQpM0JkyTXDiEJjlLEikzQqQcknNcUEhcIY171qd5vv6rbR/Wfp7nfd/f//2vp1a/3+99n2ftvdde+7vXaT+/a6/JKyWQEkgJ7CiBa3fklaxSAimBlMA1CSqpBCmBlMCuEkhQ2VWcySwlkBJIUEkdSAmkBHaVQILKruJMZimBXSXwcuP2NqNnLFx/ZD/fYvSTyVYeYvf/2uhrRm9sPEtbdy3tfWHAv8svQWVyds70dpQEZXvvmY7vogzrHRMyfpPd+1ajDxr90+i1Rs9fBnKT/bxnYlAftXvfYPSxCqjA86XL97B8hdEIVHr8MlA7MTHneiuA8g2jNTvgucrkUOOS5fECa+Afg0b+at8/x+gP7r5vLsACoAAsketpdtO3jR7QABW+x/L5oREW0QhURvwSVCKzcsb3ACg/MHrNoli9oaJMzzNKa2abQsgCeXYHWGQ9lK4KoPR5o98ZPT7Yjd/afbg9b2+AithEQWXIL92f2MygCJfcrY+03z9tdEvs8eZd4vsvu+NBRvDld5RgxJtnX2L0LCN2ob8Zfd/ozR1lLTuCIn2v0xZt3GDEjvkwo38bPXDjmK/kx99nnX+ukWIcGguyRx++ZBSJd8DnUUaAxMwF2GCtRC0VtfOJ5bma+6P2I6AS4peg0p9S7eSPsNtA+o8st8sE5M8nG3kTNaIk4guQXFqURM+xkD9s1NuN8HlfttwDCF1nBLBwsfAjfUJBXm308E6HUeIHG7E7ivfVDCoSFbv145Y/AJTSTRnpgAKdBGFH8QvPS7rxTvtwZDE+xu75utELjfgdMNoCKmF+CSr96Rd61yaDoNvtyyKeXWjii1UhoPI96QXC+I7dkiCeD9apP/D5olFvF0Sp/2TkgbInCfX3ardUJCPiHVhuXJEFXpMtAPF+IyyWUXxFzwNATzTquU66lzkjm8MzsnC2gEqYX4JKeylpV2Ah3WhUM2vvs8+xEFCOkbuilkD83y9/PL3BV0rALugtCe0WLaVSIG+0+CNWipdMgsplaQDIf3fCac1hW7Pu/0bAzsY0sjq4X3oTyfywwVxv9EojAGsrqEzxS1BpT712o3Jh+ye0iPksKktNMM+0FET3lODA5P7UqJVOBCywPnp9pl3A8LNGrZqFUioJKpclos2GT5DzE5aF29ak9jdYEbhOPRdUTzMHXzUaAZBcK++SbQGVaX7RhbBGYFfyM8RMfrwMoBcU0yLm1lEqTvLwlkqLt1yZkRtTyrhbP7DcrAxCtL88lqByWdKKZ/HJ7PyU8yWAGlk7zCtXZBNQjIbgrK6n2C9YROjbnUbEAMs4YCtQO80vQaUOfR4sej6ztzp6/mrZiiaQz8vntDMQp6EoaabICeuKqxc4FPA81O6L+vIRUAEscQGftPSBTBZXJCPFmG81IlbEReD5L0a/NPqAUSSjUp/J/T/18ZRWTCzaqjavno4pAxfN6nndavWjpqstUJnmFwUVFs/NRkp5knH4pJFKiCN+XlTQF+E+vxtFQYUS6mcGO+8LiHiEZymIItNCxJ6rDMSOWNNngn6jIjYpSXTuaXcEKrKsSmX1wePWAvSZsBcvAAJAAUYKhmrs0VTqSFZrv/dWJjweazSb+Svb/o990LJ4VHJQFsshMzKECsajT/SjtUlscX9qsuryGykWnf+cEUxYXOxydNy7B/j9MxHsNROK4LdeMwrp0TkKKqPgaNn/Elh4nlgH9Q53dBSk5IOif8aI2gl4oGy9oDFt/MYoCoC01wOVUQp85CIKwMtgt9w02mfRYc5Trn5Kq8WD5EwBWk930e3ahqTxM3Yydf6iFEDpaJ9QaGUhI6CiNHnELV4NKtpByMfXFpYW+sxiXQsMpwSVnhXmMwGzoIIsABaCb35Hjlo8TOy7FzAp5dpT+JYS9+amBSrKYJABa4FvT0b+u9rzcjWOoWMR3fSB+Rl3dyRbPAAfrC03nPJ5HyD2BXHK9pT390CAtl5vxNkgLnTnNqN7jVZZPi1LxQNKS3ha6Gvz9JFJPNU93lIZBdEkhzWgwmR/2Yj4AeCtK1rApvvh8zojCuJ09eYtClzi1QIVnwnpycm7k34n9DGpmh5FU+TH0hOVENBeZEeP9GuNOxrhe7J7WqCiyWylzLwy7OFXnkwAjYaP4f5oQWrxY+5+3Gi2MtYPwbsMLZDb01JR0Jc+9EDFuw3ezRmBilynNYC9t075vu7p8l8VoDKaaCZLyoSpFKnu23uCD83PL5ZoTGVm928dDPMWImOc4SmZeKugttD3BJWoRed1yrsyPjZXG6tApef+KGhJpWnrkJ1OB3PO6UVGkbNVpY752NCaeWnpLLEMrugBwUPr/mb+NUtFitKyUrwf3YpaEzwkp04hFhfITrEVO/EpA21RgfmdNQoqMzULihXUMiIlsMxagt5aqYEKbf/ZaI9ArQeVXuypBSrMRw+YZDHXXA29A4YT1riOrTiSwED9U8r+V/ZM9PUBZT9nKqhHOrcG5Ec8T/p9CSo+ZdZaJB6xR3l6+aBbg1rHDtT6HbQHFpGUaTnBnnfLZfDAMBuz8tW4tazcGnO7FVNZU89Tjkfvc1H2SkcikC33tip/eY4UvA7L1UBF+lxaFpq3aFxkbWk+8hkd30C3t66Pk4JI2XgJKj7wVgMMJunnRvL7ewVUHqC21rEcG1SQk6yJyGnhmcCq37V7cYi1gXABUstlEBDMWEAtUPHg13MJvF7VdEHWGRYUJ7e5fmEUsWwlz9o8tSqM9UzUjfHjjJbmq8akZxGqH6PN+UKBxqgzJaj0ago08RS+sasongJ4PNpI5bxqU4q05mj4qN/H+N4vhNYC7FliyOupRmVFrN/1ejulQGUWkJkHiqVIE5ZzgtxkKUV3aZ7p1an4CtPWJqM4T23hy1K529qpndgezXUPVNTv2lgl30hlsY+xRdLb0cOCsphmAH4kj5N/37NUvJkqQPmU9Vg+LG4BJdTUWagS0g9IihSZhJMLotEBKWXNPPWgWR4q83Gn2kIayaYVyNXuRzFUrWxbfRr5/AABFavRlwT1QMVbXjVXUbJAxLVjB1sDlT1QEXD0QCUC2h44R66Kj4mNyhGQK9dMfOuirpX/9asEFb8YuAkBcr3K6HYjTkhqorBAuC4Zlbsxn2sXn40JXCSheQXxiqniJMZYA9Qy/Vi+OsHzLReiCuKQQ8nbF1+pevZbi8BYsGQ2PrTMU0+OWKSAUqQSutSJ2s7ecptlhVDcRaFeaYmUcqLSVxfAqUrS3hvVtoLKyGLzfaRvOlJRFoZhsVMnhL4THhhlRhUeOCvXBwHVsj8IkTd4E1FHcXkpsj/UJcUGSDjxWAMUH4y80k07FgaH3ViwXHr1I+lJFmfr7AcmM2DcCjTCS5YHB+j8goL3HUal4iLX9xgxR7pQXmIRXzECoCKHBAUUo5c0MQbG7St+2UxIyWK6+7Z0oFByok/I6o8DOXmgdMP6v19bFsKhQEUZTBa9Yoi9/pXfjaxFdAdZnU0qWQIYnf2ZEaK/V77i6L0ea/nnc9sloGK7iLWyvbU2B4ASt/o2I47o6+K0s4K2WDoAW82d6IGKrOWe+zOyVA4xdiU8Zk+hH6Ivu/M8FKj0YhG7DyIZrpaAArnR2MrqhhoP0i6vPLxkVLN4/WNYNN81Kl9SdIxA7d7jZn30Xji+d3tH5XcIUIlkN9iduK6EQrijTsgJGkPB7zZak3nZ0l3t1tET07hi/P+aMqPVAxVlM0tXpPfMljFFnqVPa96kH+F9Ie45BKgoc9FLJRPxn31fyIUQ2Jl2goX6nSMDy4yLLBepdiSkBxCj4rdjJxGIofEvT05lGR5FfQ8BKkqX1uIpOqfBm8m2vNvzKMK5yhpB0Wt1LYcSg88YEWwmOeADzarz4fQ153pa//CslX5Xv1tl+gSSy5cfHWqs4ntsGR96PFX+e4IKSkBKDVNT0XLSb/iOXJh8TOLs2+dPIphs9CgS8EVltQaVfazV5EjfsHjJVHKhe7X0MwD2LiNegEUAmGrdWnbtKIM+90b2BJVzl1WO7zASUH3H9cbel+j/zP6OpsgP07PkukoCCSqrxJYPpQRSAi0JJKikbqQEUgK7SiBBZVdxJrOUQEogQSV1ICWQEthVAgkqu4ozmaUEUgIJKqkDKYGUwK4S+C/FW5JYJTQY7QAAAABJRU5ErkJggg==\" width=\"138.5\" height=\"21\" alt=\"aL = 0.83(log10(L))^2.414\" style=\"width: 138.5px; height: 21px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17\" height=\"20\" alt=\"aL\" style=\"width: 17px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.175px 8px; transform-origin: 92.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is in meters if the flow length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eL\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 250.083px 8px; transform-origin: 250.083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is in meters. Take the flow length to be the length of the plume—that is, guess a plume length, compute the new plume, and repeat until the plume length stops changing.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.15px 8px; transform-origin: 383.15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eContaminants in groundwater are subject to advection, retardation, dispersion, and degradation. If the transport is assumed to be one-dimensional, then the variation of the concentration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.0083px 8px; transform-origin: 84.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the contaminant in time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.3583px 8px; transform-origin: 72.3583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and spatial coordinate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.1667px 8px; transform-origin: 15.1667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e can be computed with\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 39.9px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19.95px; text-align: left; transform-origin: 384px 19.95px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"170\" height=\"40\" alt=\"dC/dt + (vL/R)dC/dx = (DL/R) d^2C/dx^2 - lam C\" style=\"width: 170px; height: 40px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 108px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 54px; text-align: left; transform-origin: 384px 54px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 311.05px 8px; transform-origin: 311.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe four terms represent the effects of unsteadiness, advection, dispersion, and degradation, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"81.5\" height=\"20\" alt=\"lam = ln(2)/T_1/2\" style=\"width: 81.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Retardation is included in the retardation coefficient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"122\" height=\"20\" alt=\"R = 1+rhobKoc phio/ne\" style=\"width: 122px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 151.317px 8px; transform-origin: 151.317px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe maximum length occurs when all processes have had sufficient time to operate—that is, in steady state. In that case, the first term can be ignored, and the equation becomes a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/51387\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003esecond-order linear ordinary differential equation with constant coefficients\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.9083px 8px; transform-origin: 94.9083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which can be solved with the boundary conditions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"67.5\" height=\"20\" alt=\"C(0) = C0\" style=\"width: 67.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"66\" height=\"18.5\" alt=\"C(infinity) = 0\" style=\"width: 66px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Lp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\n%  See the text suite for the definitions of the parameters\r\n   v  = K*dhdx/ne;\r\n   Lp = (C0-Clim)/v;\r\nend","test_suite":"%%  Dieldrin and styrene\r\nC0   = [1 15];                  %  Source concentrations (mg/L)\r\nClim = [2e-4 0.1];              %  Maximum contaminant levels (mg/L)\r\nK    = 87.5;                    %  Hydraulic conductivity (m/d)\r\ndhdx = 0.002;                   %  Magnitude of the hydraulic gradient \r\nne   = 0.25;                    %  Effective porosity\r\nrhob = 2.5;                     %  Bulk density (g/cm3)\r\nphio = 0.005;                   %  Soil organic fraction\r\nKoc  = [25120 380];             %  Octanol-water partition coefficient (mL/g)\r\naL   = 'X\u0026E';                   %  Dispersivity method\r\nTh   = [1825 182];              %  Half lives (d)\r\nLp_correct = [20.76 58.95];\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  Benzene, toluene, ethylbenzene, and p-xylene\r\nC0   = 30;                      %  Source concentration (mg/L)\r\nClim = [0.005 1 0.7 10];        %  Maximum contaminant levels (mg/L)\r\nK    = 11;                      %  Hydraulic conductivity (m/d)\r\ndhdx = 0.04;                    %  Magnitude of the hydraulic gradient \r\nne   = 0.22;                    %  Effective porosity\r\nrhob = 2;                       %  Bulk density (g/cm3)\r\nphio = 0.005;                   %  Soil organic fraction\r\nKoc  = [97 242 622 552];        %  Octanol-water partition coefficient (mL/g)\r\naL   = 'X\u0026E';                   %  Dispersivity method\r\nTh   = [300 20 120 190];        %  Half lives (d)\r\nLp_correct = [1501.21 20.69 54.12 24.98];\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  Glyphosate\r\nC0   = 13.9;                    %  Source concentrations (mg/L)\r\nClim = 0.7;                     %  Maximum contaminant level (mg/L)\r\nK    = 30;                      %  Hydraulic conductivity (m/d)\r\ndhdx = 0.0005;                  %  Magnitude of the hydraulic gradient \r\nne   = 0.18;                    %  Effective porosity\r\nrhob = 1.9;                     %  Bulk density (g/cm3)\r\nphio = 0.001;                   %  Soil organic fraction\r\nKoc  = 4e-5;                    %  Octanol-water partition coefficient (mL/g)\r\naL   = 2.8;                     %  Dispersivity method\r\nTh   = 300;                     %  Half life (d)\r\nLp_correct = 115.59;\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  1,4-dioxane\r\nC0   = 10;                      %  Source concentrations (mg/L)\r\nClim = 3e-4;                    %  Limit set by Massachusetts (mg/L)\r\nK    = 7.77;                    %  Hydraulic conductivity (m/d)\r\ndhdx = 0.01;                    %  Magnitude of the hydraulic gradient \r\nne   = 0.21;                    %  Effective porosity\r\nrhob = 1.8;                     %  Bulk density (g/cm3)\r\nphio = 0.003;                   %  Soil organic fraction\r\nKoc  = 1;                       %  Octanol-water partition coefficient (mL/g)\r\naL   = 3;                       %  Dispersivity method\r\nTh   = 1;                       %  Half life (d)\r\nLp_correct = 16;\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  Benzene\r\nC0   = 2;                       %  Source concentrations (mg/L)\r\nClim = 0.005;                   %  Maximum contaminant level (mg/L)\r\nK    = 11;                      %  Hydraulic conductivity (m/d)\r\ndhdx = 0.0035;                  %  Magnitude of the hydraulic gradient \r\nne   = 0.1;                     %  Effective porosity\r\nrhob = 1.7;                     %  Bulk density (g/cm3)\r\nphio = 0.002;                   %  Soil organic fraction\r\nKoc  = 97;                      %  Octanol-water partition coefficient (mL/g)\r\naL   = 6;                       %  Dispersivity method\r\nTh   = 300;                     %  Half life (d)\r\nLp_correct = 263.93;\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  p-xylene\r\nC0   = 200;                     %  Source concentrations (mg/L)\r\nClim = 10;                      %  Maximum contaminant level (mg/L)\r\nK    = 11;                      %  Hydraulic conductivity (m/d)\r\ndhdx = 0.0035;                  %  Magnitude of the hydraulic gradient \r\nne   = 0.1;                     %  Effective porosity\r\nrhob = 1.7;                     %  Bulk density (g/cm3)\r\nphio = 0.002;                   %  Soil organic fraction\r\nKoc  = 552;                     %  Octanol-water partition coefficient (mL/g)\r\naL   = 6;                       %  Dispersivity method\r\nTh   = 190;                     %  Half life (d)\r\nLp_correct = 26.74;\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  Ethylbenzene\r\nC0   = 100;                     %  Source concentrations (mg/L)\r\nClim = 0.7;                     %  Maximum contaminant level (mg/L)\r\nK    = 11;                      %  Hydraulic conductivity (m/d)\r\ndhdx = 0.0035;                  %  Magnitude of the hydraulic gradient \r\nne   = 0.1;                     %  Effective porosity\r\nrhob = 1.7;                     %  Bulk density (g/cm3)\r\nphio = 0.002;                   %  Soil organic fraction\r\nKoc  = 622;                     %  Octanol-water partition coefficient (mL/g)\r\naL   = 6;                       %  Dispersivity method\r\nTh   = 120;                     %  Half life (d)\r\nLp_correct = 29.83;\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  Nastene, phylthene, siccanol (fictitious chemicals)\r\nC0   = [10 10 20];              %  Source concentrations (mg/L)\r\nClim = [1 2 0.1];               %  Limits (mg/L)\r\nK    = 0.2;                     %  Hydraulic conductivity (m/d)\r\ndhdx = 0.008;                   %  Magnitude of the hydraulic gradient \r\nne   = 0.08;                    %  Effective porosity\r\nrhob = 2;                       %  Bulk density (g/cm3)\r\nphio = 0.003;                   %  Soil organic fraction\r\nKoc  = [15 80 2];               %  Octanol-water partition coefficient (mL/g)\r\naL   = 2;                       %  Dispersivity method\r\nTh   = [30 100 475];            %  Half lives (d)\r\nLp_correct = [2.6 1.83 72.39];\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-10-01T15:59:04.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-10-01T15:47:36.000Z","updated_at":"2026-02-12T14:03:58.000Z","published_at":"2023-10-01T15:59:04.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the maximum length of a contaminant plume for steady, one-dimensional transport in groundwater. The leaking source has a constant concentration of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the end of the plume for each contaminant is taken to be where the concentration equals some limit (e.g., the U.S. Environmental Protection Agency’s \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emaximum contaminant level\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, or MCL). Assume the aquifer to be infinite and initially clean. Relevant properties of the confined aquifer are the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the magnitude of the head gradient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"|dh/dx|\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e|dh/dx|\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, effective porosity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ne\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, bulk density \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"rhob\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rho_b\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and soil organic fraction \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"phio\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\phi_o\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Along with the MCLs, the properties of the contaminants provided to the function are the half life \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"T_1/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT_{1/2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the octanol-water partition coefficient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Koc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_{oc}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute the longitudinal dispersion coefficient as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"DL = aLvL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD_L = a_L v_\\\\ell\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"vL = (K/ne)|dh/dx|\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_\\\\ell = (K/n_e)|dh/dx|\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the average linear velocity and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"aL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the longitudinal dispersivity. The variable \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eaL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will be specified as either a number or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e‘X\u0026amp;E’\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. In the latter case, compute the longitudinal dispersivity with the empirical formula of Xu \u0026amp; Eckstein (1995):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"aL = 0.83(log10(L))^2.414\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_L = 0.83(\\\\log_{10}L)^{2.414}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"aL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is in meters if the flow length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is in meters. Take the flow length to be the length of the plume—that is, guess a plume length, compute the new plume, and repeat until the plume length stops changing.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eContaminants in groundwater are subject to advection, retardation, dispersion, and degradation. If the transport is assumed to be one-dimensional, then the variation of the concentration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the contaminant in time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and spatial coordinate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e can be computed with\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dC/dt + (vL/R)dC/dx = (DL/R) d^2C/dx^2 - lam C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{\\\\partial C}{\\\\partial t}+\\\\frac{v_\\\\ell}{R}\\\\frac{\\\\partial C}{\\\\partial x}=\\\\frac{D_L}{R}\\\\frac{\\\\partial^2 C}{\\\\partial x^2} - \\\\lambda C\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe four terms represent the effects of unsteadiness, advection, dispersion, and degradation, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"lam = ln(2)/T_1/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lambda = \\\\ln2/T_{1/2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Retardation is included in the retardation coefficient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R = 1+rhobKoc phio/ne\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR = 1+\\\\rho_b K_{oc} \\\\phi_o/n_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe maximum length occurs when all processes have had sufficient time to operate—that is, in steady state. In that case, the first term can be ignored, and the equation becomes a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/51387\\\"\u003e\u003cw:r\u003e\u003cw:t\u003esecond-order linear ordinary differential equation with constant coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, which can be solved with the boundary conditions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C(0) = C0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC(0) = C_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C(infinity) = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC(\\\\infty) = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59002,"title":"Compute piezometric head in a leaky confined aquifer","description":"Problem statement\r\nWrite a function to compute the piezometric head  in a leaky confined aquifer and the position of a groundwater divide  given the boundary heads  at  and  at  and head  (assumed constant) in the unconfined aquifer above the leaky confining layer. The hydraulic conductivity and thickness of the aquifer are  and , and the hydraulic conductivity and thickness of the leaking confining layer are  and . If there is no groundwater divide, set xd to the empty set []. \r\nBackground\r\nAs in other problems in this series, the movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. For steady, one-dimensional flow, conservation of mass applied to the control volume indicated by the dashed line says that the flow into the volume equals the flow out of the volume. If  is the specific discharge in the aquifer, or the flow per unit area, the flow into the left side is , and the flow out of the right side is . If  is the specific discharge through the leaky confining layer, the flow into the volume through the top is . Then the mass (or volume) balance is\r\n\r\nRearranging, dividing by , and taking the limit as  goes to zero gives\r\n\r\nDarcy’s law allows the specific discharge through the aquifer to be written as  and the specific discharge through the leaky confining layer to be approximated as . Then \r\n\r\nOne can solve this second-order linear ordinary differential equation using the boundary heads to get the piezometric head in the aquifer. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 939.1px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 469.55px; transform-origin: 407px 469.55px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 107px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 53.5px; text-align: left; transform-origin: 384px 53.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 153.9px 8px; transform-origin: 153.9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the piezometric head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211.233px 8px; transform-origin: 211.233px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a leaky confined aquifer and the position of a groundwater divide \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"20\" alt=\"xd\" style=\"width: 15px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e given the boundary heads \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAACRUlEQVRYR+1WuUoEQRTczY00MlLQQNHAxANEERGNTD1+wCMwVNDAUEExMPKIBY/MUFNBPDAQFAw0EEQjTTTXKugHr3tnpmd2e3cRtqFolunt6n5V773O56o48lXkztXIqxL9fxP2FhOel1BhSrr5KEhGgEGgA6gDNoGlSpCTox44BHgQjjHgvFLk5DkGJoAPoBP4qiT5O8gazY1582DD5/ZuMN0YtnnMu8GYsZGPfBlr1gxhK+ZgTueePvIzY7YnzP0h9U5D/o1FTLF9YNZEgM7fBtqAH2AYuC1GDl+e8+YcUwBdvweMAwcAPcCDXQN9ock3sOGiuV0T5h1DsIKZ2ksWlIX8CgS95manmIeAaYB5rrNAS5IpAHFhZ2X7NDudYB4wELfrLBBJMhFzcRz5JL4dqd3csipZQMNREl31eHCRiFvw+wJQYMo4chprxpBHhVWywNWbxK/ApZJIotTjHiCOXMzEm3UBurhovWm+dRUh6QNupHjYN6BdaxNFzr79rPSmBHrEVT3tkwZHCjGvdago8jmlWVQLFb0l5IwE+/4dwG+shtYN8VvS1pIwitzXQkVvhpzeeACYDayArAtJ5JZHoshlcz4a3Baq9eZGHKsA18rtksitby65r4XSDxcA+zvJhZiHKJnc8Vamn2LEom+eic1ZzG5XsuFKOcCv+bMrp6SaVYp9j4msB0kqMjSy9QANTS7l9RFE0uPFCwUNKDQ5I8WM4LuPDeUeaAa2TDpakSwHeWqpauSpQxVyYS3sIaOZeq8/pdSJKRBBS50AAAAASUVORK5CYII=\" width=\"15.5\" height=\"20\" alt=\"h0\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17\" height=\"20\" alt=\"hL\" style=\"width: 17px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"18\" alt=\"x = L\" style=\"width: 39px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.0667px 8px; transform-origin: 33.0667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eH\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 164.933px 8px; transform-origin: 164.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (assumed constant) in the unconfined aquifer above the leaky confining layer. The hydraulic conductivity and thickness of the aquifer are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59.125px 8px; transform-origin: 59.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the hydraulic conductivity and thickness of the leaking confining layer are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAAkCAYAAADl9UilAAACSklEQVRYR+2Wuy9EQRTGd3saKhoSGolG4ZFIFAoaKglCIlt5/AEk1IIQtUct8WhESUTt0RCNgoSGioY/wPfJnORkzNy5s+4mK7mTfNmZu2dmfvebmTO3WKjSUqxSrkIOFrsyuWP/ybFOwC5Dm9CZDR5aygF0GIGGoQar8xHat9Cqeb6O3z6oW8W9ob4HrUEfVv9DtEehXWgmFkzix1A5UJ2XFJAeU8cRnHFPnmX8NM/54tGOucDoQrvDAS7NBVRjgMRJF5e8AIEGXQGhpZQ+YjvbdIID6yJQdKHkcsCK30F7AnK6xdi0YK+IlT02h/q2mmgW9S3oCpqEfEun2Tjevc+ttGAtCHxUo7aayevwuw/xgGxArg1uGfXTFHf7Ub9xBaQFW0TgihngAb+9EGFPoFpo3nLQN5c853jN0K+TqDumWcpT4wr78Wg/G1BCTiW9tYeQYOehfmnAuKF50lh4IrnXCDUEpdlPIQed/4fAuB+uPSOP4zlPa0VKCIzZnHuIhafuDpo2bbrWVhEqDBoCu0SMXDFy8l7U0tqpIzPOJDCmg3c1EzM0M7V28QttnszMSxKYvvcI0ATJRawTLp1cyJosCYzXhuwn+06TbC889Qo6E8YkMO2K62tC7z/X/fknQB+YfQ11YRb7+uBVxOQrxRVTNpwPTC+V7zOHk2rXmE56yiaxOvrA9IQEa/RMqE8oQzJLHzYYnSpB+vOYE3LzH0PyucO4DojfVHJdCbsdW5aJoQRb1qBZdMrBYl3MHcsdi3UgNj7fY7GOfQPxAGwlAOQJGwAAAABJRU5ErkJggg==\" width=\"19\" height=\"18\" alt=\"K'\" style=\"width: 19px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"18\" alt=\"b'\" style=\"width: 15px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 118.625px 8px; transform-origin: 118.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If there is no groundwater divide, set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003exd\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to the empty set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58997\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eother\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52070\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eproblems\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55825\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ein\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/56205\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ethis\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58966\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eseries\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 264.883px 8px; transform-origin: 264.883px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. For steady, one-dimensional flow, conservation of mass applied to the control volume indicated by the dashed line says that the flow into the volume equals the flow out of the volume. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ev\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97.2417px 8px; transform-origin: 97.2417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the specific discharge in the aquifer, or the flow per unit area, the flow into the left side is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"27\" height=\"18\" alt=\"vbw\" style=\"width: 27px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.008px 8px; transform-origin: 112.008px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the flow out of the right side is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"73\" height=\"18.5\" alt=\"(v+Deltav)bw\" style=\"width: 73px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.70833px 8px; transform-origin: 9.70833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14\" height=\"18\" alt=\"v'\" style=\"width: 14px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.825px 8px; transform-origin: 18.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the specific discharge through the leaky confining layer, the flow into the volume through the top is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"42.5\" height=\"18\" alt=\"v'wDeltax\" style=\"width: 42.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.6083px 8px; transform-origin: 62.6083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Then the mass (or volume) balance is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"316.5\" height=\"18.5\" alt=\"0 = vbw - (v+Deltav)bw + v'wDeltax = -bwDeltav + v'wDeltax\" style=\"width: 316.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.425px 8px; transform-origin: 77.425px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRearranging, dividing by \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"38.5\" height=\"18\" style=\"width: 38.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73.5083px 8px; transform-origin: 73.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and taking the limit as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"21.5\" height=\"18\" style=\"width: 21.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.7333px 8px; transform-origin: 58.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e goes to zero gives\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"71\" height=\"35\" alt=\"dv/dx - v'/b = 0\" style=\"width: 71px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 238.317px 8px; transform-origin: 238.317px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDarcy’s law allows the specific discharge through the aquifer to be written as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"98.5\" height=\"18.5\" alt=\"v = -K(dh/dx)\" style=\"width: 98.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.8px 8px; transform-origin: 84.8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the specific discharge through the leaky confining layer to be approximated as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"117\" height=\"18.5\" alt=\"v' = K'(H-h)/b'\" style=\"width: 117px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.775px 8px; transform-origin: 21.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Then \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"152\" height=\"36.5\" alt=\"K d2h/dx2 + (K'/(bb'))(H-h) = 0\" style=\"width: 152px; height: 36.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59.5083px 8px; transform-origin: 59.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOne can solve this \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/51387\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003esecond-order linear ordinary differential equation\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 170.767px 8px; transform-origin: 170.767px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e using the boundary heads to get the piezometric head in the aquifer. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 376.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 188.35px; text-align: left; transform-origin: 384px 188.