A civil engineer is designing a storm drainage system for a large commercial development. The system needs to accommodate a peak runoff rate of 15 cubic feet per second (CFS). The design calls for a storm sewer pipe with a Manning's roughness coefficient (n) of 0.013 and a slope of 0.005 ft/ft. If the pipe is to flow full, what is the approximate minimum diameter (in inches) required for a circular concrete pipe to handle this flow, assuming a velocity of 5 ft/s?
- A24 inches
- B36 inches
- C30 inches
- D18 inches
Show answer & explanationAnswer & explanation
Correct answer: A. 24 inches
First, calculate the required cross-sectional area (A) using the flow rate (Q) and velocity (V): A = Q / V = 15 cfs / 5 ft/s = 3 sq ft. For a circular pipe, A = π * (D/2)^2. So, 3 = π * (D/2)^2. (D/2)^2 = 3 / π ≈ 0.9549. D/2 = sqrt(0.9549) ≈ 0.977 ft. D ≈ 1.954 ft. To convert to inches: 1.954 ft * 12 in/ft ≈ 23.45 inches. The closest standard pipe size is 24 inches. (Manning's 'n' and slope are distractors here, as velocity is given directly).
Why the other options are wrong
- B. 36 inches is significantly larger than required.
- C. 30 inches is larger than necessary, leading to higher costs.
- D. 18 inches is too small for the calculated area.
Storm Sewer Pipe Sizing (Q=AV)
The fundamental principle for sizing pipes, where Flow Rate (Q) equals Cross-sectional Area (A) multiplied by Velocity (V). This formula helps determine the required pipe diameter for a given flow.
- Q = A * V is the basic hydraulic formula.
- A = π * (D/2)^2 for circular pipes.
- Pipe velocity is often limited to prevent scour or sedimentation.
Memory trick: Quantity equals Area times Velocity: QAV is the key to pipe capacity.