Practice Question: Continuity Between Two Pipe Section

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Solution

Answer: D) 60 psi

 

Reference Civil Reference Handbook Section 6.2 for relevant hydraulic equations.

Applying the energy equation at both points a & c:

\[\frac{ V_{a}^2}{2g} +  \frac{ P_{a} }{\gamma} + Z_{a} =  \frac{ V_{c}^2}{2g} +  \frac{ P_{c} }{\gamma} + Z_{c} + h_{f}\\\]

 where:
Gravity: \(g=32.2 ft/sec^2  \\\)

Unit Weight of Water: \(\gamma=62.4\ lbf/ft^3\\\)

\(Z_{a} = Z_{c}\ \text{ elevation term is cancelled}\\\)

\[Q_{a}=V_{a} A_{a} = V_{c} A_{c}\]\[Q_a=\frac{\pi}{4} \times (\frac{12}{12})^2 \times 10 = \frac{\pi}{4} \times (\frac{8}{12})^2 \times V_{c}\\\]
\[\to V_{c}\ = 22.5\ ft/sec\]

\[\text{Total losses}\  h_{f}  = h_{fab} + h_{fb} + h_{fbc} = 0.03 \times 500 + 7 + 0.05 \times 350 = 39.5 ft\\\]
\[102 / (2 \times 32.2) + 80\times144/62.4 = 22.52 / (2 \times 32.2) + P_{c}/62.4 +39.5\\\]
\[Get\ P_{c} = 8661\ lb/ft^2 = 8661/144 = 60.1\ psi\\\]

 

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