# Froude Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Froude number, abbreviated as Fr, a dimensionless number, is the ratio of inertial force to gravitational force.  It is used for wave and surface behavior for mixed natural and forced convection.

## Froude number formula

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

### Where:

 Units US Metric $$\large{ Fr }$$ = Froude number $$\large{dimensionless}$$ $$\large{ g }$$ = gravitational acceleration $$\large{ \frac{ft}{sec^2}}$$ $$\large{ \frac{m}{s^2}}$$ $$\large{ h_m }$$ = mean depth $$\large{ft}$$ $$\large{m}$$ $$\large{ v }$$ = velocity of flow $$\large{ \frac{ft}{sec}}$$ $$\large{ \frac{m}{s}}$$

### Solve For:

 $$\large{ g = \frac{ v^2 }{ h_m \; Fr^2 } }$$ $$\large{ h_m = \frac{ v^2 }{ g \; Fr^2 } }$$ $$\large{ v = Fr \; \sqrt{ g \; h_m } }$$