Overview
PE depth exam study guide for closed conduit (pipe) hydraulics: Hazen-Williams, Darcy-Weisbach, minor losses, pump selection, NPSH, and water hammer.
This topic accounts for 5 out of 40 questions on the PE Civil Water Resources Depth (PM) exam.
Key Concepts
Hazen-Williams Equation
V = 1.318 x C x R^0.63 x S^0.54 (US). Head loss form: hf = (4.73 x L x Q^1.852)/(C^1.852 x D^4.87) with Q in cfs, D in ft. C values: PVC 150, ductile iron 140, concrete 130, old cast iron 100. Valid for water at normal temperatures only. Convert between psi and feet: 1 psi = 2.31 ft H2O.
Darcy-Weisbach Equation
hf = f x (L/D) x V^2/(2g). Friction factor f from Moody diagram: depends on Re and relative roughness e/D. Laminar flow (Re < 2000): f = 64/Re. Turbulent flow: use Colebrook-White or Swamee-Jain approximation. More accurate than Hazen-Williams for non-water fluids and extreme temperatures.
Minor Losses
hm = K x V^2/(2g). K values: entrance (sharp 0.5, rounded 0.04), exit (1.0), 90-degree elbow (0.9), gate valve fully open (0.2), check valve (2.5). Equivalent length method: Le = K x D / f. Total system losses = friction + minor losses. For long pipes, minor losses are often < 5% of friction losses.
Pump Selection and NPSH
System curve: H = static head + hf(Q) + hm(Q). Operating point is where pump curve intersects system curve. NPSH_A = P_atm/gamma + z_s - P_v/gamma - hf_suction. Must have NPSH_A > NPSH_R. Cavitation occurs when NPSH_A < NPSH_R. Affinity laws: Q varies with N, H varies with N^2, Power varies with N^3.
Water Hammer
Pressure surge from rapid valve closure: deltaP = rho x a x deltaV. Wave speed: a = sqrt(Ev / rho) / sqrt(1 + (Ev x D)/(E x t)). Joukowsky equation: deltaH = a x deltaV / g. Critical time: tc = 2L/a. If closure time < tc, full water hammer occurs. Pressure rise can be hundreds of psi. Mitigation: slow-closing valves, surge tanks.
Common Exam Question Types
- Calculate head loss in a pipe system using Hazen-Williams or Darcy-Weisbach
- Determine pump operating point from system and pump curves
- Check NPSH availability vs. required
- Compute pressure surge from water hammer
- Find friction factor from Moody diagram
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