Grashof Number

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)
Ts = 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
Ca,s = concentration of species a at surface
Ca,a = concentration of species a in ambient medium
L = characteristic length
ν = kinematic viscosity
ρ = fluid density
Ca = concentration of species a
T = constant temperature
p = constant pressure

Read more about Grashof Number:  Derivation of Grashof Number

Famous quotes containing the word number:

    At thirty years a woman asks her lover to give her back the esteem she has forfeited for his sake; she lives only for him, her thoughts are full of his future, he must have a great career, she bids him make it glorious; she can obey, entreat, command, humble herself, or rise in pride; times without number she brings comfort when a young girl can only make moan.
    Honoré De Balzac (1799–1850)