Froude Number

Froude number: Fr = v/√(g·L)

The Froude number is a dimensionless ratio that weighs inertial forces against gravitational ones: Fr = v/√(g·L), where v is velocity (m/s), g = 9.81 m/s² and L is a characteristic length (m). Take water moving at v = 2 m/s over a depth L = 1 m. That works out to Fr ≈ 0.64, which puts you in subcritical flow. What the value tells you changes with the regime. When Fr < 1 the flow is subcritical: calm water, gravity in charge, and disturbances able to travel back upstream. Fr = 1 sits right at critical, and Fr > 1 means the flow is supercritical, fast and inertia-driven, the kind that throws hydraulic waves down a spillway. There's a nice parallel with ships, where Fr = v/√(g·L_hull). Cargo vessels stay under Fr < 0.3 to save fuel, whereas a planing speedboat pushes past Fr > 1. The same threshold shows up in animal locomotion: Fr ≈ 1 is roughly where walking turns into running, and dolphins hit their best hydrodynamic efficiency near that mark too.

Applications

It turns up in open-channel hydraulics for rivers and irrigation canals, in the design of hydraulic jumps in spillways and stilling basins, in naval architecture when sizing up hull resistance, in biomechanics for gait analysis, and in scale models of ports and dams.

FAQ

What is the characteristic length L? That varies with the problem you're solving. In an open channel, L is the hydraulic depth (area divided by top width). For a ship it's the waterline length, and for an animal it's the leg length. Pick whatever L matches the geometry you're dealing with.

What is a hydraulic jump? It's the sudden shift from supercritical (Fr > 1) back to subcritical flow, and a lot of energy gets dissipated in the process. You'll find them just downstream of spillways and gates, where engineers use them on purpose to keep the channel bed from eroding.

Why do cargo ships stay at Fr < 0.3? Push past that and the wave-making resistance climbs non-linearly, so fuel consumption goes through the roof. Only fast hulls like speedboats and hydrofoils bother operating above Fr > 1.