Variation of Atmospheric Pressure With Altitude
The pressure in the ocean is well approximated by the expression
where
is atmospheric pressure at sea level,
is the density of seawater (
) and
is the depth of water. This equation works because water is virtually incompressible so pressure is proportional to depth of water (
).
The same cannot be said for atmospheric pressure. Air is a gas, much more compressible than water, so the pressure at any point below the top of the atmosphere increases more rapidly because the density of the atmosphere increases as you descend, or alternatively the pressure decreases more rapidly with altitude because of the decreasing density of the air as you ascend.
The pressure may be better described, for example by an exponential function of the form
where
is a constant and
is the height above sea level, but this is only one of many possible models.
