The variation of pressure with density in a thick gas layer is given by where C and n are constants. Noting that the pressure change across a differential fluid layer of thickness dz in the vertical z–direction is given as dP= ‒ρg dz, obtain a relation for pressure as a function of elevation z. Take the pressure and density at z = 0 to be P0 and ρ0, respectively.

Step 1:

To obtain the relation for the variation of pressure with altitude with respect to the density of the air. The change in pressure P with altitude is given by

= ----(1)

Where is density of the air

g is the acceleration due to gravity (assuming constant)

z is the vertical height (altitude)