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"581\" height=\"371\" style=\"vertical-align: baseline;width: 581px;height: 371px\" 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\" alt=\"leaky confined aquifer\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [h,xd] = leakyConfAq(x,L,h0,hL,K,b,Kp,bp,H)\r\n  h = H + (hL-h0*(x/L)*sin(Kp*x^2/(Kp*b*bp));\r\n  xd = x\r\nend","test_suite":"%%\r\nL = 3300;                                     %  Length (m)    \r\nx = 1000;                                     %  Position where head is desired (m)\r\nh0 = 32;                                      %  Piezometric head at x = 0 (m)\r\nhL = 29;                                      %  Piezometric head at x = L (m)\r\nH = 39;                                       %  Head in unconfined aquifer (m)\r\nK = 12;                                       %  Hydraulic conductivity of aquifer (m/d)\r\nKp = 8e-5;                                    %  Hydraulic conductivity of leaky confining layer (m/d)\r\nb = 15;                                       %  Thickness of aquifer (m)\r\nbp = 2;                                       %  Thickness of leaky confining layer (m)\r\n[h,xd] = leakyConfAq(x,L,h0,hL,K,b,Kp,bp,H);\r\nh_correct = 32.7897;\r\nxd_correct = 1060.65;\r\nassert(abs(h-h_correct)\u003c1e-3)\r\nassert(abs(xd-xd_correct)\u003c1e-2)\r\n\r\n%%\r\nL = 3300;                                     %  Length (m)    \r\nx = 700:700:2800;                             %  Position where head is desired (m)\r\nh0 = 32;                                      %  Piezometric head at x = 0 (m)\r\nhL = 29;                                      %  Piezometric head at x = L (m)\r\nH = 39;                                       %  Head in unconfined aquifer (m)\r\nK = 12;                                       %  Hydraulic conductivity of aquifer (m/d)\r\nKp = 3e-4;                                    %  Hydraulic conductivity of leaky confining layer (m/d)\r\nb = 15;                                       %  Thickness of aquifer (m)\r\nbp = 2;                                       %  Thickness of leaky confining layer (m)\r\n[h,xd] = leakyConfAq(x,L,h0,hL,K,b,Kp,bp,H);\r\nh_correct = [34.6548 35.4741 34.8040 32.3615];\r\nxd_correct = 1433.93;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-2)\r\n\r\n%%\r\nL = 2500;                                     %  Length (m)    \r\nx = 0:500:2500;                               %  Position where head is desired (m)\r\nh0 = 45;                                      %  Piezometric head at x = 0 (m)\r\nhL = 42;                                      %  Piezometric head at x = L (m)\r\nH = 50;                                       %  Head in unconfined aquifer (m)\r\nK = 4;                                        %  Hydraulic conductivity of aquifer (m/d)\r\nKp = 2e-5;                                    %  Hydraulic conductivity of leaky confining layer (m/d)\r\nb = 30;                                       %  Thickness of aquifer (m)\r\nbp = 3;                                       %  Thickness of leaky confining layer (m)\r\n[h,xd] = leakyConfAq(x,L,h0,hL,K,b,Kp,bp,H);\r\nh_correct = [45 44.5664 44.0573 43.4656 42.7830 42];\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(isempty(xd))\r\n\r\n%%\r\nL = 2500;                                     %  Length (m)    \r\nx = 0:500:2500;                               %  Position where head is desired (m)\r\nh0 = 45;                                      %  Piezometric head at x = 0 (m)\r\nhL = 42;                                      %  Piezometric head at x = L (m)\r\nH = 50;                                       %  Head in unconfined aquifer (m)\r\nK = 4;                                        %  Hydraulic conductivity of aquifer (m/d)\r\nKp = 2e-4;                                    %  Hydraulic conductivity of leaky confining layer (m/d)\r\nb = 30;                                       %  Thickness of aquifer (m)\r\nbp = 3;                                       %  Thickness of leaky confining layer (m)\r\n[h,xd] = leakyConfAq(x,L,h0,hL,K,b,Kp,bp,H);\r\nh_correct = [45 45.6796 45.7522 45.2279 44.0331 42];\r\nxd_correct = 811.72;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-2)\r\n\r\n%%\r\nL = 3300;                                     %  Length (m)    \r\nx = 700:700:2900;                             %  Position where head is desired (m)\r\nh0 = 32;                                      %  Piezometric head at x = 0 (m)\r\nhL = 29;                                      %  Piezometric head at x = L (m)\r\nH = 39;                                       %  Head in unconfined aquifer (m)\r\nK = 12;                                       %  Hydraulic conductivity of aquifer (m/d)\r\nKp = 3e-4;                                    %  Hydraulic conductivity of leaky confining layer (m/d)\r\nb = 15;                                       %  Thickness of aquifer (m)\r\nbp = 2;                                       %  Thickness of leaky confining layer (m)\r\n[h,xd] = leakyConfAq(x,L,h0,hL,K,b,Kp,bp,H);\r\nh_correct = [34.6548 35.4741 34.8040 32.3615];\r\nxd_correct = 1433.93;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-2)\r\n\r\n%%\r\nL = 1000;                                     %  Length (m)    \r\nx = [130 280 390 560 710 940];                %  Position where head is desired (m)\r\nh0 = 34;                                      %  Piezometric head at x = 0 (m)\r\nhL = 33;                                      %  Piezometric head at x = L (m)\r\nH = 38;                                       %  Head in unconfined aquifer (m)\r\nK = 0.5;                                      %  Hydraulic conductivity of aquifer (m/d)\r\nKp = 2e-4;                                    %  Hydraulic conductivity of leaky confining layer (m/d)\r\nb = 24;                                       %  Thickness of aquifer (m)\r\nbp = 1;                                       %  Thickness of leaky confining layer (m)\r\n[h,xd] = leakyConfAq(x,L,h0,hL,K,b,Kp,bp,H);\r\nh_correct = [35.5547 36.4902 36.7941 36.7832 36.2740 34.0536];\r\nxd_correct = 471.73;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-2)\r\n\r\n%%\r\nfiletext = fileread('leakyConfAq.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-09-23T13:55:41.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-09-23T13:48:39.000Z","updated_at":"2026-02-12T13:57:58.000Z","published_at":"2023-09-23T13:51:50.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the piezometric head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in a leaky confined aquifer and the position of a groundwater divide \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"xd\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_d\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e given the boundary heads \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"hL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (assumed constant) in the unconfined aquifer above the leaky confining layer. The hydraulic conductivity and thickness of the aquifer are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the hydraulic conductivity and thickness of the leaking confining layer are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K'\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\\\\prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b'\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\\\\prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If there is no groundwater divide, set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003exd\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to the empty set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58997\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eother\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52070\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eproblems\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55825\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ein\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/56205\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethis\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58966\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eseries\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. For steady, one-dimensional flow, conservation of mass applied to the control volume indicated by the dashed line says that the flow into the volume equals the flow out of the volume. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the specific discharge in the aquifer, or the flow per unit area, the flow into the left side is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"vbw\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003evbw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the flow out of the right side is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"(v+Deltav)bw\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(v+\\\\Delta v)bw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v'\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev\\\\prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the specific discharge through the leaky confining layer, the flow into the volume through the top is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v'wDeltax\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev\\\\prime w\\\\Delta x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Then the mass (or volume) balance is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"0 = vbw - (v+Deltav)bw + v'wDeltax = -bwDeltav + v'wDeltax\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 = vbw - (v+\\\\Delta v)bw+v\\\\prime w\\\\Delta x = -bw\\\\Delta v+v\\\\prime w\\\\Delta x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRearranging, dividing by \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ebw\\\\Delta x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and taking the limit as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Delta x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e goes to zero gives\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dv/dx - v'/b = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{dv}{dx}-\\\\frac{v\\\\prime}{b} = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDarcy’s law allows the specific discharge through the aquifer to be written as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v = -K(dh/dx)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev = -K(dh/dx)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the specific discharge through the leaky confining layer to be approximated as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v' = K'(H-h)/b'\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev\\\\prime = K\\\\prime(H-h)/b\\\\prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Then \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K d2h/dx2 + (K'/(bb'))(H-h) = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\\\\frac{d^2h}{dx^2} + \\\\frac{K\\\\prime}{bb\\\\prime}(H-h) = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOne can solve this \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/51387\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esecond-order linear ordinary differential equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e using the boundary heads to get the piezometric head in the aquifer. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"371\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"581\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"leaky confined aquifer\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58966,"title":"Compute the head for steady 1D flow in a homogeneous aquifer","description":"Problem statement\r\nWrite a function that computes the head  (i.e., piezometric head for a confined aquifer or water table elevation above the aquifer bottom for an unconfined aquifer) at specified locations . The input will include a Boolean variable that is true for confined aquifers and false for unconfined aquifers as well as the length  of the aquifer, hydraulic conductivity , aquifer thickness  (set to [] for unconfined aquifers), width , and a vector BC, which contains two of three of the head  at , the head  at , and the flow . The function should also return the flow.\r\nBackground\r\nThe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. The latter relates the flow of water to the gradient in piezometric head by\r\n\r\nwhere  is the flow area. For a confined aquifer, the flow area is , whereas for an unconfined aquifer .\r\nThe spatial variation of the head can be computed with these two principles. For steady, one-dimensional flow, conservation of mass says that the flow must by constant (i.e., the same at any cross section). Then Darcy’s law provides a differential equation that can be integrated using two of the three boundary conditions listed above\r\n ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 738.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 369.25px; transform-origin: 407px 369.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 107px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 53.5px; text-align: left; transform-origin: 384px 53.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 125.5px 8px; transform-origin: 125.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes the head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 247.392px 8px; transform-origin: 247.392px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (i.e., piezometric head for a confined aquifer or water table elevation above the aquifer bottom for an unconfined aquifer) at specified locations \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 175.433px 8px; transform-origin: 175.433px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The input will include a Boolean variable that is true for confined aquifers and false for unconfined aquifers as well as the length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eL\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.742px 8px; transform-origin: 114.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the aquifer, hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.225px 8px; transform-origin: 27.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, aquifer thickness \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (set to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97.6333px 8px; transform-origin: 97.6333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for unconfined aquifers), width \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ew\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3333px 8px; transform-origin: 44.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and a vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eBC\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.183px 8px; transform-origin: 127.183px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which contains two of three of the head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.0583px 8px; transform-origin: 33.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17\" height=\"20\" style=\"width: 17px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"18\" style=\"width: 39px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 43.5583px 8px; transform-origin: 43.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.575px 8px; transform-origin: 127.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The function should also return the flow.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.442px 8px; transform-origin: 381.442px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. The latter relates the flow of water to the gradient in piezometric head by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"85\" height=\"35\" style=\"width: 85px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 173.467px 8px; transform-origin: 173.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the flow area. For a confined aquifer, the flow area is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"49.5\" height=\"18\" style=\"width: 49.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 111.642px 8px; transform-origin: 111.642px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, whereas for an unconfined aquifer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"50\" height=\"18\" style=\"width: 50px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe spatial variation of the head can be computed with these two principles. For steady, one-dimensional flow, conservation of mass says that the flow must by constant (i.e., the same at any cross section). Then Darcy’s law provides a differential equation that can be integrated using two of the three boundary conditions listed above\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 365.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 182.85px; text-align: left; transform-origin: 384px 182.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"640\" height=\"360\" style=\"vertical-align: baseline;width: 640px;height: 360px\" 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data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [h,Q] = homogAq(x,confined,L,K,b,w,BC)\r\n% h = head at position x\r\n% Q = flow\r\n% x = position at which head is requested\r\n% L = length of aquifer\r\n% K = hydraulic conductivity\r\n% b = thickness of confined aquifer ([] if unconfined)\r\n% w = width of aquifer\r\n% BC = [h0 hL Q]--one of which is NaN\r\n\r\n  h = conservation of mass + Darcy's law;\r\n  Q = -K*dhdx*A\r\nend","test_suite":"%%  Confined, boundary heads specified\r\nK = 0.5;                %  Hydraulic conductivity (m/d)\r\nL = 24;                 %  Length (m)\r\nb = 2.5;                %  Thickness (m)\r\nw = 400;                %  Width (m)\r\nBC = [4 2.5 NaN];       %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 12;                 %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,true,L,K,b,w,BC);\r\nh_correct = 3.25;\r\nQ_correct = 31.25;\r\nassert(abs(h-h_correct)\u003c1e-4)\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Confined, head at x = 0 and flow specified\r\nK = 8;                  %  Hydraulic conductivity (m/d)\r\nL = 2300;               %  Length (m)\r\nb = 31;                 %  Thickness (m)\r\nw = 1800;               %  Width (m)\r\nBC = [45 NaN 892.8];    %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = [800 1800];         %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,true,L,K,b,w,BC);\r\nh_correct = [43.4 41.4];\r\nQ_correct = 892.8;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Confined, head at x = L and flow specified\r\nK = 0.04;               %  Hydraulic conductivity (m/d)\r\nL = 1850;               %  Length (m)\r\nb = 25;                 %  Thickness (m)\r\nw = 1400;               %  Width (m)\r\nBC = [NaN 133 28];      %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 300:300:1800;       %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,true,L,K,b,w,BC);\r\nh_correct = [164 158 152 146 140 134];\r\nQ_correct = 28;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Unconfined, boundary heads specified\r\nK = 0.5;                %  Hydraulic conductivity (m/d)\r\nL = 24;                 %  Length (m)\r\nw = 400;                %  Width (m)\r\nBC = [4 2.5 NaN];       %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 12;                 %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,false,L,K,[],w,BC);\r\nh_correct = 3.3354;\r\nQ_correct = 40.625;\r\nassert(abs(h-h_correct)\u003c1e-4)\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Unconfined, head at x = 0 and flow specified\r\nK = 8;                  %  Hydraulic conductivity (m/d)\r\nL = 2300;               %  Length (m)\r\nw = 1800;               %  Width (m)\r\nBC = [45 NaN 892.8];    %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = [800 1800];         %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,false,L,K,[],w,BC);\r\nh_correct = [43.8839 42.4476];\r\nQ_correct = 892.8;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Unconfined, head at x = L and flow specified\r\nK = 0.04;               %  Hydraulic conductivity (m/d)\r\nL = 1850;               %  Length (m)\r\nw = 1400;               %  Width (m)\r\nBC = [NaN 133 28];      %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 300:300:1800;       %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,false,L,K,[],w,BC);\r\nh_correct = [138.7047 137.6190 136.5247 135.4216 134.3093 133.1878];\r\nQ_correct = 28;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Confined, random selection of boundary conditions\r\nK = 2.3;                %  Hydraulic conductivity (m/d)\r\nL = 2000;               %  Length (m)\r\nb = 34;                 %  Thickness (m)\r\nw = 1650;               %  Width (m)\r\nBC = [54 51 193.545];   %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 400:400:1600;       %  Position in aquifer (m)\r\nk = randi(3);\r\nBC(k) = NaN;\r\n[h,Q] = homogAq(x,true,L,K,b,w,BC);\r\nh_correct = [53.4 52.8 52.2 51.6];\r\nQ_correct = 193.545;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(all(abs(Q-Q_correct)\u003c1e-4))\r\n\r\n%%  Unconfined, random selection of boundary conditions\r\nK = 2.3;                %  Hydraulic conductivity (m/d)\r\nL = 2000;               %  Length (m)\r\nw = 1650;               %  Width (m)\r\nBC = [54 51 298.85625]; %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 400:400:1600;       %  Position in aquifer (m)\r\nk = randi(3);\r\nBC(k) = NaN;\r\n[h,Q] = homogAq(x,false,L,K,[],w,BC);\r\nh_correct = [53.4135 52.8205 52.2207 51.6140];\r\nQ_correct = 298.85625;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(all(abs(Q-Q_correct)\u003c1e-4))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-09-09T15:47:31.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2023-09-09T15:42:41.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-09-09T15:33:16.000Z","updated_at":"2026-02-10T14:45:49.000Z","published_at":"2023-09-09T15:42:41.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes the head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (i.e., piezometric head for a confined aquifer or water table elevation above the aquifer bottom for an unconfined aquifer) at specified locations \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The input will include a Boolean variable that is true for confined aquifers and false for unconfined aquifers as well as the length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the aquifer, hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, aquifer thickness \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (set to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for unconfined aquifers), width \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ew\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and a vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBC\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which contains two of three of the head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The function should also return the flow.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. The latter relates the flow of water to the gradient in piezometric head by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K\\\\frac{dh}{dx}A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the flow area. For a confined aquifer, the flow area is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA = bw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, whereas for an unconfined aquifer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA = hw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe spatial variation of the head can be computed with these two principles. For steady, one-dimensional flow, conservation of mass says that the flow must by constant (i.e., the same at any cross section). Then Darcy’s law provides a differential equation that can be integrated using two of the three boundary conditions listed above\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"360\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"640\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e 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the water table elevation in an unconfined aquifer with recharge","description":"Problem statement\r\nWrite a function to compute the water table elevation  above the bottom of the aquifer and the position of a groundwater divide  given the water table elevations  at ,  at , hydraulic conductivity , and recharge rate . If there is no groundwater divide, set xd to the empty set []. \r\nBackground\r\nAs in other problems in this series, the movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. In an unconfined aquifer, the latter relates the flow of water to the gradient in water table elevation above the bottom of the aquifer by\r\n\r\nwhere  is the width of the aquifer. For steady, one-dimensional flow, conservation of mass says that the flow at any position  is \r\n\r\nwhere  is the (unknown) flow at . Using Darcy’s law to replace  provides a differential equation that can be integrated using the water table elevations at the boundaries to determine  and a constant of integration.\r\nUnlike the flows in Cody Problem 58966, the flows here can have a groundwater divide, or a point in the profile that separates flow to the left from flow to the right. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 838.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 419.25px; transform-origin: 407px 419.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 164.792px 8px; transform-origin: 164.792px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the water table elevation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 206.542px 8px; transform-origin: 206.542px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e above the bottom of the aquifer and the position of a groundwater divide \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"20\" alt=\"xd\" style=\"width: 15px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.917px 8px; transform-origin: 101.917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e given the water table elevations \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"h0\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x  = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17\" height=\"20\" alt=\"hL\" style=\"width: 17px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"18\" alt=\"x = L\" style=\"width: 39px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.35px 8px; transform-origin: 72.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 61.0667px 8px; transform-origin: 61.0667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and recharge rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABgAAAAoCAYAAADkDTpVAAAByElEQVRIS+2VPS8FQRSG7+1VVBoKCiJB4qsQOjQUGpdf4KMnqFQIP8BHpaVV8QuERkcjUSk19DwnmbOZGbs7u+PeKOwmb3Y3Z+a857znnJl6rcVPvcX+axVBUOH/IdEROmyCK9AIauItKCLRl7Vnju/bMiRFCC5xuASewSR4bzaB+BsDD2Uc69oiGcT4Tfb8OcEsoYyA4ZgOkjSyMjjDNg36TK5RBc4jEJtEf2MIomYgRLDGghNDsM77NKbaeUXW/he/HWX7v0ibvrGoE4j+/THR50kkg3VvnB7z3kohkDNqCLyahtjjLVk7T5ZEO6zaNyvTzp87bF1gCrwADWiX7wObIYtAuke66BN0e/pr8f3MdI9TryyCD5y2ATk5JQP7eeJH5mPZk0SPdYc4jcDWX1OWzYcmEz2+/c7SuXGaIo3A1r8XpzNgEayAUaDDl0Ug2SZ+0wg0VVkoEzwI5k0x7enOI0hsaQQ9OHu0arBhnAthUwi8mjq/dn2iM8gjENuvixwikCGbAP4Aau3Osa2qk5gbLTRo4zhP7u8YAglOshgAOuVaGyd6p19Dunj2dv63wQK4BnL7XYAfd0ZsBoXjqQiCUlUSBSX6BtLJXikPaIchAAAAAElFTkSuQmCC\" width=\"12\" height=\"20\" alt=\"i0\" style=\"width: 12px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.6px 8px; transform-origin: 27.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If there is no groundwater divide, set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003exd\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.6583px 8px; transform-origin: 53.6583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to the empty set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.3917px 8px; transform-origin: 35.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs in other \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52070\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eproblems\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55825\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ein\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/56205\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ethis\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58966\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eseries\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 264.883px 8px; transform-origin: 264.883px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. In an unconfined aquifer, the latter relates the flow of water to the gradient in water table elevation above the bottom of the aquifer by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"91.5\" height=\"35\" alt=\"Q = -K(dh/dx)hw\" style=\"width: 91.5px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ew\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 333.967px 8px; transform-origin: 333.967px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the width of the aquifer. For steady, one-dimensional flow, conservation of mass says that the flow at any position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.94167px 8px; transform-origin: 8.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"91\" height=\"20\" alt=\"Q = Q0 + i0 w x\" style=\"width: 91px; height: 20px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.4px 8px; transform-origin: 77.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the (unknown) flow at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94px 8px; transform-origin: 94px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Using Darcy’s law to replace \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 135.633px 8px; transform-origin: 135.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e provides a differential equation that can be integrated using the water table elevations at the boundaries to determine \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" alt=\"Q0\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.1833px 8px; transform-origin: 92.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and a constant of integration.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.35px 8px; transform-origin: 58.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUnlike the flows in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58966\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 58966\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 233.383px 8px; transform-origin: 233.383px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the flows here can have a groundwater divide, or a point in the profile that separates flow to the left from flow to the right. