Overview

PE exam study guide for hydraulics and hydrology covering Manning's equation, Bernoulli, Hazen-Williams, pump systems, rational method, SCS curve number, and hydraulic jump.

This topic accounts for 7 out of 40 questions on the PE Civil Civil Breadth (AM) exam.

Key Concepts

Manning's Equation

Open channel flow: V = (1.486/n) x R^(2/3) x S^(1/2) (US units). Q = VA. Hydraulic radius R = A/P (area / wetted perimeter). For circular pipes flowing full: R = D/4. For rectangular channels: R = (b x y)/(b + 2y). Manning's n values: concrete 0.013, corrugated metal 0.024, natural channels 0.030-0.050. Normal depth is found iteratively when Q, n, S, and geometry are known.

Mannings Equation Mannings Discharge Mannings Velocity

Energy Equation (Bernoulli)

P1/gamma + V1^2/2g + z1 = P2/gamma + V2^2/2g + z2 + hL. Total head = pressure head + velocity head + elevation head. Head loss hL = friction losses + minor losses. For pumps: add hp (pump head). For turbines: subtract ht. The HGL (Hydraulic Grade Line) = P/gamma + z. The EGL (Energy Grade Line) = HGL + V^2/2g.

Bernoulli Equation Continuity Energy Slope

Hazen-Williams Equation

For pressure pipe flow: V = 1.318 x C x R^0.63 x S^0.54 (US units). Or hf = (4.73 x L x Q^1.852) / (C^1.852 x D^4.87). C values: new cast iron 130, PVC 150, old unlined pipe 80-100. Most common PE exam pipe flow equation. For distribution systems, convert pressure to head (1 psi = 2.31 ft of head).

Hazen Williams Pipe Headloss

Pump Systems

Pump power: P(hp) = Q x gamma x TDH / (550 x eta) where Q is in cfs, or P(hp) = Q(gpm) x TDH(ft) / (3960 x eta). TDH = static lift + friction losses + velocity head. NPSH available must exceed NPSH required. Affinity laws: Q2/Q1 = N2/N1, H2/H1 = (N2/N1)^2, P2/P1 = (N2/N1)^3.

Pump Horsepower Calc Hp Pump Horsepower Calc Kw Npsha Pump Affinity Laws

Rational Method

Peak runoff: Q = CiA. Q in cfs, C = runoff coefficient (0-1), i = rainfall intensity (in/hr) for duration = time of concentration, A = drainage area (acres). The 1.008 conversion factor is typically dropped. Runoff coefficients: impervious 0.90, lawns 0.10-0.35, commercial 0.70-0.95. Valid for areas < 200 acres.

Rational Method Rational Method Peak Flow

SCS Curve Number Method

Runoff depth: Q = (P - 0.2S)^2 / (P + 0.8S), where S = (1000/CN) - 10. P = rainfall depth (inches), Q = runoff depth (inches). CN ranges from 30 (woods, good condition) to 98 (impervious). For composite CN: weighted average by area. Higher CN = more runoff. Initial abstraction Ia = 0.2S.

Runoff Curve Number Method

Hydraulic Jump and Froude Number

Froude number: Fr = V / sqrt(g x y) for rectangular channels, Fr = V / sqrt(g x D) for non-rectangular (D = A/T). Fr < 1: subcritical (deep, slow). Fr = 1: critical. Fr > 1: supercritical (shallow, fast). Conjugate depth ratio: y2/y1 = 0.5(-1 + sqrt(1 + 8Fr1^2)). Energy loss in jump: dE = (y2-y1)^3 / (4 x y1 x y2).

Froude Number Froude Number Rectangular Critical Depth Rectangular

Common Exam Question Types

Calculate flow or velocity using Manning's equation
Apply Bernoulli equation with head loss to pipe systems
Compute head loss in a pipe using Hazen-Williams
Size a pump or calculate required horsepower
Determine peak runoff using the Rational Method
Calculate runoff depth using SCS Curve Number
Determine Froude number and classify flow regime

Exam Tips & Strategies

Manning's uses 1.486 in US customary, 1.0 in SI. The most common mistake is forgetting to convert units

For Bernoulli problems, always define your datum and sign conventions before starting

Hazen-Williams C values: PVC=150, ductile iron=140, concrete=130. Memorize the common ones

For rational method: Q=CiA. Remember i must correspond to tc (time of concentration) duration

SCS CN: S = 1000/CN - 10. Initial abstraction = 0.2S. Higher CN = more impervious = more runoff

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Hydraulics and Hydrology Study Guide