Archimedes number

An Archimedes number (not to be confused with Archimedes' constant, π), named after the ancient Greek scientist Archimedes—used to determine the motion of fluids due to density differences—is a dimensionless number in the form:

$\{rm\; Ar\}\; =\; frac\{g\; L^3\; rho\_ell\; (rho\; -\; rho\_ell)\}\{mu^2\}$

where:

• g = gravitational acceleration (9.81 m/s²),
• ρ_l = density of the fluid, $kg/m^3$
• ρ = density of the body, $kg/m^3$
• μ = dynamic viscosity, $kg/sm$
• L = characteristic length of body, m

See also

• Fluid dynamics