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If the fluid is at rest under gravity (that is in equilibrium), the
forces must all balance so that (2.9) reduces to
 |
(2.12) |
If gravity is directed vertically downwards, then this reduces to
 |
(2.13) |
Example 2. .3How 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. .4At 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. .5If 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,
Next: Rotating Liquids
Up: Fluids and Nonmagnetic Plasmas
Previous: The Equation of State
Prof. Alan Hood
2000-11-06