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