# Grashof Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Grashof number, abbreviated as Gr, a dimensionless number, is the ratio of buoyant to viscous forces.

## Grashof Number formulas

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

### Where:

 Units English Metric $$\large{ Gr }$$ = Grashof number $$\large{dimensionless}$$ $$\large{ T_{\infty} }$$ = bulk temperature $$\large{F}$$ $$\large{C}$$ $$\large{ g }$$ = gravitational acceleration $$\large{\frac{ft}{sec^2}}$$ $$\large{\frac{m}{s^2}}$$ $$\large{ \nu }$$  (Greek symbol nu) = kinematic viscosity of fluid $$\large{\frac{ft^2}{sec}}$$ $$\large{\frac{m^2}{s}}$$ $$\large{ l }$$ = vertical length $$\large{ft}$$ $$\large{m}$$ $$\large{ T_s }$$ = temperature of surface $$\large{F}$$ $$\large{C}$$ $$\large{ \alpha_c }$$  (Greek symbol alpha) = thermal expansion coefficient of fluid $$\large{\frac{in}{in\;F}}$$ $$\large{\frac{mm}{mm\;C}}$$ 