Chézy Formula

Definition

A theoretical relationship that relates mean velocity of flowing water to key channel parameters.

The Chézy formula was developed in about 1775 by French engineer Antoine de Chézy. The mean velocity of water ($\overline{v}$) is related to hydraulic radius (R), slope of the channel taken to be the slope of the energy grade line (S_e), and a parameter called the Chézy coefficient (C):

$$ \overline{v}\ \ =\ \ C\sqrt{RS_e} $$

(1)

where $\overline{v}$ is in m/s, R is in m (cross-section area, A, divided by wetted perimeter, P), and S_e is in m/m, resulting in C, a term related to friction losses, having the units of m^1/2/s. Expressions describing friction losses are applicable to uniform flow conditions but have been used for estimating energy losses in gradually varying nonuniform flow. Friction losses are governed by the dimensionless Reynolds number (Re), which is the mean velocity times the hydraulic radius divided by the kinematic viscosity of water (ν).

$$...