Galileo number#

Named after: Galileo Galilei (1564-1642).

$$\text{Ga} \stackrel{\text{def}}{=} \frac{g L^{3}}{\nu^{2}} \sim \frac{\text{gravity driven motion}}{\text{viscous diffusion}}$$

Measures gravity-driven motion relative to viscous diffusion. It is useful for settling, rising bubbles, and natural motion set by body forces.

Name	Symbol	SI units	Dimension
gravitational acceleration	$g$	$\mathrm{m}\,\mathrm{s}^{-2}$	$\text L\,\text T^{-2}$
characteristic length	$L$	$\mathrm{m}$	$\text L$
kinematic viscosity	$\nu$	$\mathrm{m}^{2}\,\mathrm{s}^{-1}$	$\text L^{2}\,\text T^{-1}$

Settling and natural motion

Range	Regime	Description
0 – 1	viscous settling	Viscous resistance controls motion. Falling particles or bubbles move slowly and remain in a creeping flow regime.
1 – 1000	transitional settling	Gravity driven motion is affected by both viscosity and inertia. Wakes and path instabilities may begin to appear.
1000 – ∞	inertial settling	Inertial effects dominate gravitational motion. Wakes, vortex shedding, and unsteady trajectories become important.

Name	Symbol	SI units	Dimension
gravitational acceleration	\(g\)	\(\mathrm{m}\,\mathrm{s}^{-2}\)	\(\text L\,\text T^{-2}\)
characteristic length	\(L\)	\(\mathrm{m}\)	\(\text L\)
kinematic viscosity	\(\nu\)	\(\mathrm{m}^{2}\,\mathrm{s}^{-1}\)	\(\text L^{2}\,\text T^{-1}\)