How can I calculate the value in an equation?

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Ali Deniz
Ali Deniz 2022-4-26
编辑： Sam Chak 2022-4-27
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.

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采纳的回答

Sam Chak
Sam Chak 2022-4-26
@Ali Deniz
Please verify if the nonlinear equation is correct.
Looks like there are no real solutions for this one.
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Ali Deniz
Ali Deniz 2022-4-27
That's right, I should find another way. Thank you.
Sam Chak
Sam Chak 2022-4-27
编辑：Sam Chak 2022-4-27
@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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更多回答（1 个）

Torsten
Torsten 2022-4-26
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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