Info

This question is closed. Reopen it to edit or answer.

Trying to solve for P in the equation. Been told fzero does not give correct solution.

1 view (last 30 days)
%clc; clear; close all; format short g;
%knowns
gamma = 1.66;
R = 8.314;
m = 4.0e-3;
RoM = R/m;
P0 = 10e5;
T0 = 300;
r0 = 0.01;
L = 0.05;
rho0 = P0/(RoM*T0);
%function for area
x = [0:0.001:2*L];
func = @(x) r0*((2*x./L)+ exp(-2*x./L));
y = func(x);
plot(x,y);
At = pi*r0*r0;
% equations
mc = At*(sqrt(gamma*P0*rho0))*(2/(gamma+1))^((gamma+1)/(2*(gamma-1))); %mass flux choking
%solving for P
f = @(P) ((P/P0)^(2/gamma)) - ((P/P0)^(1+(1/gamma))) == ((gamma-1)/(2*gamma))*((mc^2)/((At^2)*P0*rho0));
r = solve (f,eps)

Answers (1)

Samatha Aleti
Samatha Aleti on 26 Feb 2020
Hi,
I think you need to specify the variables as “sym” to use “solve”. You may also solve for “P” using “fsolve function.
Here is the documentation link for “fsolve”.
  4 Comments
Walter Roberson
Walter Roberson on 26 Feb 2020
If you convert everything to rational, except using the transcendentatal pi instead of an approximation of it, then 281250*sqrt(3) becomes an exact solution. That is approximately 487139.2898.
dpb
dpb on 28 Feb 2020
Ah, indeed! I hadn't really looked at the algebra, just the numerical solution. Nicely done, Walter!

Community Treasure Hunt

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

Start Hunting!