# Using vpasolve to iterate/solve for flowrate in a piping network

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Jonathan Siow on 19 May 2020
Answered: Alex Sha on 20 May 2020
Dear Matlab community,
I am trying to use vpasolve to solve for the Fanning friction factor (f1), Reynolds number (Re1), and velocity (v1) of water flowing through a single pipe with the following code:
>> syms f1 v1 Re1 %% not sure why 'f1' isn't in pink font on this post, it is pink on my computer
eqn1 = 14.63 == ((f1*(3200/0.3))+6.8)*((v1^2)/(2*9.81));
eqn2 = Re1 == v1*0.3/(1.004E-6);
eqn3 = 1/(f1^0.5) == -2*log(((1.5e-6)/(3.7*0.3))+(2.51/(Re1*(f1^0.5))));
sol = vpasolve(eqn1,eqn2,eqn3, f1, v1, Re1);
sol.f1
sol.v1
sol.Re1
However, matlab returns:
ans =
Empty sym: 0-by-1
ans =
Empty sym: 0-by-1
ans =
Empty sym: 0-by-1
>> double(sol.Re1)
ans =
0×1 empty double column vector
I have tried iterating using the Goal Seek function on Excel by first typing in a suggested a Reynolds number.
By suggesting a Re number, excel will iterate to find a value for 'f1' that ensures LHS - RHS = 0
eqn3 = 1/(f1^0.5) == -2*log(((1.5e-6)/(3.7*0.3))+(2.51/(Re1*(f1^0.5))));
What is preventing the matlab code from successfully iterating?
I am trying to solve this simpler example first because I will later be trying this on a more complicated pipe network with several Fanning friction values, Reynolds numbers, velocities, etc.
I have read the vpasolve matlab help page and am still stuck.
Any help appreciated!
Thanks,
Jonathan

Alex Sha on 20 May 2020
refer to the result below:
f1: 0.013713131883721
v1: 1.36937309476078
re1: 409175.227518161

R2020a

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