A 10.0 in diameter distribution pipe delivers 1,287,000 gal of water in exactly 24 hours. What is the average flow during the 24 hours in feet per second?

• A. 0.75 fps
• B. 1.50 fps
• C. 1.99 fps
• D. 2.50 fps

Answer: (C)

The key idea is that velocity in a pipe equals the volumetric flow rate divided by the cross-sectional area: v = Q / A.

First, convert the pipe diameter to feet and find the area:

• Diameter is 10 inches, which is 10/12 = 0.8333 ft. Radius is 0.4167 ft.

• Cross-sectional area A = πr^2 ≈ π × (0.4167)^2 ≈ 0.545 ft^2.

Next, convert the total water volume and time to consistent units:

• 1,287,000 gallons to cubic feet: 1 gal = 1/7.48052 ft^3, so Qvol ≈ 1,287,000 / 7.48052 ≈ 172,047 ft^3.

• Time of 24 hours to seconds: 24 × 3600 = 86,400 s.

So the volumetric flow rate is Q = Qvol / time ≈ 172,047 / 86,400 ≈ 1.993 ft^3/s.

Now find the average velocity:

• v = Q / A ≈ 1.993 / 0.545 ≈ 3.66 ft/s.

Thus, the average flow speed is about 3.66 feet per second. The value 1.99 would be the volumetric flow rate in cubic feet per second, not the velocity.