# Manning's Formula for Gravity Flow

## Manning's equation for calculating gravity flow in open channels

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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 mean velocity (ft/s, m/s)

k_{n}= 1.486 for English units and k_{n}= 1.0 for SI units

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 (ft^{2}, m)

P = wetted perimeter (ft, m)

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 (ft^{3}/s, m^{3}/s)

A = cross-sectional area of flow (ft^{2}, m^{2})

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