changing a variable in an equation

Hi, I wrote this little piece of code to evaluate

 mass_flow  

I then find out I have mass_flow, and I need to evaluate ER. Is there an automatic way to do so without doing the math?

 clear
clc
close all


load 
datas.mat

k = 1.4;          %Gas constant ratio, cp/cv()
R = 287.05;       %ideal gas constant [J/Kg*K]
A_eff = .0069;    %[m^2]

mass_flow = phi_10Hz; %expansion ratio

mass_flow = A_eff.*((k./R).^0.5).*((1./E_R).^(1/k)).*(((2./k-1).*(1-(1./E_R).^((k-1)./k))).*0.5);


figure()
plot(E_R,mass_flow)

In attached the datas.mat you need to run the file

[Alan Stevens]

You don't specify E_R anywhere!

[Paul Rogers]

yes, because I have mass_flow and I need to find E_R.

[Alan Stevens]

Ah yes. Because you want to plot mass-flow agaist E_R, I assume you want to find a different E_R for each value of mass_flow (rather than a single overall best-fit), in which case one way is to do the following:

load datas.mat

k = 1.4;          %Gas constant ratio, cp/cv()
R = 287.05;       %ideal gas constant [J/Kg*K]
A_eff = .0069;    %[m^2]

mass_flow = phi_10Hz; %expansion ratio
mass_flowfn = @(E_R) A_eff.*((k./R).^0.5).*((1./E_R).^(1/k)).*(((2./k-1).*(1-(1./E_R).^((k-1)./k))).*0.5);

E_R = zeros(1,numel(mass_flow));
ER0 = 1;  % Initial guess
for i = 1:numel(mass_flow)
    E_R(i) = fminsearch(@(ER)fn(ER,mass_flowfn,mass_flow(i)),ER0);
    ER0 = E_R(i);
end

figure()
plot(E_R,mass_flow)


function F = fn(ER, mass_flowfn, mass_flow)

         F = norm(mass_flowfn(ER) - mass_flow);
         
end

Most of the values of E_R seem to be the same, so perhaps this isn't the best method!

[Paul Rogers]

mmm, thanks, but basically what I wanted is to write the following euation as a function of m and not ER like it is now.

Since it's pretty rought I wanted to know if there is some matlab tricks I don't know to do so.

In short I have m=f(ER), and I want ER=f(m)