Archimedes number


In viscous fluid dynamics, the Archimedes number (Ar) (not to be confused with Archimedes’ constant, π), named after the ancient Greek scientist Archimedes is used to determine the motion of fluids due to density differences. It is a dimensionless number defined as the ratio of external forces to internal viscous forces and has the form shown here.

Related formulas


ArArchimedes number (dimensionless)
glocal external field (for example gravitational acceleration) (m/s2)
Lcharacteristic length of body (m)
ρldensity of the fluid (kg/m3)
ρdensity of the body (kg/m3)
μdynamic viscosity (kg/m*s)