Froude Number Calculator

Fr = V / √(gL) — ratio of flow velocity to shallow-water wave celerity. Determines whether open-channel flow is subcritical, critical, or supercritical.

Fluid Mechanics II

Inputs

Flow velocity V (m/s)

Characteristic depth L (m)

Use hydraulic depth y = A/T for non-rectangular channels, or flow depth for rectangular.

Theory

Froude number and wave celerity:

Fr = V / c = V / √(gL) [dimensionless]

c = √(gL) [m/s] (shallow-water wave speed)

L is the hydraulic depth = A/T for any cross-section (A = flow area, T = top width). For rectangular channels, hydraulic depth = flow depth y.

Flow regime classification:

Regime	Fr	Characteristics
Subcritical	Fr < 1	Slow / tranquil. Waves travel upstream & downstream. Downstream controls.
Critical	Fr = 1	Maximum discharge for given specific energy. Boundary condition for transitions.
Supercritical	Fr > 1	Fast / rapid. Waves only travel downstream. Upstream conditions control.

Common applications:

Open-channel flow: rivers, canals, spillways
Hydraulic jump: transition from supercritical to subcritical (Fr₁ → Fr₂)
Ship hull resistance: Fr based on hull length L
Critical depth calculation: y_c where Fr = 1
Weir and sluice gate analysis

Where:

Fr = Froude number (dimensionless)
V = mean flow velocity [m/s]
c = wave celerity = √(gL) [m/s]
g = gravitational acceleration = 9.81 m/s²
L = characteristic length (hydraulic depth or flow depth) [m]