Suppose the density of air at Madras is ρ 0 and atmospheric pressure is P 0 . If we go up, the density and the pressure both decrease. Suppose we wish to calculate the pressure at a height 10 kin above Madras. If we use the equation P 0 - P = ρ 0 gz, will we get a pressure more than the actual or less than the actual? Neglect the variation in g. Does your answer change if you also consider the variation in g?

Question

Philoid · Accepted Answer

For the first case, the density of air decreases as altitude increases. Let the density at a certain altitude be ρ. Then, ρ<ρ₀ and the pressure equation becomes,

Thus pressure is less than the actual value.

In the second case, the value of acceleration due to gravity(g) decreases as we increase height but by small amount. The value of ρgz will still be smaller than P₀ and thus the pressure will be less than actual.