Grashof Number - Derivation of Grashof Number

Derivation of Grashof Number

The first step to deriving the Grashof Number Gr is manipulating the volume expansion coefficient, as follows:

\mathrm{\beta}=\frac{1}{v}\left(\frac{\partial v}{\partial T}\right)_p \mathrm=\frac{-1}{\rho}\left(\frac{\partial\rho}{\partial T}\right)_p

This partial relation of the volume expansion coefficient, with respect to fluid density, and constant pressure can be rewritten as

and

- bulk fluid density - boundary layer density - temperature difference between boundary layer and bulk fluid

There are two different ways to find the Grashof Number from this point. One involves the energy equation while the other incorporates the buoyant force due to the difference in density between the boundary layer and bulk fluid.

Read more about this topic:  Grashof Number

Famous quotes containing the word number:

    “The Oregon [matter] and the annexation of Texas are now all- important to the security and future peace and prosperity of our union, and I hope there are a sufficient number of pure American democrats to carry into effect the annexation of Texas and [extension of] our laws over Oregon. No temporizing policy or all is lost.”
    —Andrew Jackson (1767–1845)