Archimedes number

English

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

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: ${\begin{aligned}\mathrm {Ar} &={\frac {gL^{3}{\frac {\rho -\rho _{\ell }}{\rho _{\ell }}}}{\nu ^{2}}}={\frac {gL^{3}\rho _{\ell }(\rho -\rho _{\ell })}{\mu ^{2}}}\\\end{aligned}},$ where $g$ is the local external field, $L$ is the characteristic length of body, ${\frac {\rho -\rho _{\ell }}{\rho _{\ell }}}$ is the submerged specific gravity, $\rho _{\ell }$ is the density of the fluid, $\rho$ is the density of the body, $\nu ={\frac {\mu }{\rho _{\ell }}}$ is the kinematic viscosity, and $\mu$ is the dynamic viscosity.