pmp_spd=@(D) Vfr*(Vfr_dim * D^3);
That creates a function handle. The only things you can do with a function handle are:
- display it
- create a character vector version of it
- copy it (such as passing it to a function)
- invoke it (typically passing in parameters)
- use functions() to inquire about it
- ask how many inputs or outputs it has with nargin() and nargout()
e5 = P_pmp==P_dim*rho*(pmp_spd^3)*D^5;
but there you try to raise the function handle to the third power. The ^3 operation is not any of the above permitted operations.
Perhaps you want
e5 = P_pmp==P_dim*rho*(pmp_spd(D)^3)*D^5;
However! solve() is for requesting the complete set of indefinitely precise exact closed-form solutions whenever those can be computed. In any case in which you have floating point numbers in your calculation, using solve() is almost certainly the wrong thing to do. For example look at your line
g=9.81;
Why are you asking for an infinitely precise solution to your equations when you know that 9.81 is just an approximation, with g being 9.789 at the equator and 9.832 at the poles? What is the point of doing computations to a minimum of 117 digits when your inputs are only valid to 2 digits? Especially when the computation involves the roots of a polynomial of degree 18, 10191242662004313*Pi^2*z^18 - 300388392382226505177600*Pi^2*z^4 - 17069893026094080000*Pi*sqrt(2) - 52219967275837440000*Pi - 3249025000000000000000 (this can be reduced to a polynomial of degree 9)
You are doing a scientific calculation. You should be doing appropriate error analysis. How do you justify OL=1287.48 being 6 digits when your 3 digit g is not even correct?
vpasolve(). And not to very many digits either. And when vpasolve() complains about numeric instability, reflect upon the fact that your inputs are potentially not precise enough to justify any output.
