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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, $k g / m 3$
ρ = density of the body, $k g / m 3$
μ = dynamic viscosity, $k g / s m$
L = characteristic length of body, m

See also

Fluid dynamics

v • d • e

Dimensionless numbers in fluid dynamics

Archimedes • Atwood • Bagnold • Bejan • Biot • Bond • Brinkman • Capillary • Cauchy • Damköhler • Dean • Deborah • Eckert • Ekman • Eötvös • Euler • Froude • Galilei • Graetz • Grashof • ‎Görtler • Hagen • Knudsen • Laplace • Lewis • Mach • Marangoni • Morton • Nusselt • Ohnesorge • Péclet • Prandtl (magnetic, turbulent) • Rayleigh • Reynolds (magnetic) • Richardson • Roshko • Rossby • Rouse • Ruark • Schmidt • Sherwood • Stanton • Stokes • Strouhal • Suratman • Taylor • Ursell • Weber • Weissenberg • Womersley

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