Grashof Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Grashof number ( \(Gr\) ) (dimensionless number) is the ratio of buoyant to viscous forces.

Grashof Number FORMULA

\(\large{ Gr = \frac { g \; l^3 \; \alpha \; \left( T_s - T_{\infty}  \right) }    {\nu^2} \; }\) (for vertical flat places)         

\(\large{ Gr = \frac { g \; l^3 \; \alpha \; \left( T_s^{\nu^2} - T_{\infty}  \right) }    {\nu^2} \; }\) (for bulk bodies and pipes)           

Where:

\(\large{ Gr }\) = Grashof number

\(\large{ T_{\infty} }\) = bulk temperature

\(\large{ g }\) = gravitational acceleration

\(\large{ \nu }\)  (Greek symbol nu) = kinematic viscosity of the fluid

\(\large{ T_s }\) = temperature of the surface

\(\large{ \alpha }\)  (Greek symbol alpha) = thermal expansion coefficient of the fluid

\(\large{ l }\) = vertical length

 

Tags: Equations for Force