Froude Number⚠ unverified
Physics / Fluids · Compute the Froude number of a flow
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| velocity | velocity | m/s | 1.0 | Flow speed |
| length | length | m | 1.0 | Characteristic length scale |
| gravity | gravity | m/s**2 | 1.0 | Gravitational acceleration |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | Fr | — | Froude number, dimensionless |
The science & history
Understanding the Parameters
- $v$ — higher speed → higher Fr (more inertia-dominated / supercritical tendency in open channels).
- $L$ — larger length raises $\sqrt{gL}$ and lowers Fr.
- $g$ — use ≈ 9.81 m/s² on Earth; registry default
1.0is a placeholder for some calcs — set it. - Fr — ship models match Fr (and struggle to match Re simultaneously). Open-channel: Fr = 1 is critical flow.
Derivation (Approaching a Proof)
Gravity wave celerity in shallow water scales as $c \sim \sqrt{g L}$. The ratio of flow speed to that scale is $\mathrm{Fr} = v/\sqrt{g L}$. Equivalently, from nondimensional free-surface equations, Fr appears as the gravity–inertia group. Distinct from Reynolds Number (viscosity) and Weber Number (surface tension).
History
William Froude’s ship-model scaling (19th century) made Fr the standard free-surface similarity parameter.
Related Concepts: Reynolds Number, Weber Number, Dynamic Pressure, Bernoulli Total Pressure
Notes: Registry calculator froude-number (unverified). Set physical $g$. Definition uses
$\sqrt{gL}$ (not $2gL$ etc.).