Practice Question: Flow Rate for a Closed Pipe

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Solution

Answer: C) 4.8 cfs

Flow Depth:
\[h=9\ in\]Radius:
\[r=18 \ in\]

Calculate the angle theta for a partially filled pipe:

 \[\theta=2{\ast\cos}^{-1}\left(\frac{r-h}{r}\right)=2.09\ radians\]
Calculate area of flow:
\[A={\frac{r^2\left(\theta-\sin{\theta}\right)}{2}}=1.38{\rm ft}^2\]

Calculate wetted perimeter: 
\[P=r\theta=37.7\ in\]
Calculate hydraulic radius:
\[R=\frac{A}{P}=0.440\]Calculate flow based on Manning’s equation:
\[Q=\frac{1.49}{n}{AR}^{2/3}S^{1/2}=4.76\frac{{ft}^3}{s}\]

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