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 403.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 201.85px; text-align: left; transform-origin: 384px 201.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"586\" height=\"398\" style=\"vertical-align: baseline;width: 586px;height: 398px\" 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\" alt=\"Unconfined aquifer with recharge\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0)\r\n  h = (h0+hL)/2;\r\n  xd = x;\r\nend","test_suite":"%%\r\nL = 10;                                       %  Length (m)    \r\nx = L/2;                                      %  Position where WTE is desired (m)\r\nh0 = 19.11;                                   %  Water table elevation at x = 0 (m)\r\nhL = 19.11;                                   %  Water table elevation at x = L (m)\r\nK = 5e-7;                                     %  Hydraulic conductivity (m/s)\r\ni0 = 6.9e-8;                                  %  Recharge rate (m/s)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = 19.2;\r\nxd_correct = 5;\r\nassert(abs(h-h_correct)\u003c1e-3)\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 1200;                                       %  Length (m)                                                   \r\nx = 0:300:1200;                                 %  Positions where WTE is desired (m)\r\nh0 = 25;                                        %  Water table elevation at x = 0 (m)\r\nhL = 23;                                        %  Water table elevation at x = L (m)\r\nK = 4;                                          %  Hydraulic conductivity (m/d)\r\ni0 = 2e-4;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [25.000 24.789 24.393 23.801 23.000];\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(isempty(xd))\r\n\r\n%%\r\nL = 1200;                                       %  Length (m)                                                   \r\nx = 0:300:1200;                                 %  Positions where WTE is desired (m)\r\nh0 = 25;                                        %  Water table elevation at x = 0 (m)\r\nhL = 23;                                        %  Water table elevation at x = L (m)\r\nK = 4;                                          %  Hydraulic conductivity (m/d)\r\ni0 = 8e-4;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [25.000 25.593 25.475 24.637 23.000];\r\nxd_correct = 400;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 2500;                                       %  Length (m)                                                   \r\nx = [100 200 300 700 1200 1800 2400];           %  Positions where WTE is desired (m)\r\nh0 = 35;                                        %  Water table elevation at x = 0 (m)\r\nhL = 33.5;                                      %  Water table elevation at x = L (m)\r\nK = 50;                                         %  Hydraulic conductivity (m/d)\r\ni0 = 1e-3;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [35.010 35.014 35.012 34.949 34.74 34.296 33.633];\r\nxd_correct = 222.5;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 2500;                                       %  Length (m)                                                   \r\nx = [100 200 300 700 1200 1800 2400];           %  Positions where WTE is desired (m)\r\nh0 = 35;                                        %  Water table elevation at x = 0 (m)\r\nhL = 33.5;                                      %  Water table elevation at x = L (m)\r\nK = 60;                                         %  Hydraulic conductivity (m/d)\r\ni0 = 1e-3;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [34.998 34.992 34.981 34.889 34.665 34.235 33.621];\r\nxd_correct = 17;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 20;                                         %  Length (m)                                                   \r\nx = 0:4:20;                                     %  Positions where WTE is desired (m)\r\nh0 = 5;                                         %  Water table elevation at x = 0 (m)\r\nhL = 3.5;                                       %  Water table elevation at x = L (m)\r\nK = 0.5;                                        %  Hydraulic conductivity (m/d)\r\ni0 = 1e-3;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [5 4.752 4.482 4.188 3.864 3.5];\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(isempty(xd))\r\n\r\n%%\r\nL = 20;                                         %  Length (m)                                                   \r\nx = 0:4:20;                                     %  Positions where WTE is desired (m)\r\nh0 = 5;                                         %  Water table elevation at x = 0 (m)\r\nhL = 3.5;                                       %  Water table elevation at x = L (m)\r\nK = 0.1;                                        %  Hydraulic conductivity (m/d)\r\ni0 = 5e-3;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [5 5.065 4.97 4.706 4.243 3.5];\r\nxd_correct = 3.625;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 1000*rand;                                  %  Length (m)                                                   \r\nx = L/17;                                       %  Positions where WTE is desired (m)\r\nh0 = randi(100);                                %  Water table elevation at x = 0 (m)\r\nhL = h0;                                        %  Water table elevation at x = L (m)\r\nK = 5;                                          %  Hydraulic conductivity (m/d)\r\ni0 = 5e-3;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nassert(abs(xd-L/2)\u003c1e-3)\r\n\r\n%%\r\nfiletext = fileread('unconfWithRecharge.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-09-23T13:56:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-09-23T01:49:39.000Z","updated_at":"2026-02-12T13:52:11.000Z","published_at":"2023-09-23T01:49:48.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the water table elevation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e above the bottom of the aquifer and the position of a groundwater divide \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"xd\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_d\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e given the water table elevations \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x  = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"hL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and recharge rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"i0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If there is no groundwater divide, set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003exd\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to the empty set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs in other \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52070\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eproblems\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55825\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ein\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/56205\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethis\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58966\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eseries\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. In an unconfined aquifer, the latter relates the flow of water to the gradient in water table elevation above the bottom of the aquifer by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = -K(dh/dx)hw\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K\\\\frac{dh}{dx}hw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"w\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ew\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the width of the aquifer. For steady, one-dimensional flow, conservation of mass says that the flow at any position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = Q0 + i0 w x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = Q_0 + i_0 w x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the (unknown) flow at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Using Darcy’s law to replace \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e provides a differential equation that can be integrated using the water table elevations at the boundaries to determine \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and a constant of integration.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUnlike the flows in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58966\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 58966\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the flows here can have a groundwater divide, or a point in the profile that separates flow to the left from flow to the right. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59029,"title":"Compute the water table in a layered unconfined aquifer","description":"Write a function to compute the flow per unit width and the elevation of the water table above the bottom of unconfined aquifer with two soil layers. The input to the function will be the positions where the water table elevation (WTE) is requested, the hydraulic conductivities of the two layers, the thickness of the bottom layer, the WTEs at  and , and the length  of the aquifer.\r\nBackground \r\nCody Problem 52070 dealt with the effective conductivity of a heterogeneous confined aquifer. In that case, the effective conductivity  for the case of flow through soil units in parallel could be computed by realizing that the head difference is same for the two soils and the total flow is the sum of the flows through the soils. The effective conductivity then is the weighted average of the individual conductivities, using the layer thicknesses as weights. \r\nFor an unconfined aquifer, the effective conductivity is computed in a similar way, but because the WTE  varies with , so does :\r\n\r\nThen using Darcy’s law as in Cody Problem 58966, one can write the flow  through the aquifer as\r\n\r\nConservation of mass says that in steady one-dimensional flow, the flow  past any section is constant. Then the WTE can be computed by inserting the effective conductivity, integrating, and using the boundary conditions  and  to determine the flow  and the constant of integration. \r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 836.3px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 418.15px; transform-origin: 407px 418.15px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 367.442px 8px; transform-origin: 367.442px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the flow per unit width and the elevation of the water table above the bottom of unconfined aquifer with two soil layers. The input to the function will be the positions where the water table elevation (WTE) is requested, the hydraulic conductivities of the two layers, the thickness of the bottom layer, the WTEs at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAkCAYAAADFGRdYAAACwUlEQVRoQ+2YPU8VQRSGoYcQsMICCyi0ILEBbSi0gITQ2CiGHqUmkGisJdEfoPILlIRQY6kxASk10UIKjdGKr2iP70vOSc6dnd09e+GyxJ1N3sy9u7OzM8+er9nurnSUEugu7ZE6dCVIDiNIkBIkBwFHl2RJCZKDgKNL0yxpGEyeQleEzRDaT9ATaCePV5MgPQSEF9A2NA3tC5Q3aO9Cq9CDGKimQJrE4jehv9B1aNfAGMDvz9Ag9BhaCUE1BdIvgbCG9l7EWh6JGxIiXVGt7KRrEyCpm3G9C9DLCKQxnPso55+jXbZ9mgCJbkZ34zEO5QXoY+nzFe21pkHSxdOVeiNWpKe28OOG/LlkXa7IkhjQGPVvQRMQA5s1V15ntmCf39DlggnUdYkp/5s8vAqkKdzzViddBIkm2g8dQOtQj4FBQB9kkKvSjqC1WSMGRrPMaaFFs1BkUPu8KpBaxvfGpFeYwLwxRVrQIcS6gm+L0HKLMTP5OiGxPrpZ8HbsGtuCxLT5Wh6gZngf/1tS5WnNowP325fCedON8o5nuLAkF9uCREvZkwFiBVkH1ncmQ56ru3HGXyDGn0yKPJPldGaQ8OV6s5s7cIfT1j1OWQDszHLbH/UPbmXSKZu3lgDsd9vGWG/gDgNuC+kK8z/vwM2p2WKyKAMrzEw544FEk/0uQY1ZjUemdHeCqgOS3ZbMYp70iPCw9VTma4AHEs3wHcT9jMYlm045CW4cL3Kmq7LBDb8SRDe43OzxYN2j1FlpE4KtJQiYgO5AF70csBbcsuWQtSpE16cSuxtmAPsJzUBaSdt6ib57FFx3el0t3dTtwuxc+aMbffM9xH0aXWrOANKVaRbIu14LAedDaVGL0Cj0A+qTdgNt7BPKybCemOR8/v/bLUFyvNsEKUFyEHB0SZaUIDkIOLokS0qQHAQcXZIlOSD9A6nxkiWxjY9EAAAAAElFTkSuQmCC\" width=\"36.5\" height=\"18\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"18\" alt=\"x = L\" style=\"width: 39px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eL\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3333px 8px; transform-origin: 44.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the aquifer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.775px 8px; transform-origin: 42.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 85px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42.5px; text-align: left; transform-origin: 384px 42.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52070-compute-the-effective-conductivity-of-a-heterogeneous-aquifer?s_tid=ta_cody_results\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 52070\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 306.625px 8px; transform-origin: 306.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e dealt with the effective conductivity of a heterogeneous confined aquifer. In that case, the effective conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"24.5\" height=\"20\" alt=\"Keff\" style=\"width: 24.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 330.125px 8px; transform-origin: 330.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for the case of flow through soil units in parallel could be computed by realizing that the head difference is same for the two soils and the total flow is the sum of the flows through the soils. The effective conductivity then is the weighted average of the individual conductivities, using the layer thicknesses as weights. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 321.408px 8px; transform-origin: 321.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor an unconfined aquifer, the effective conductivity is computed in a similar way, but because the WTE \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36.95px 8px; transform-origin: 36.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e varies with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.2167px 8px; transform-origin: 13.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, so does \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"24.5\" height=\"20\" alt=\"Keff\" style=\"width: 24.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVgAAABGCAYAAACJx4wfAAAPSUlEQVR4Xu2da+h32RTHn3nnBbm9MgnjUhQhuTTTCLmUSCj3y1PkVpImwgs9SQglqXFJmqRxC4kUCpFiUK5RLg2JVxjxnvWZfmustnPZ+5y99znn//ue2j3/5/8/Z1++a6/vXnvttfe+6pIeISAEhIAQaILAVU1yVaZCQAgIASFwSQSrTiAEhIAQaISACLYRsMpWCAgBISCCVR8QAkJACDRCQATbCFhlKwSEgBAQwaoPCAEhIAQaISCCbQTsQLb3sN+9xdJLLF3dr1iVJASEwFYIiGDbI+/E+lor6s6W/m3pLu2LVQlCQAhsjYAItq0Enm/ZP8fSbZZedSpKBNsWc+UuBHaDgAi2rSgeYNn//lTED+zfx8qCbQu4chcCe0JABNtPGiLYflirJCGwCwREsP3EIILth7VKEgK7QEAE208MIth+WKskIbALBESw/cSwlmDx5756pLofDb7efi1SSULgvBB4jTX3/gNN/oP97iNDUIhg+3WQtQT7VKvq1y39cKDKr7ff/ahfU1TSzhAgFJDB9907q9cRqoNe/SNTfzBkHp406j72/z9ZepwIdltx1yJYDYrbynFvpUOuX7OkQXaZZMDv05a+NGaFzmT7Xvv740Wwy8Cv+dU5EixuDTqwrOuaPel/eYHt9y29rADjR9u7hA7+vU2VuuSK1fnjim1wHD+4gGRXESwNea6lZ1q6VwLd5+z/P7Xk0xIviFhPf/5qP3zK0nsqgtFFgg0K6U2w7rNFdg9O2oOb4btBLviWnmjpeeE9NkTcbOnjBcpLmTdauqsl7wcfs5/HfMcNYO6a5db6QZ9Cjm+eaDWyfaQlprYuk6fZz9/oitS6wt5qnz/LEtNx56F7VuYUSPaXp3JKDIJVBOuwsCPpMwGjt9nPQ/6e+B4EzHseaL8O4uN/3ZtgHTE6zt8CfMiFbbupBRPf+439vcQqSqWDr8p3rr3Afv7s8cU32YIt9APFzj3XgoHveydyYuC8b2Vy6iHetH8+pEGhEDn9viTv6gSLVfrQAQEx9fiWJfbbjxFwA0wOk+VeCPYxhlg6QvsUCUt3jIBLgKbTven0QW1Lo6Qevd6NBNtDP5DXH08YD65eDzT8LyeCxXLFgj3i859TpVvOisCJWffUrCBiV4VgsUB8+ogC0qHi4+T6L/vlZUtHmn706mhbESxTxA+fGollep2laL06ud7bfv8uSzVWon9t+UDWuCIGV1d7gX4qB+x5XmypxYyqt36UWK+0Gwv2dycMjmr8xEGspYsDbJnh5R7IVIVgffRDRhQeR01XYJSpVQfurI9NituKYKeUv8XAGKdy7zMkcy2BJqCfMnXLZ8h6r1Fub/3AkME/nuvbZurL4MnzwEaDTA0cp/Jwt1NrF4cPRinPjdVtNcHG0S8KyMMbcPSjSFrImu5iWxHsmPL7NJ7ZxusqKl20mFtaGiUK3ZJge+uHW3Ilvm3ip9HToRlMCY5bvuv9uMesiLJ+YSnHlbKaYOPo5wKiU33ZEmY0vrZcP9CWAtq67C0IFgv1ltBwrBeCqombZEW5xcDoFvOYL3ILObQk2N764ZZciW8bi5e1kSH33hbyKC2zt4uDAenaE7/N1XU1wfroR0E4l2+1xHRj7UrzXMUv0t99UYJOzlOiHI6D7+Qq2WiQKv8bLLMvnDJ8pf3bYnU/XUyh3jdY4l8eiPeNjcoe6zMtCba3fvhAndsP4iAbrV76BpsTCHvau2UbZ0W4efCj++0gHrZVY3HW+4/P7nLcKasJ1kc/Vw4XyDNODd07EXqHXFPPpYdkQyqvsPR0S06u1MNjTIm6yCW5JQQblR9i887YyhcZlRkfFg9WMv5CnhcFHEqmuGtkx7ctCba3flDeryzlLh6mER3gwQyG52eWPJxuL/7yIVlHFwe881VL/7REDDC7qDy+l4GiJMRqrF85ZjkurlUEm04xY4V6KsgaBduSYNfUO/12CcFG5Y/5tQpziRYzCssmhzgQexuoS89woVYEu4V+0JYSP6T3f75hoGfn1yct4Wq4uyWPLtgzwXo/ps+w2YD6x2iXqOM1jAfvpzkLXasINo5+CCiOeLVGi5okdJHzKiXYSGZYzPjKPVwLnJa4KebwjX7mPyfk6t862fXsP60Idgv9KCVYbzsEym4udNgjO+KAuFeDKfZj3xmaRqZEOdRoh5eZM+isItg4MviCCAHOPt3NYfg5pdTf8xAoJdhU+ZlSRnnWXvBId4yNdXRX+BIrbA6hrWYpW+hHCcGmOyvvZkC+0JLHQUcXUu6AG/vVnFzG/l4Sixt3BboVnu5CjHXKmdbP1bsLwaYK4xWPjVnqm5xrIB3jUZbiOYusJLLZgWnNOZ5/WkqwHuwP1j4SR2uA3+dMp5gGv9MSq6oMrGOLVFGZx6b/sfxoHeSWMdZvtiDYFvoBhh+wNLUIWEKwkZyQ2/WW4kYLn3qXDHa9CTb247H+GmdOcRswdY1nceQuhJWEwi22YKPCpMG9MbYyx4yeI9T4dxZ9GGk5PowpLfl/3hJhYXS8K5bYJZS7ilpS9p7fLSHYMeWnfXHjwZxiQXzg/iFLP7HEwT9jiyIx3zFFiArvK7QlZSyVTwsXQU39QLYR26lpLro3ev5oAlAkpzTP6D+urcNL5ZR+F8Ozxgbt2NfjrMx55BOWKUYZETTwRs5GhS6LXFEZ0sbFsAlAyZ1ezAFPw3A7POL0IjtVIIGbLLESzf8pm1PFc3cIbWHdzLVzyd9LCHZqb3waGD+lzEwh6aAx0sH9dunsJQaCs5gydJiMu5eiIpSUsQQ3vmlBsDX1A7LjfAjvq1MyyQ3TinIemlpH/2vOTGYp9mu+izwzhomTIf3xSSccwROjIPZDPy2LSJo5F4XnmcNriy3YaKUOVai2P89jRdMQlJLRZEiYPQmWNlyzsEdx4tWtE9+WEGy0JodG/jjNY+p49Ui5YJeSZbQYvAPmBII7IbG4FSMLcstYCOvtn7Ug2Bb6kUOwLru5GM1ITkNrJUfY3TW3aYV+x5Gp6QFTYMSMKw2B9D44F0WDHIhWGNOL2BcXEWxq5QyNcEv8eVNK4h0iJXM6Ms/QCV5rlK7Fty+1TAkhWfLw3csrEeyc8qcbH+ZG9LRaEFbcqTVnDblFjZXBVDjnMKC0jCWY+je1CbaVfuQQrE/t51bLnZzGpsTuf3X3APrHmkeObNbIouTbGJ41tG3VXSC5vlUfnOb6O+USK5weajVU90UEG0e/qS2P0Tqc8+dROToHO4h47meJFc2nWGJBy53R5HOLpTtZQjGiz2/0crESqTV890GW9xMW5v9b++47E9/mWrA5yk8x6WJl7hmhnn+0jKdWo/1AGcrMJdehMhbCevtntQm2lX7kECztYQDlfNcpAvBBdmgGE/2vGE/4KN9haci1swb3Nd/GOg5ZnD6A5JIrdfFvplwirme50QiLCDYS59QUMl1RHAvb8oNhMLtxNiN0On30xbnFElc6Pf+9OuHXdKDSb3MJNpXJ2FQynYFEWUzVDXJBHu7v4t24oSH6rbwupQfKDJVRild8vzbB1tYPr2suwfpaxdigGMlpyFqLMw7kTj57Owkv1jESLG1jtsfxmqXnoOQMTJAwHJTjHkBuRQRLx75sKV77QiYoSLwUjPe4hiJuffROkr4bzxt1pXQLwAnZO0RqBbtllDuarFHCvX87R7D8nW258doX2oTP8yuWfFGQ955sidPwfeustz19dwgTOml6IDEWJ/kzC+FhlZtrY35u6YuWUl/YHNZDZcx9M/X3WgTbQj9ivXMJdu7A7UhOQwMsli9XAfkBMJBwi3Ny18iMb8H72Zbos3ADfYotskS2MDCU1Jm83m4pDVWLdXRcS87pKCLYtYAMfe9muVuhLlxCsNIdJelUAMuIh6iCEjBbtGPrPOcItkf96ExYOwyMrS7Na1EGxMWz95tXcwmWtrge5bp2evSPvZbhEQSXrYJTPmYWwdjtlnvOA+3dlGCjPxDyJL71Nkuc6BQb6iQcHff+bc8tla07yJobPbcmWBSaOOSWfroeZbSW8Zr8SwiWcnxmkLMYs6ZeR/+WxbArAa+h9qBf8FLpgLUpwborYGyLmzcUAPCpREvVV57nQir2LHx3pdS40XNLgvW4wpZ+uh5l7LmvULdSgvVvbrIfdCbzsHQZhOLt10NvLb1Rlrw2JVhf5BhaQPHgairpC1zRsezfji2c7V1ZvH61bvSMq5tp22veEZ/m7TuthnxXdN4a7oIeZRyhvywhWNqFHL4tkv0/EYMLM+b0ah10icglTuSCXAnJynEf0U+JuIgP6x5YvYNuhdbbTeNqpjvbaRwhIey5BgAnjpSEvbPNBVQfQXGmQmZy65+u+sfvWi0CeiA3mz84ezM+nMPJyUy590KNtbNHGbkYb/2ex3XOxbgO1ZMZX+li4tbtbVk+/lQW4W+2xMKYPyyUsRjrBgN6lWugxOiRWPfRENXWBEslPOSGFUs/aJoVTL862i3VtFNh1V4E/2vOLqeWHW1p3vEq77E81m6x7FHG0vb3/M7jwz3mm35/xdI3LbVaTOzZvt5lxTjlobLHzjWoXs8eBDtXaUKxHhZGFN53y/cixL/OhczM4aO/CwEhcFAE9kCwQ9vSICVi82Iw+0EhvnSEPd9HxVb1FgK7RmALgnXrFALlhlN2dnH4x42WrrXETbX4LDkNJ14LsWsgJyp39Bs9j4q76i0ENkdgC4L1VTsaz/F177eEP9Z9te6Uzj2OcHMQJyoQF/mOeqPnnvFV3YTArhHYgmB3DUjlysVzAdijz3O0Gz0rQ6LshMD5ICCCbStrD+vwjRZHvNGzLULKXQhcYAREsG2Fe/QbPduio9yFwAVHQATbTsAtbvRsV1vlLASEQHUERLDVIb0jwxY3erarrXIWAkKgOgIi2OqQ3pHh0W/0bIeMchYCZ4KACLaNoC/CjZ5tkFGuQuCMEBDBthF23At91Bs92yCjXIXAGSEggm0j7Itwo2cbZJSrEDgjBESwbYR99Bs926CiXIXAmSEggq0v8Itwo2d9VJSjEDhDBESw9YU+dzzhUW70rI+MchQCZ4aACPbMBK7mCgEh0A8BEWw/rFWSEBACZ4aACPbMBK7mCgEh0A8BEWw/rFWSEBACZ4aACPbMBK7mCgEh0A8BEWw/rFWSEBACZ4aACPbMBK7mCgEh0A8BEWw/rFWSEBACZ4aACPbMBK7mCgEh0A8BEWw/rFWSEBACZ4bAfwH+HWODLGqD3AAAAABJRU5ErkJggg==\" width=\"172\" height=\"35\" alt=\"Keff = (1/h)[(K2-K1) b2 + K1(h-b2)]\" style=\"width: 172px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.8917px 8px; transform-origin: 90.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThen using Darcy’s law as in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58966-compute-the-head-for-steady-1d-flow-in-a-homogeneous-aquifer\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 58966\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73.5083px 8px; transform-origin: 73.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, one can write the flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70.0167px 8px; transform-origin: 70.0167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e through the aquifer as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"183\" height=\"35\" alt=\"Q = -Keff(dh/dx)A = -Keff(dh/dx)hw\" style=\"width: 183px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 224.825px 8px; transform-origin: 224.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConservation of mass says that in steady one-dimensional flow, the flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.058px 8px; transform-origin: 152.058px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e past any section is constant. Then the WTE can be computed by inserting the effective conductivity, integrating, and using the boundary conditions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"61\" height=\"20\" alt=\"h(0) = h0\" style=\"width: 61px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"64.5\" height=\"20\" alt=\"h(L) = hL\" style=\"width: 64.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0.991667px 8px; transform-origin: 0.991667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to determine the flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.9583px 8px; transform-origin: 99.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the constant of integration. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 346.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 173.35px; text-align: left; transform-origin: 384px 173.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"559\" height=\"341\" style=\"vertical-align: baseline;width: 559px;height: 341px\" 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alt=\"unconfined aquifer with soils in parallel\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L)\r\n%  h  = water table elevation above the aquifer bottom\r\n%  Qp = flow per unit width\r\n%  x  = locations where WTE is requested\r\n%  K1 = hydraulic conductivity of upper layer\r\n%  K2 = hydraulic conductivity of lower layer\r\n%  b2 = thickness of lower layer\r\n%  h0 = water table elevation on the left side (x = 0)\r\n%  hL = water table elevation on the right side (x = L)\r\n%  L  = length of the aquifer\r\n\r\n   Qp = mean([K1 K2])*(h0-hL)*b2/L;\r\n   h  = h0 + (hL-h0)*x/L;","test_suite":"%%\r\nx  = [0 251.884 503.2297 754.0371 1004.3062 1254.0371 1503.2297 1751.884 2000];\r\nK1 = 900;                       %  Hydraulic conductivity of upper layer (m/d)\r\nK2 = 8000;                      %  Hydraulic conductivity of lower layer (m/d)\r\nh0 = 37;                        %  Water table elevation on the left side (m)\r\nhL = 33;                        %  Water table elevation on the right side (m)\r\nL  = 2000;                      %  Length of aquifer (m)\r\nb2 = 25;                        %  Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 37:-0.5:33;\r\nQp_correct = 418;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx  = [0 284.1463 558.5366 823.1707 1078.0488 1323.1707 1558.5366 1784.1463 2000];\r\nK1 = 8000;                      %  Hydraulic conductivity of upper layer (m/d)\r\nK2 = 900;                       %  Hydraulic conductivity of lower layer (m/d)\r\nh0 = 37;                        %  Water table elevation on the left side (m)\r\nhL = 33;                        %  Water table elevation on the right side (m)\r\nL  = 2000;                      %  Length of aquifer (m)\r\nb2 = 25;                        %  Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 37:-0.5:33;\r\nQp_correct = 205;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx  = [0 230.8945 460.1048 687.631 913.4731 1137.631 1360.1048 1580.8945 1800];\r\nK1 = 4;                         %  Hydraulic conductivity of upper layer (m/d)\r\nK2 = 0.1;                       %  Hydraulic conductivity of lower layer (m/d)\r\nh0 = 50;                        %  Water table elevation on the left side (m)\r\nhL = 48;                        %  Water table elevation on the right side (m)\r\nL  = 1800;                      %  Length of aquifer (m)\r\nb2 = 16;                        %  Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 50:-0.25:48;\r\nQp_correct = 0.1484;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx  = [0 225.2925 450.5015 675.6269 900.6686 1125.6269 1350.5015 1575.2925 1800];\r\nK1 = 0.1;                       %  Hydraulic conductivity of upper layer (m/d)\r\nK2 = 4;                         %  Hydraulic conductivity of lower layer (m/d)\r\nh0 = 50;                        %  Water table elevation on the left side (m)\r\nhL = 48;                        %  Water table elevation on the right side (m)\r\nL  = 1800;                      %  Length of aquifer (m)\r\nb2 = 16;                        %  Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 50:-0.25:48;\r\nQp_correct = 7.48e-2;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx  = [0 2.6558 5.2033 7.6423 9.9729 12.1951 14.3089 16.3144 18.2114 20];\r\nK1 = 0.5;                       %  Hydraulic conductivity of upper layer (m/d)\r\nK2 = 0.1;                       %  Hydraulic conductivity of lower layer (m/d)\r\nh0 = 3.7;                       %  Water table elevation on the left side (m)\r\nhL = 2.8;                       %  Water table elevation on the right side (m)\r\nL  = 20;                        %  Length of aquifer (m)\r\nb2 = 1.5;                       %  Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 3.7:-0.1:2.8;\r\nQp_correct = 4.613e-2;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx  = [0 2.6558 5.2033 7.6423 9.9729 12.1951 14.3089 16.3144 18.2114 20];\r\nK1 = 0.5;                       %  Hydraulic conductivity of upper layer (m/d)\r\nK2 = 0.1;                       %  Hydraulic conductivity of lower layer (m/d)\r\nh0 = 3.7;                       %  Water table elevation on the left side (m)\r\nhL = 2.8;                       %  Water table elevation on the right side (m)\r\nL  = 20;                        %  Length of aquifer (m)\r\nb2 = 1.5;                       %  Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 3.7:-0.1:2.8;\r\nQp_correct = 4.613e-2;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx  = [0 2.3183 4.6126 6.8829 9.1291 11.3514 13.5495 15.7237 17.8739 20];\r\nK1 = 0.1;                       %  Hydraulic conductivity of upper layer (m/d)\r\nK2 = 0.5;                       %  Hydraulic conductivity of lower layer (m/d)\r\nh0 = 3.7;                       %  Water table elevation on the left side (m)\r\nhL = 2.8;                       %  Water table elevation on the right side (m)\r\nL  = 20;                        %  Length of aquifer (m)\r\nb2 = 1.5;                       %  Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 3.7:-0.1:2.8;\r\nQp_correct = 4.163e-2;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx  = 0:325:1300;\r\nK1 = 5;                         %  Hydraulic conductivity of upper layer (m/d)\r\nK2 = 5;                         %  Hydraulic conductivity of lower layer (m/d)\r\nh0 = 10;                        %  Water table elevation on the left side (m)\r\nhL = 9;                         %  Water table elevation on the right side (m)\r\nL  = 1300;                      %  Length of aquifer (m)\r\nb2 = 4;                         %  Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = [10 9.7596 9.5131 9.2601 9];\r\nQp_correct = 3.65e-2;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nfiletext = fileread('unconfParallel.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-09-30T19:04:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-09-30T15:05:42.000Z","updated_at":"2023-09-30T19:04:22.000Z","published_at":"2023-09-30T15:09:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the flow per unit width and the elevation of the water table above the bottom of unconfined aquifer with two soil layers. The input to the function will be the positions where the water table elevation (WTE) is requested, the hydraulic conductivities of the two layers, the thickness of the bottom layer, the WTEs at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the aquifer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52070-compute-the-effective-conductivity-of-a-heterogeneous-aquifer?s_tid=ta_cody_results\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 52070\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e dealt with the effective conductivity of a heterogeneous confined aquifer. In that case, the effective conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Keff\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_{eff}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for the case of flow through soil units in parallel could be computed by realizing that the head difference is same for the two soils and the total flow is the sum of the flows through the soils. The effective conductivity then is the weighted average of the individual conductivities, using the layer thicknesses as weights. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor an unconfined aquifer, the effective conductivity is computed in a similar way, but because the WTE \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e varies with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, so does \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Keff\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_{eff}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Keff = (1/h)[(K2-K1) b2 + K1(h-b2)]\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_{eff} = \\\\frac{1}{h}[K_2 b_2 + K_1(h-b_2)]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThen using Darcy’s law as in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58966-compute-the-head-for-steady-1d-flow-in-a-homogeneous-aquifer\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 58966\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, one can write the flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e through the aquifer as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = -Keff(dh/dx)A = -Keff(dh/dx)hw\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K_{eff} \\\\frac{dh}{dx} A =  -K_{eff} \\\\frac{dh}{dx} h w\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConservation of mass says that in steady one-dimensional flow, the flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e past any section is constant. Then the WTE can be computed by inserting the effective conductivity, integrating, and using the boundary conditions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h(0) = h0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh(0) = h_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h(L) = hL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh(L) = h_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to determine the flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the constant of integration. