Understanding Pressure Variation with Altitude in a Horizontal Slab of Air

[greencheeseca]

"consider a horizontal slab of air whose thickness(height) is dz. if this slab is at rest, the pressure holding it up from below must balance both the pressure from above and the weight of the slab. use this fact to find an expression for dP/dz, the variation of pressure with altitude, in terms of the density of air"

P = $$\rho$$gh

(h = dz)

dP = $$\rho$$g dz

dP = $$\rho$$g
dz

 

[cepheid]

You can't start with P= rho*g*h. That is basically the result the problem is asking you to derive. You need to express the balance of differential forces on the slab of air. In other words, write the force balance equation that corresponds to Newton's second law for the slab.