# Froude Number

on . Posted in Dimensionless Numbers

Froude number, abbreviated as Fr, a dimensionless number, is the ratio of inertial force to gravitational forces  acting on a fluid flow.  It is used for wave and surface behavior for mixed natural and forced convection.  It is used used in fluid dynamics to characterize the flow regime and behavior of fluids, particularly in open channel flow or flow around objects.

The Froude number is important in various applications, such as open channel hydraulics, river engineering, and ship hydrodynamics.  It helps in understanding the behavior of flow, determining flow patterns, and predicting the occurrence of hydraulic phenomena.

### Froude number formula

$$Fr \;=\; v \;/\; \sqrt { g \; h_m }$$    (Froude Number)

$$v \;=\; Fr \; \sqrt { g \; h_m }$$

$$g \;=\; v^2 \;/\; h_m \; Fr^2$$

$$h_m \;=\; v^2 \;/\; g \; Fr^2$$

### Solve for Fr

 velocity, v gravitational acceleration, g mean depth, hm

### Solve for v

 Froude number, Fr gravitational acceleration, g mean depth, hm

### Solve for g

 velocity, v mean depth, hm Froude number, Fr

### Solve for hm

 velocity, v gravitational acceleration, g Froude number, Fr

Symbol English Metric
$$Fr$$ = Froude number $$dimensionless$$
$$v$$ = velocity of flow $$ft\;/\;sec$$ $$m\;/\;s$$
$$g$$ = gravitational acceleration $$ft\;/\;sec^2$$ $$m\;/\;s^2$$
$$h_m$$ = mean depth $$ft$$ $$m$$