Question

SOLVE USING MATLAB The following implicit equation offers a way to estimate the critical free stream velocity M_cr (Mach number) at which one can expect to observe a sonic flow (M=1) at a certain point on an airfoil. Solve the following implicit equation for M_cr when C_p.0=-0.43 and γ=1.4 (Use iteration or Newton's Method to solve the implicit equation). Avoid using symbolic toolbox servers.

Cp,0 / √(1-M2cr) = 2/(γM2cr) { [(2+(γ-1) M2cr) / (γ+1)] ^ (γ / ((γ-1))) -1}

Answer #1

**PLEASE GIVE IT A THUMBS UP, I SERIOUSLY NEED ONE, IF YOU
NEED ANY MODIFICATION THEN LET ME KNOW, I WILL DO IT FOR
YOU**

**Output:**

**Code:**

```
%Newton Ralphson to find M
clc
clear
C_p0 = -0.43;
g = 1.4; % g = gamma
syms M % M = critical free stream velocity
f1(M) = C_p0/sqrt(1-M^2) - (2/(g*M^2))*(((2+(g-1)*M^2)/(g+1))^(g/(g-1))-1);
fd = diff(f1);
p0 = 0.5; % initial approximation
n = 100; % maximum number of iterations
tol = 0.001; % tolerance required
i=1;
while i <= n
p = p0 - (f1(p0)/fd(p0)); %Newton-Raphson method
if (abs(p - p0)/abs(p)) < tol %stopping criterion when difference between iterations is below tolerance
fprintf('Solution is %f \n', double(p))
return
end
i = i + 1;
p0 = p; %update p0
end
```

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 26 minutes ago

asked 46 minutes ago

asked 46 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago