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. It is named after the German engineer Franz Grashof.

- for vertical flat plates

- for pipes
- for bluff bodies

where the L and D subscripts indicates the length scale basis for the Grashof Number.

*g*= acceleration due to Earth's gravity*β*= volumetric thermal expansion coefficient (equal to approximately 1/T, for ideal fluids, where T is absolute temperature)*T*_{s}= surface temperature*T*_{∞}= bulk temperature*L*= length*D*= diameter*ν*= kinematic viscosity

The transition to turbulent flow occurs in the range 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.

The product of the Grashof number and the Prandtl number gives the Rayleigh number, a dimensionless number that characterizes convection problems in heat transfer.

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

where

and

*g*= acceleration due to Earth's gravity*C*_{a,s}= concentration of species*a*at surface*C*_{a,a}= concentration of species*a*in ambient medium*L*= characteristic length*ν*= kinematic viscosity*ρ*= fluid density*C*_{a}= concentration of species*a**T*= constant temperature*p*= constant pressure

Read more about Grashof Number: Derivation of Grashof Number

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