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How to get the value of an extra variable with fsolve

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As an example, we have the following approach to find f:
%% Known data
D=0.1;%m
V=10;%m/s
nu=8.94e-7;%m^2/s
epsilon=4.6e-5;%m
%% Calculation of f
f_est=0.02;
f=fsolve(@f_Col,f_est,[],V,nu,D,epsilon);
%% Functions
function [F]=f_Col(f_est,V,nu,D,epsilon)
% function that calculates the friction factor with the Colebrook equation
% for a specific V, D and epsilon
Re=D.*V/nu;
rr=epsilon/D;
F=1./sqrt(f_est)+2*log10(rr/3.7+2.51./(Re.*sqrt(f_est)));
F=F';
end
Is there a way to receive the rr and Re values ​​when using the fsolve? In this case these two values ​​do not depend on the value of f that solves the equation, but just as an example, is there a way to do it?

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John D'Errico
John D'Errico 2020 年 7 月 7 日
編集済み: John D'Errico 2020 年 7 月 7 日
The simple trick is to use the output arguments from a function.
Change your function header to look like this:
function [F,rr,Re]=f_Col(f_est,V,nu,D,epsilon)
When you use a function that return multiple output arguments, if you only ask for one output, it only gives you the first output. Fsolve will ignore those other outputs.
Now, after fsolve returns a value for f, call the function ONE more time, with the final value of f, but now with additional outputs. Call it like this:
[~,rr,Re]=f_Col(f,V,nu,D,epsilon);
You see that now you are taking the values of rr and Re, as computed when f is the final value from fsolve. We are not interested in the first output argument, so tell MATLAB to dump it in the bit bucket.

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Santiago Rivera González
Santiago Rivera González 2020 年 7 月 7 日
Thank you very much, it is an elegant solution.

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