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Hailey
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How to iterate with fsolve to find Mach number

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

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1 Answer

Answer by Torsten
on 10 Sep 2019
Edited by Torsten
on 10 Sep 2019
 Accepted Answer

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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