A plumber is installing a water distribution system in a new commercial building. The design calls for a main cold water supply line to be sized to deliver 60 GPM with a maximum velocity of 8 feet per second (fps). Using the formula Q = A × V (where Q = flow rate in ft³/s, A = cross-sectional area in ft², V = velocity in ft/s) and knowing 1 GPM = 0.002228 ft³/s, what is the minimum nominal pipe size (inside diameter) required for this application? (Note: Schedule 40 pipe inside diameters are approximately: 2" = 2.067", 2.5" = 2.469", 3" = 3.068", 4" = 4.026")
- A2 inches
- B2 1/2 inches
- C3 inches
- D4 inches
Show answer & explanationAnswer & explanation
Correct answer: C. 3 inches
First, convert GPM to ft³/s: 60 GPM * 0.002228 ft³/s/GPM = 0.13368 ft³/s. Then, calculate the required area: A = Q / V = 0.13368 ft³/s / 8 ft/s = 0.01671 ft². Convert area to square inches: 0.01671 ft² * 144 in²/ft² = 2.406 in². Calculate the required diameter from the area: A = πr² => r = sqrt(A/π) = sqrt(2.406/π) = 0.874 inches. Diameter = 2r = 1.748 inches. This is the minimum required inside diameter. Comparing this to the given nominal pipe sizes, a 2.5-inch pipe has an ID of 2.469 inches, which is sufficient.
Why the other options are wrong
- A. Incorrect. A 2-inch pipe (ID ~2.067 inches) is too small as the required diameter is calculated to be 1.748 inches. If the question was asking for the next size up, it would be 2.5 inch.
- B. Incorrect. A 2 1/2 inch pipe (ID ~2.469 inches) is too small. The calculation shows a minimum required ID of 1.748 inches is needed to maintain max velocity, and then you need to select the next larger standard pipe size.
- D. Incorrect. This is oversized and not the minimum required.
Water Pipe Sizing (Velocity Method)
Determining minimum pipe diameter based on desired flow rate and maximum allowable water velocity to prevent erosion, noise, and excessive pressure drop.
- Higher velocity can cause erosion and noise.
- Lower velocity can lead to sediment buildup.
- Common maximum velocities are 5-8 ft/s for cold water, 4-6 ft/s for hot water.
Memory trick: Flow's Area Velocity, then pick the pipe that's free.