A 24-inch wastewater interceptor is flowing half-full at a rate of 3 fps. What is the approximate volume of wastewater flowing through the line in gpm?

To calculate the volume of wastewater flowing through a 24-inch diameter interceptor that is flowing half full at a velocity of 3 feet per second (fps), we first need to determine the cross-sectional area of the flow and then use that to find the flow rate in gallons per minute (gpm).

1. Calculate the radius: Since the diameter is 24 inches, the radius is 12 inches or 1 foot (since there are 12 inches in a foot).

2. Determine the flow area: When the pipe is half full, the effective flow area can be approximated as a full circle divided by 2. The area of a full circle is calculated using the formula:

[

A = \pi r^2

]

For a radius of 1 foot:

[

A = \pi (1)^2 = \pi \text{ square feet}

]

3. Flow area when half full: Since the pipe is flowing half-full, the effective flow area remains approximately:

[

A_{half} \approx \frac{A}{2} = \frac{\pi}{2} \text{ square feet}

]

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