# 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

$$\large{ Ar = \frac{ g \; l^3 \; \rho_f \; \left( \rho_b \;-\; \rho _f \right)}{\mu^2} }$$
Symbol English Metric
$$\large{ Ar }$$ = Archimedes number $$\large{dimensionless}$$
$$\large{ \rho_f }$$ = density of fluid $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$
$$\large{ \rho_b }$$ = density of the body flowing through the fluid $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$
$$\large{ \mu }$$ = dynamic viscosity of fluid $$\large{\frac{lbf-sec}{ft^2}}$$ $$\large{ Pa-s }$$
$$\large{ g }$$ = gravitational acceleration  $$\large{\frac{ft}{sec^2}}$$   $$\large{\frac{m}{s^2}}$$
$$\large{ l }$$ = length $$\large{in}$$ $$\large{mm}$$

Tags: Gravity Equations