Chézy formula

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

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

where

• $v$ is the mean velocity [m/s],
• $C$ is the Chézy coefficient [m^½/s],
• $R$ is the hydraulic radius (~ water depth) [m], and
• $i$ 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:

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

where

• $C$ is the Chézy coefficient [m^½/s],
• $R$ is the hydraulic radius (~ water depth) [m], and
• $n$ is Manning's roughness coefficient.

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

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
2. Martin & McCutcheon, 1999, Hydrodynamics and Transport, Lewis

External links

• History of the Chézy Formula