air pressure at various height

Atmospheric pressure various with altitude, because the temperature, and hence density, of air decreases with increase in height.

A simple (but approximate) relationship between the air density with height is given by,

p = (po).exp(-h/H)
where p and po are the densities of air at height h and sea level respectively
H is a constant which represents the mean height of the atmosphere
Commonly accepted values for po and H are 1.21 kg/m^3 and 8000 m respectively

Thus, the pressure P at height h is,
P = integral { p.g.dh} with limit of integration from h to infinitiy
where g is the acceleration due to gravity
After integration, P = Hg(po).exp(-h/H)
i.e. P = 8000 x 9.81 x 1.21 x exp(-h/8000)
or P = 94960.exp(-h/8000) Pa

This equation underestimates the actual atmospheric pressure as water vapour pressure has not been taken into account.

A more accurate equation for atmospheris pressure at various altitudes is given in the following web-page,

http://www.engineeringtoolbox.com/air-altitude-pressure-d_462.html


Q:Is there an air buoyant force acting on an object in air like the case immersed in a liquid?

The answer is YES. Archimedes Principle applies to fluids, which include both liquids and gases.