changing a variable in an equation

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Paul Rogers 2020-12-11

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https://ww2.mathworks.cn/matlabcentral/answers/690915-changing-a-variable-in-an-equation

编辑： Paul Rogers 2020-12-11

datas.mat

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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

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Alan Stevens 2020-12-11

编辑：Alan Stevens 2020-12-11

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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