If gravity is directed vertically downwards, then this reduces to

__Example 2. .3__How does the pressure increase with depth in the ocean?
*Assume* a uniform, *incompressible* liquid in
equilibrium. With taken as a constant (2.13) gives

where at at the surface of the ocean. Thus, the pressure increases linearly with depth.

__Example 2. .4__At what depth is the pressure double the atmospheric value of
Newtons m. Use kg m for water,
m s and 1 Newton = 1kg m s.

Thus, the depth is approximately 10 metres.

__Example 2. .5__If the Sun's atmosphere is compressible and isothermal, how does the
pressure, , decrease with height above the solar surface? We may
assume that the atmosphere is treated as a plane and that the pressure
at the surface is .

but, using the gas law , we may eliminate the density to obtain

where is called the pressure scaleheight. Hence,

Hence,