Froude number

Remarks

It is a dimensionless number: $[g L] = \mathsf{L}^2 \mathsf{T}^{-2} = [U^2]$. Some authors call $U^2 / (g L)$ the Froude number; this is the square of the definition above. Example: water of depth $h = 0.1\ \mathrm{m}$ flowing at $U = 2\ \mathrm{m/s}$ has $\mathrm{Fr} = 2 / \sqrt{0.981} \approx 2.0$, so the flow is supercritical. Non-example: $U / (g L)$ is not a Froude number; it has dimension $\mathsf{L}^{-1} \mathsf{T}$. In shallow water, $\sqrt{g h}$ is the speed of long surface waves, so $\mathrm{Fr}$ compares the current with the wave speed.