Grashof number

The Grashof number is a dimensionless parameter which, unlike the Rayleigh number, contains information of a mechanical nature only. It contrasts the exclusive effects of viscosity with the floating force:

\[Gr=\dfrac{F_g}{(F_v)^2}\]

once the motion is triggered (Ra > 1708) to understand if the motion is laminar or turbulent (in natural convection) the Grashof number is evaluated; if (Gr > \(10^9\)) the motion is laminar, if instead (Gr < \(10^9\)) the motion is turbulent.

In natural convection:

\[Gr=\dfrac{\rho^2g\beta\Delta TL^3}{\mu^2}\]

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