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Grashof number, ground to 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$^8$ < $Gr_L$ < 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
$\frac{g \beta_{gas} \left(T_{gas}-T_{bulk}\right) {L_{cm}}^3}{{\nu_{gas}}^2}$for vertical flat planes
$\frac{g \beta_{gas} \left(T_{gas}-T_{bulk}\right) {D_o}^3}{{\nu_{gas}}^2}$for pipes
Related
$\beta_{gas}$
Volumetric thermal expansion coefficient for gas [1/K]
$D_o$
Outer diameter [m]
$g$
Standard acceleration of gravity [m/s$^2$]
$L_{cm}$
Depth of laying [m]
$\nu_{gas}$
Kinematic viscosity for gas [m$^2$/s]
$T_{bulk}$
Bulk temperature [K]
$T_{gas}$
Absolute gas temperature [K]
Used in
$\mathrm{Ra}_L$
Rayleigh number, ground to air