Chézy and Manning's Equation

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Manning's equation, which is based on Chezy's equation, is a common method to calculate the free surface flow or fluid flow within a channel.

For Manning's equation, the roughness coefficient in Chezy's equation is calculated as:

C = k [ R^(0.125) / n]

Where:

C = Chezy's roughness coefficient (ft ^1/2/sec, m ^1/2/sec)
R = Hydraulic Radius (ft, m)
n = Manning's roughness (s/m^1/3)
k = Constant (1 m^1/3/m^1/3, 1.49 ft^1/3/ft^1/3)

Substituting the calculated roughness into Chezy's equation, one can obtain Manning's equation:

Q = [k / n] A R^2/3 S^1/2

Where:

Q = Discharge (ft³/sec, m³/sec)
k = Constant ( 1.49 ft^1/3/ sec, 1.00 m^1/3/ sec)
n = Manning's roughness coefficient
A = Flow area (ft²,m²⁾
R = Hydraulic Radius (ft, m)
S = Slope Friction (ft/ft, m/m)

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