How Does Pressure Change with Altitude?

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SUMMARY

The discussion focuses on deriving the expression for the variation of pressure with altitude, specifically dP/dz, using a horizontal slab of air. The key conclusion is that the change in pressure with altitude is directly related to the density of the air slab and gravitational acceleration, resulting in the formula dP/dz = -gρ, where ρ represents the density of the air. Participants emphasized the importance of visualizing the problem and relating the weight of the air slab to the pressure difference.

PREREQUISITES
  • Understanding of basic physics concepts, particularly fluid statics.
  • Familiarity with the relationship between pressure, density, and gravitational force.
  • Knowledge of calculus, specifically differentiation.
  • Concept of hydrostatic equilibrium in fluids.
NEXT STEPS
  • Study the principles of fluid statics and hydrostatic pressure.
  • Learn about the ideal gas law and its applications in atmospheric science.
  • Explore the concept of barometric formula and its derivation.
  • Investigate the effects of altitude on atmospheric pressure and density.
USEFUL FOR

This discussion is beneficial for physics students, atmospheric scientists, and anyone interested in understanding the relationship between pressure and altitude in fluid dynamics.

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

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