Archimedes Number

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