# Archimedes Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Archimedes number, abbreviated as Ar, a dimensionless number, analyzes flow as it relates to a system of density differences.  It is used when dealing with gravitational settling of particles in fluid.

## Archimedes Number formula

 $$\large{ Ar = \frac{ g \; l^3 \; \rho_f \; \left( \rho_b \;-\; \rho _f \right)}{\mu^2} }$$

### Where:

$$\large{ Ar }$$ = Archimedes number

$$\large{ \rho_f }$$ = density of fluid

$$\large{ \rho_b }$$ = density of the body flowing through the fluid

$$\large{ \mu }$$ = dynamic viscosity of fluid

$$\large{ g }$$ = gravitational acceleration (9.80665 m/s2 or 32.1740 ft/s2)

$$\large{ l }$$ = length