Chézy formula

In fluid dynamics, the Chézy formula describes the mean flow velocity of turbulent open channel flow. The formula is

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

where

• ${\displaystyle v}$ is average velocity [m/s],
• ${\displaystyle C}$ is Chezy's coefficient [m^1/2/s],
• ${\displaystyle R}$ is the hydraulic radius, which is the cross-sectional area of flow divided by the wetted perimeter (for a wide channel this is approximately equal to the water depth) [m], and
• ${\displaystyle i}$ is the hydraulic gradient, which for normal depth of flow equals 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 [m^1/2/s],
• ${\displaystyle R}$ is the hydraulic radius, which is the cross-sectional area of flow divided by the wetted perimeter (for a wide channel this approximately equal to the water depth) [m], and
• ${\displaystyle n}$ is Manning's roughness coefficient.

Both formulae are empirical, but the Manning formula is widely accepted as more accurate and is the base formula still in current use for all open channel flow analysis.

See also

• Hydraulics
• Manning formula

References

1. Manning, R., "On the flow of Water in Open Channels and Pipes." Transactions Institute of Civil Engineers of Ireland, vol. 20, pp 161-209, Dublin, 1891, Supplement, vol 24, pp. 179-207, 1895

External links

• History of the Chézy Formula