Manning's equation is one of the most frequently tested formulas on the PE Civil and Environmental exams. Whether you're calculating flow velocity in a storm drain, sizing a channel, or analyzing a wastewater conveyance system, this equation is essential. In this comprehensive guide, we'll cover everything you need to know to master Manning's equation for the PE exam.

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What is Manning's Equation?

Manning's equation calculates the average velocity of water flowing in an open channel under steady, uniform flow conditions. It was developed by Irish engineer Robert Manning in 1889 and remains the standard for open channel hydraulics today.

Manning's Equation

US Customary Units: V = (1.486/n) × R^2/3 × S^1/2

SI Units: V = (1/n) × R^2/3 × S^1/2

Where:

V = Average flow velocity (ft/s or m/s)
n = Manning's roughness coefficient (dimensionless)
R = Hydraulic radius = A/P (ft or m)
S = Channel slope (ft/ft or m/m)
1.486 = Unit conversion factor for US customary units

Critical PE Exam Tip: The most common mistake is using k=1 with US customary units. Always use k=1.486 for feet/seconds and k=1 for meters/seconds.

Calculating Hydraulic Radius

The hydraulic radius is the ratio of the flow cross-sectional area to the wetted perimeter. It's a measure of channel efficiency - a larger hydraulic radius means less friction per unit of flow.

Hydraulic Radius

R = A / P

Where: A = Cross-sectional flow area, P = Wetted perimeter

Common Channel Shapes

Shape	Area (A)	Wetted Perimeter (P)	Hydraulic Radius (R)
Rectangular	b × y	b + 2y	by / (b + 2y)
Trapezoidal	(b + zy)y	b + 2y√(1 + z²)	A / P
Circular (full)	πD²/4	πD	D/4
Triangular	zy²	2y√(1 + z²)	zy / (2√(1 + z²))

Manning's Roughness Coefficient (n)

Selecting the correct roughness coefficient is crucial. Here are common values you'll encounter on the PE exam:

Channel Material	n (min)	n (typical)	n (max)
Concrete, smooth finished	0.011	0.013	0.015
Concrete, rough	0.014	0.017	0.020
Corrugated metal pipe	0.021	0.024	0.030
Earth channel, clean	0.018	0.022	0.025
Earth channel, weedy	0.025	0.030	0.033
Natural stream, clean	0.025	0.033	0.040
PVC/HDPE pipe	0.009	0.010	0.011

Exam Strategy: If the problem doesn't specify n, look for it in the reference handbook. For smooth concrete, 0.013 is the most commonly used value.

Worked Example: Rectangular Channel

Problem

A rectangular concrete channel is 4 ft wide, carries water 2 ft deep, and has a slope of 0.002 ft/ft. Using n = 0.013, find the average velocity and discharge.

Solution

Step 1: Calculate the hydraulic radius

A = width × depth = 4 × 2 = 8 ft²
P = width + 2×depth = 4 + 2(2) = 8 ft
R = A/P = 8/8 = 1.0 ft

Step 2: Apply Manning's equation

V = (1.486/0.013) × (1.0)^2/3 × (0.002)^1/2
V = 114.3 × 1.0 × 0.0447
V = 5.11 ft/s

Step 3: Calculate discharge

Q = V × A = 5.11 × 8
Q = 40.9 ft³/s (cfs)

Excel Formula for Manning's Equation

Here's how to set up Manning's equation in Excel for quick calculations:

Excel Formula (US Units)

=(1.486/A1)*B1^(2/3)*C1^(1/2)

Where: A1 = n, B1 = R, C1 = S

For a complete template with automatic unit conversion and discharge calculation, use our online calculator which exports Excel-ready formulas.

Common Mistakes to Avoid

Wrong unit constant: Using k=1 instead of k=1.486 for US customary units
Confusing R with radius: Hydraulic radius R is not the same as geometric radius
Slope as percentage: Manning's equation uses decimal slope (0.02), not percentage (2%)
Wrong n value: Using roughness coefficient for wrong material or condition
Ignoring flow regime: Manning's equation is for turbulent flow only

When to Use Manning's Equation

Manning's equation is appropriate for:

Open channel flow (not pressurized pipes)
Steady, uniform flow conditions
Turbulent flow (Re > 4000)
Gravity-driven flow

For pressurized pipe flow, use Hazen-Williams or Darcy-Weisbach instead.

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