Fluid Mechanics: Determine volumetric flowrate

cheme333

1. The problem statement, all variables and given/known data


*See attachment for diagram*

With steady-state operation, an energy balance between point 1 and point 2 along the A side dictates:

*See attachment for equation 1*

And an energy balance between points 1 and 2 along the B side dictates:

*see attachment for equation 2*

Comparing the two balances, the following can be determined:

*See attachment for equation 3*

Which states that frictional losses over parallel segments are equal. With this in mind, develop a model for the system and fill in the missing entries in the table below.

Qtot LA DA LB DB QA QB
gpm ft in ft in gpm gpm

150 85 4 100 4 ? ?
80 100 4 400 3 ? ?
300 120 2 120 3 ? ?
300 120 6 50 4 ? ?
180 80 ? 80 4 60 ?
300 ? 3 70 3 140 ?
? 300 6 100 4 100 ?

2. Relevant equations
Use chen equation for friction factor:

1/(f)^1/2 = -2.0log((e/D)/3.7065 – 5.0452A/Re)
A = log((e/D)^1.1098/2.8257 + (5.8506/Re^0.8981))

3. The attempt at a solution

We are allowed to use Excel goal seek (I think we HAVE to). However, i cannot seem to get a system of equations that will solve for Va and Vb. I believe that if I had those terms, I could easily calculate Qa and Qb. If that's not the direction I need to be going, then I am completely lost.

For the first row, we were given the answers so that we could check our model. Qa=83.1 gpm and Qb=66.9 gpm.

Thanks for any help!

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