(a) Consider a fluid whose mass density \(ho\) varies with height \(y\) above sea level. Use Eq. 18.6, \(P_{1}+ho g y_{1}=\) \(P_{2}+ho g y_{2}\), to obtain an expression that shows how \(d P\), the change in pressure along a column of the fluid of infinitesimal height \(d y\), varies with y.

(b) Using the simplification that the mass density of air at any given height \(y\) above sea level is proportional to atmospheric pressure at that height, integrate the differential equation you found in part \(a\) to obtain an expression that shows how atmospheric pressure varies with height \(y\) above sea level.

Data from Eq. 18.6

Ppgy P+pgy2 (stationary liquid).