Froude number#
Named after: William Froude (1810-1879).
$$\text{Fr} \stackrel{\text{def}}{=} \frac{U}{\sqrt{g} \sqrt{L}} \sim \frac{\text{flow velocity}}{\text{gravity wave speed}}$$
Description#
Measures flow speed relative to gravity wave speed. It indicates whether gravity can communicate disturbances upstream in free-surface and stratified flows.
Quantities#
| Name | Symbol | SI units | Dimension |
|---|---|---|---|
| velocity | \(U\) | \(\mathrm{m}\,\mathrm{s}^{-1}\) | \(\text L\,\text T^{-1}\) |
| gravitational acceleration | \(g\) | \(\mathrm{m}\,\mathrm{s}^{-2}\) | \(\text L\,\text T^{-2}\) |
| characteristic length | \(L\) | \(\mathrm{m}\) | \(\text L\) |
Regimes#
Open channel flow
| Range | Regime | Description |
|---|---|---|
| 0 – 1 | subcritical (tranquil) | Flow velocity is less than wave speed. Disturbances can propagate upstream. Common in rivers and open channels. |
| 1 – ∞ | supercritical (rapid) | Flow velocity exceeds wave speed. Disturbances cannot propagate upstream. Occurs in steep channels and spillways. |