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

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

Answer 1

[Alex Sha]

refer to the result below:

f1: 0.013713131883721
v1: 1.36937309476078
re1: 409175.227518161