Archimedes number

An Archimedes number Ar (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 / m³
• ρ = density of the body, kg / m³
• μ = dynamic viscosity, kg / ms
• L = characteristic length of body, m

When analyzing potentially mixed convection of a liquid, the Archimedes number parametrizes the relative strength of free and forced convection by representing the ratio of Grashof number and the square of Reynolds number. This represents the ratio of buoyancy and inertial forces, which stands in for the contribution of natural convection. When Ar >> 1, natural convection dominates and when Ar << 1, forced convection dominates.

$Ar= \frac{Gr}{Re^2}$

See also

• Fluid dynamics
• Convective heat transfer