How can I calculate the value in an equation?

조회 수: 1 (최근 30일)
Ali Deniz
Ali Deniz . 2022년 4월 26일
편집: Sam Chak . 2022년 4월 27일
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.

채택된 답변

Sam Chak
Sam Chak 2022년 4월 26일
Please verify if the nonlinear equation is correct.
Looks like there are no real solutions for this one.
  댓글 수: 4
Sam Chak
Sam Chak 2022년 4월 27일
편집: Sam Chak 님. 2022년 4월 27일
@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 =

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추가 답변 (1개)

Torsten 2022년 4월 26일
I don't see a root:
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;


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