# Galileo Number

on . Posted in Dimensionless Numbers

Galileo number, abbreviated as Ga, a dimensionless number, also called Galilei number, is used in fluid dynamics to characterize the relative importance of gravitational forces to viscous forces in a fluid flow.  The Galileo number is particularly useful when analyzing flows in which both gravitational and viscous forces are significant.  The Galileo number helps determine whether gravitational forces dominate the flow (larger Galileo number) or viscous forces dominate (small Galileo number).

### Galileo number categorizes fluids into different regimes

• Ga < 1  -  It means that viscous forces are dominant, and the flow is relatively slow compared to the effects of gravity. In this case, you might expect the flow to be more influenced by viscous effects.
• Ga > 1  -  It means that gravitational forces are dominant, and the flow is relatively fast compared to the effects of viscosity.  In this case, you might expect the flow to be more influenced by gravitational effects.

The Galileo number is particularly important in areas such as fluid mechanics, chemical engineering, and geophysics, where it helps engineers and scientists understand and predict the behavior of fluid flows under different conditions.

## Galileo number formula

$$\large{ Ga = \frac{ g \; l_c^3 \; \mu^2 } { \rho^2 } }$$
Symbol English Metric
$$\large{ Ga }$$ = Galileo number $$\large{dimensionless}$$
$$\large{ g }$$ = gravitational acceleration $$\large{ \frac{ft}{sec^2}}$$ $$\large{ \frac{m}{s^2}}$$
$$\large{ l_c }$$ = characteristic length $$\large{ft}$$ $$\large{m}$$
$$\large{ \mu }$$  (Greek symbol mu) = viscosity $$\large{\frac{lbf - sec}{ft^2}}$$ $$\large{ Pa - s }$$
$$\large{ \rho }$$  (Greek symbol rho) = density $$\large{ \frac{lbm}{ft^3}}$$ $$\large{ \frac{kg}{m^3}}$$

Tags: Flow Viscosity