Archimedes number

Meanings

1. A dimensionless number used to determine the motion of fluids due to density differences, defined as the ratio of gravitational forces to viscous forces: Ar=(gL³(ρ-ρ_ℓ)/(ρ_ℓ))/(ν²)=(gL³ρ_ℓ(ρ-ρ_ℓ))/(μ²)\, where g is the local external field, L is the characteristic length of body, (ρ-ρ_ℓ)/(ρ_ℓ) is the submerged specific gravity, ρ_ℓ is the density of the fluid, ρ is the density of the body, ν=μ/(ρ_ℓ) is the kinematic viscosity, and μ is the dynamic viscosity.

Etymology

Named after Archimedes of Syracuse (c. 287 – c. 212 BC), a Greek mathematician, physicist, engineer, inventor, and astronomer.