### Chézy and Manning's Equation Method and Calculator

**Fluid Flow Table of Contents**

Hydraulic and Pneumatic Knowledge

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**Manning's Roughness Coefficient**

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^{(1/6) }/ 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 (ft^{3}/sec, m^{3}/sec)

k = Constant ( 1.49 ft^{1/3}/ sec, 1.00 m^{1/3}/ sec)

n = Manning's roughness coefficient

A = Flow area (ft^{2},m^{2)}

R = Hydraulic Radius (ft, m)

S = Slope Friction (ft/ft, m/m)