Archimedes number

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

Archimedes number (plural Archimedes numbers)

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

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