Drainage and Hydrology

Manning's Equation Calculator

Calculate open-channel velocity and discharge from area, hydraulic radius, slope, and Manning roughness.

Engineering schematic

Open-channel flow geometry

Static symbolic figure. Enter project values in the calculator fields below.

Two-part Manning equation schematic with channel flow area A, wetted perimeter P, hydraulic radius R equals A over P, roughness n, discharge Q, and longitudinal energy slope S. — Symbols
A
flow area
P
wetted perimeter
R
hydraulic radius, A/P
S, n, Q
energy slope, Manning roughness, and discharge

Result

Discharge: 27.12 cfs

Velocity

3.39

Discharge

27.12

Coefficient

1.486

Step-by-step calculation

Unit-system coefficient
$k=1.486$
Mean velocity
$V=\frac{1.486}{0.035}(1.2)^{2/3}(0.005)^{1/2}=3.39$
Discharge
$Q=AV=8\times3.39=27.12$

What this means

Check that the hydraulic radius and roughness are appropriate for the actual channel shape and flow regime.

Assumptions

Uniform steady open-channel flow
Positive bed slope
Hydraulic radius already accounts for wetted perimeter

Formula Used

\begin{aligned}V&=\frac{k}{n}R^{2/3}S^{1/2}\\Q&=VA\end{aligned}

Step-by-Step Example

For A=8 ft2, R=1.2 ft, S=0.005, and n=0.035, flow is about 28.8 cfs.

Engineering Notes

Check units, assumptions, boundary conditions, groundwater, drainage, and whether the simplified method is appropriate before using a result in any project decision.

FAQ

What is hydraulic radius?

It is flow area divided by wetted perimeter.