We can understand how pressure in water depends on depth by considering a stack of bricks. The pressure below the bottom brick is determined by the weight of the entire stack. Halfway up the stack, the pressure is half because the weight of the bricks above is half. To explain atmospheric pressure, we should consider compressible bricks, like those made of foam rubber. Why is this so?

The pressure at any point in a column of gas is an exponential function

Explanation:

In the case of water due to the hydrostatic paradox, a liquid of any quantity can support any weight it is subjected to, as such the pressure at a point in a liquid is directly proportional to the depth. Analogous to stack of bricks

P = ρ×g×h

For gases we have that gas density depends on the gas pressure and  pressure depends on  gas density

This is as a result of the comprehensibility of gases in the atmosphere which is analogous to compressible bricks. A gas quickly spreads out to occupy a containing volume as such when subject to a force they are compressed to occupy a lesser volume.

However as the elevation increases it results in a lesser column of fluid exerting a force at that point hence reducing the pressure at that point.

We have for gases

where

= Pressure at height h

P₀ = Pressure at reference point

m = unit mass of air molecule

g = Acceleration due to gravity

h = Height from the reference point

k = Boltzmann constant

T = Temperature in Kelvin

The pressure at any point in a column of gas is an exponential function