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"341\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"559\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" 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an ODE: Ekman spiral on a solid surface","description":"Problem \r\nWrite a function to solve for  and  as a function of  in this system of ordinary differential equations:\r\n\r\n\r\nwhere , , , and  are constants. The boundary conditions are that  at  and  and  as .\r\nBackground\r\nThis set of equations results from simplifying the Navier-Stokes equations (i.e., conservation of momentum for a fluid with a linear stress-rate of strain relation) for large-scale flow subjected to rotation. The horizontal velocity components are  and . The Coriolis parameter  is related to Earth’s rotation rate and the latitude, and  is the kinematic viscosity, which can be interpreted as an eddy viscosity to account for the effects of turbulence. \r\nThe velocities far above the surface,  and , result from the pressure gradient:  and , where  is pressure and  is density. Notice that far above the surface, the flow is along the isobars, or lines of constant pressure. As the surface is approached, the velocity vector rotates—or spirals. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 388.2px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 194.1px; transform-origin: 407px 194.1px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.9417px 8px; transform-origin: 29.9417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 86.6px 8px; transform-origin: 86.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to solve for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eu\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ev\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.3333px 8px; transform-origin: 51.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as a function of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 147.683px 8px; transform-origin: 147.683px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in this system of ordinary differential equations:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"121\" height=\"36.5\" alt=\"-fv = -fV + eta d^2u/dz^2\" style=\"width: 121px; height: 36.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"102.5\" height=\"36.5\" alt=\"fu = fU + eta d^2v/dz^2\" style=\"width: 102.5px; height: 36.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ef\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eU\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eV\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eη\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.083px 8px; transform-origin: 152.083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are constants. The boundary conditions are that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"62\" height=\"18\" alt=\"u = v = 0\" style=\"width: 62px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"35\" height=\"18\" alt=\"z = 0\" style=\"width: 35px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"40\" height=\"18\" alt=\"u = U\" style=\"width: 40px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"18\" alt=\"v = V\" style=\"width: 39px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.275px 8px; transform-origin: 11.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"45\" height=\"18\" alt=\"z --\u003e infinity\" style=\"width: 45px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.342px 8px; transform-origin: 382.342px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis set of equations results from simplifying the Navier-Stokes equations (i.e., conservation of momentum for a fluid with a linear stress-rate of strain relation) for large-scale flow subjected to rotation. The horizontal velocity components are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eu\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ev\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.0167px 8px; transform-origin: 77.0167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The Coriolis parameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ef\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.283px 8px; transform-origin: 168.283px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is related to Earth’s rotation rate and the latitude, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eη\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 115px 8px; transform-origin: 115px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the kinematic viscosity, which can be interpreted as an eddy viscosity to account for the effects of turbulence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.35px 8px; transform-origin: 114.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe velocities far above the surface, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eU\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eV\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 108.9px 8px; transform-origin: 108.9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, result from the pressure gradient: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"123.5\" height=\"18.5\" alt=\"U = -(1/rho f) dp/dy\" style=\"width: 123.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOEAAAAlCAYAAAC0yo7YAAAKOUlEQVR4Xu2cS6h2YxTHmZMwIqEYEGHgViIUSiTJraSvyGUgGRAGkgHCRAYuISn3kEgxMFDkMnGNAcKAkVvMWT/t/2l9z/fc937f/Z7T3rV6zznvc13P+q/bs/bZe6/lWTiwcGBWDuw96+zL5AsHFg7stYBwEYKFAzNzYAHhzAcQmf5c+9sfRp9u3tJ21Io2hs8LCNNydbl99cMMYPjF5nzE6L4NEfk7NmgtU7JkY/i8gDB+rDfYn88yAojrfE6yyT4xOtDo93VOnJkLHtxidP4GrWksazaKzwsI9zxOAHix0XljT7qj/+PW5/A1zn2AzXW90ZnDWl+3z8ci64YnNxudtkOAuG4+Z0UhBUKYvsvolKD3y/b7Z0YxV+kB+/uFRkcNff6xz+eNcGc2RauXcEGc8KrRYQ1rps89Rm8k+FKa03//t/1yawIILePUtMUaPDs0vMA+bzO6zugJI4AZPpwvfGnxDmh7dyATb9vvdxp9X7PIFbWp4TMK6lEjPIB9hnV8a58PT30+OUvIIn5yCwCApQM4wtp8Nyz4xqkXu6ID0bDaby0IBD4pKgRrTBwHb58cBH3VSou9fmB0iNEJAyA+sk/28rHRqRFe0+crI1zTlyrPAnngEeC0R4T6ioZxKqeratbCZ8743WFU9nKv0WVGgPHoqtkqGpXcUR0MQ6U0pJ8GC4r2YOFXGq1amCq2WN0ETX+V0cGFHgjj7UZYheOMZPnHglCCXVJ01RvKNGSvKBuvWLGMlxq9YpTKzHK+Dw577z1bxWN4Si0exxT7ZoyxfH7HxgCc8AHvYfRTAqEOi4kAVilOArTHGJ2dOcjRi17BAC1WkLY8CCGHwaHwjAGh5r/WCckKtvn/kN7D4Tyl6WvmU18swhirP7kg1yze7X0Mn6VEmLKEn6pllQZBK784jFQywWo7mYao2sE0jYhbEazWrORUIMTC3GVUssJT7FbeSq8lwpKcPnKt4ndJpqbYrx9jKj4TU07mUpdA6FHPZnJCyr3LX0bbMYP2zXBSrX7+VCDEMvxoFEuITC2I7BUXOhX7leYTiE+2hr0FBeIbimDf0oQTfj8VnxWmjfF+trZVAiEN/3VMONJ+jmW15LbOFWyPOSdcrN+MamLecJ4pQKhk1hihrt2/9kr7nv3ST4p5jAB6vpX2DX9YtwDPzycOG25xpafks0BYE6IVz6YGhNKcDBYDmeKED+37UsxYXNAMDSQQPW70FCDENbvaqNUKwyp4T2x2hhFeCNnNX418xU3ozcRYXJP59v1QzDV94M81RrivBxlh+biieMpIsXQIQsCCR+Cvu5ToI+lHdtI/tVn4Vj7rDvWiga/MifvMfSlXUvA6BCEhGfkQzgNvI+QRxor14spuGbQaECqIZhEx7UeMwF2KUt0Bj6p/9ZnY6k5Bwx73RvFJa5KCqacAIUqO+7rWRAfges/I37vJVWRtMZBwVhLi1vjXsxoQltxZLsS5d0QpILSsZ3+jtwYB1XgpS+jzEfQFyH4c7qt1f1eypszVwmd4y70vioO5HzLCEktWtHYPQpTHOUaUOgqktBPYFEvjfrPuLeVRA0KfIQ1dGAnhGNdEG5oLhNrfHCCUlUq5+V7w/c8C4Nf2x7CcjNgc4eEJgSavBo0+JnbnrA41SiWSBHYAiCXxsaNXFCjNlPL27Rhnl5F3PwVy9lmSvxY+i7cAJeaye/6mXHqvQPAeUT6sn7PiwZ3e2ksNCP2AofbjMHi2c13hnCDsKZ+S+w/fY1dBXpn58MHHgzWu5HC00Q/NEZMf8ROAXRIAh8G895DzXLzVjoVBOeMQLrqWz/76JhXvef6mwO95DWb2M6IqKVolVANCzzSfUpam6rEguQNe93dzghCtiusSq9dM8UHCmQJSCoT+HGvjqNQaUiD0Qpxan19HzqXVNUDKansQlixhLZ+9AknddXv+5mS/lEvZ4m0NCGnsM6S4ODyUtBGPrKPCY5XAnAuELeVT2r8vC0zFQRJe+nh31AttTQyV43nqSkcxU8oKMqZfRyoZ5pNJqTY+V5EDQwufxbtc1lNYKN2zenc5G3/XgtD7wRwg5U2UeBEsz1mIOwU4x1j0MYmZnvIpn+w41jYflo55kIZWRkJLfBXr28LLVGJGViJ3Ce8tREoZ+ARISdmU9lPLZ3+Wqas2H5qVrid8TJtVerUgDP1gqkvGujThoc+VmJnjiqK3TE3KMOXqeSsTClKNlq8FIiCMJSVkJVLr80oiB1QP5lgCyQt4zhVt4XONK1qKU8W/8OWH7PVXLQj94TIRWnbqZMxcIJS73ZOs6LWECBEH01It4l20mAIMkwq+gN4Lf899qAen9hxbg0CYAkatEGucVPaxBFKtt4XPHoSxc6lVIMzN+j430n1h9jqnFoRe8zDJ2JiiVuOuqx2uGin31gvzXhD2lE95RRi70tD3WJgwE+fdqLGJNLmKsTXIUsdA6IU458qV3EIfd5ZeFGjhs2Q8lbGVAsnFu8gr53C8EUqQu1/uSnmENfa32/8QqgWhZ0xvudO6ANUzjw6g9b6uB4RKX7cqspz21/pjAIQfiiVLyYQa3ulaKvbOoQQ1tLZ6f/Eom6DkReUSGv41qNj1h19/K5+9kghx4QEavm9KPwjFQjsqaqQEQ+UH+CjM2E1J1oKQzeEilILgmkPcxDZy5SiLanlHrOWuSvtGk99k1PLGhL93CmMpWQaUI+uJJcoE4FKVS+lsJKipfADfU8nCo0t4FBVvowNAlZ/l3kX0iRufVVSWkwIF+FcqHu/hsxSADI3eHQV4qvwJr5MUa6PgeLxy8OfG97TdNfBhi9ctIMTVaHmrunSgm/Y9AlzzUi/rpq2vbdReEPL3je43SglaS/mUxg1fKfvCvvjT6HCjH414Iz8nlIqxxsaD2nfObcdaUbtKbSUPSuNno6eNlKlMnb0XWoT+SyNiK9w79vtaxRgau4fP9GWPqu8EOICeMwWgOQUXq+rReALxLvvDHkXnLSBMMW4n/Z2De9OoxRq27F+WpNXtrb5ziizGJ3Ra5/XDycqV3MAWfoRtfe5hzBs5vXwes/buvgsId2edCnfDesduBgcdARNaPRZP5eZQwqPHnZS72tPXrwmXFouwKgXFXD57OqbAvJfPU51z0zgLCPdkl2KYMQXOqUOoLZ8KLZD+eVaNO4kV8G6TYqwxlgUXrfU/rTUJ4tBYymbsG/c9fO5Z7yR9FhDG2ai4Zsq7UGVSWzW8d9FK1wtyW3UFILesVN2REybmP8to1eWJ3m0ek4Hv5fMkgOoZZAFhmmvhG909/PV9asunwnmU2azJTKs0TVlIanuzFfwVmwJ8pYRKxTDFJj7uHVON1cvn4gJX1WAB4ao4u+e4pKdb/8sXiuC5Yahn7LP0tgXZxReMsAbK1KayeuvbeX4m9kicSazsn1xGMjdiD59n5cUCwvWxnwRJ69vz61vdzplp2/F5AeHOEb5lJ9uUAwsIt+nBLcveORxYQLhzznLZyTblwH88VulE2UZPZQAAAABJRU5ErkJggg==\" width=\"112.5\" height=\"18.5\" alt=\"V = (1/rho f) dp/dx\" style=\"width: 112.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.8917px 8px; transform-origin: 24.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.7333px 8px; transform-origin: 51.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is pressure and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eρ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 237.9px 8px; transform-origin: 237.9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is density. Notice that far above the surface, the flow is along the isobars, or lines of constant pressure. As the surface is approached, the velocity vector rotates—or spirals. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [u,v] = EkmanSolid(z,eta,f,U,V)\r\n%  u,v  =   velocities in the x- and y-directions\r\n%  z    =   distance above the solid surface\r\n%  eta  =   kinematic viscosity (can be interpreted as an eddy viscosity for turbulent flow)\r\n%  f    =   Coriolis parameter\r\n%  U,V  =   velocities in the x- and y-directions far above the surface\r\n\r\n   [u,v] = deal(U,V);","test_suite":"%%\r\neta = 1e-6;             %  Kinematic viscosity (m2/s)\r\nf  = 1e-4;              %  Coriolis parameter (1/s)\r\nU  = 1;                 %  x-velocity far above the surface (m/s)\r\nV  = 0;                 %  y-velocity far above the surface (m/s)\r\nz = [0 0.05 0.1 0.15 0.2:0.1:0.5 0.7];    %  Distance above surface (m)\r\n[u,v] = EkmanSolid(z,eta,f,U,V);\r\nu_correct = [0 0.34124 0.62515 0.83094 0.96209 1.0627 1.0562 1.0269 0.99833];\r\nv_correct = [0 0.24312 0.32032 0.30214 0.24014 0.10216 0.018209 -0.011186 -0.0068865];\r\nassert(isequal([u(1) v(1)],[0 0]))\r\nassert(all(abs(u(2:end)-u_correct(2:end))./u_correct(2:end) \u003c 1e-4))\r\nassert(all(abs(v(2:end)-v_correct(2:end))./v_correct(2:end) \u003c 1e-4))\r\n\r\n%%\r\neta = 1e-6;             %  Kinematic viscosity (m2/s)\r\nf  = 1e-4;              %  Coriolis parameter (1/s)\r\nU  = 0;                 %  x-velocity far above the surface (m/s)\r\nV  = 1;                 %  y-velocity far above the surface (m/s)\r\nz = [0 0.05 0.1 0.15 0.2:0.1:0.5 0.7];    %  Distance above surface (m)\r\n[u,v] = EkmanSolid(z,eta,f,U,V);\r\nu_correct = [0 -0.24312 -0.32032 -0.30214 -0.24014 -0.10216 -0.018209 0.011186 0.0068865];\r\nv_correct = [0 0.34124 0.62515 0.83094 0.96209 1.0627 1.0562 1.0269 0.99833];\r\nassert(isequal([u(1) v(1)],[0 0]))\r\nassert(all(abs(u(2:end)-u_correct(2:end))./u_correct(2:end) \u003c 1e-4))\r\nassert(all(abs(v(2:end)-v_correct(2:end))./v_correct(2:end) \u003c 1e-4))\r\n\r\n%%\r\neta = 3;                %  Eddy viscosity (m2/s)\r\nf  = 1e-4;              %  Coriolis parameter (1/s)\r\nU  = 0.5;               %  x-velocity far above the surface (m/s)\r\nV  = 0.8;               %  y-velocity far above the surface (m/s)\r\nz = [10 50 80 130 190 240 300 400 500 1000 2000];    %  Distance above surface (m)\r\n[u,v] = EkmanSolid(z,eta,f,U,V);\r\nu_correct = [-0.010943 -0.031442 -0.026767 0.0081958 0.077758 0.14605 0.22904 0.3501 0.43683 0.51587 0.49983];\r\nv_correct = [0.052233 0.24389 0.36912 0.54304 0.69822 0.78853 0.85848 0.9072 0.90497 0.80113 0.80021];\r\nassert(all(abs(u-u_correct)./u_correct \u003c 1e-4))\r\nassert(all(abs(v-v_correct)./v_correct \u003c 1e-4))\r\n\r\n%%\r\neta = 0.5;              %  Eddy viscosity (m2/s)\r\nf  = 1e-4;              %  Coriolis parameter (1/s)\r\nU  = 2;                 %  x-velocity far above the surface (m/s)\r\nV  = 0.4;               %  y-velocity far above the surface (m/s)\r\nz = [10 50 80 130 190 240 300 400 500 1000 2000];    %  Distance above surface (m)\r\n[u,v] = EkmanSolid(z,eta,f,U,V);\r\nu_correct = [0.16323 0.81912 1.245 1.7492 2.0401 2.1093 2.0958 2.0295 1.9988 2.0001 2];\r\nv_correct = [0.22054 0.76866 0.91944 0.89604 0.70242 0.54931 0.43377 0.37707 0.38631 0.39997 0.4];\r\nassert(all(abs(u-u_correct)./u_correct \u003c 1e-4))\r\nassert(all(abs(v-v_correct)./v_correct \u003c 1e-4))\r\n\r\n%%\r\neta = 10;               %  Eddy viscosity (m2/s)\r\nf  = 8e-5;              %  Coriolis parameter (1/s)\r\nU  = 8;                 %  x-velocity far above the surface (m/s)\r\nV  = 6;                 %  y-velocity far above the surface (m/s)\r\nz = 200:200:2000;       %  Distance above surface (m)\r\n[u,v] = EkmanSolid(z,eta,f,U,V);\r\nu_correct = [1.4945 3.5616 5.4425 6.8363 7.7122 8.1675 8.3361 8.3398 8.2686 8.1789];\r\nv_correct = [4.3838 6.7003 7.591 7.6499 7.3224 6.8916 6.5067 6.2251 6.0503 5.9609];\r\nassert(all(abs(u-u_correct)./u_correct \u003c 1e-4))\r\nassert(all(abs(v-v_correct)./v_correct \u003c 1e-4))\r\n\r\n%%\r\neta = 12;               %  Eddy viscosity (m2/s)\r\nf  = 8e-5;              %  Coriolis parameter (1/s)\r\nU  = 10;                %  x-velocity far above the surface (m/s)\r\nV  = 5;                 %  y-velocity far above the surface (m/s)\r\nz = 300:300:3000;       %  Distance above surface (m)\r\n[u,v] = EkmanSolid(z,eta,f,U,V);\r\nu_correct = [3.5576 6.9831 9.1755 10.1948 10.468 10.397 10.2354 10.0997 10.0197 9.9861];\r\nv_correct = [5.5429 7.208 6.9985 6.2349 5.551 5.1311 4.9452 4.902 4.9216 4.9554];\r\nassert(all(abs(u-u_correct)./u_correct \u003c 1e-4))\r\nassert(all(abs(v-v_correct)./v_correct \u003c 1e-4))\r\n\r\n%%\r\nfiletext = fileread('EkmanSolid.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":46909,"edited_by":46909,"edited_at":"2024-03-11T02:38:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2024-03-11T02:38:47.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-03-10T16:24:15.000Z","updated_at":"2025-09-16T00:37:21.000Z","published_at":"2024-03-10T16:24:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to solve for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as a function of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"z\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in this system of ordinary differential equations:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"-fv = -fV + eta d^2u/dz^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e-fv = -fV+\\\\eta\\\\frac{d^2u}{dz^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"fu = fU + eta d^2v/dz^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003efu = fU+\\\\eta\\\\frac{d^2v}{dz^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"eta\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\eta\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are constants. The boundary conditions are that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u = v = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu = v = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"z = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u = U\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu = U\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v = V\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev = V\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"z --\u0026gt; infinity\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\\\\to\\\\infty\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis set of equations results from simplifying the Navier-Stokes equations (i.e., conservation of momentum for a fluid with a linear stress-rate of strain relation) for large-scale flow subjected to rotation. The horizontal velocity components are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The Coriolis parameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"f\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is related to Earth’s rotation rate and the latitude, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"eta\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\eta\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the kinematic viscosity, which can be interpreted as an eddy viscosity to account for the effects of turbulence. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe velocities far above the surface, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, result from the pressure gradient: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"U = -(1/rho f) dp/dy\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU = -(1/\\\\rho f)\\\\partial p/\\\\partial y\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"V = (1/rho f) dp/dx\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV = (1/\\\\rho f)\\\\partial p/\\\\partial x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is pressure and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"rho\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is density. Notice that far above the surface, the flow is along the isobars, or lines of constant pressure. As the surface is approached, the velocity vector rotates—or spirals. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55335,"title":"Generate Bernoulli polynomials","description":"The Bernoulli polynomial  is a polynomial of order  with the properties that  and for  \r\n,\r\nwhere the prime denotes differentiation with respect to , and\r\n.\r\nTherefore, , , , etc. Notice that  is the th Bernoulli number.\r\nWrite a function to generate the Bernoulli polynomial of order . Use MATLAB's approach for specifying the coefficients. For example, the function should return [1 -1/2] for  and [1 -1 1/6] for .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 201px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 100.5px; transform-origin: 407px 100.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78.5917px 8px; transform-origin: 78.5917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Bernoulli polynomial \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B_n(x)\" style=\"width: 36.5px; height: 20px;\" width=\"36.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 76.2417px 8px; transform-origin: 76.2417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a polynomial of order \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74.675px 8px; transform-origin: 74.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the properties that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B_0(x) = 1\" style=\"width: 62.5px; height: 20px;\" width=\"62.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.6667px 8px; transform-origin: 25.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n \u003e 0\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B'_n(x) = n B_{n-1}(x)\" style=\"width: 113.5px; height: 20px;\" width=\"113.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 169.858px 8px; transform-origin: 169.858px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere the prime denotes differentiation with respect to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 27px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 13.5px; text-align: left; transform-origin: 384px 13.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-8px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Integral[B_n(x),{x,0,1}] = 0\" style=\"width: 80px; height: 27px;\" width=\"80\" height=\"27\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.225px 8px; transform-origin: 34.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTherefore, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B_1(x) = x-1/2\" style=\"width: 81px; height: 20px;\" width=\"81\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B_2(x) = x^2 – x + 1/6\" style=\"width: 121.5px; height: 21px;\" width=\"121.5\" height=\"21\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASoAAAAqCAYAAAAETRabAAANHElEQVR4Xu2d6+t/2RTHZ/4Adw+HfhkeKEUGI/GAwoREyDX9yjSuKcZl3PLA/ZZSGDL1S4QiEtPMKB6Q3CPkgUsT8cgl/gHWK+fNan/3/ezz+ZzP97tPrb7f3++cs/faa6/13muvtfb5Xn3VvKYEpgSmBHYugat3zt9kb0pgSmBK4KoJVFMJpgSmBHYvgQlUu5+iyeCUwJTABKqLpwP3syE/2eiBy9Bvs59/OydieJCN4zHL2P5pP798jsZ2TqaobxgTqPrkdqpvPdwY/47R75cBPMp+/sPomUbfO9VBLXy/wH5+wejOBazus4ztJfbz9o6xPd7eeZzRBzveveivvNwE8KdOuUdlt3egYvV/l9E7Bq2MT7N2HmD0qQuqST+2cb/TKRAKdavRl4ww9FO9AJUrRtc7PfmE/f7KBawe0qE/X7R3/m70qlMVyhH5ltyQ4ZBrz0AFSH3e6M1Gvxgy2v828iajSxdQATHma4xC5fm3/d9PjB49UMaHbgpQ+oZR6DlhMHhWT4/cy/GI7v3V6BGDde/QcjlGfzgDnzO678jOS0CFUZcuYgHfMvpD6cGG+yjKHUavM9piS4Jis+V5WwNP5/FRGeQrbHBbeJm0j5fzsEV4399oPjGO2PYOHXqqUStQ4V2+2+jBmUn38TAe+5XRD43OS7yvV9+xLa6cJ0oI4rFG96rVixJQ0Y4QkpWJCwP/pBEARUe419wjNsDkjgAWVn3iKFsCye+s/dca9cQveidxb++xED3SaItt33us3bdGBoz3dqPRSC85JVcB1f3tgRYAYYt8V0L/AN/XJ8aGbfTGxPamGz38aOFLLQyAO0DG4hFeWb2oASoa1ITzexjPoHM6UfDyiSuVEKNhMD1xhRbhshX6+gH6aeHpUM96Y2PR+bDRSI+Y+WMe32+EF3VPo2cYsahxsQj5eNJW42Zb2xp/Q5/h79qETGQLPMNihyxJSvir1YPbavyHbjfniSKn3xqBE+AFCwceK3LWhUyfY3RmEasFKiZc1wvtlzDO4VfPVsUIhcnkf9roENkWVk7oIgVMUZiXGV0yEnDgDd8wSKtR1suLTEPwU/CerrY2Zi14gEgLCMMjHl8sZif+QxsA3N5r9PxFhiOBmG3SPYz+0jiOQdPZ1ExuJ8S9pxiFjgwOw0eNBPZR/KgBKgT1c8dubKVhC/GB5Zk1gVmlmFtd9SZpuocP3V8vn1u9p3IFVrmUB9HaN8AP6MW2Wtoa0OZWcTHaph/iRW83as08sVB+yCgWs8vdo1/uy0N4gv0+IgwiD25LebXOcex5eaKxBETuHm3pPr+zfT6zm6oBKr8KpkDIAxWrSS4ImRMKSo6Cj1rdSxOwdTC51P8e7gusR3g4yJPMYi7+JO98lCHHZMjWEx5aEwRalGMLpVb+XHbU28ooYDkVoMp5ouAD8exczJkFRR7pGbCrASofn8K9jXXmO+nd+glVKUc4xLZPCn5ocNwDOHkeMMDvGm0JHOpPQLDG6y7JD4Nhe9GTICCEgUcUexc5ceW8JMmS5y4aUGFHn0ksDsjzR0a5Lbh3drqAysenYsrsJwe3rTeYrpW91WB8mpgjE14Y3Huu0R+NUlsAFQbWgHbJSI5x36d6Q4BXdXWuLEBZ3a2TF8hGcYrauJH4j80f+sIxID/n/N+zIkCDjLhKmca1hYreFkbVYG3pUfnykVBHuIft4AmVHActQGvCBwIqMORMDVbJOFHiby6THO4dFZS9xe4T40hG7CutV4zWTjC8vdTo3kZKd3pvTsCn7lNCbO3XD0fGUjnE5GMlRYi9qNICxqVApF/FBcC8iweDp8G2JTz/hiH81GjLUhCdMEBeNel7eGeR8Vkh6YVq7DRmspYkQ5RxCrOJSom/2J7JlSiMKFTU1m+kx7gFUCn4j+1wNlL2K9n52CX6E0ugeZ3MeaK1tqFdWXTXVgIqn80DiACC65aeBQ4oCrGA0mpVYlgTUuIp1o7eFZg+1B66YkSdFGlxEDq1FZBytXpy8OG3xaXxpe5HV5CGxnzaV9k7QOxJRh8zAsx/trRHwoP+3mL0a6MXLf/eCqS0Kr/R+vFpaPTo1Ual2ibvoSgkIGD9pb1/eRnjn+2nT/iE4hOY5cRaU6hYmhYZW8mwS+34+1sAlW/fb7mwgd8YkYggoYA3hR6xEOS2bSQRehIXng+dIog6FCVQYN/pV667l5Yv2U8MX0i8lkmaXQNUPoiJsK8sSlyTdZEx9MQURnhUFM62Bn1DRZeBsJgAzgBUrE7J83uISmqdbEBfSE17sKotiZACA24AbqxAlflXlXMoG/4dhgTCZ5RU6Vms1JZirLXjivEZ+7+tgcpn9bGBZxt9tUEnR4QOtPtJxqdzQOVThggwRDpf6Mn9HkP3E7MGqLyw8RhYAWrT0gKqQwfxaxW15jkP1Gu34DX99T4Dn+8z0imHmkyjQJh5BbR6M8o5nrVtXNN2a/xN/CgOl+LvpsX2BNSp50pgnBu/FgNkzDha6grXeqIqJcErS27Pc0DlYzypkgNvIAwyFiQF0Pj+EStezntYA1RMgoTdWh5xHoDKA3XNNqcXaEa853UmlUX2/fjnR26pwkVyTZxOtlIbX/V9+63XGvn29K3+fNa+JSCusENN3DE1NoAObzt7UiEHVD4Ym1L+0OsKFUkTiDuswCiBRuolwj3vWqCSsFsDmb3ZxjVKtcW7Auoa40/1v8ZoWhYIv51LxQ7FowfhGg+sVbalIzOl9hR47jXWWo8KG/p2hpk1H0D0i0FLsfVaT5T3wZliFjgHVFImZJNbyXz5gjcSFICDnaClQElgEtsmKnDfIijNW5gJalkVZJw98YkRMSrG0JP18zrrszQtgBHqPfEGfemgZKDh/VwJSPisFqUa78979jXPt/KdK1QstbUWpErtc3/rGBV9eKekxWtd8/GAapCCwRRQ1Ryb4X2flQkBDQX4gZHPBur52Kq/JvuGoEm9K/DfImwBZCmxEFOqvWT94INL428B6hpjGf2M5FaaJ/TwK0vnjGkNCKfGUDoWk3rvECB1CKCSV0RmnNhh7WJQOhaT05kmkMoBVc2xGd4PtwolA1FdVmw/LXBsDcpL0OxxdTq7VthSBDyyng/HjfCo1mb9AGmUjCC1UvQlABgNPK3t4a1z5YpM5SVT7cx1qwOslkPGOd56CxVrYzPYx1pveUuPSgvBZePzNUaEZGoXAzCCspPWBATOCl8tyW33VMT9v4RYyovwnkIq5uHrd1CGmtgI7eZSn6xubBdrsw4StD4N4dP0CFDKHouJwbPS0jW8txrjIZ4PYwTarguokQ+G3gPCvfzTJ6f9U6UhqS8QhP35bJL38AXCtENl+poasJ5CRelU6ntVGgf8k2Bawx9tbQVUGsdHrA/sxjsncjj4/88a3R5RhtyRmZTu1Hih4st/Mju69fMn3FMApAOa2U8zOG5VHUwVLEaUmjwUh0+PpD5jCm8fX9rljxTgRfggZpghutnuayJiwpOHV/IEe4129HtMNEWbeBR3G91i5FcmD9TUtvEhw+j3fUYztrTnAYWkRviF1ly9DPcuG5F9YwsCuHqAFQgTVGax61nNw2G3Fir6WCh8pC4ljkbo1Uigwr4o2EZ+fMrGg62fOxZulZDEnIaeBIRACplx7i91gRFnylBCjwoG3mCk7xTRGKuCvujJv59nJIBCGXNAwPMwSBU7Fa6qZk/VLEkAqa1LGBMLt4lhFrK0jcSwOUZwQ0Zwe7rlt9rMS/jXY3zgOXZ/67GEXjb9+Y+k8TuLS+wUg/fiY99z8gHfEd97ai1UDBM2JVmOKvwcCVQ+8RX7eADAraLc3McFBHi1duOTPSW5cf8MPnig0gHemoY4wNjzIS8ZUm4fXBKC4kKpg7Y1B3EZ45pgYI2MtnjGHxRNFfhJPmsKANfwDo/+7wYSg+O4DkczckdmpH88H/t7fBo7vI34e32thYqlMoJQZgDV2mNltDkSqHKHvGUTpUP8PNfqibbGcs+UWvRkutYoMe9qZUyVIahSdcSxnByvKMCaIr+1cpjvH08CtcHw43H4/54V8+txDLbgX7uanjKibn6OAVRsX4it5DI+CpL7GqzuQUZeXFM7M5KP2dZxJBAmIY7DxWn22uqJDhnlMYCqtLXTwIghcMC29HmOVkEoE8b+unR6v7Xt+fxpSGBNoeJpjHA7Lgl091bhd3O1JVDhIl5j5A8Ht7rcynKNAiva4xMnNZ8Y6RbqfHHXEjjF2OReBKpCzaF/XLRmcFsClYKAygz+yxji20hfC8CrxCfgNsrzQUlHFQuW+J739ymBue3vn5ejeaJbApXPUCGarf5Kbr/Y55sXUQKlouOLKJPaMVPesOYrDbX9nHluS6DqZmq+OCWwoQTY/o8oG9iQxd02fTTZTaDarU5MxqYEpgQkgQlUUxemBKYEdi+BCVS7n6LJ4JTAlMAEqqkDUwJTAruXwASq3U/RZHBKYEpgAtXUgSmBKYHdS+A/9gtJWNMfwWUAAAAASUVORK5CYII=\" alt=\"B_3(x) = x^3 – 3 x^2/2 + x/2\" style=\"width: 149px; height: 21px;\" width=\"149\" height=\"21\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.4917px 8px; transform-origin: 52.4917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, etc. Notice that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B_n(0)\" style=\"width: 36.5px; height: 20px;\" width=\"36.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6083px 8px; transform-origin: 20.6083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45831\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eBernoulli number\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 190.092px 8px; transform-origin: 190.092px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to generate the Bernoulli polynomial of order \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.658px 8px; transform-origin: 188.658px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Use MATLAB's approach for specifying the coefficients. For example, the function should return [1 -1/2] for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAkCAYAAADFGRdYAAACUklEQVRoQ+2YuUoEQRCG3QcQz0iM1EQQNBAjETRR9AHUTFDwyj0wFLzARPAKhM3UB1A0MjBURDFVQyOvN9D/h25sm3G7lp5lYLcGfnp2uma665vqqt7JVekRJJALWqhBlUISBIFCUkgCAgITjSSFFCTQAIsa6KWQZaVGEuFMQkvQMnSokP4SWDBw6szlGYX0C6jFRM8j2j5oViEVTke96L5WSAopWLVCBqlHEitBM/TgjMz13QS9hspnaLYZ9UdDGsbEO6ABqAdiFbAVgHD2oEHj3Cfafg9gIb8JvD0FMLEvJxqSjZI8nGk1DrGthq6gDXNt07RraFeEjruTE96SaBYs24GHR0Oyz7/BSTd0Cc1Bt07UuIOM4/qJ0ONO2Fm4wlsSzXZw9TziAalA4rJ4M5PgW5uCth0Y0zg/MP2NaN8jJpzFralAYl46M7NnJPG/DaPJHsxL3IyxbygLLyPHTAWShcC5PENt3qQ+8JsJfRHaipxwFrenAukJM7dJewTn7vpnXrk3nnWhdbcGIYfLprq5EE7h9Zjnuc1HLP/1ISpef9lUNzcp+1FEny8g7pP2ITdPSXiVTXWzEJIixa16tvSz/K8XuewkQEtpE52Tvs3skiKFS+/Y9LP0r0KEKd1MltLxYp4dBckt/UlLzV2K3Fyy8vk5q5jJZmHL1bALjZrBmXfnoX/3ev7nWzo8YW5O2v/YAWphk4ekO+0sYCSNya+S/E/qH1+4cAcdJcGq1G/cRb00hSTApZAUkoCAwEQjSSEJCAhMNJIUkoCAwEQjSQDpB91GeCVOeCsXAAAAAElFTkSuQmCC\" alt=\"n = 1\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 55.2167px 8px; transform-origin: 55.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and [1 -1 1/6] for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAkCAYAAADFGRdYAAAC5klEQVRoQ+2YPUscURSGd3+AoNFKUplYCIIWYpUUWiQhtimUpLAQ1PwAFSyF+AFJEciH3XYmaKvEKqBio4X2aplKk5+g7wv3LHdnzr1zk5khK3MHXobd+zFznjlfM/VaPDIJ1DNnxAm1CCnACSKkCCmAQMCU6EkRkpPAEEY6zOhRFqeqedICgCxBXQkw7/D7A3SjAasSpBMAGPF4zT7GXmugqgKJHrQOzUE7BkQfzq8SnkWPWk6CrAKkbhh9DU1B3xRPeoL/Ds3/f3B+UEVIszB6DJr0hJodisOYd27PrYInMdSOIV8Vk3Akm3+CRHd9mKDLeO6FfkFXnid0X4YEEsOt3+Ss5r1rnvQSo4PQODQKsVwy4W1ChPMZem7FMF25xT09ZAh8oAByRT8c2jQPfYdSYalBEi9pYMEjYxDPbL5+QmvmP1YLHmpFcICwk2QeVvLQ8uxhr70wtj7FORWWvpwkyYz9w1voFBKvsY11VQ3NAHa6AjePgR+xeC/PBtZasUX1Is5zQZKyyTl8ajPQe0hKKCvGV3OhHpzVTrUgI8re5gcu8Bh6Bqn51QWJeWnX3B09iYvpTXJIDHPsRdlWlLg/H/Yq5M2rLkgCgfd3aUjb9/obP5jQF6GNEo0oc2uG/hk0AXlD1wVJEhlvMrmJbM6xVE+RYVW7VDfawCL0JgsQ7dEg2RC0ZCb5SG3hMyC1Q3X7K0AuSHZS1lyRiY590hfIzlMhofG/qxvbG1ZpnweJtzdbAc2TBILmKXbVk9LPisfkF9pQhsAsYw7vnbZtZ+RR5uMDqPkyrEG6NXeoeQq70S0zztK/AhFm6vNCGVbm2FMAsSmWZljbTt4yWl5NkpDs0q+Fmh2KdFtWPt/bdQ67ClsqgHwf3OyLpd4gkpBo8LRZofU/vOAnqBNq2C5ZmEnFb8SXV3pI6MG2pnKfSkLhOOdV4XtShJSbQMAG0ZMipAACAVOiJ0VIAQQCpkRPipACCARMuQPmxYMluJzL1wAAAABJRU5ErkJggg==\" alt=\"n = 2\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = BernoulliPolynomial(n)\r\n  y = sum(nchoosek(n,k).*x.^(0:n));\r\nend","test_suite":"%%\r\nn = 0;\r\ny = BernoulliPolynomial(n);\r\ny_correct = 1;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -1/2];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 2;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -1 1/6];\r\nassert(all(abs(y-y_correct)\u003c1e-11))\r\n\r\n%%\r\nn = 3;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -3/2 1/2 0];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 4;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -2 1 0 -1/30];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 5;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -5/2 5/3 0 -1/6 0];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 8;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -4 14/3 0 -7/3 0 2/3 0 -1/30];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 11;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -11/2 55/6 0 -11 0 11 0 -11/2 0 5/6 0];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 14;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -7 91/6 0 -1001/30 0 143/2 0 -1001/10 0 455/6 0 -691/30 0 7/6];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 21;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -21/2 35 0 -399/2 0 1292 0 -6783 0 293930/11 0 -223193/3 0 135660 0 -1443183/10 0 219335/3 0 -1222277/110 0];\r\nassert(all(abs(y-y_correct)\u003c2e-9))\r\n\r\n%%\r\nn = 30;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -15 145/2 0 -1827/2 0 28275/2 0 -390195/2 0 4552275/2 0 -43785215/2 0 339319575/2 0 -2062720845/2 0 9509268925/2 0 -31795091601/2 0 72484065225/2 0 -102818379585/2 0 78132595905/2 0 -23749461029/2 0 8615841276005/14322];\r\nassert(all(abs(y-y_correct)\u003c1e-3))\r\n\r\n%%\r\nn = 12;\r\ny = BernoulliPolynomial(n);\r\nn2 = round(y(7));\r\ny2 = BernoulliPolynomial(n2);\r\ny2_15_correct = 373065;\r\nassert(isequal(round(y2(15)),y2_15_correct))\r\n\r\n%%\r\nfiletext = fileread('BernoulliPolynomial.