How can I calculate the value in an equation?

조회 수: 6 (최근 30일)
Ali Deniz
Ali Deniz 2022년 4월 26일
편집: Sam Chak 2022년 4월 27일
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.

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
Ali Deniz
Ali Deniz 2022년 4월 27일
That's right, I should find another way. Thank you.
Sam Chak
Sam Chak 2022년 4월 27일
편집: Sam Chak 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 =
17.9584

댓글을 달려면 로그인하십시오.

추가 답변 (1개)

Torsten
Torsten 2022년 4월 26일
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))

카테고리

Help CenterFile Exchange에서 Gamma Functions에 대해 자세히 알아보기

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by