Grashof Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Grashof Number

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

Grashof Number FORMULA

\(Gr = \frac { g \; l^3 \; \alpha \; \left( T_s - T_{\infty}  \right) }    {\nu^2} \) (for vertical flat places)          \( Grashof \; number  \;=\;   \frac { gravitational \; acceleration \;\;x\;\;  length^3 \;\;x\;\;  thermal \; expansion \; coefficient \; of \; the \; fluid    \; \left( \;surface \; temperature  \;-\;  bulk \; temperature \; \right) }    { kinematic \; viscosity \; of \; the \; fluid^2} \)

\(Gr = \frac { g \; l^3 \; \alpha \; \left( T_s^{\nu^2} - T_{\infty}  \right) }    {\nu^2} \) (for bulk bodies and pipes)          \( Grashof \; number  \;=\;   \frac { gravitational \; acceleration \;\;x\;\;  length^3 \;\;x\;\;  thermal \; expansion \; coefficient \; of \; the \; fluid    \; \left( \;surface \; temperature^{ kinematic \; viscosity \; of \; the \; fluid^2 }   \;-\;  bulk \; temperature \; \right) }    { kinematic \; viscosity \; of \; the \; fluid^2} \)   

Where:

\(Gr\) = Grashof number

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

\(d\) = diameter

\(g\) = gravitational acceleration

\(l\) = vertical length

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

\(T_s\) = surface temperature

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

 

Tags: Equations for Force