Definition: Froude number

Froude number ($F_r$) is the dimensionless ratio of the inertia force to the gravity force in a flowing fluid. It is the most important number for open channel flow.

$$F_r = \sqrt{\frac{\text{Inertia force}}{\text{Gravity force}}} = \frac{V}{\sqrt{gD}}$$

where $V$ = mean velocity, $g$ = acceleration due to gravity, $D = A/T$ = hydraulic depth (equal to $y$ for a rectangular channel).

Classification of flow:

Uses: hydraulic jump calculations below spillways, model studies (Froude model law for spillways and dams), and design of channels. Example: $V = 2$ m/s, $y = 1$ m gives $F_r = 2/\sqrt{9.81 \times 1} = 0.64$ (subcritical).