Question

Wastewater is pumped through an 8-inch force main at the rate of 448 gallons per minute. Calculate velocity of flow in the line and answer in feet per second (fps).)?

a. 2.86
b. 42.95
c. 66.40
d. 100.00

Answer 1

The velocity of water flow through an 8-inch force main at 448 gallons per minute is approximately 2.86 feet per second. This is calculated by converting the flow rate to cubic feet per minute and dividing by the cross-sectional area of the pipe.

Step-by-step explanation:

To calculate the velocity of flow in feet per second (fps) for water being pumped through an 8-inch diameter force main at 448 gallons per minute, we first convert the flow rate to cubic feet per minute (cfm) and then use the formula velocity (fps) = flow rate (cfm) / cross-sectional area (sq ft) of the pipe.

Let's start with the conversions:
1 gallon = 0.133681 cubic feet,
1 inch = 1/12 feet.

First, convert the flow rate:
448 gallons/min * 0.133681 cubic feet/gallon ≈ 59.89 cubic feet/min (cfm)

Now, find the cross-sectional area of the pipe:
The radius is half of the diameter, so r = 4 inches = 4/12 feet = 1/3 feet,
Area = π * r^2 ≈ 3.14159 * (1/3)^2 ≈ 0.349 square feet.

Finally, calculate the velocity:
Velocity (fps) = 59.89 cfm / 0.349 sq ft ≈ 171.60 fps.

Converting this to feet per second:
1 minute = 60 seconds, so 171.60 fps / 60 ≈ 2.86 fps.

Therefore, the correct flow velocity is approximately 2.86 fps, which corresponds to option (a).