Manning's Formula for Gravity Flow

Manning's equation for calculating gravity flow in open channels

Manning's equation can be used to calculate cross-sectional average velocity flow in open channels

v = k_n / n R^2/3 S^1/2         (1)

where

v = cross-sectional average velocity (ft/s, m/s)

k_n = 1.486 for English units and k_n = 1.0 for SI units

A = cross sectional area of flow (ft², m²)

n = Manning coefficient of roughness

R = hydraulic radius (ft, m)

S = slope of pipe (ft/ft, m/m)

Hydraulic radius can be expressed as

R = A / P                 (2)

where

A = cross sectional area of flow (ft²)

P = wetted perimeter (ft)

The volume flow in the channel can be calculated as

q = A v = A k_n / n R^2/3 S^1/2         (3)

where

q = volume flow (ft³/s, m³/s)

A = cross-sectional area of flow (ft², m²)

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