Manning’s Equation

V = \frac{1}{n} R^{2/3} S^{1/2} (SI), Q = V A

Mean velocity in a fully rough open channel. Hydraulic radius R = A/P, S is friction slope (≈ bed slope for uniform flow). n is Manning’s roughness from Handbook tables. US form multiplies by 1.486.

$n$: Manning roughness
$R$ (m): Hydraulic radius A/P
$S$: Energy slope

Step-by-step solved example

A 3 m wide rectangular channel, depth 1.2 m, S = 0.001, n = 0.015. Find Q (SI).

Open-channel uniform flow. R = A/P, V from Manning n, S.

1. R
A = 3.6 m², P = 3 + 2×1.2 = 5.4 m, R = 0.667 m.
2. V and Q
V = (1/0.015)(0.667)^{2/3}(0.001)^{1/2} = 1.61 m/s. Q = 5.79 m³/s.
$Q = 5.79 m^{3} / s$

Answer: Q ≈ 5.8 m³/s

10 practice questions

0/10 correct

1.Hydraulic radius of a full circular pipe is

2.Increasing n (same S, R) will

3.Uniform flow means

4.Most efficient rectangle has

5.US Manning uses a coefficient

6.Froude number Fr = V/√(gy) < 1 means

7.A trapezoid with A = 10 m², P = 8 m: R =

8.If slope quadruples, V (Manning) multiplies by

9.Concrete lining n is nearest

10.Critical depth for a wide rectangle is