Solving 4 equations and 4 unknowns - help please

Hi, I've been looking around for quite some time and I can't seem to find how to answer my problem. I basically have 2 equations which I then separate into relationships for each variable. I have a number of initial conditions, i.e. A=A therefore A1=A2 (in both equations) and similarly X=X therefore X1=X2. I have initial conditions of M=7 and X=1.36. From the initial equation relationships I know that the relationship to B has 6 solutions but I know the actual solution is the equation in row 5, so this is selected. So then, I have 4 equations: A1=A2, X1=X2, B==b1 (f(A)) and B2==b2 (f(A,M2)). Here's where my problem lies, I run a solve for the equations and it says it solves, or as far as I can tell but I can't get the answer. Can anyone please help.

Here is the full code I'm running:

[Andrew Newell]

I cannot figure out what you are trying to solve. Maybe you need to step back a little - where did these equations come from?

[Fergus Conway]

OK, the original equation is from Oblique Shock Wave formation. The equation is from the theta, beta, Mach relationship. The original equation is: tan(theta1)=(2/tan(beta1))*((M1^2 sin^2(beta1)-1)/(M1^2(gamma+cos(2beta1))+2) ( Original Equation) .

From using this equation I have 2 points which it is being measured at (the same with theta2, M2 and beta2). I have the initial Mach number, Gamma and the relationship between them is that Theta in the first point = Theta at the second point (Theta1=Theta2). So from here what I did was try to get relationships for each variable and use the initial conditions (M1=7 and gamma=1.36) to reduce the equations to have 4 unknowns: Theta1, Beta1, Beta2 and M2. So from here I'm trying to find their values. The one I'm particularly interested in is Theta so just finding this would be sufficient. I hope this explains it a bit more

Thanks

Ferg

Answer 1

[Andrew Newell]

I think that you are misinterpreting the theta-beta-M equation. It does not involve initial and final conditions because the boundary conditions have already been used to derive this equation (have a look at one of the sources for the Wikipedia article). Instead, you have an equation of the form

f(theta,beta,M) = 0

If you know two of the variables, you can find the other. However, you only seem to know M, so you don't have enough information to solve the equation.

[Andrew Newell]

An alternative is that you could solve for theta as a function of beta to get a curve.

[Fergus Conway]

Thanks for your help, I found an alternative method for doing it which uses iterating repeatedly until certain conditions are satisfied based on the standard oblique shock relationships.