How Does Pressure Change with Altitude?

[jason177]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

I have no idea, neither the professor nor the textbook have gone over anything like this.

 

[nickjer]

I recommend first drawing a picture of a slab of air with thickness dz. Then finding a way to write out its mass and hence weight in terms of dz and density.

 

[sagardip]

see ,the change in pressure from bottom to top of the slab (dP) is equal to the pressure due to the weight of the slab.If you can figure this out then by writing out the equation, dP/dz can be easily solved and the answer comes out to be density of slab times g.

 

[jason177]

alright, so I got dP/dz = -g\rho does that sound about right?

 

[nickjer]

Yes.