Practice Question: Flow to a Parallel Pipe System Based on Head Loss

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Solution

Answer: A) 1.3 cfs

Head loss for a parallel system is equal for each pipe:
\[h_{f-total}=h_{fA}=h_{fB}\]
Head loss per the Darcy-Weisbach equation:
\[h_f=f * \frac LD * \frac{v^2}{2g}\]
Calculate velocity in Pipe A:
\[5 ft=0.025 * \frac{100\ ft}{5/12\ ft} * \frac{v_A^2}{2(32.2\ ft/s)}\]
\[v_A=7.32\ ft/s\]
Calculate velocity in Pipe B:
\[5\ ft=0.025 * \frac{75\ ft}{3/12\ ft} * \frac{v_B^2}{2(32.2\ ft/s)}\]\[v_B=6.55\ ft/s\]

Total input flow is equal to flow through Pipes A and B:
\[Q_{total}=Q_A+Q_B\]
Calculate total input flow:
\[Q_{total}=A_A\ v_A+A_B\ v_B\]
\[Q_{total}=\frac{\pi * (5/12\ ft)^2}{4}\ast(7.32\ ft/s)+\frac{\pi * (3/12\ ft)^2}{4}*(6.55\ ft/s)\approx1.3\ cfs\]
 

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