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Question
Pressure decreases as one ascends the atmosphere. If the density of air is ρ, what is the change in pressure dp over a differential height dh?
Solution
Consider a horizontal parcel of air with cross-section A and height dh.
Let the pressure on the top surface and bottom surface be p and p + do. If the parcel is in equilibrium, then the net upward force must be balanced by the weight.
i.e., `(p + dp)A - pA = - pgAdh` ......(∵ Weight = Density × Volume × g)
= `- p xx Adh xx g`
⇒ `dp = - ρgdh` .....(ρ = density of air)
A negative sign shows that pressure decreases with height.
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