Grashof Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Grashof number is the ratio of buoyant to viscous forces.

FORMULA

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

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

Where:

\(Gr\) = Grashof number

\(g\) = gravitational acceleration

\(l\) = vertical length

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

\(T_s\) = surface temperature

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

\(d\) = diameter

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