Question

Suppose the density of air at Madras is ρ₀ and atmospheric pressure is P₀. If we go up, the density and pressure both decrease. Suppose we wish to calculate the pressure at a height 10 km above Madras. If we use the equation P₀ -P =ρ₀gz, will we get the 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?

Answer 1

In First Case : (When the Variation is g is not considered) ⇒

If we will go at the top then pressure will decrease.

Atmospheric pressure in madras = P₀

Pressure at the top of height be P.

Now, Pressure at depth or atmospheric pressure will be given by,

P₀ = P + ρ₀gz

This means, P = P₀ - ρ₀gz

Now, pressure is less than the actual.

P ∠ P₀

In Second Case : (When the Variation is g is considered) ⇒

When change in g is considered, then we know that value of g decreases as we move up.

Thus, equation becomes,

P = P₀ - ρ₀g'z, g' is less than g, thus it will make ρ₀g'z as small.

Thus, P will still be less than P₀.

Thus, Our answer will not change in both cases.

Hope it helps.