Archimedes number

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

Noun

 * 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: $$\begin{align}\mathrm{Ar} & = \frac{g L^3 \frac{\rho - \rho_\ell}{\rho_\ell}}{\nu^2} = \frac{g L^3 \rho_\ell (\rho - \rho_\ell)}{\mu^2} \\ \end{align},$$ 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.