Grashof number

The Grashof number is a dimensionless number in fluid dynamics which approximates the ratio of the buoyancy force to the viscous force acting on a fluid.

$Gr = \frac{g \beta (T_s - T_\infty ) L^3}{\nu ^2}\,$

where

T_s = source temperature

T_∞ = quiescent temperature

L = characteristic length

ν = kinematic viscosity

There is another form of the Grashof number used in cases of natural convection mass transfer problems.

$Gr_D = \frac{g l^3 \Delta \rho }{\rho} (\frac{\rho}{\mu})^2\,$ de:Grashof-Zahl