The Chézy formula describes mean flow velocity in turbulent open channel flow and is used broadly in fields related to fluid mechanics and fluid dynamics.Open channels refer to any open conduit, such as rivers, ditches, canals, or partially full pipes. The Chézy formula is defined for uniform equilibrium and non-uniform gradually varied flows.
The formula is written as:
where,
* is average velocity [length/time];
* is the hydraulic radius [length], 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); and
* is the hydraulic gradient, which for uniform normal depth of flow is the slope of the channel bottom [unitless; length/length]; and
* is Chézy's coefficient [length/time]. The value of this coefficient must be determined by experiments. The Chézy coefficient ranges typically from 30 m/s (small rough channel) up to 90 m/s (large smooth channel).
The formula is named after Antoine de Chézy, the French hydraulics engineer who devised it in 1775.
For many years following Antoine de Chézys development of this formula, researchers assumed that  was a constant independent of flow conditions. However, additional research proved the coefficients dependence upon the Reynolds number as well as channel roughness. Accordingly, although the Chézy formula does not appear to incorporate either of these terms, the Chézy coefficient empirically and indirectly represents them.
Hydraulic radius, R, is 1/4 the hydraulic diameter and is defined as the area of the flow section divided by the wetted perimeter, P.