Archimedes number

== English == === Etymology === Named after Archimedes of Syracuse (c. 287 – c. 212 BC), a Greek mathematician, physicist, engineer, inventor, and astronomer. === Noun === Archimedes number (plural Archimedes numbers) (fluid dynamics) A dimensionless number used to determine the motion of fluids due to density differences, defined as the ratio of gravitational forces to viscous forces: A r = g L 3 ρ − ρ ℓ ρ ℓ ν 2 = g L 3 ρ ℓ ( ρ − ρ ℓ ) μ 2 , {\displaystyle {\begin{aligned}\mathrm {Ar} &={\frac {gL^{3}{\frac {\rho -\rho _{\ell }}{\rho _{\ell }}}}{\nu ^{2}}}={\frac {gL^{3}\rho _{\ell }(\rho -\rho _{\ell })}{\mu ^{2}}}\\\end{aligned}},} where g {\displaystyle g} is the local external field, L {\displaystyle L} is the characteristic length of body, ρ − ρ ℓ ρ ℓ {\displaystyle {\frac {\rho -\rho _{\ell }}{\rho _{\ell }}}} is the submerged specific gravity, ρ ℓ {\displaystyle \rho _{\ell }} is the density of the fluid, ρ {\displaystyle \rho } is the density of the body, ν = μ ρ ℓ {\displaystyle \nu ={\frac {\mu }{\rho _{\ell }}}} is the kinematic viscosity, and μ {\displaystyle \mu } is the dynamic viscosity. === Further reading === Archimedes number on Wikipedia.Wikipedia