Froude Number Calculator — Open-Channel Flow Regime

Formula

How this is calculated

The Froude number compares flow inertia to the restoring force of gravity in open-channel hydraulics. It is defined as Fr = v / √(gy), where v is the mean flow velocity, g = 9.81 m/s² and y is the flow depth (or hydraulic depth A/T for non-rectangular sections). The denominator √(gy) is the celerity (wave speed) of a small gravity wave on the surface — the speed at which a disturbance such as a ripple or surge travels upstream.

When Fr < 1 (subcritical or tranquil flow), gravity waves can propagate upstream, so information about a downstream obstruction reaches the approaching flow and adjusts it smoothly. When Fr > 1 (supercritical or rapid/shooting flow), inertia overwhelms gravity and disturbances cannot travel upstream — the flow accelerates and surface waves are swept downstream. At Fr = 1 (critical flow) these two speeds are equal, standing waves can form, and the flow is at minimum specific energy for a given discharge. The transition from supercritical to subcritical is abrupt and turbulent: a hydraulic jump.

For rectangular channels, the critical depth yc = (q²/g)^(1/3) where q is discharge per unit width. This calculator computes critical depth from velocity alone as yc = v²/g (rearranging Fr = 1 at the input velocity) and critical velocity from depth as vc = √(gy). These are useful for channel design, spillway dimensioning and flood analysis. The formula assumes steady, uniform flow and a flat channel; slope effects and non-hydrostatic pressure distributions are not included.