Overview

PE depth exam study guide for open channel hydraulics: Manning's equation, critical depth, specific energy, hydraulic jump, gradually varied flow, and weir/orifice flow.

This topic accounts for 5 out of 40 questions on the PE Civil Water Resources Depth (PM) exam.

Key Concepts

Normal Depth and Manning's Equation

Normal depth occurs when gravity and friction forces balance (uniform flow). V = (1.486/n) x R^(2/3) x S^(1/2). For a given Q, n, S, and channel geometry, solve iteratively for normal depth. Trapezoidal: A = (b + zy)y, P = b + 2y*sqrt(1+z^2). Circular: use geometric tables for partial flow.

Mannings Equation Mannings Discharge

Critical Depth and Specific Energy

Critical depth: Fr = 1. For rectangular channels: yc = (q^2/g)^(1/3) where q = Q/b. Specific energy: E = y + V^2/(2g) = y + Q^2/(2gA^2). At critical depth, specific energy is minimum. Alternating depths (same E): subcritical (y > yc) and supercritical (y < yc) are conjugate depths on the E-y curve.

Critical Depth Rectangular Froude Number Energy Slope

Hydraulic Jump

Occurs when supercritical flow transitions to subcritical. Conjugate depth: y2/y1 = 0.5(-1 + sqrt(1 + 8Fr1^2)). Energy loss: deltaE = (y2-y1)^3/(4y1y2). Momentum equation: used for force analysis on structures. Hydraulic jumps dissipate energy and are used in stilling basins downstream of spillways.

Froude Number Rectangular

Weir and Orifice Flow

Sharp-crested rectangular weir: Q = Cd x (2/3) x sqrt(2g) x L x H^(3/2). Typical Cd = 0.62. V-notch weir: Q = Cd x (8/15) x sqrt(2g) x tan(theta/2) x H^(5/2). Broad-crested weir: Q = Cd x L x sqrt(g) x (2H/3)^(3/2). Orifice: Q = Cd x A x sqrt(2gH), Cd typically 0.61. Submerged orifice: use difference in head.

Rectangular Sharp Crested Weir V Notch Weir Broad Crested Weir Orifice Equation Orifice Free Discarge Orifice Submerged

Common Exam Question Types

Calculate normal depth for given Q, n, S, and geometry
Determine critical depth and classify flow regime
Compute conjugate depth and energy loss in a hydraulic jump
Calculate discharge over a weir or through an orifice
Determine flow profiles (M1, M2, S1, S2, etc.)

Exam Tips & Strategies

Normal depth: use Manning's and iterate. Critical depth for rectangular: yc = (q^2/g)^(1/3)

Froude number < 1 is subcritical (deep, slow), > 1 is supercritical (shallow, fast)

Weir discharge: sharp-crested uses H^(3/2), V-notch uses H^(5/2)

Hydraulic jump always goes from supercritical to subcritical (y1 < yc < y2)

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Open Channel Hydraulics Study Guide