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The variation of pressure with density in a thick gas
Chapter 3, Problem 138P(choose chapter or problem)
Problem 138P
The variation of pressure with density in a thick gas layer is given by where C and n are constants. Noting that the pressure change across a differential fluid layer of thickness dz in the vertical z–direction is given as dP= ‒ρg dz, obtain a relation for pressure as a function of elevation z. Take the pressure and density at z = 0 to be P0 and ρ0, respectively.
Questions & Answers
QUESTION:
Problem 138P
The variation of pressure with density in a thick gas layer is given by where C and n are constants. Noting that the pressure change across a differential fluid layer of thickness dz in the vertical z–direction is given as dP= ‒ρg dz, obtain a relation for pressure as a function of elevation z. Take the pressure and density at z = 0 to be P0 and ρ0, respectively.
ANSWER:
Step 1:
To obtain the relation for the variation of pressure with altitude with respect to the density of the air. The change in pressure P with altitude is given by
=
----(1)
Where is density of the air
g is the acceleration due to gravity (assuming constant)
z is the vertical height (altitude)