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How to iterate with fsolve to find Mach number

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Hailey
Hailey on 10 Sep 2019
Edited: Torsten on 10 Sep 2019
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:
Capture.PNG
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);

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Hailey
Hailey on 10 Sep 2019
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
Torsten on 10 Sep 2019
They are stored in the fsolve return parameter (pt2pinf_test in your case).
Hailey
Hailey on 10 Sep 2019
The values are too small to be a Mach number after a shock wave.
Not sure what I did wrong.

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Accepted Answer

Torsten
Torsten on 10 Sep 2019
Edited: Torsten on 10 Sep 2019
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

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