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Archimedes number

An Archimedes number (not to be confused with Archimedes' constant, π), named after the ancient Greek scientist Archimedes, 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),
• ρl = density of the fluid, kg / m3
• ρ = density of the body, kg / m3
• μ = dynamic viscosity, kg / sm
• L = characteristic length of body, m