Archimedes number

Archimedes' number is named after the Greek Archimedes.

In viscous fluid dynamics, the Archimedes number (Ar) ^[1] is used when the motion of fluids is affected by density differences. It is a dimensionless number, the ratio of gravitational forces to viscous forces.^[2]

The relationship and has the form:^[3]

${\displaystyle \mathrm {Ar} ={\frac {gL^{3}\rho _{\ell }(\rho -\rho _{\ell })}{\mu ^{2}}}}$

where:

• ${\displaystyle g}$ is the local external field (for example gravitational acceleration), ${\displaystyle m/s^{2}}$,
• ${\displaystyle \rho _{\ell }}$ is the density of the fluid, ${\displaystyle kg/m^{3}}$,
• ${\displaystyle \rho }$ is the density of the body, ${\displaystyle kg/m^{3}}$,
• ${\displaystyle \mu }$ is the dynamic viscosity, ${\displaystyle kg/ms}$,
• ${\displaystyle L}$ is the characteristic length of body, ${\displaystyle m}$.