Froude Number Calculator

The Froude number, Fr, is a dimensionless quantity that compares a flow's velocity to the speed at which gravity-driven surface waves can travel. It is the free-surface flow analogue of the Mach number, which compares speed to the speed of sound.

Fr = v/√(gL), where v is flow velocity, g is gravitational acceleration, and L is a characteristic length (such as water depth for open-channel flow, or waterline length for a ship hull).

Subcritical flow (Fr<1) means the flow is slower than surface waves can travel, so disturbances can propagate both upstream and downstream, and the flow is controlled from downstream. Supercritical flow (Fr>1) means the flow outruns its own surface waves, so disturbances can only travel downstream, and the flow is controlled from upstream.

Fr=1 is called critical flow, where flow velocity exactly equals the speed of a shallow-water surface wave. This is analogous to Mach 1 in aerodynamics, the boundary condition where upstream-traveling disturbances become impossible.

A hydraulic jump is the sudden, turbulent rise in water surface level that occurs when supercritical flow (Fr>1) abruptly transitions to subcritical flow (Fr<1), commonly seen below dam spillways or where fast water hits an obstruction. The jump is the flow's way of dissipating excess kinetic energy while crossing the Fr=1 boundary.

Naval architects use the Froude number, based on a ship's waterline length, to predict wave-making resistance and to scale test results from small physical models up to full-size vessels. Matching the Froude number between a scale model and the real ship is the standard similarity condition for these free-surface tests.

It depends on the application: water depth for open-channel flow, waterline length for a ship hull, or another relevant length scale for the specific free-surface flow problem being analyzed. Choosing the right length for your geometry is essential to a physically meaningful Fr.

A displacement-hull boat's practical maximum speed (often called hull speed) corresponds to a Froude number around 0.4 to 0.5, where the boat's own bow and stern waves begin to interfere destructively, requiring disproportionately more power to go faster without the hull planing onto the water surface.

No, they measure different physical effects: Reynolds number compares inertial to viscous forces (predicting laminar versus turbulent flow), while Froude number compares flow speed to gravity-wave speed (predicting subcritical versus supercritical free-surface behavior). Both can matter simultaneously in the same flow.

No, the Froude number is specifically meaningful for flows with a free surface (open channels, ship hulls, spillways) where gravity waves can form. For fully enclosed pipe flow with no free surface, it is not a relevant parameter, unlike the Reynolds number which applies universally.