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-09-17T15:39:23.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2022-09-17T15:39:23.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-08-20T20:19:44.000Z","updated_at":"2026-01-26T13:39:36.000Z","published_at":"2022-08-20T20:21:33.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Bernoulli polynomial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_n(x)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_n(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a polynomial of order \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with the properties that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_0(x) = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_0(x) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n \u0026gt; 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en \u0026gt; 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B'_n(x) = n B_{n-1}(x)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\\\\prime_n(x) = nB_{n-1}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere the prime denotes differentiation with respect to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Integral[B_n(x),{x,0,1}] = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\int_0^1 B_n(x) = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_1(x) = x-1/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_1(x) = x – ½\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_2(x) = x^2 – x + 1/6\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_2(x) = x^2 – x + 1/6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_3(x) = x^3 – 3 x^2/2 + x/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_3(x) = x^3 – 3 x^2/2 + x/2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, etc. Notice that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_n(0)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_n(0)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45831\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBernoulli number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to generate the Bernoulli polynomial of order \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Use MATLAB's approach for specifying the coefficients. For example, the function should return [1 -1/2] for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and [1 -1 1/6] for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n = 2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":59034,"title":"Compute the maximum length of a contaminant plume in groundwater","description":"Problem statement \r\nWrite a function to compute the maximum length of a contaminant plume for steady, one-dimensional transport in groundwater. The leaking source has a constant concentration of , and the end of the plume for each contaminant is taken to be where the concentration equals some limit (e.g., the U.S. Environmental Protection Agency’s maximum contaminant level, or MCL). Assume the aquifer to be infinite and initially clean. Relevant properties of the confined aquifer are the hydraulic conductivity , the magnitude of the head gradient , effective porosity , bulk density , and soil organic fraction . Along with the MCLs, the properties of the contaminants provided to the function are the half life  and the octanol-water partition coefficient .\r\nCompute the longitudinal dispersion coefficient as , where  is the average linear velocity and  is the longitudinal dispersivity. The variable aL will be specified as either a number or ‘X\u0026E’. In the latter case, compute the longitudinal dispersivity with the empirical formula of Xu \u0026 Eckstein (1995):\r\n\r\nwhere  is in meters if the flow length  is in meters. Take the flow length to be the length of the plume—that is, guess a plume length, compute the new plume, and repeat until the plume length stops changing.\r\nBackground\r\nContaminants in groundwater are subject to advection, retardation, dispersion, and degradation. If the transport is assumed to be one-dimensional, then the variation of the concentration  of the contaminant in time  and spatial coordinate  can be computed with\r\n\r\nThe four terms represent the effects of unsteadiness, advection, dispersion, and degradation, where . Retardation is included in the retardation coefficient . The maximum length occurs when all processes have had sufficient time to operate—that is, in steady state. In that case, the first term can be ignored, and the equation becomes a second-order linear ordinary differential equation with constant coefficients, which can be solved with the boundary conditions  and . ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 605.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 302.95px; transform-origin: 407px 302.95px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.95px 8px; transform-origin: 64.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 151px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 75.5px; text-align: left; transform-origin: 384px 75.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 350.983px 8px; transform-origin: 350.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the maximum length of a contaminant plume for steady, one-dimensional transport in groundwater. The leaking source has a constant concentration of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"18\" height=\"20\" alt=\"C0\" style=\"width: 18px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.525px 8px; transform-origin: 157.525px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the end of the plume for each contaminant is taken to be where the concentration equals some limit (e.g., the U.S. Environmental Protection Agency’s \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003emaximum contaminant level\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 325.967px 8px; transform-origin: 325.967px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, or MCL). Assume the aquifer to be infinite and initially clean. Relevant properties of the confined aquifer are the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.358px 8px; transform-origin: 114.358px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the magnitude of the head gradient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"49.5\" height=\"18.5\" alt=\"|dh/dx|\" style=\"width: 49.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.2083px 8px; transform-origin: 58.2083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, effective porosity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"20\" alt=\"ne\" style=\"width: 15px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7833px 8px; transform-origin: 42.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, bulk density \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"rhob\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.125px 8px; transform-origin: 29.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and soil organic fraction \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17.5\" height=\"20\" alt=\"phio\" style=\"width: 17.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 302.217px 8px; transform-origin: 302.217px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Along with the MCLs, the properties of the contaminants provided to the function are the half life \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"26.5\" height=\"20\" alt=\"T_1/2\" style=\"width: 26.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the octanol-water partition coefficient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"22.5\" height=\"20\" alt=\"Koc\" style=\"width: 22.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32.5px; text-align: left; transform-origin: 384px 32.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 155.875px 8px; transform-origin: 155.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute the longitudinal dispersion coefficient as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIMAAAAoCAYAAADdRklLAAAFm0lEQVR4Xu2bTcgWVRTHc1+bWtXCwFoECbrRAqldBRFECzVdhCBYrSKiyBbRqqKPRStTSiRCy0UQSFCBSSL0sYkIcmFRLmpVFLWv/0/mPJzmvR9n5tXpGZ87cJhH587MPef8zzn/e+68G65pR7NAZ4ENzRLNAmaBBoaGhYUFGhgaGBoYGgbWWqBlhoaKlhkaBoZnhld0y92SOyrG+1XXz0relnzSDD1PC0TLxPdS77ZORRx/l+SH7t/bdN4pedpdf1C/v56nSVZ31lEw/CIT3diZ6VWdn0mYDFCcllzbXdveADEvYEXAcItUuuDUuq9QCh7TtUNu7A36/fu8TLK6s42AwTuYErG54mCfRY5o7KOra955aR4Bw/tSaVenFuSQzFA6DuvigW7A3zpfNy+TrO5sI2D4y/GA5/T7pYq5+qXiVo03srm6lp6B5jUwQAq/cnpEHHuvxn/s7nlYv8kuV/OBzk9JNkr+7OSozk9KWJaXeFbJLtfr4rOSmzu5XecXEwFp2TiSubPvq4HhYPdyHnBeskNSI4T9zHAlwdAH3ljARTJe6tk464SEefAMnIJ9fBBRKnFmzW6luUPiv5GwUks53Jfm0faugYEIR1GOk5LdAWvTqLKeA8PHRkXgVZfm5rNQ5J7UmDFgAAjnJPRfUvf/071oXdHqJmvcDRJ/U0IJ81UkeyftVAODKcTNUcR5AHHf1bi89EDIrZjMdmOAlnKWz7gpm5Idtkjul4zKQiUw9KMu6lRPOL/UxO4cG65LfJ8BPrfU9rYbHak9/f0zU4HJkh6OMpqflcDg033UqZSR95wSlysqlgkX3ik5/ayGR3lWRD+y0W/dwMd1ftPdBLdjCyCaFcgyD0nOSBarwxIY/H5ErgXdV+IL/YdtapWiZr/GWe+Cce9KXh6b3iKWvIxjTMecfjjtZwlkL8ezIIQ044xbQTKPS96SlPZ0rPT40sSz2CSM7AcZ4f1D4wHyKcliUZADg0chdozsMwxZUnq2HeUiKX9OTSB9az7naJ9R+xHc18FKarRTmxoPOI9JfKZI2cp4zre6yLzgFdy7yCY5MPh0H2lB86LvJLaZVVPOyFB/B3RoAE8NBk/iUo72S0B0KfEsD6zoisuykgHR+EFklQfPoQ/ygIQmIKD90YMoB4YhLWjPrDEAQKCGlRitPT/KRYaC5EqN91Hfz2hmB5pOlErjCzh9k6RP7MYEhIGBZ78j2eqivKSzzdtAB6f5SfKfbnIODJEta15OZB7rMgJ1L9UdS03Snj83gukzg5+7AQEHPSKh90D0vib5UJKq5xYQQ/oQnpNx355C0FGK4R+WPRl/ppsLPltTVlJg6KfefvSC9Hsk+yRGFk3xyActni9EuEgJ8VNf8+SQd5MFOfa6QDCSRwnkwE6pr7+s/g8JCJ8ZLN3nbEDpeEECMAnUjyQfSD6VJLO2BwNOJrKN5ZcMDUBgzJ91Dx+yEWUt7lwnbWoHD30fwfJGz8hkAAsE60EAgNczQPABMaQPQTZhJVArw6aTLXFrRPbS+FoHcqihIuPNWNH2duSZcxszRUAYQSVwQ/2H/wMMlkbXs6Scm/P787V0X1t1rUdP4yThUjw1GGzJSg2DCafKC2OydW091lmSe30PJxcQlBGOCAdLqWXv8OSU/2P1kP3ybGowWA3LLSlJbXTFauRoSfw6ahoWEKUeC93fJyQp4hl5qb3DlpIAAQL5fOmZU4PBlpQpvmBAuKgJ1z6tixhkWceUtqJxGh8U86cItW9NS/oZJ6HpxVEFAoOmAkO/F8+7AQQrEg62Xu27iWg3blmdnZsXjmalxj6P/TkBGfLz7gY+gIHocS26F1R6FwCgAcbqw692snabCgxzc9xKzreBYSXdnla6gaGBYWGBBoYGhgaGhoG1FmiZoaGiZYaGgbUW+Bf20VM4+con7wAAAABJRU5ErkJggg==\" width=\"65.5\" height=\"20\" alt=\"DL = aLvL\" style=\"width: 65.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.8917px 8px; transform-origin: 24.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"123.5\" height=\"20\" alt=\"vL = (K/ne)|dh/dx|\" style=\"width: 123.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 105.808px 8px; transform-origin: 105.808px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the average linear velocity and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17\" height=\"20\" alt=\"aL\" style=\"width: 17px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 136.417px 8px; transform-origin: 136.417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the longitudinal dispersivity. The variable \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eaL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 121.367px 8px; transform-origin: 121.367px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be specified as either a number or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.25px 8px; transform-origin: 19.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e‘X\u0026amp;E’\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.275px 8px; transform-origin: 88.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. In the latter case, compute the longitudinal dispersivity with the empirical formula of Xu \u0026amp; Eckstein (1995):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"138.5\" height=\"21\" alt=\"aL = 0.83(log10(L))^2.414\" style=\"width: 138.5px; height: 21px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17\" height=\"20\" alt=\"aL\" style=\"width: 17px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.175px 8px; transform-origin: 92.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is in meters if the flow length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eL\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 250.083px 8px; transform-origin: 250.083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is in meters. Take the flow length to be the length of the plume—that is, guess a plume length, compute the new plume, and repeat until the plume length stops changing.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.15px 8px; transform-origin: 383.15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eContaminants in groundwater are subject to advection, retardation, dispersion, and degradation. If the transport is assumed to be one-dimensional, then the variation of the concentration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.0083px 8px; transform-origin: 84.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the contaminant in time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.3583px 8px; transform-origin: 72.3583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and spatial coordinate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.1667px 8px; transform-origin: 15.1667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e can be computed with\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 39.9px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19.95px; text-align: left; transform-origin: 384px 19.95px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"170\" height=\"40\" alt=\"dC/dt + (vL/R)dC/dx = (DL/R) d^2C/dx^2 - lam C\" style=\"width: 170px; height: 40px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 108px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 54px; text-align: left; transform-origin: 384px 54px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 311.05px 8px; transform-origin: 311.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe four terms represent the effects of unsteadiness, advection, dispersion, and degradation, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"81.5\" height=\"20\" alt=\"lam = ln(2)/T_1/2\" style=\"width: 81.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Retardation is included in the retardation coefficient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"122\" height=\"20\" alt=\"R = 1+rhobKoc phio/ne\" style=\"width: 122px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 151.317px 8px; transform-origin: 151.317px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe maximum length occurs when all processes have had sufficient time to operate—that is, in steady state. In that case, the first term can be ignored, and the equation becomes a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/51387\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003esecond-order linear ordinary differential equation with constant coefficients\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.9083px 8px; transform-origin: 94.9083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which can be solved with the boundary conditions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"67.5\" height=\"20\" alt=\"C(0) = C0\" style=\"width: 67.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"66\" height=\"18.5\" alt=\"C(infinity) = 0\" style=\"width: 66px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Lp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\n%  See the text suite for the definitions of the parameters\r\n   v  = K*dhdx/ne;\r\n   Lp = (C0-Clim)/v;\r\nend","test_suite":"%%  Dieldrin and styrene\r\nC0   = [1 15];                  %  Source concentrations (mg/L)\r\nClim = [2e-4 0.1];              %  Maximum contaminant levels (mg/L)\r\nK    = 87.5;                    %  Hydraulic conductivity (m/d)\r\ndhdx = 0.002;                   %  Magnitude of the hydraulic gradient \r\nne   = 0.25;                    %  Effective porosity\r\nrhob = 2.5;                     %  Bulk density (g/cm3)\r\nphio = 0.005;                   %  Soil organic fraction\r\nKoc  = [25120 380];             %  Octanol-water partition coefficient (mL/g)\r\naL   = 'X\u0026E';                   %  Dispersivity method\r\nTh   = [1825 182];              %  Half lives (d)\r\nLp_correct = [20.76 58.95];\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  Benzene, toluene, ethylbenzene, and p-xylene\r\nC0   = 30;                      %  Source concentration (mg/L)\r\nClim = [0.005 1 0.7 10];        %  Maximum contaminant levels (mg/L)\r\nK    = 11;                      %  Hydraulic conductivity (m/d)\r\ndhdx = 0.04;                    %  Magnitude of the hydraulic gradient \r\nne   = 0.22;                    %  Effective porosity\r\nrhob = 2;                       %  Bulk density (g/cm3)\r\nphio = 0.005;                   %  Soil organic fraction\r\nKoc  = [97 242 622 552];        %  Octanol-water partition coefficient (mL/g)\r\naL   = 'X\u0026E';                   %  Dispersivity method\r\nTh   = [300 20 120 190];        %  Half lives (d)\r\nLp_correct = [1501.21 20.69 54.12 24.98];\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  Glyphosate\r\nC0   = 13.9;                    %  Source concentrations (mg/L)\r\nClim = 0.7;                     %  Maximum contaminant level (mg/L)\r\nK    = 30;                      %  Hydraulic conductivity (m/d)\r\ndhdx = 0.0005;                  %  Magnitude of the hydraulic gradient \r\nne   = 0.18;                    %  Effective porosity\r\nrhob = 1.9;                     %  Bulk density (g/cm3)\r\nphio = 0.001;                   %  Soil organic fraction\r\nKoc  = 4e-5;                    %  Octanol-water partition coefficient (mL/g)\r\naL   = 2.8;                     %  Dispersivity method\r\nTh   = 300;                     %  Half life (d)\r\nLp_correct = 115.59;\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  1,4-dioxane\r\nC0   = 10;                      %  Source concentrations (mg/L)\r\nClim = 3e-4;                    %  Limit set by Massachusetts (mg/L)\r\nK    = 7.77;                    %  Hydraulic conductivity (m/d)\r\ndhdx = 0.01;                    %  Magnitude of the hydraulic gradient \r\nne   = 0.21;                    %  Effective porosity\r\nrhob = 1.8;                     %  Bulk density (g/cm3)\r\nphio = 0.003;                   %  Soil organic fraction\r\nKoc  = 1;                       %  Octanol-water partition coefficient (mL/g)\r\naL   = 3;                       %  Dispersivity method\r\nTh   = 1;                       %  Half life (d)\r\nLp_correct = 16;\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  Benzene\r\nC0   = 2;                       %  Source concentrations (mg/L)\r\nClim = 0.005;                   %  Maximum contaminant level (mg/L)\r\nK    = 11;                      %  Hydraulic conductivity (m/d)\r\ndhdx = 0.0035;                  %  Magnitude of the hydraulic gradient \r\nne   = 0.1;                     %  Effective porosity\r\nrhob = 1.7;                     %  Bulk density (g/cm3)\r\nphio = 0.002;                   %  Soil organic fraction\r\nKoc  = 97;                      %  Octanol-water partition coefficient (mL/g)\r\naL   = 6;                       %  Dispersivity method\r\nTh   = 300;                     %  Half life (d)\r\nLp_correct = 263.93;\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  p-xylene\r\nC0   = 200;                     %  Source concentrations (mg/L)\r\nClim = 10;                      %  Maximum contaminant level (mg/L)\r\nK    = 11;                      %  Hydraulic conductivity (m/d)\r\ndhdx = 0.0035;                  %  Magnitude of the hydraulic gradient \r\nne   = 0.1;                     %  Effective porosity\r\nrhob = 1.7;                     %  Bulk density (g/cm3)\r\nphio = 0.002;                   %  Soil organic fraction\r\nKoc  = 552;                     %  Octanol-water partition coefficient (mL/g)\r\naL   = 6;                       %  Dispersivity method\r\nTh   = 190;                     %  Half life (d)\r\nLp_correct = 26.74;\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  Ethylbenzene\r\nC0   = 100;                     %  Source concentrations (mg/L)\r\nClim = 0.7;                     %  Maximum contaminant level (mg/L)\r\nK    = 11;                      %  Hydraulic conductivity (m/d)\r\ndhdx = 0.0035;                  %  Magnitude of the hydraulic gradient \r\nne   = 0.1;                     %  Effective porosity\r\nrhob = 1.7;                     %  Bulk density (g/cm3)\r\nphio = 0.002;                   %  Soil organic fraction\r\nKoc  = 622;                     %  Octanol-water partition coefficient (mL/g)\r\naL   = 6;                       %  Dispersivity method\r\nTh   = 120;                     %  Half life (d)\r\nLp_correct = 29.83;\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n\r\n%%  Nastene, phylthene, siccanol (fictitious chemicals)\r\nC0   = [10 10 20];              %  Source concentrations (mg/L)\r\nClim = [1 2 0.1];               %  Limits (mg/L)\r\nK    = 0.2;                     %  Hydraulic conductivity (m/d)\r\ndhdx = 0.008;                   %  Magnitude of the hydraulic gradient \r\nne   = 0.08;                    %  Effective porosity\r\nrhob = 2;                       %  Bulk density (g/cm3)\r\nphio = 0.003;                   %  Soil organic fraction\r\nKoc  = [15 80 2];               %  Octanol-water partition coefficient (mL/g)\r\naL   = 2;                       %  Dispersivity method\r\nTh   = [30 100 475];            %  Half lives (d)\r\nLp_correct = [2.6 1.83 72.39];\r\nLp = maxPlumeLength(C0,Clim,K,dhdx,ne,rhob,phio,Koc,aL,Th);\r\nassert(all(abs(Lp-Lp_correct)\u003c0.01))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-10-01T15:59:04.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-10-01T15:47:36.000Z","updated_at":"2026-02-12T14:03:58.000Z","published_at":"2023-10-01T15:59:04.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the maximum length of a contaminant plume for steady, one-dimensional transport in groundwater. The leaking source has a constant concentration of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the end of the plume for each contaminant is taken to be where the concentration equals some limit (e.g., the U.S. Environmental Protection Agency’s \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emaximum contaminant level\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, or MCL). Assume the aquifer to be infinite and initially clean. Relevant properties of the confined aquifer are the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the magnitude of the head gradient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"|dh/dx|\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e|dh/dx|\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, effective porosity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ne\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, bulk density \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"rhob\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rho_b\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and soil organic fraction \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"phio\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\phi_o\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Along with the MCLs, the properties of the contaminants provided to the function are the half life \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"T_1/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT_{1/2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the octanol-water partition coefficient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Koc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_{oc}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute the longitudinal dispersion coefficient as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"DL = aLvL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD_L = a_L v_\\\\ell\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"vL = (K/ne)|dh/dx|\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_\\\\ell = (K/n_e)|dh/dx|\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the average linear velocity and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"aL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the longitudinal dispersivity. The variable \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eaL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will be specified as either a number or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e‘X\u0026amp;E’\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. In the latter case, compute the longitudinal dispersivity with the empirical formula of Xu \u0026amp; Eckstein (1995):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"aL = 0.83(log10(L))^2.414\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_L = 0.83(\\\\log_{10}L)^{2.414}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"aL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is in meters if the flow length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is in meters. Take the flow length to be the length of the plume—that is, guess a plume length, compute the new plume, and repeat until the plume length stops changing.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eContaminants in groundwater are subject to advection, retardation, dispersion, and degradation. If the transport is assumed to be one-dimensional, then the variation of the concentration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the contaminant in time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and spatial coordinate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e can be computed with\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dC/dt + (vL/R)dC/dx = (DL/R) d^2C/dx^2 - lam C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{\\\\partial C}{\\\\partial t}+\\\\frac{v_\\\\ell}{R}\\\\frac{\\\\partial C}{\\\\partial x}=\\\\frac{D_L}{R}\\\\frac{\\\\partial^2 C}{\\\\partial x^2} - \\\\lambda C\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe four terms represent the effects of unsteadiness, advection, dispersion, and degradation, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"lam = ln(2)/T_1/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lambda = \\\\ln2/T_{1/2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Retardation is included in the retardation coefficient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R = 1+rhobKoc phio/ne\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR = 1+\\\\rho_b K_{oc} \\\\phi_o/n_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe maximum length occurs when all processes have had sufficient time to operate—that is, in steady state. In that case, the first term can be ignored, and the equation becomes a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/51387\\\"\u003e\u003cw:r\u003e\u003cw:t\u003esecond-order linear ordinary differential equation with constant coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, which can be solved with the boundary conditions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C(0) = C0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC(0) = C_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C(infinity) = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC(\\\\infty) = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59002,"title":"Compute piezometric head in a leaky confined aquifer","description":"Problem statement\r\nWrite a function to compute the piezometric head  in a leaky confined aquifer and the position of a groundwater divide  given the boundary heads  at  and  at  and head  (assumed constant) in the unconfined aquifer above the leaky confining layer. The hydraulic conductivity and thickness of the aquifer are  and , and the hydraulic conductivity and thickness of the leaking confining layer are  and . If there is no groundwater divide, set xd to the empty set []. \r\nBackground\r\nAs in other problems in this series, the movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. For steady, one-dimensional flow, conservation of mass applied to the control volume indicated by the dashed line says that the flow into the volume equals the flow out of the volume. If  is the specific discharge in the aquifer, or the flow per unit area, the flow into the left side is , and the flow out of the right side is . If  is the specific discharge through the leaky confining layer, the flow into the volume through the top is . Then the mass (or volume) balance is\r\n\r\nRearranging, dividing by , and taking the limit as  goes to zero gives\r\n\r\nDarcy’s law allows the specific discharge through the aquifer to be written as  and the specific discharge through the leaky confining layer to be approximated as . Then \r\n\r\nOne can solve this second-order linear ordinary differential equation using the boundary heads to get the piezometric head in the aquifer. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 939.1px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 469.55px; transform-origin: 407px 469.55px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 107px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 53.5px; text-align: left; transform-origin: 384px 53.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 153.9px 8px; transform-origin: 153.9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the piezometric head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 211.233px 8px; transform-origin: 211.233px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a leaky confined aquifer and the position of a groundwater divide \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"20\" alt=\"xd\" style=\"width: 15px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e given the boundary heads \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"h0\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17\" height=\"20\" alt=\"hL\" style=\"width: 17px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"18\" alt=\"x = L\" style=\"width: 39px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.0667px 8px; transform-origin: 33.0667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eH\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 164.933px 8px; transform-origin: 164.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (assumed constant) in the unconfined aquifer above the leaky confining layer. The hydraulic conductivity and thickness of the aquifer are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59.125px 8px; transform-origin: 59.