A solution of the differential equation for the pressure
is given by
P(y) = P(0) e-y/H
When we choose y=0 at sea level,
then P(0)=1 atm.
By taking an average temperature of
T=0oC
for our atmosphere and an average molecular weight of
28.97
of air molecules, one obtains for the scale height of air
a value of about H=8 km
which is almost as high as the Mount Everest.
Below we show a graph of the atmospheric pressure
versus the altitude for the latter value of
H.
Atmospheric pressure according to the
isothermal-barotropic approximation.
For the density of a gaseous fluid we find, moreover, the expression
