# Chézy formula

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In fluid dynamics, the **Chézy formula** describes the mean flow velocity of steady, turbulent open channel flow:

where

- is the mean velocity [m/s],
- is the Chézy coefficient [m
^{½}/s], - is the hydraulic radius (~ water depth) [m], and
- is the bottom slope [m/m].

The formula is named after Antoine de Chézy, the French hydraulics engineer who devised it in 1775.

## Usage with Manning coefficient

This formula can also be used with Manning's Roughness Coefficient, instead of Chézy's coefficient. Manning derived^{[1]} the following relation to C based upon experiments:

where

- is the Chézy coefficient [m
^{½}/s], - is the hydraulic radius (~ water depth) [m], and
- is Manning's roughness coefficient.

Unlike the Manning equation, which is empirical, the Chézy equation is derived from hydrodynamics theory.^{[2]}