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 \(\large{\frac{in}{in\;F}}\) \(\large{\frac{mm}{mm\;C}}\)

 

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Tags: Heat Transfer Equations Force Equations