Navier Stokes Equations - General Question

[gilgtc]

(This is from the perspective of Geophysical Fluid Dynamics)

In the Navier Stokes equations I am confused as to why there is both a pressure term and a gravity term. Is this pressure resulting from differences in densities and temperature differences alone? I would think that the gravity term would be lumped into the pressure term. Can someone please clarify?

I am sorry if this makes no sense I am just trying to understand,

Thanks for your help.

g

 

[caslav.ilic]

Engineering-wise a look into energy balance is always comfortable. If in the system there are two distinct bodies of fluid, having same velocity, density, pressure and temperature, but at different altitudes, the system still has the energy potential to do something. If the gravity term would be missing from Navier-Stokes equations, then they would not show this potential.

--
Chusslove Illich (Часлав Илић)

 

[jaap de vries]

gravity is usually shown for the body force component. However this can also be centrifugal force etc.

 

[luben]

the pressure term should be for the pressure force driving the fluid. In compressible flow this is the same pressure that change with temperature and density. The body force is of different nature. It cannot be lump into the pressure term. Perhaps because all terms on RHS are forces, and this gives you the impression that they can be lump together. In fact, they are different.

the momentum equation:

Change of momentum = pressure force + viscous force + body force