A 3,500-foot section of 12-inch C=130 ductile iron water main carries 1,200 GPM. Using the Hazen-Williams friction loss equation, what is the approximate friction head loss in feet?

Formula Used: hf (ft) = 10.44 × L × Q^1.852 ÷ (C^1.852 × d^4.87)

Step-by-Step Mathematical Derivation:

1. Identify parameters: L = 3,500 ft, Q = 1,200 GPM, C = 130, d = 12 inches.
2. Calculate hydraulic gradient = ~3.554 ft head loss per 1,000 ft of pipe length.
3. Total friction head loss = 3.5 × 3.554 ft = 12.44 ft (~12.4 ft).

⚠️ Common Exam Trap: Higher C-values represent smoother pipes with LESS friction loss (e.g. C=140 for smooth PVC vs C=100 for aged cast iron).