# Chézy formula

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

${\displaystyle v=C{\sqrt {R\,i}},\,}$

where

• ${\displaystyle v}$ is average velocity [m/s],
• ${\displaystyle C}$ is Chezy's coefficient [m½/s],
• ${\displaystyle R}$ is the hydraulic radius (~ water depth) [m], and
• ${\displaystyle i}$ 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:

${\displaystyle C={\frac {1}{n}}R^{1/6}}$

where

• ${\displaystyle C}$ is the Chézy coefficient [m½/s],
• ${\displaystyle R}$ is the hydraulic radius (~ water depth) [m], and
• ${\displaystyle n}$ is Manning's roughness coefficient.

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