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the hydraulic conductivity and thickness of the leaking confining layer are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"18\" alt=\"K'\" style=\"width: 19px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAkCAYAAACe0YppAAACB0lEQVRYR+1WyyvFQRR290qxsqJYUBY2WMjGgpKd8toqj4WsKJYSImuPLJXHf0CysPJYWrBgI7EiYs/33c7U9LtnXt1ykzv1NdP9nTPfOd+cM3NzFSUauRLxVpSJf035PyF1G+R4Ax4iZaH9ErABnGR9fBn3wHgRqAKaxHEY82EkMe0GgR1gIoXY2N5axDWSdQz3pxgNpGZsNr/AogO4A5pjGGEzBBwIYa/mEyquaji9iuM65rlI4m3YjQJqttwjRGwipy0jLygSRyDP+P1GfFSTELEpkC9410WeL6v5DOgGrl0KhYgZea3vrJSN5/FbPVBQybatj7gBhvdivIB5BZgEZgDTXpdYT2cyI/GpL9vQGXODZSFulHUX5j2RnT1qRkqb5X18GR/jOy8RttEj8A5MAby9ONaAWVkbRaxY/Esf8be4vmBmhY5YpPzEoBgch3o7+ahdxHYbsaJbgewdbROn9Hg+HhcxL4DxgIy21Ck97iU2bUSZWzISGwXNHc4a6HTYONXWMrbbyHV2tswsuK3oqhJDjZi9uinf2zFrt4/J9gjf7UqP5teITRu5ZDbnT4n7laKLIteI+Y5WAtozaNQoilSral7wVxKyTczncR/g2bJ1VlOLKSuDljE3HwP6gCfgA+Dfn3Ng13HmUfLaRqHXKXnDWIcycaxSRduVpS5awtgN/p/UP1TMZSXbpcoRAAAAAElFTkSuQmCC\" width=\"15\" height=\"18\" alt=\"b'\" style=\"width: 15px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 118.625px 8px; transform-origin: 118.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If there is no groundwater divide, set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003exd\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to the empty set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58997\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eother\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52070\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eproblems\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55825\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ein\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/56205\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ethis\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58966\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eseries\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 264.883px 8px; transform-origin: 264.883px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. For steady, one-dimensional flow, conservation of mass applied to the control volume indicated by the dashed line says that the flow into the volume equals the flow out of the volume. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ev\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97.2417px 8px; transform-origin: 97.2417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the specific discharge in the aquifer, or the flow per unit area, the flow into the left side is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"27\" height=\"18\" alt=\"vbw\" style=\"width: 27px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.008px 8px; transform-origin: 112.008px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the flow out of the right side is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"73\" height=\"18.5\" alt=\"(v+Deltav)bw\" style=\"width: 73px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.70833px 8px; transform-origin: 9.70833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14\" height=\"18\" alt=\"v'\" style=\"width: 14px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.825px 8px; transform-origin: 18.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the specific discharge through the leaky confining layer, the flow into the volume through the top is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"42.5\" height=\"18\" alt=\"v'wDeltax\" style=\"width: 42.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.6083px 8px; transform-origin: 62.6083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Then the mass (or volume) balance is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"316.5\" height=\"18.5\" alt=\"0 = vbw - (v+Deltav)bw + v'wDeltax = -bwDeltav + v'wDeltax\" style=\"width: 316.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.425px 8px; transform-origin: 77.425px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRearranging, dividing by \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"38.5\" height=\"18\" style=\"width: 38.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73.5083px 8px; transform-origin: 73.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and taking the limit as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"21.5\" height=\"18\" style=\"width: 21.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.7333px 8px; transform-origin: 58.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e goes to zero gives\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"71\" height=\"35\" alt=\"dv/dx - v'/b = 0\" style=\"width: 71px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 238.317px 8px; transform-origin: 238.317px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDarcy’s law allows the specific discharge through the aquifer to be written as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"98.5\" height=\"18.5\" alt=\"v = -K(dh/dx)\" style=\"width: 98.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.8px 8px; transform-origin: 84.8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the specific discharge through the leaky confining layer to be approximated as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"117\" height=\"18.5\" alt=\"v' = K'(H-h)/b'\" style=\"width: 117px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.775px 8px; transform-origin: 21.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Then \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"152\" height=\"36.5\" alt=\"K d2h/dx2 + (K'/(bb'))(H-h) = 0\" style=\"width: 152px; height: 36.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59.5083px 8px; transform-origin: 59.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOne can solve this \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/51387\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003esecond-order linear ordinary differential equation\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 170.767px 8px; transform-origin: 170.767px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e using the boundary heads to get the piezometric head in the aquifer. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 376.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 188.35px; text-align: left; transform-origin: 384px 188.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"581\" height=\"371\" style=\"vertical-align: baseline;width: 581px;height: 371px\" 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\" alt=\"leaky confined aquifer\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [h,xd] = leakyConfAq(x,L,h0,hL,K,b,Kp,bp,H)\r\n  h = H + (hL-h0*(x/L)*sin(Kp*x^2/(Kp*b*bp));\r\n  xd = x\r\nend","test_suite":"%%\r\nL = 3300;                                     %  Length (m)    \r\nx = 1000;                                     %  Position where head is desired (m)\r\nh0 = 32;                                      %  Piezometric head at x = 0 (m)\r\nhL = 29;                                      %  Piezometric head at x = L (m)\r\nH = 39;                                       %  Head in unconfined aquifer (m)\r\nK = 12;                                       %  Hydraulic conductivity of aquifer (m/d)\r\nKp = 8e-5;                                    %  Hydraulic conductivity of leaky confining layer (m/d)\r\nb = 15;                                       %  Thickness of aquifer (m)\r\nbp = 2;                                       %  Thickness of leaky confining layer (m)\r\n[h,xd] = leakyConfAq(x,L,h0,hL,K,b,Kp,bp,H);\r\nh_correct = 32.7897;\r\nxd_correct = 1060.65;\r\nassert(abs(h-h_correct)\u003c1e-3)\r\nassert(abs(xd-xd_correct)\u003c1e-2)\r\n\r\n%%\r\nL = 3300;                                     %  Length (m)    \r\nx = 700:700:2800;                             %  Position where head is desired (m)\r\nh0 = 32;                                      %  Piezometric head at x = 0 (m)\r\nhL = 29;                                      %  Piezometric head at x = L (m)\r\nH = 39;                                       %  Head in unconfined aquifer (m)\r\nK = 12;                                       %  Hydraulic conductivity of aquifer (m/d)\r\nKp = 3e-4;                                    %  Hydraulic conductivity of leaky confining layer (m/d)\r\nb = 15;                                       %  Thickness of aquifer (m)\r\nbp = 2;                                       %  Thickness of leaky confining layer (m)\r\n[h,xd] = leakyConfAq(x,L,h0,hL,K,b,Kp,bp,H);\r\nh_correct = [34.6548 35.4741 34.8040 32.3615];\r\nxd_correct = 1433.93;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-2)\r\n\r\n%%\r\nL = 2500;                                     %  Length (m)    \r\nx = 0:500:2500;                               %  Position where head is desired (m)\r\nh0 = 45;                                      %  Piezometric head at x = 0 (m)\r\nhL = 42;                                      %  Piezometric head at x = L (m)\r\nH = 50;                                       %  Head in unconfined aquifer (m)\r\nK = 4;                                        %  Hydraulic conductivity of aquifer (m/d)\r\nKp = 2e-5;                                    %  Hydraulic conductivity of leaky confining layer (m/d)\r\nb = 30;                                       %  Thickness of aquifer (m)\r\nbp = 3;                                       %  Thickness of leaky confining layer (m)\r\n[h,xd] = leakyConfAq(x,L,h0,hL,K,b,Kp,bp,H);\r\nh_correct = [45 44.5664 44.0573 43.4656 42.7830 42];\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(isempty(xd))\r\n\r\n%%\r\nL = 2500;                                     %  Length (m)    \r\nx = 0:500:2500;                               %  Position where head is desired (m)\r\nh0 = 45;                                      %  Piezometric head at x = 0 (m)\r\nhL = 42;                                      %  Piezometric head at x = L (m)\r\nH = 50;                                       %  Head in unconfined aquifer (m)\r\nK = 4;                                        %  Hydraulic conductivity of aquifer (m/d)\r\nKp = 2e-4;                                    %  Hydraulic conductivity of leaky confining layer (m/d)\r\nb = 30;                                       %  Thickness of aquifer (m)\r\nbp = 3;                                       %  Thickness of leaky confining layer (m)\r\n[h,xd] = leakyConfAq(x,L,h0,hL,K,b,Kp,bp,H);\r\nh_correct = [45 45.6796 45.7522 45.2279 44.0331 42];\r\nxd_correct = 811.72;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-2)\r\n\r\n%%\r\nL = 3300;                                     %  Length (m)    \r\nx = 700:700:2900;                             %  Position where head is desired (m)\r\nh0 = 32;                                      %  Piezometric head at x = 0 (m)\r\nhL = 29;                                      %  Piezometric head at x = L (m)\r\nH = 39;                                       %  Head in unconfined aquifer (m)\r\nK = 12;                                       %  Hydraulic conductivity of aquifer (m/d)\r\nKp = 3e-4;                                    %  Hydraulic conductivity of leaky confining layer (m/d)\r\nb = 15;                                       %  Thickness of aquifer (m)\r\nbp = 2;                                       %  Thickness of leaky confining layer (m)\r\n[h,xd] = leakyConfAq(x,L,h0,hL,K,b,Kp,bp,H);\r\nh_correct = [34.6548 35.4741 34.8040 32.3615];\r\nxd_correct = 1433.93;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-2)\r\n\r\n%%\r\nL = 1000;                                     %  Length (m)    \r\nx = [130 280 390 560 710 940];                %  Position where head is desired (m)\r\nh0 = 34;                                      %  Piezometric head at x = 0 (m)\r\nhL = 33;                                      %  Piezometric head at x = L (m)\r\nH = 38;                                       %  Head in unconfined aquifer (m)\r\nK = 0.5;                                      %  Hydraulic conductivity of aquifer (m/d)\r\nKp = 2e-4;                                    %  Hydraulic conductivity of leaky confining layer (m/d)\r\nb = 24;                                       %  Thickness of aquifer (m)\r\nbp = 1;                                       %  Thickness of leaky confining layer (m)\r\n[h,xd] = leakyConfAq(x,L,h0,hL,K,b,Kp,bp,H);\r\nh_correct = [35.5547 36.4902 36.7941 36.7832 36.2740 34.0536];\r\nxd_correct = 471.73;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-2)\r\n\r\n%%\r\nfiletext = fileread('leakyConfAq.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-09-23T13:55:41.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-09-23T13:48:39.000Z","updated_at":"2026-02-12T13:57:58.000Z","published_at":"2023-09-23T13:51:50.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the piezometric head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in a leaky confined aquifer and the position of a groundwater divide \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"xd\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_d\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e given the boundary heads \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"hL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (assumed constant) in the unconfined aquifer above the leaky confining layer. The hydraulic conductivity and thickness of the aquifer are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the hydraulic conductivity and thickness of the leaking confining layer are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K'\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\\\\prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b'\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\\\\prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If there is no groundwater divide, set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003exd\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to the empty set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58997\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eother\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52070\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eproblems\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55825\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ein\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/56205\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethis\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58966\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eseries\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. For steady, one-dimensional flow, conservation of mass applied to the control volume indicated by the dashed line says that the flow into the volume equals the flow out of the volume. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the specific discharge in the aquifer, or the flow per unit area, the flow into the left side is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"vbw\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003evbw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the flow out of the right side is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"(v+Deltav)bw\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(v+\\\\Delta v)bw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v'\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev\\\\prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the specific discharge through the leaky confining layer, the flow into the volume through the top is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v'wDeltax\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev\\\\prime w\\\\Delta x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Then the mass (or volume) balance is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"0 = vbw - (v+Deltav)bw + v'wDeltax = -bwDeltav + v'wDeltax\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 = vbw - (v+\\\\Delta v)bw+v\\\\prime w\\\\Delta x = -bw\\\\Delta v+v\\\\prime w\\\\Delta x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRearranging, dividing by \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ebw\\\\Delta x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and taking the limit as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Delta x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e goes to zero gives\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dv/dx - v'/b = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{dv}{dx}-\\\\frac{v\\\\prime}{b} = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDarcy’s law allows the specific discharge through the aquifer to be written as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v = -K(dh/dx)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev = -K(dh/dx)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the specific discharge through the leaky confining layer to be approximated as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v' = K'(H-h)/b'\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev\\\\prime = K\\\\prime(H-h)/b\\\\prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Then \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K d2h/dx2 + (K'/(bb'))(H-h) = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\\\\frac{d^2h}{dx^2} + \\\\frac{K\\\\prime}{bb\\\\prime}(H-h) = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOne can solve this \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/51387\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esecond-order linear ordinary differential equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e using the boundary heads to get the piezometric head in the aquifer. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"371\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"581\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"leaky confined aquifer\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58966,"title":"Compute the head for steady 1D flow in a homogeneous aquifer","description":"Problem statement\r\nWrite a function that computes the head  (i.e., piezometric head for a confined aquifer or water table elevation above the aquifer bottom for an unconfined aquifer) at specified locations . The input will include a Boolean variable that is true for confined aquifers and false for unconfined aquifers as well as the length  of the aquifer, hydraulic conductivity , aquifer thickness  (set to [] for unconfined aquifers), width , and a vector BC, which contains two of three of the head  at , the head  at , and the flow . The function should also return the flow.\r\nBackground\r\nThe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. The latter relates the flow of water to the gradient in piezometric head by\r\n\r\nwhere  is the flow area. For a confined aquifer, the flow area is , whereas for an unconfined aquifer .\r\nThe spatial variation of the head can be computed with these two principles. For steady, one-dimensional flow, conservation of mass says that the flow must by constant (i.e., the same at any cross section). Then Darcy’s law provides a differential equation that can be integrated using two of the three boundary conditions listed above\r\n ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 738.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 369.25px; transform-origin: 407px 369.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 107px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 53.5px; text-align: left; transform-origin: 384px 53.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 125.5px 8px; transform-origin: 125.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes the head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 247.392px 8px; transform-origin: 247.392px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (i.e., piezometric head for a confined aquifer or water table elevation above the aquifer bottom for an unconfined aquifer) at specified locations \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 175.433px 8px; transform-origin: 175.433px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The input will include a Boolean variable that is true for confined aquifers and false for unconfined aquifers as well as the length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eL\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.742px 8px; transform-origin: 114.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the aquifer, hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.225px 8px; transform-origin: 27.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, aquifer thickness \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.325px 8px; transform-origin: 23.325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (set to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97.6333px 8px; transform-origin: 97.6333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for unconfined aquifers), width \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ew\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3333px 8px; transform-origin: 44.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and a vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eBC\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.183px 8px; transform-origin: 127.183px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which contains two of three of the head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.0583px 8px; transform-origin: 33.0583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the head \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACIAAAAoCAYAAACb3CikAAACPUlEQVRYR+1XOy9FQRC+t1fpaBQUEgqNkAgRERKJ1uMPeFQqEgolCZXKI0rx6pSUNB6thIKWioYf4PtkRsaxe/bknrvuLc4mX/Ym59yZ78x8M7NbLtXJKtcJj1JBJJmJIiJ5ItIqf36OIfC01IzA4TAwAHQADcAmsPTfROivETgCSIprFLioBRH6PAEmgFegE3ivFZEXOG6SSDAiUVaofLvh9VY8z2PficICRkNElvHOmjhvwx6lYmg/RORchPqIvS+WPrIQ+cBLLNs9YFYiwwraAtqBT2AIuMubslAfYUS4pgBWzy4wDhwA1AxJ3gC9MYlswPiifHUL9m1xtoKdWtFqik7kGs565IvPsA8C0wD7iK0mm7aKA+NLDTvqm1g9xd4v0Kqx1aRpq5gE/+gjMolnx8ZysrVrNVGsTFvubusjQlHOCBFX6LWafPrgpGaVUWNcJHwI7APOCvMRUSHSQBdgG5nVB4W7npITV/k7X3cR4dc8GX0wTXZl7bbWTnBqu4jMwauWqsuA6kPTwgjx3JKMjNrh1KbYU8eDi0ho7Gu4mRZq6d7jSO3w/BKc2i4i6shlwOqDEeFaBVyHJUs4TUffRpJEQmOfeb8CeD4hER8JayfT1A5N35SCSH2kgqY+mrMYiUVEx0Pm9h+DiB0PvvbP1HH9NLcYRHQ8pJXtA0gsWJHHIGLLP6kPRos9in3l142gmkTohNcOXsJ4YOJiZV3Kbw7HMXn256JWTSJZisP7TkEkGZoiIkVEQiX1BQjHeSlahDCkAAAAAElFTkSuQmCC\" width=\"17\" height=\"20\" style=\"width: 17px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"18\" style=\"width: 39px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 43.5583px 8px; transform-origin: 43.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.575px 8px; transform-origin: 127.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The function should also return the flow.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.442px 8px; transform-origin: 381.442px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. The latter relates the flow of water to the gradient in piezometric head by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKoAAABGCAYAAABc8A97AAAKGklEQVR4Xu2dW+hvQxTH/+ed3B7kEoUHIpTbiZI8UCJFuadT5PYiiZCH8+SaJOUWJXk4CImUSx6IXHMtHlBHLnlA4p31qb1qnTkze2Zff7N//7Vrtf//32/vmTVrvrNmzVpr5rdlwy+XwAIksGUBPDqLLoENB6qDYBEScKAuopucSQeqY2AREnCgLqKbnEkH6ubEwOHS7BOFnks0/yz5/M2aRONArak3puMF4N0stJfQKU01J8v9k+bv++R+qNCxQkcK/dv8/+d0LHUr2YHaTV5Lf/rbBoi/yf0YIQtEwPxG08CP5L61psY6UGvqjel5+bDRqEzrZwfVYQ5833x2h9zvnp6d8hocqOWyWocn/2sacb3cHwsadJ38/2jzmTULqmi3A7WKbpiFiYullh1NTUfI/YegVqZ9pv/vhE4LzIJZGGyrxIG68i6YjYHHpaZrWoD4j3y3h9DzQoC6qsuBWlV3TMrMr1L6AQkgniSff9zUHjMLJmWspHAHaomUlvXMvsLubULnCf0tdIjQTUI67V8if4f+09vls7uaZu4nd7wBlMOC6rIaNK0DdVkgzHHLguh+oZ+FrhTCT2q1Je8rEG1Z6g3APj2qeecVub8ntLcQtisXnoKVBAIcqLmuX873bTaorvZT/lH9HpC/IARI0cJoXusNcKAuBw9VcqpTNxGl44XCFb0F4q1BC6yjH7PgQaFtRnOqNyCljWcRSF+NyqrwAiENuSmzTAsvC4U+ulkaU2ElhCaPE9KpU1kkMvRso72Ynvn+QiG1B/U5VuAvNZot1TwLtNhCyH4f84+qJoann4TeFbJgVm+AmgVjihmTAzs6DD7sVkdXoAJQRpyuHp8yIw+BPCRErLhKX9yYEu5YloYueQ3ZnCsUaj2+0+fQjFdnAKos6DtM6+cIhfF5BsstQrGwqa2Tv1E0l5oyrH2LWRBq445i2OVxHUBFA6AUqKwAiVpcJNQmRJ7bKYQ/roiBIS1d0LsWqKnwJPYg8m0Dcthk68RPlatuqVjYlP76oyk0ZjZYb8DY9qnyRfWxBd4ubS0BKo15XwhNyRVzb9hCdSrhs+pixisAt42hU30sKqQgfUK+BxylWUvWfoyVmzML7EKJuq8N5KPlp7RxX3Gqltf3s4OgBKjquqDQWGNCZq1waOCBfVuzJu9ZMIQmkSqBg6Wt+DG7JoKoVkqZWlaTtw2Q1ACaIlrFwP2i6VtmXq5skCEHVKsdS0eVBWpKAGuCwaJmqLbkYRueZNp+Ugif541CffyTupqPmVlWaymQ4YFggNqaCvSY28rap6rxwEMXjR8TEPIg9/VLIUK6XFkF2AbUEHC5KV+Z6vteUa8v8CHVSlZzqAIAnDcIxRZWJU1VoIWJzoDpfKGjhTR+j9bChNNBkUvrU/tUFRQAJ/E6NA9K+AyxgffhBCHN1srmv7YB1U75pdoUhuxUx/+lAO/S4KU8G0aF6KBnhLD3sd8BbKk9GmtzqDVflYdObwCFZ0HzS+k/3EDUreaFXSjF3FbW/kXjEaEC7EP4xRT5SojZpJOJmAJqqBW7uCasuYBwsyu6pgdCA7svGGvKpbRgQOtxoeHGWmSG8Xj1z97TAErBhuZ+QMiaF7m0Pu0P+EbzaZl9+0XDuzYgoaZLFicpoFq7ikJihniKYWvAd9HE6whUq5WsvDab607dlgDe+mKti6p15Z8Cqi2gi/Pe+uXomJjvru+IXOJ7VmMwbTIz6Up3M5lEzLJkc4X7tKx52bryjwE1BFt2RWYQtET71IKpz2Bgatwz8qI1n3Sxw4KEKBHXZnHd6aItBkQ7i7biLAbU0D7N+rhMJ9lpPxXS6wOGKd+ZCqjWVtdVrY3c0aaxbNUp5TO0bKs128pqXfmXALV0inK31K7dYAetXYzaWae6/fNDURm8ryHe1AK3eOVfMvWXAtWOnD77btZpMRWaT2FH2TVAF9NqZBxNXhzt/FqoLTuqaOVfspgqmfqtG6bvlL9OQLVaM3fYA2jp4lVRdB0kf+w/OdR2r+AX+ej3gnq1P3PuQhsQSa78U0C1oMlpR+vU7pL5U9DWxT5i3Xspz4edgfp4R3Dcszib+6LOezOVqi3+QUabUkzRyj8FVCr6Roi8U66U0x4b40UhG6YbErmYW+hT1Wen9tSCKbTpsxlEAbNoKpznc1/MmMTp2y4dqDltShlhBCwaom0LoaIp2TsDWJm+iB3roVq4HMj2IX+S73R/zdxCq7G+Ll4Ta5+ti7vKmj0lUckwVB/NtstlT9mtt5qPCjhYraLW2XaCaeBadGODwUvUJdxOoiFI3FUkn/AcWoOYvJ6spwMufLbGgViiSfUZtO/TQrGtSXqCIMrOXtF3ckDVAtRmLfUA8B4d0jcraGkd5PxOLIESoKq9gcF/p5BO/22s4T/bLpTaGzRxs7z4AgnQR58uRZm0ARWN+JqQnfK1/dhTpJR9LvSWaSz22VVCbDJjV2WfZOACGfsjPSSA7bhNiJxS+rRLwlCP6sZ9JQVUm31OHiNXaE+lOMHGuHwpI3VccVZfmg1E9HGJrayBqcgUxv7bQuE0D4DPFGKvumaPwzz+U/aDvyOEqeBXvRJQT8Oi8gxKbNR6Re6cdZWAdZ31iYZ1rW+05x2oo4lyEQW1nU9VdQMcqFV3z+jMaUZXLiw+esVDC3SgDpXgct63u05LEo2qapkDtaruGI0ZDXFziB1eG1xS7EAl7M1lQ5s8S3ToDKFThcjbsPYrofSHhfD6rEwTO1BHw0Y1BakdCqhY2RMdtGmY4cZC/Ks/Ch0mpPvsFZCAFE8Oh2Ss9PA7B2o1+BrMCD7S1xOaz67227a+qw2rGzo5sGK7EC5HQEtOx0rC4g7UwfiopgBNl4slrlugtqUT2n1eBARI5xvzqMnewnKg9hZdVS/awyIIyISBmtwZqdoYe4xl350akwjGgTqJWGctVE/HYxGU2n+lOZ+5sKkNsVa1l8uBOiumJqnMTtexjPrcYWghU7o7IQfqSRqTKtSBOqu4J6nMnrEf+2lIu/8tFzYNN1hWg49qGJmkC9e/UKstYz5OaxbkjmbS/W/4WtXf2nUf12QSd6BOJtpZCrar+ZhNGTtrgXf2aVxOyqTuGiWHmGRqPdffurLwxXY9EXs0IThQRxPlSgqyGtUeiaM/DmJ/dY+w6WdCRKjYeaFbhf6Sv/GX2rNT7S+tbG1AvVPuK3NVOVBXgq9RKw3PB8D3eYUQPw/Jb1TtaGoDyPwu6jYhTnvW6Z0NhQQK7CG94ZH4lDX0EN9BjXagDhJfFS+jGR8RYkrnwhbl977Y+annM3DaIGDUkKru4FCXVnguP2UCTrbKY1IMPbd/sKAcqINF6AXMIQEH6hxS9joGS8CBOliEXsAcEnCgziFlr2OwBByog0XoBcwhAQfqHFL2OgZLwIE6WIRewBwScKDOIWWvY7AEHKiDRegFzCEBB+ocUvY6BkvgfyzdX2UpVypGAAAAAElFTkSuQmCC\" width=\"85\" height=\"35\" style=\"width: 85px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 173.467px 8px; transform-origin: 173.467px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the flow area. For a confined aquifer, the flow area is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"49.5\" height=\"18\" style=\"width: 49.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 111.642px 8px; transform-origin: 111.642px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, whereas for an unconfined aquifer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"50\" height=\"18\" style=\"width: 50px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe spatial variation of the head can be computed with these two principles. For steady, one-dimensional flow, conservation of mass says that the flow must by constant (i.e., the same at any cross section). Then Darcy’s law provides a differential equation that can be integrated using two of the three boundary conditions listed above\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 365.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 182.85px; text-align: left; transform-origin: 384px 182.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"640\" height=\"360\" style=\"vertical-align: baseline;width: 640px;height: 360px\" 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data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [h,Q] = homogAq(x,confined,L,K,b,w,BC)\r\n% h = head at position x\r\n% Q = flow\r\n% x = position at which head is requested\r\n% L = length of aquifer\r\n% K = hydraulic conductivity\r\n% b = thickness of confined aquifer ([] if unconfined)\r\n% w = width of aquifer\r\n% BC = [h0 hL Q]--one of which is NaN\r\n\r\n  h = conservation of mass + Darcy's law;\r\n  Q = -K*dhdx*A\r\nend","test_suite":"%%  Confined, boundary heads specified\r\nK = 0.5;                %  Hydraulic conductivity (m/d)\r\nL = 24;                 %  Length (m)\r\nb = 2.5;                %  Thickness (m)\r\nw = 400;                %  Width (m)\r\nBC = [4 2.5 NaN];       %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 12;                 %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,true,L,K,b,w,BC);\r\nh_correct = 3.25;\r\nQ_correct = 31.25;\r\nassert(abs(h-h_correct)\u003c1e-4)\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Confined, head at x = 0 and flow specified\r\nK = 8;                  %  Hydraulic conductivity (m/d)\r\nL = 2300;               %  Length (m)\r\nb = 31;                 %  Thickness (m)\r\nw = 1800;               %  Width (m)\r\nBC = [45 NaN 892.8];    %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = [800 1800];         %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,true,L,K,b,w,BC);\r\nh_correct = [43.4 41.4];\r\nQ_correct = 892.8;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Confined, head at x = L and flow specified\r\nK = 0.04;               %  Hydraulic conductivity (m/d)\r\nL = 1850;               %  Length (m)\r\nb = 25;                 %  Thickness (m)\r\nw = 1400;               %  Width (m)\r\nBC = [NaN 133 28];      %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 300:300:1800;       %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,true,L,K,b,w,BC);\r\nh_correct = [164 158 152 146 140 134];\r\nQ_correct = 28;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Unconfined, boundary heads specified\r\nK = 0.5;                %  Hydraulic conductivity (m/d)\r\nL = 24;                 %  Length (m)\r\nw = 400;                %  Width (m)\r\nBC = [4 2.5 NaN];       %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 12;                 %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,false,L,K,[],w,BC);\r\nh_correct = 3.3354;\r\nQ_correct = 40.625;\r\nassert(abs(h-h_correct)\u003c1e-4)\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Unconfined, head at x = 0 and flow specified\r\nK = 8;                  %  Hydraulic conductivity (m/d)\r\nL = 2300;               %  Length (m)\r\nw = 1800;               %  Width (m)\r\nBC = [45 NaN 892.8];    %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = [800 1800];         %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,false,L,K,[],w,BC);\r\nh_correct = [43.8839 42.4476];\r\nQ_correct = 892.8;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Unconfined, head at x = L and flow specified\r\nK = 0.04;               %  Hydraulic conductivity (m/d)\r\nL = 1850;               %  Length (m)\r\nw = 1400;               %  Width (m)\r\nBC = [NaN 133 28];      %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 300:300:1800;       %  Position in aquifer (m)\r\n[h,Q] = homogAq(x,false,L,K,[],w,BC);\r\nh_correct = [138.7047 137.6190 136.5247 135.4216 134.3093 133.1878];\r\nQ_correct = 28;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(abs(Q-Q_correct)\u003c1e-4)\r\n\r\n%%  Confined, random selection of boundary conditions\r\nK = 2.3;                %  Hydraulic conductivity (m/d)\r\nL = 2000;               %  Length (m)\r\nb = 34;                 %  Thickness (m)\r\nw = 1650;               %  Width (m)\r\nBC = [54 51 193.545];   %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 400:400:1600;       %  Position in aquifer (m)\r\nk = randi(3);\r\nBC(k) = NaN;\r\n[h,Q] = homogAq(x,true,L,K,b,w,BC);\r\nh_correct = [53.4 52.8 52.2 51.6];\r\nQ_correct = 193.545;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(all(abs(Q-Q_correct)\u003c1e-4))\r\n\r\n%%  Unconfined, random selection of boundary conditions\r\nK = 2.3;                %  Hydraulic conductivity (m/d)\r\nL = 2000;               %  Length (m)\r\nw = 1650;               %  Width (m)\r\nBC = [54 51 298.85625]; %  Boundary conditions [h0 hL Q] (m m m3/d)\r\nx = 400:400:1600;       %  Position in aquifer (m)\r\nk = randi(3);\r\nBC(k) = NaN;\r\n[h,Q] = homogAq(x,false,L,K,[],w,BC);\r\nh_correct = [53.4135 52.8205 52.2207 51.6140];\r\nQ_correct = 298.85625;\r\nassert(all(abs(h-h_correct)\u003c1e-4))\r\nassert(all(abs(Q-Q_correct)\u003c1e-4))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-09-09T15:47:31.