Grashof number ground-air

The Grashof number is a dimensionless number in fluid dynamics and heat transfer which approximates the ratio of the buoyancy to viscous force acting on a fluid. It frequently arises in the study of situations involving natural convection. The transition to turbulent flow occurs in the range $10^8 < Gr < 10^9$ for natural convection from vertical flat plates. At higher Grashof numbers, the boundary layer is turbulent; at lower Grashof numbers, the boundary layer is laminar.

Symbol
$\mathrm{Gr}_{L}$
Formulae
$\frac{L_{cm}^{3} \beta_{gas} g \left(T_{gas} - T_{\infty}\right)}{\nu_{gas}^{2}}$for vertical flat planes
$\frac{D_{o}^{3} \beta_{gas} g \left(T_{gas} - T_{\infty}\right)}{\nu_{gas}^{2}}$for pipes
$D_{o}$
$L_{cm}$
$\nu_{gas}$
Used in
$\mathrm{Ra}_{L}$