Froude Number — froude • rivr

Calculate the Froude Number.

froude(Q, g, A, DH)

Arguments

Q: Flow rate [$L^3 T^{-1}$].
g: Gravitational acceleration [$L T^{-2}$].
A: Flow area [$L^2$].
DH: Hydraulic depth [$L$].

Value

The Froude Number (dimensionless).

Details

The Froude number is a dimensionless measure of bulk flow characteristics that represents the relative importance of inertial forces and gravitational forces. For open channel flow, the Froude number of open channel flow is defined as $$Fr = \frac{v}{\sqrt{gD_H}}$$ where $v = \frac{Q}{A}$ is the flow velocity, $g$ is the gravitational acceleration and $D_H$ is the hydraulic depth. The Froude number is related to the energy state of the flow and can be used to identify flows as either supercritical ($Fr < 1$) or subcritical ($Fr > 1$).

Examples

froude(250, 32.2, 171, 1.71) # subcritical flow
#> [1] 0.1970234
froude(250, 32.2, 57.9, 0.579) # critical flow
#> [1] 0.9999867
froude(250, 32.2, 45, 0.45) # supercritical flow
#> [1] 1.459464