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2023-09-09T15:42:41.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-09-09T15:33:16.000Z","updated_at":"2026-02-10T14:45:49.000Z","published_at":"2023-09-09T15:42:41.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes the head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (i.e., piezometric head for a confined aquifer or water table elevation above the aquifer bottom for an unconfined aquifer) at specified locations \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The input will include a Boolean variable that is true for confined aquifers and false for unconfined aquifers as well as the length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the aquifer, hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, aquifer thickness \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (set to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for unconfined aquifers), width \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ew\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and a vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBC\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which contains two of three of the head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the head \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The function should also return the flow.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. The latter relates the flow of water to the gradient in piezometric head by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K\\\\frac{dh}{dx}A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the flow area. For a confined aquifer, the flow area is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA = bw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, whereas for an unconfined aquifer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA = hw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe spatial variation of the head can be computed with these two principles. For steady, one-dimensional flow, conservation of mass says that the flow must by constant (i.e., the same at any cross section). Then Darcy’s law provides a differential equation that can be integrated using two of the three boundary conditions listed above\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"360\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"640\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e 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the water table elevation in an unconfined aquifer with recharge","description":"Problem statement\r\nWrite a function to compute the water table elevation  above the bottom of the aquifer and the position of a groundwater divide  given the water table elevations  at ,  at , hydraulic conductivity , and recharge rate . If there is no groundwater divide, set xd to the empty set []. \r\nBackground\r\nAs in other problems in this series, the movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. In an unconfined aquifer, the latter relates the flow of water to the gradient in water table elevation above the bottom of the aquifer by\r\n\r\nwhere  is the width of the aquifer. For steady, one-dimensional flow, conservation of mass says that the flow at any position  is \r\n\r\nwhere  is the (unknown) flow at . Using Darcy’s law to replace  provides a differential equation that can be integrated using the water table elevations at the boundaries to determine  and a constant of integration.\r\nUnlike the flows in Cody Problem 58966, the flows here can have a groundwater divide, or a point in the profile that separates flow to the left from flow to the right. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 838.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 419.25px; transform-origin: 407px 419.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 164.792px 8px; transform-origin: 164.792px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the water table elevation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 206.542px 8px; transform-origin: 206.542px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e above the bottom of the aquifer and the position of a groundwater divide \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"20\" alt=\"xd\" style=\"width: 15px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.917px 8px; transform-origin: 101.917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e given the water table elevations \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"h0\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x  = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17\" height=\"20\" alt=\"hL\" style=\"width: 17px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"18\" alt=\"x = L\" style=\"width: 39px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.35px 8px; transform-origin: 72.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 61.0667px 8px; transform-origin: 61.0667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and recharge rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"12\" height=\"20\" alt=\"i0\" style=\"width: 12px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.6px 8px; transform-origin: 27.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If there is no groundwater divide, set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003exd\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.6583px 8px; transform-origin: 53.6583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to the empty set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.3917px 8px; transform-origin: 35.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs in other \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52070\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eproblems\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55825\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ein\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/56205\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ethis\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58966\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eseries\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 264.883px 8px; transform-origin: 264.883px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. In an unconfined aquifer, the latter relates the flow of water to the gradient in water table elevation above the bottom of the aquifer by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"91.5\" height=\"35\" alt=\"Q = -K(dh/dx)hw\" style=\"width: 91.5px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ew\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 333.967px 8px; transform-origin: 333.967px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the width of the aquifer. For steady, one-dimensional flow, conservation of mass says that the flow at any position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.94167px 8px; transform-origin: 8.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"91\" height=\"20\" alt=\"Q = Q0 + i0 w x\" style=\"width: 91px; height: 20px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.4px 8px; transform-origin: 77.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the (unknown) flow at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94px 8px; transform-origin: 94px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Using Darcy’s law to replace \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 135.633px 8px; transform-origin: 135.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e provides a differential equation that can be integrated using the water table elevations at the boundaries to determine \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAAoCAYAAACSN4jeAAAC30lEQVRYR+1XTUhVQRTWvW1qZZsWtTDUbBNJ7VwoiCIkVNCysFq2MDJciIiCLsSVP9i+BImoTRkuhMJq0SaojaAgtUoI2tf3wRw4d+7MvWce78kD78DHfe/dmTnf+c6Zc+a1tjTpaG1SXi0VsdTIVIqdeMVuQYEbwCWgQ6nxDp9fAiupCvnzU3OMhBaBdmADeAaQDEc/sOSI/sDzOnBUK0ErsdMwsAzcBP4C94AXAaOcdwC0ASR3sZHEaOyDU4J2bkdICYdVfBhzX57iOVcLOYtiu9j4qtt8Dc/7JYYY0rduzi88zzaCmPaeRroMeaOJkdMFYC+VXJFivoGyEIrtWtdluBcR0yG0qsXNHwA8KDKsDpmI+V4vYNVjYzh0+LnkjCH8ua1jirEUsDTISMmT71gkRTdFaZNiPzGLRZQjpViytPxWFlh8B4xKlxLzN7eUCNm0LvnFzUKh9PPrIeZZe58O4yesG/Ty6wq+zwD7QA/ALsH9c63LQsx6qsrKhLzXB4mFuBvI1ccQMT+UVmK6vLDBs+Hrwbw9BZxTClHBz0AuXWKnUie/JZQT2HzWsQiFkCSfA6HG/s+ty3CJEZvH5HG3IOS9VkK85m80PAT4LUj2Cx0kUToTmRgxhvMbICUjViSZN5sArzl0IJjI+F2MFxHLFPGilkQlXjlyLJQjwBcn1XkXOhZhvnsEhO5noqyFWIZ02bWHyj0BhgF9heZl8SPAazSVKrup1p2YeCw5Yj2hXEdVJddYFhj2olAmKUYD0jfZXiZVOIV06MlTOAXIQahb8ovHb7wQCgnm1WvgK7CllKEqdwFW/FFA/1GhaiwlvZ4nUi4yByyWY/R4HTgE/riN5HpdpBTf0fgdRVbmS23UNqXU5Jp9rPLzXv8+EDYS7gPY5zoBlgkO1q8dYBuInc5YS7qGNZd9R8pOZZk6qe9Jbhpg85bBf1K5/wTHTczsSEXMLJWbWClWKZaqQOr8/+6UrClQAbvIAAAAAElFTkSuQmCC\" width=\"19\" height=\"20\" alt=\"Q0\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.1833px 8px; transform-origin: 92.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and a constant of integration.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.35px 8px; transform-origin: 58.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUnlike the flows in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58966\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 58966\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 233.383px 8px; transform-origin: 233.383px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the flows here can have a groundwater divide, or a point in the profile that separates flow to the left from flow to the right. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 403.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 201.85px; text-align: left; transform-origin: 384px 201.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"586\" height=\"398\" style=\"vertical-align: baseline;width: 586px;height: 398px\" 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\" alt=\"Unconfined aquifer with recharge\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0)\r\n  h = (h0+hL)/2;\r\n  xd = x;\r\nend","test_suite":"%%\r\nL = 10;                                       %  Length (m)    \r\nx = L/2;                                      %  Position where WTE is desired (m)\r\nh0 = 19.11;                                   %  Water table elevation at x = 0 (m)\r\nhL = 19.11;                                   %  Water table elevation at x = L (m)\r\nK = 5e-7;                                     %  Hydraulic conductivity (m/s)\r\ni0 = 6.9e-8;                                  %  Recharge rate (m/s)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = 19.2;\r\nxd_correct = 5;\r\nassert(abs(h-h_correct)\u003c1e-3)\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 1200;                                       %  Length (m)                                                   \r\nx = 0:300:1200;                                 %  Positions where WTE is desired (m)\r\nh0 = 25;                                        %  Water table elevation at x = 0 (m)\r\nhL = 23;                                        %  Water table elevation at x = L (m)\r\nK = 4;                                          %  Hydraulic conductivity (m/d)\r\ni0 = 2e-4;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [25.000 24.789 24.393 23.801 23.000];\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(isempty(xd))\r\n\r\n%%\r\nL = 1200;                                       %  Length (m)                                                   \r\nx = 0:300:1200;                                 %  Positions where WTE is desired (m)\r\nh0 = 25;                                        %  Water table elevation at x = 0 (m)\r\nhL = 23;                                        %  Water table elevation at x = L (m)\r\nK = 4;                                          %  Hydraulic conductivity (m/d)\r\ni0 = 8e-4;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [25.000 25.593 25.475 24.637 23.000];\r\nxd_correct = 400;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 2500;                                       %  Length (m)                                                   \r\nx = [100 200 300 700 1200 1800 2400];           %  Positions where WTE is desired (m)\r\nh0 = 35;                                        %  Water table elevation at x = 0 (m)\r\nhL = 33.5;                                      %  Water table elevation at x = L (m)\r\nK = 50;                                         %  Hydraulic conductivity (m/d)\r\ni0 = 1e-3;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [35.010 35.014 35.012 34.949 34.74 34.296 33.633];\r\nxd_correct = 222.5;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 2500;                                       %  Length (m)                                                   \r\nx = [100 200 300 700 1200 1800 2400];           %  Positions where WTE is desired (m)\r\nh0 = 35;                                        %  Water table elevation at x = 0 (m)\r\nhL = 33.5;                                      %  Water table elevation at x = L (m)\r\nK = 60;                                         %  Hydraulic conductivity (m/d)\r\ni0 = 1e-3;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [34.998 34.992 34.981 34.889 34.665 34.235 33.621];\r\nxd_correct = 17;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 20;                                         %  Length (m)                                                   \r\nx = 0:4:20;                                     %  Positions where WTE is desired (m)\r\nh0 = 5;                                         %  Water table elevation at x = 0 (m)\r\nhL = 3.5;                                       %  Water table elevation at x = L (m)\r\nK = 0.5;                                        %  Hydraulic conductivity (m/d)\r\ni0 = 1e-3;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [5 4.752 4.482 4.188 3.864 3.5];\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(isempty(xd))\r\n\r\n%%\r\nL = 20;                                         %  Length (m)                                                   \r\nx = 0:4:20;                                     %  Positions where WTE is desired (m)\r\nh0 = 5;                                         %  Water table elevation at x = 0 (m)\r\nhL = 3.5;                                       %  Water table elevation at x = L (m)\r\nK = 0.1;                                        %  Hydraulic conductivity (m/d)\r\ni0 = 5e-3;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [5 5.065 4.97 4.706 4.243 3.5];\r\nxd_correct = 3.625;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 1000*rand;                                  %  Length (m)                                                   \r\nx = L/17;                                       %  Positions where WTE is desired (m)\r\nh0 = randi(100);                                %  Water table elevation at x = 0 (m)\r\nhL = h0;                                        %  Water table elevation at x = L (m)\r\nK = 5;                                          %  Hydraulic conductivity (m/d)\r\ni0 = 5e-3;                                      %  Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nassert(abs(xd-L/2)\u003c1e-3)\r\n\r\n%%\r\nfiletext = fileread('unconfWithRecharge.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-09-23T13:56:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-09-23T01:49:39.000Z","updated_at":"2026-02-12T13:52:11.000Z","published_at":"2023-09-23T01:49:48.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the water table elevation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e above the bottom of the aquifer and the position of a groundwater divide \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"xd\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_d\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e given the water table elevations \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x  = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"hL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and recharge rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"i0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If there is no groundwater divide, set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003exd\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to the empty set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs in other \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52070\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eproblems\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55825\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ein\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/56205\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethis\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58966\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eseries\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. In an unconfined aquifer, the latter relates the flow of water to the gradient in water table elevation above the bottom of the aquifer by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = -K(dh/dx)hw\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K\\\\frac{dh}{dx}hw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"w\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ew\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the width of the aquifer. For steady, one-dimensional flow, conservation of mass says that the flow at any position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = Q0 + i0 w x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = Q_0 + i_0 w x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the (unknown) flow at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Using Darcy’s law to replace \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e provides a differential equation that can be integrated using the water table elevations at the boundaries to determine \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and a constant of integration.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUnlike the flows in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58966\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 58966\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the flows here can have a groundwater divide, or a point in the profile that separates flow to the left from flow to the right. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59029,"title":"Compute the water table in a layered unconfined aquifer","description":"Write a function to compute the flow per unit width and the elevation of the water table above the bottom of unconfined aquifer with two soil layers. The input to the function will be the positions where the water table elevation (WTE) is requested, the hydraulic conductivities of the two layers, the thickness of the bottom layer, the WTEs at  and , and the length  of the aquifer.\r\nBackground \r\nCody Problem 52070 dealt with the effective conductivity of a heterogeneous confined aquifer. In that case, the effective conductivity  for the case of flow through soil units in parallel could be computed by realizing that the head difference is same for the two soils and the total flow is the sum of the flows through the soils. The effective conductivity then is the weighted average of the individual conductivities, using the layer thicknesses as weights. \r\nFor an unconfined aquifer, the effective conductivity is computed in a similar way, but because the WTE  varies with , so does :\r\n\r\nThen using Darcy’s law as in Cody Problem 58966, one can write the flow  through the aquifer as\r\n\r\nConservation of mass says that in steady one-dimensional flow, the flow  past any section is constant. Then the WTE can be computed by inserting the effective conductivity, integrating, and using the boundary conditions  and  to determine the flow  and the constant of integration. \r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 836.3px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 418.15px; transform-origin: 407px 418.15px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 367.442px 8px; transform-origin: 367.442px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the flow per unit width and the elevation of the water table above the bottom of unconfined aquifer with two soil layers. The input to the function will be the positions where the water table elevation (WTE) is requested, the hydraulic conductivities of the two layers, the thickness of the bottom layer, the WTEs at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"18\" alt=\"x = L\" style=\"width: 39px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eL\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3333px 8px; transform-origin: 44.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the aquifer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.775px 8px; transform-origin: 42.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 85px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42.5px; text-align: left; transform-origin: 384px 42.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52070-compute-the-effective-conductivity-of-a-heterogeneous-aquifer?s_tid=ta_cody_results\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 52070\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 306.625px 8px; transform-origin: 306.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e dealt with the effective conductivity of a heterogeneous confined aquifer. In that case, the effective conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"24.5\" height=\"20\" alt=\"Keff\" style=\"width: 24.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 330.125px 8px; transform-origin: 330.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for the case of flow through soil units in parallel could be computed by realizing that the head difference is same for the two soils and the total flow is the sum of the flows through the soils. The effective conductivity then is the weighted average of the individual conductivities, using the layer thicknesses as weights. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 321.408px 8px; transform-origin: 321.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor an unconfined aquifer, the effective conductivity is computed in a similar way, but because the WTE \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36.95px 8px; transform-origin: 36.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e varies with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.2167px 8px; transform-origin: 13.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, so does \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"24.5\" height=\"20\" alt=\"Keff\" style=\"width: 24.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"172\" height=\"35\" alt=\"Keff = (1/h)[(K2-K1) b2 + K1(h-b2)]\" style=\"width: 172px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.8917px 8px; transform-origin: 90.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThen using Darcy’s law as in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58966-compute-the-head-for-steady-1d-flow-in-a-homogeneous-aquifer\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 58966\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73.5083px 8px; transform-origin: 73.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, one can write the flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70.0167px 8px; transform-origin: 70.0167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e through the aquifer as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"183\" height=\"35\" alt=\"Q = -Keff(dh/dx)A = -Keff(dh/dx)hw\" style=\"width: 183px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 224.825px 8px; transform-origin: 224.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConservation of mass says that in steady one-dimensional flow, the flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.058px 8px; transform-origin: 152.058px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e past any section is constant. Then the WTE can be computed by inserting the effective conductivity, integrating, and using the boundary conditions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"61\" height=\"20\" alt=\"h(0) = h0\" style=\"width: 61px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"64.5\" height=\"20\" alt=\"h(L) = hL\" style=\"width: 64.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0.991667px 8px; transform-origin: 0.991667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to determine the flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.9583px 8px; transform-origin: 99.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the constant of integration. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 346.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 173.35px; text-align: left; transform-origin: 384px 173.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"559\" height=\"341\" style=\"vertical-align: baseline;width: 559px;height: 341px\" 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alt=\"unconfined aquifer with soils in parallel\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L)\r\n%  h  = water table elevation above the aquifer bottom\r\n%  Qp = flow per unit width\r\n%  x  = locations where WTE is requested\r\n%  K1 = hydraulic conductivity of upper layer\r\n%  K2 = hydraulic conductivity of lower layer\r\n%  b2 = thickness of lower layer\r\n%  h0 = water table elevation on the left side (x = 0)\r\n%  hL = water table elevation on the right side (x = L)\r\n%  L  = length of the aquifer\r\n\r\n   Qp = mean([K1 K2])*(h0-hL)*b2/L;\r\n   h  = h0 + (hL-h0)*x/L;","test_suite":"%%\r\nx  = [0 251.884 503.2297 754.0371 1004.3062 1254.0371 1503.2297 1751.884 2000];\r\nK1 = 900;                       %  Hydraulic conductivity of upper layer (m/d)\r\nK2 = 8000;                      %  Hydraulic conductivity of lower layer (m/d)\r\nh0 = 37;                        %  Water table elevation on the left side (m)\r\nhL = 33;                        %  Water table elevation on the right side (m)\r\nL  = 2000;                      %  Length of aquifer (m)\r\nb2 = 25;                        %  Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 37:-0.5:33;\r\nQp_correct = 418;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx  = [0 284.1463 558.5366 823.1707 1078.0488 1323.1707 1558.5366 1784.1463 2000];\r\nK1 = 8000;                      %  Hydraulic conductivity of upper layer (m/d)\r\nK2 = 900;                       %  Hydraulic conductivity of lower layer (m/d)\r\nh0 = 37;                        %  Water table elevation on the left side (m)\r\nhL = 33;                        %  Water table elevation on the right side (m)\r\nL  = 2000;                      %  Length of aquifer (m)\r\nb2 = 25;                        %  Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 37:-0.5:33;\r\nQp_correct = 205;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx  = [0 230.8945 460.1048 687.631 913.4731 1137.631 1360.1048 1580.8945 1800];\r\nK1 = 4;                         %  Hydraulic conductivity of upper layer (m/d)\r\nK2 = 0.1;                       %  Hydraulic conductivity of lower layer (m/d)\r\nh0 = 50;                        %  Water table elevation on the left side (m)\r\nhL = 48;                        %  Water table elevation on the right side (m)\r\nL  = 1800;                      %  Length of aquifer (m)\r\nb2 = 16;                        %  Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 50:-0.25:48;\r\nQp_correct = 0.1484;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx  = [0 225.2925 450.5015 675.6269 900.6686 1125.6269 1350.5015 1575.2925 1800];\r\nK1 = 0.1;                       %  Hydraulic conductivity of upper layer (m/d)\r\nK2 = 4;                         %  Hydraulic conductivity of lower layer (m/d)\r\nh0 = 50;                        %  Water table elevation on the left side (m)\r\nhL = 48;                        %  Water table elevation on the right side (m)\r\nL  = 1800;                      %  Length of aquifer (m)\r\nb2 = 16;                        %  Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 50:-0.25:48;\r\nQp_correct = 7.48e-2;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx  = [0 2.6558 5.2033 7.6423 9.9729 12.1951 14.3089 16.3144 18.2114 20];\r\nK1 = 0.5;                       %  Hydraulic conductivity of upper layer (m/d)\r\nK2 = 0.1;                       %  Hydraulic conductivity of lower layer (m/d)\r\nh0 = 3.7;                       %  Water table elevation on the left side (m)\r\nhL = 2.8;                       %  Water table elevation on the right side (m)\r\nL  = 20;                        %  Length of aquifer (m)\r\nb2 = 1.5;                       %  Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 3.7:-0.1:2.8;\r\nQp_correct = 4.613e-2;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx  = [0 2.6558 5.2033 7.6423 9.9729 12.1951 14.3089 16.3144 18.2114 20];\r\nK1 = 0.5;                       %  Hydraulic conductivity of upper layer (m/d)\r\nK2 = 0.1;                       %  Hydraulic conductivity of lower layer (m/d)\r\nh0 = 3.7;                       %  Water table elevation on the left side (m)\r\nhL = 2.8;                       %  Water table elevation on the right side (m)\r\nL  = 20;                        %  Length of aquifer (m)\r\nb2 = 1.5;                       %  Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 3.7:-0.1:2.8;\r\nQp_correct = 4.613e-2;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx  = [0 2.3183 4.6126 6.8829 9.1291 11.3514 13.5495 15.7237 17.8739 20];\r\nK1 = 0.1;                       %  Hydraulic conductivity of upper layer (m/d)\r\nK2 = 0.5;                       %  Hydraulic conductivity of lower layer (m/d)\r\nh0 = 3.7;                       %  Water table elevation on the left side (m)\r\nhL = 2.8;                       %  Water table elevation on the right side (m)\r\nL  = 20;                        %  Length of aquifer (m)\r\nb2 = 1.5;                       %  Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 3.7:-0.1:2.8;\r\nQp_correct = 4.163e-2;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx  = 0:325:1300;\r\nK1 = 5;                         %  Hydraulic conductivity of upper layer (m/d)\r\nK2 = 5;                         %  Hydraulic conductivity of lower layer (m/d)\r\nh0 = 10;                        %  Water table elevation on the left side (m)\r\nhL = 9;                         %  Water table elevation on the right side (m)\r\nL  = 1300;                      %  Length of aquifer (m)\r\nb2 = 4;                         %  Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = [10 9.7596 9.5131 9.2601 9];\r\nQp_correct = 3.65e-2;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nfiletext = fileread('unconfParallel.