Chézy Equation Calculator

V = C√(R_hS) — the original open-channel velocity formula. Solves for velocity, Chézy coefficient C, slope S, or hydraulic radius R_h. Includes Manning and Darcy-Weisbach equivalents.

Open Channel Flow · Hydraulics

Inputs

Solve for:

R_h input method:

Hydraulic radius Rh (m)

R_h = A / P (cross-section area / wetted perimeter)

Chézy coefficient C (m^(1/2)/s)

Channel slope S (m/m)

Derive C from Manning's n — C = R_h^1/6 / n

Also compute Q = V × A — enter cross-section area

Theory

Chézy's equation and derived forms:

V = C × √(R_h × S) [m/s]

Q = C × A × √(R_h × S) [m³/s]

S = V² / (C² × R_h) [m/m]

R_h = V² / (C² × S) [m]

Relationships to other friction representations:

Manning–Chézy: C = R_h^1/6 / n [SI, m^1/2/s]

Darcy–Chézy: C = √(8g / f) [f = Darcy-Weisbach]

Bazin (1865): C = 87 / (1 + γ/√R_h) [γ = Bazin roughness]

Because C = R_h^1/6/n depends on depth, the Manning form (with constant n) is more convenient than Chézy for variable-depth calculations.

Typical Chézy C values (SI, m^1/2/s):

Channel surface	C	Manning n equiv
Smooth concrete flume	60–90	0.011–0.015
Lined concrete channel	55–75	0.013–0.018
Unlined earth, good condition	45–65	0.018–0.025
Natural channel, clean	30–55	0.025–0.040
Rough/rocky channel	20–35	0.040–0.060

Historical note:

Antoine de Chézy derived this formula in 1769 from measurements on the Seine and Canal de l'Yvette. It predates Manning's equation (1891) and Darcy-Weisbach (1845). All three are equivalent for fully turbulent flow; the preference today is Manning's n because n is more nearly constant across depth changes than C.