The Froude number is the open-channel-flow counterpart to the Reynolds number — instead of comparing inertial forces to viscous friction, it compares them to gravity. That single ratio predicts whether a river, canal, or ship hull is moving in a deep, gravity-dominated regime or a shallow, inertia-dominated one, and it pinpoints exactly where a hydraulic jump will form. This calculator applies Fr = v/√(gL) to your own flow conditions, classifies the result, and can solve backward for a missing variable when you know the Froude number you're targeting.
How the Froude Number Calculator works
The Froude number is a ratio of a flow's velocity to the speed of a small gravity wave traveling on its surface, √(gL). When Fr is below 1, the flow moves slower than that wave speed, so surface disturbances can propagate both upstream and downstream — this is subcritical flow. When Fr exceeds 1, the flow outruns its own surface waves, so disturbances can only travel downstream — this is supercritical flow. The transition at Fr = 1 is not gradual: it shows up physically as a hydraulic jump, an abrupt, turbulent rise in surface elevation that dissipates the flow's excess kinetic energy.
Inputs and what they mean
Velocity (m/s) is the average flow speed. Characteristic length (m) depends on context: for open-channel flow it's usually the hydraulic depth (cross-sectional flow area divided by the free-surface width), while for a ship hull it's the waterline length. Gravitational acceleration (m/s²) defaults to standard Earth gravity, 9.81 m/s², and rarely needs adjustment — but the field exists for specialized modeling contexts. Because L sits under a square root, doubling it only raises the denominator by about 41%, while doubling velocity doubles Fr directly — velocity is usually the input with the biggest leverage on the result.
Limits and edge cases
The Froude number assumes a single, well-defined free surface and a length scale that meaningfully represents the flow's depth or hull geometry — it doesn't capture three-dimensional effects, wave interference between multiple hulls, or compressibility. For ships, the Fr ≈ 0.4 hull-speed rule of thumb is a useful planing/displacement guideline, not a hard physical limit — many hulls operate somewhat above or below it depending on hull form. For channel and spillway design, always cross-check hydraulic-jump predictions against site-specific hydraulic modeling; this calculator gives the classification and threshold, not a full energy-loss or jump-length calculation.