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-09-30T19:04:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-09-30T15:05:42.000Z","updated_at":"2023-09-30T19:04:22.000Z","published_at":"2023-09-30T15:09:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the flow per unit width and the elevation of the water table above the bottom of unconfined aquifer with two soil layers. The input to the function will be the positions where the water table elevation (WTE) is requested, the hydraulic conductivities of the two layers, the thickness of the bottom layer, the WTEs at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the aquifer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52070-compute-the-effective-conductivity-of-a-heterogeneous-aquifer?s_tid=ta_cody_results\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 52070\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e dealt with the effective conductivity of a heterogeneous confined aquifer. In that case, the effective conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Keff\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_{eff}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for the case of flow through soil units in parallel could be computed by realizing that the head difference is same for the two soils and the total flow is the sum of the flows through the soils. The effective conductivity then is the weighted average of the individual conductivities, using the layer thicknesses as weights. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor an unconfined aquifer, the effective conductivity is computed in a similar way, but because the WTE \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e varies with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, so does \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Keff\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_{eff}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Keff = (1/h)[(K2-K1) b2 + K1(h-b2)]\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_{eff} = \\\\frac{1}{h}[K_2 b_2 + K_1(h-b_2)]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThen using Darcy’s law as in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58966-compute-the-head-for-steady-1d-flow-in-a-homogeneous-aquifer\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 58966\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, one can write the flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e through the aquifer as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = -Keff(dh/dx)A = -Keff(dh/dx)hw\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K_{eff} \\\\frac{dh}{dx} A =  -K_{eff} \\\\frac{dh}{dx} h w\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConservation of mass says that in steady one-dimensional flow, the flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e past any section is constant. Then the WTE can be computed by inserting the effective conductivity, integrating, and using the boundary conditions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h(0) = h0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh(0) = h_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h(L) = hL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh(L) = h_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to determine the flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the constant of integration. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"341\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"559\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" 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an ODE: Ekman spiral on a solid surface","description":"Problem \r\nWrite a function to solve for  and  as a function of  in this system of ordinary differential equations:\r\n\r\n\r\nwhere , , , and  are constants. The boundary conditions are that  at  and  and  as .\r\nBackground\r\nThis set of equations results from simplifying the Navier-Stokes equations (i.e., conservation of momentum for a fluid with a linear stress-rate of strain relation) for large-scale flow subjected to rotation. The horizontal velocity components are  and . The Coriolis parameter  is related to Earth’s rotation rate and the latitude, and  is the kinematic viscosity, which can be interpreted as an eddy viscosity to account for the effects of turbulence. \r\nThe velocities far above the surface,  and , result from the pressure gradient:  and , where  is pressure and  is density. Notice that far above the surface, the flow is along the isobars, or lines of constant pressure. As the surface is approached, the velocity vector rotates—or spirals. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 388.2px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 194.1px; transform-origin: 407px 194.1px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.9417px 8px; transform-origin: 29.9417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 86.6px 8px; transform-origin: 86.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to solve for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eu\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ev\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.3333px 8px; transform-origin: 51.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as a function of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 147.683px 8px; transform-origin: 147.683px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in this system of ordinary differential equations:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"121\" height=\"36.5\" alt=\"-fv = -fV + eta d^2u/dz^2\" style=\"width: 121px; height: 36.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"102.5\" height=\"36.5\" alt=\"fu = fU + eta d^2v/dz^2\" style=\"width: 102.5px; height: 36.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ef\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eU\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eV\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eη\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.083px 8px; transform-origin: 152.083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are constants. The boundary conditions are that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"62\" height=\"18\" alt=\"u = v = 0\" style=\"width: 62px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"35\" height=\"18\" alt=\"z = 0\" style=\"width: 35px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFAAAAAkCAYAAAAeor16AAADK0lEQVRoQ+2Yy6tPURTH750beIxMKAwoAwOviDKhTCSFMvf4AygGBgYUJkYeycAA10xKoQzlNVQMUEqMkJjz/WqtWne391nrtDu/362zT3279/zOWvvxOWuvvfaZnWlXFYHZKu/mPNMAVgZBA9gAVhKodG8R2ABWEqh0H0MEXgSjldDBhNUf3N+BnkFzybPjuN+V+DzB/a3UdgwAlQ0hKUTC2wB9dALwBZ5vgW5Ax3K2YwKoMMjhPnQosHrVZ00J9pgA/jXA9uB/Lknvos9LaGvJcCwAdwPAY4HA5cuc+MOhpz5nYHdh7ACvA8BRgcDIYwR6l/pshuHrIQAuRaMbpeE3gTfqDXjI5+/Q+FrpoDOizCDow2t719xyS5hguOMsgXZCK6CH8pudpH2ryxYwwNUY2wcz8M6IEjsy+A65m00pB7KBuxDzAK9c0v2K35dDnUk2CSubi5JHvW6jUcRGWdNdldbfexEldurjbjZdmwiTLiecS7osAe5JZ5fw91Rw+tMAaOs/N6JkHvTZC7mbTRfArgizg3LfUhDuUGa/0fAiafww/qanjly/9HkuK69zXCWANm+ky8U+i5YEQ8Hx2t0Eg1fGKJKr1SeUJkoAbd5Ik66Nvj75z5vsEM/T/Lcu0AnPzieh4unDtlECqJC+wXg9pEVnuqOF3lJg0EOZ2EqheJ5NOg+VL+pTAqj5L026bPwXxAM2r0hJYMc36U3Enn8j+a/X8uXEcgBtlJ2AzTUhoJ+FFuOeINLojETRQgfIymMbFPlS83++OYA2b2ge4MSvQKzKP0Pc1fRIRPtPch+BOEmb0+jsvHToLWEtzTy7eePPAdS8waKTSZdh/QDaBzEXalXP6CS4cxBrJu9wPklw2hcPBG8hFvy8SimH8G5CXyRIwnPJAUy/mxHOAYkwuwS5A/OYtwPyPkxOA572yQC4DelZWL8s/8Rvq6D9EOfF+RzpO5fSEubpgtcj6DKkXyPsG2WHZwXsNAFF+2aqISzmOC2sWceyYOan+qdQOPK007F8D4xC7m3XAPZGNt+hAWwAKwlUurcIbAArCVS6twhsACsJVLq3CKwE+A/0maglIn+EtQAAAABJRU5ErkJggg==\" width=\"40\" height=\"18\" alt=\"u = U\" style=\"width: 40px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"18\" alt=\"v = V\" style=\"width: 39px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.275px 8px; transform-origin: 11.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"45\" height=\"18\" alt=\"z --\u003e infinity\" style=\"width: 45px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.342px 8px; transform-origin: 382.342px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis set of equations results from simplifying the Navier-Stokes equations (i.e., conservation of momentum for a fluid with a linear stress-rate of strain relation) for large-scale flow subjected to rotation. The horizontal velocity components are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eu\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ev\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.0167px 8px; transform-origin: 77.0167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The Coriolis parameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ef\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.283px 8px; transform-origin: 168.283px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is related to Earth’s rotation rate and the latitude, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eη\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 115px 8px; transform-origin: 115px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the kinematic viscosity, which can be interpreted as an eddy viscosity to account for the effects of turbulence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.35px 8px; transform-origin: 114.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe velocities far above the surface, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eU\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eV\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 108.9px 8px; transform-origin: 108.9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, result from the pressure gradient: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"123.5\" height=\"18.5\" alt=\"U = -(1/rho f) dp/dy\" style=\"width: 123.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"112.5\" height=\"18.5\" alt=\"V = (1/rho f) dp/dx\" style=\"width: 112.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.8917px 8px; transform-origin: 24.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.7333px 8px; transform-origin: 51.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is pressure and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eρ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 237.9px 8px; transform-origin: 237.9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is density. Notice that far above the surface, the flow is along the isobars, or lines of constant pressure. As the surface is approached, the velocity vector rotates—or spirals. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [u,v] = EkmanSolid(z,eta,f,U,V)\r\n%  u,v  =   velocities in the x- and y-directions\r\n%  z    =   distance above the solid surface\r\n%  eta  =   kinematic viscosity (can be interpreted as an eddy viscosity for turbulent flow)\r\n%  f    =   Coriolis parameter\r\n%  U,V  =   velocities in the x- and y-directions far above the surface\r\n\r\n   [u,v] = deal(U,V);","test_suite":"%%\r\neta = 1e-6;             %  Kinematic viscosity (m2/s)\r\nf  = 1e-4;              %  Coriolis parameter (1/s)\r\nU  = 1;                 %  x-velocity far above the surface (m/s)\r\nV  = 0;                 %  y-velocity far above the surface (m/s)\r\nz = [0 0.05 0.1 0.15 0.2:0.1:0.5 0.7];    %  Distance above surface (m)\r\n[u,v] = EkmanSolid(z,eta,f,U,V);\r\nu_correct = [0 0.34124 0.62515 0.83094 0.96209 1.0627 1.0562 1.0269 0.99833];\r\nv_correct = [0 0.24312 0.32032 0.30214 0.24014 0.10216 0.018209 -0.011186 -0.0068865];\r\nassert(isequal([u(1) v(1)],[0 0]))\r\nassert(all(abs(u(2:end)-u_correct(2:end))./u_correct(2:end) \u003c 1e-4))\r\nassert(all(abs(v(2:end)-v_correct(2:end))./v_correct(2:end) \u003c 1e-4))\r\n\r\n%%\r\neta = 1e-6;             %  Kinematic viscosity (m2/s)\r\nf  = 1e-4;              %  Coriolis parameter (1/s)\r\nU  = 0;                 %  x-velocity far above the surface (m/s)\r\nV  = 1;                 %  y-velocity far above the surface (m/s)\r\nz = [0 0.05 0.1 0.15 0.2:0.1:0.5 0.7];    %  Distance above surface (m)\r\n[u,v] = EkmanSolid(z,eta,f,U,V);\r\nu_correct = [0 -0.24312 -0.32032 -0.30214 -0.24014 -0.10216 -0.018209 0.011186 0.0068865];\r\nv_correct = [0 0.34124 0.62515 0.83094 0.96209 1.0627 1.0562 1.0269 0.99833];\r\nassert(isequal([u(1) v(1)],[0 0]))\r\nassert(all(abs(u(2:end)-u_correct(2:end))./u_correct(2:end) \u003c 1e-4))\r\nassert(all(abs(v(2:end)-v_correct(2:end))./v_correct(2:end) \u003c 1e-4))\r\n\r\n%%\r\neta = 3;                %  Eddy viscosity (m2/s)\r\nf  = 1e-4;              %  Coriolis parameter (1/s)\r\nU  = 0.5;               %  x-velocity far above the surface (m/s)\r\nV  = 0.8;               %  y-velocity far above the surface (m/s)\r\nz = [10 50 80 130 190 240 300 400 500 1000 2000];    %  Distance above surface (m)\r\n[u,v] = EkmanSolid(z,eta,f,U,V);\r\nu_correct = [-0.010943 -0.031442 -0.026767 0.0081958 0.077758 0.14605 0.22904 0.3501 0.43683 0.51587 0.49983];\r\nv_correct = [0.052233 0.24389 0.36912 0.54304 0.69822 0.78853 0.85848 0.9072 0.90497 0.80113 0.80021];\r\nassert(all(abs(u-u_correct)./u_correct \u003c 1e-4))\r\nassert(all(abs(v-v_correct)./v_correct \u003c 1e-4))\r\n\r\n%%\r\neta = 0.5;              %  Eddy viscosity (m2/s)\r\nf  = 1e-4;              %  Coriolis parameter (1/s)\r\nU  = 2;                 %  x-velocity far above the surface (m/s)\r\nV  = 0.4;               %  y-velocity far above the surface (m/s)\r\nz = [10 50 80 130 190 240 300 400 500 1000 2000];    %  Distance above surface (m)\r\n[u,v] = EkmanSolid(z,eta,f,U,V);\r\nu_correct = [0.16323 0.81912 1.245 1.7492 2.0401 2.1093 2.0958 2.0295 1.9988 2.0001 2];\r\nv_correct = [0.22054 0.76866 0.91944 0.89604 0.70242 0.54931 0.43377 0.37707 0.38631 0.39997 0.4];\r\nassert(all(abs(u-u_correct)./u_correct \u003c 1e-4))\r\nassert(all(abs(v-v_correct)./v_correct \u003c 1e-4))\r\n\r\n%%\r\neta = 10;               %  Eddy viscosity (m2/s)\r\nf  = 8e-5;              %  Coriolis parameter (1/s)\r\nU  = 8;                 %  x-velocity far above the surface (m/s)\r\nV  = 6;                 %  y-velocity far above the surface (m/s)\r\nz = 200:200:2000;       %  Distance above surface (m)\r\n[u,v] = EkmanSolid(z,eta,f,U,V);\r\nu_correct = [1.4945 3.5616 5.4425 6.8363 7.7122 8.1675 8.3361 8.3398 8.2686 8.1789];\r\nv_correct = [4.3838 6.7003 7.591 7.6499 7.3224 6.8916 6.5067 6.2251 6.0503 5.9609];\r\nassert(all(abs(u-u_correct)./u_correct \u003c 1e-4))\r\nassert(all(abs(v-v_correct)./v_correct \u003c 1e-4))\r\n\r\n%%\r\neta = 12;               %  Eddy viscosity (m2/s)\r\nf  = 8e-5;              %  Coriolis parameter (1/s)\r\nU  = 10;                %  x-velocity far above the surface (m/s)\r\nV  = 5;                 %  y-velocity far above the surface (m/s)\r\nz = 300:300:3000;       %  Distance above surface (m)\r\n[u,v] = EkmanSolid(z,eta,f,U,V);\r\nu_correct = [3.5576 6.9831 9.1755 10.1948 10.468 10.397 10.2354 10.0997 10.0197 9.9861];\r\nv_correct = [5.5429 7.208 6.9985 6.2349 5.551 5.1311 4.9452 4.902 4.9216 4.9554];\r\nassert(all(abs(u-u_correct)./u_correct \u003c 1e-4))\r\nassert(all(abs(v-v_correct)./v_correct \u003c 1e-4))\r\n\r\n%%\r\nfiletext = fileread('EkmanSolid.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":46909,"edited_by":46909,"edited_at":"2024-03-11T02:38:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2024-03-11T02:38:47.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-03-10T16:24:15.000Z","updated_at":"2025-09-16T00:37:21.000Z","published_at":"2024-03-10T16:24:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to solve for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as a function of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"z\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in this system of ordinary differential equations:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"-fv = -fV + eta d^2u/dz^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e-fv = -fV+\\\\eta\\\\frac{d^2u}{dz^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"fu = fU + eta d^2v/dz^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003efu = fU+\\\\eta\\\\frac{d^2v}{dz^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"eta\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\eta\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are constants. The boundary conditions are that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u = v = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu = v = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"z = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u = U\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu = U\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v = V\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev = V\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"z --\u0026gt; infinity\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\\\\to\\\\infty\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis set of equations results from simplifying the Navier-Stokes equations (i.e., conservation of momentum for a fluid with a linear stress-rate of strain relation) for large-scale flow subjected to rotation. The horizontal velocity components are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"v\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The Coriolis parameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"f\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is related to Earth’s rotation rate and the latitude, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"eta\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\eta\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the kinematic viscosity, which can be interpreted as an eddy viscosity to account for the effects of turbulence. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe velocities far above the surface, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, result from the pressure gradient: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"U = -(1/rho f) dp/dy\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU = -(1/\\\\rho f)\\\\partial p/\\\\partial y\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"V = (1/rho f) dp/dx\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV = (1/\\\\rho f)\\\\partial p/\\\\partial x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is pressure and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"rho\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is density. Notice that far above the surface, the flow is along the isobars, or lines of constant pressure. As the surface is approached, the velocity vector rotates—or spirals. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55335,"title":"Generate Bernoulli polynomials","description":"The Bernoulli polynomial  is a polynomial of order  with the properties that  and for  \r\n,\r\nwhere the prime denotes differentiation with respect to , and\r\n.\r\nTherefore, , , , etc. Notice that  is the th Bernoulli number.\r\nWrite a function to generate the Bernoulli polynomial of order . Use MATLAB's approach for specifying the coefficients. For example, the function should return [1 -1/2] for  and [1 -1 1/6] for .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 201px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 100.5px; transform-origin: 407px 100.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78.5917px 8px; transform-origin: 78.5917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Bernoulli polynomial \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B_n(x)\" style=\"width: 36.5px; height: 20px;\" width=\"36.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 76.2417px 8px; transform-origin: 76.2417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a polynomial of order \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74.675px 8px; transform-origin: 74.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the properties that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B_0(x) = 1\" style=\"width: 62.5px; height: 20px;\" width=\"62.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.6667px 8px; transform-origin: 25.6667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n \u003e 0\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B'_n(x) = n B_{n-1}(x)\" style=\"width: 113.5px; height: 20px;\" width=\"113.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 169.858px 8px; transform-origin: 169.858px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere the prime denotes differentiation with respect to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 27px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 13.5px; text-align: left; transform-origin: 384px 13.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-8px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"Integral[B_n(x),{x,0,1}] = 0\" style=\"width: 80px; height: 27px;\" width=\"80\" height=\"27\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.225px 8px; transform-origin: 34.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTherefore, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B_1(x) = x-1/2\" style=\"width: 81px; height: 20px;\" width=\"81\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B_2(x) = x^2 – x + 1/6\" style=\"width: 121.5px; height: 21px;\" width=\"121.5\" height=\"21\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B_3(x) = x^3 – 3 x^2/2 + x/2\" style=\"width: 149px; height: 21px;\" width=\"149\" height=\"21\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.4917px 8px; transform-origin: 52.4917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, etc. Notice that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"B_n(0)\" style=\"width: 36.5px; height: 20px;\" width=\"36.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6083px 8px; transform-origin: 20.6083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45831\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eBernoulli number\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 190.092px 8px; transform-origin: 190.092px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to generate the Bernoulli polynomial of order \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.658px 8px; transform-origin: 188.658px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Use MATLAB's approach for specifying the coefficients. For example, the function should return [1 -1/2] for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n = 1\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 55.2167px 8px; transform-origin: 55.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and [1 -1 1/6] for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAkCAYAAADFGRdYAAAC5klEQVRoQ+2YPUscURSGd3+AoNFKUplYCIIWYpUUWiQhtimUpLAQ1PwAFSyF+AFJEciH3XYmaKvEKqBio4X2aplKk5+g7wv3LHdnzr1zk5khK3MHXobd+zFznjlfM/VaPDIJ1DNnxAm1CCnACSKkCCmAQMCU6EkRkpPAEEY6zOhRFqeqedICgCxBXQkw7/D7A3SjAasSpBMAGPF4zT7GXmugqgKJHrQOzUE7BkQfzq8SnkWPWk6CrAKkbhh9DU1B3xRPeoL/Ds3/f3B+UEVIszB6DJr0hJodisOYd27PrYInMdSOIV8Vk3Akm3+CRHd9mKDLeO6FfkFXnid0X4YEEsOt3+Ss5r1rnvQSo4PQODQKsVwy4W1ChPMZem7FMF25xT09ZAh8oAByRT8c2jQPfYdSYalBEi9pYMEjYxDPbL5+QmvmP1YLHmpFcICwk2QeVvLQ8uxhr70wtj7FORWWvpwkyYz9w1voFBKvsY11VQ3NAHa6AjePgR+xeC/PBtZasUX1Is5zQZKyyTl8ajPQe0hKKCvGV3OhHpzVTrUgI8re5gcu8Bh6Bqn51QWJeWnX3B09iYvpTXJIDHPsRdlWlLg/H/Yq5M2rLkgCgfd3aUjb9/obP5jQF6GNEo0oc2uG/hk0AXlD1wVJEhlvMrmJbM6xVE+RYVW7VDfawCL0JgsQ7dEg2RC0ZCb5SG3hMyC1Q3X7K0AuSHZS1lyRiY590hfIzlMhofG/qxvbG1ZpnweJtzdbAc2TBILmKXbVk9LPisfkF9pQhsAsYw7vnbZtZ+RR5uMDqPkyrEG6NXeoeQq70S0zztK/AhFm6vNCGVbm2FMAsSmWZljbTt4yWl5NkpDs0q+Fmh2KdFtWPt/bdQ67ClsqgHwf3OyLpd4gkpBo8LRZofU/vOAnqBNq2C5ZmEnFb8SXV3pI6MG2pnKfSkLhOOdV4XtShJSbQMAG0ZMipAACAVOiJ0VIAQQCpkRPipACCARMuQPmxYMluJzL1wAAAABJRU5ErkJggg==\" alt=\"n = 2\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = BernoulliPolynomial(n)\r\n  y = sum(nchoosek(n,k).*x.^(0:n));\r\nend","test_suite":"%%\r\nn = 0;\r\ny = BernoulliPolynomial(n);\r\ny_correct = 1;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -1/2];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 2;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -1 1/6];\r\nassert(all(abs(y-y_correct)\u003c1e-11))\r\n\r\n%%\r\nn = 3;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -3/2 1/2 0];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 4;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -2 1 0 -1/30];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 5;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -5/2 5/3 0 -1/6 0];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 8;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -4 14/3 0 -7/3 0 2/3 0 -1/30];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 11;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -11/2 55/6 0 -11 0 11 0 -11/2 0 5/6 0];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 14;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -7 91/6 0 -1001/30 0 143/2 0 -1001/10 0 455/6 0 -691/30 0 7/6];\r\nassert(all(abs(y-y_correct)\u003c1e-12))\r\n\r\n%%\r\nn = 21;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -21/2 35 0 -399/2 0 1292 0 -6783 0 293930/11 0 -223193/3 0 135660 0 -1443183/10 0 219335/3 0 -1222277/110 0];\r\nassert(all(abs(y-y_correct)\u003c2e-9))\r\n\r\n%%\r\nn = 30;\r\ny = BernoulliPolynomial(n);\r\ny_correct = [1 -15 145/2 0 -1827/2 0 28275/2 0 -390195/2 0 4552275/2 0 -43785215/2 0 339319575/2 0 -2062720845/2 0 9509268925/2 0 -31795091601/2 0 72484065225/2 0 -102818379585/2 0 78132595905/2 0 -23749461029/2 0 8615841276005/14322];\r\nassert(all(abs(y-y_correct)\u003c1e-3))\r\n\r\n%%\r\nn = 12;\r\ny = BernoulliPolynomial(n);\r\nn2 = round(y(7));\r\ny2 = BernoulliPolynomial(n2);\r\ny2_15_correct = 373065;\r\nassert(isequal(round(y2(15)),y2_15_correct))\r\n\r\n%%\r\nfiletext = fileread('BernoulliPolynomial.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-09-17T15:39:23.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2022-09-17T15:39:23.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-08-20T20:19:44.000Z","updated_at":"2026-01-26T13:39:36.000Z","published_at":"2022-08-20T20:21:33.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Bernoulli polynomial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_n(x)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_n(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a polynomial of order \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with the properties that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_0(x) = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_0(x) = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n \u0026gt; 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en \u0026gt; 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B'_n(x) = n B_{n-1}(x)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\\\\prime_n(x) = nB_{n-1}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere the prime denotes differentiation with respect to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Integral[B_n(x),{x,0,1}] = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\int_0^1 B_n(x) = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_1(x) = x-1/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_1(x) = x – ½\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_2(x) = x^2 – x + 1/6\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_2(x) = x^2 – x + 1/6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_3(x) = x^3 – 3 x^2/2 + x/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_3(x) = x^3 – 3 x^2/2 + x/2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, etc. Notice that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B_n(0)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB_n(0)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45831\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBernoulli number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to generate the Bernoulli polynomial of order \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Use MATLAB's approach for specifying the coefficients. For example, the function should return [1 -1/2] for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and [1 -1 1/6] for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n = 2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"ordinary differential 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