How can I calculate the value in an equation?

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gamma=1.4
V_M_2 = 20;
V_M_2 = sqrt((gamma+1)/(gamma-1)) * atan(sqrt((gamma-1)/(gamma+1)*(M_2^2-1)))-atan(sqrt(M_2^2-1))
How can I find the M_2 from this equation? Thank you.

Accepted Answer

Sam Chak
Sam Chak on 26 Apr 2022
Please verify if the nonlinear equation is correct.
Looks like there are no real solutions for this one.
  4 Comments
Ali Deniz
Ali Deniz on 27 Apr 2022
That's right, I should find another way. Thank you.
Sam Chak
Sam Chak on 27 Apr 2022
Edited: Sam Chak on 27 Apr 2022
@Ali Deniz, Thanks for the correction.
By the way, the nonlinear function has a limit, .
So, if , then it has roots. Please check again.
gamma = 1.4;
V_M_2 = 2.0;
% function to be solved
f = @(x) sqrt((gamma + 1)/(gamma - 1))*atan(sqrt((gamma - 1)/(gamma + 1)*(x^2 - 1))) - atan(sqrt(x^2 - 1)) - V_M_2;
% initial guess
x0 = 20;
% root-finding solver
xsol = fzero(f, x0)
xsol =
17.9584

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More Answers (1)

Torsten
Torsten on 26 Apr 2022
I don't see a root:
gamma=1.4
V_M_2 = 20;
fun = @(M_2)V_M_2 - (sqrt((gamma+1)/(gamma-1)) * atan(sqrt((gamma-1)/(gamma+1)*(M_2-1)))-atan(sqrt(M_2-1)));
M_2 = -20:0.1:200;
plot(M_2,fun(M_2))

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