How to iterate with fsolve to find Mach number

I'm trying to interate static pressure ratio to find Mach number using fsolve, but I can't get the syntax correct. The Mathworks explaination didn't really help me. Could anyone out there help?

I have a set range for the pressure ratio, but the Mach number is unknown. Here is the equation:

This is what I have so far for the code:

pt2pinf = [1.9, 2.7, 3.5, 4.3, 5.1, 5.9, 6.7, 7.5, 27.5, 47.5, 67.5 ,87.5 ,107.5,127.5, 147.5, 200, 252.5, 305, 357.5, 410, 462.5 ,515 ,567.5, 620, 672.5, 725, 777.5, 830 ,882.5, 935, 987.5, 1000];
Me0=ones(1,32);
g=1.2;
pt2pinf_test = fsolve(@(Me)(((1+((g-1)/2)*Me.^2)^(g/(g-1)))/((((2*g)/(g+1))*Me.^2)-((g-1)/(g+1)))),Me0);

[Torsten]

In the function you passed to "fsolve", you forgot to subtract the pressure ratio.

And for all ^, / and * operators, use .^, ./ and .* (elementwise operation).

[Hailey]

So it should look like this? But I get an error doing this. I'm sorry, I'm still confused. Because I have Me0 set as ones, should it be zeros while fsolve is trying to solve the problem?

pt2pinf_test = fsolve(@(Me)((((1+((g-1)/2).*Me.^2)^(g/(g-1)))/((((2*g)/(g+1)).*Me.^2)-((g-1)/(g+1))))-pt2pinf),Me0);

[Torsten]

You did not substitute all ^ by .^ and all / by ./ .

[Hailey]

I'm getting this, but I have the same array size:

Equation solved, fsolve stalled.

fsolve stopped because the relative size of the current step is less than the

value of the step size tolerance squared and the vector of function values

is near zero as measured by the value of the function tolerance.

<stopping criteria details>

[Torsten]

Thus you were successful.

[Hailey]

But I need to have the Mach number values. I need an array of Mach numbers that match up with it's respective pressure ratio value. This did not do that.

[Torsten]

They are stored in the fsolve return parameter (pt2pinf_test in your case).

[Hailey]

The values are too small to be a Mach number after a shock wave.

Not sure what I did wrong.

Answer 1

[Torsten]

function main
  pt2pinf = [1.9, 2.7, 3.5, 4.3, 5.1, 5.9, 6.7, 7.5, 27.5, 47.5, 67.5 ,87.5 ,107.5,127.5, 147.5, 200, 252.5, 305, 357.5, 410, 462.5 ,515 ,567.5, 620, 672.5, 725, 777.5, 830 ,882.5, 935, 987.5, 1000];
  Me0 = 5.0;
  g = 1.2;
  fun = @(Me,pquot)((((1+((g-1)/2)*Me.^2).^(g/(g-1)))./((((2*g)/(g+1))*Me.^2)-((g-1)/(g+1))))-pquot).^2
  for i = 1:numel(pt2pinf)
    pquot = pt2pinf(i);
    machnumber(i) = fminsearch(@(Me)fun(Me,pquot),Me0,optimset('TolFun',1e-10));
  end
  machnumber
  fun(machnumber,pt2pinf)
end