Pressure in a rotating cylinder

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SUMMARY

The discussion centers on calculating the ratio of air pressure at the center of a rotating cylinder to the pressure at its rim, given a constant temperature and a centripetal acceleration equivalent to gravitational acceleration at the rim. The ideal gas law, represented by the equation PV=NRT, is relevant for this analysis. Participants seek guidance on how to approach this problem, indicating a need for foundational understanding of fluid dynamics and thermodynamics in rotating systems.

PREREQUISITES
  • Understanding of the ideal gas law (PV=NRT)
  • Basic principles of fluid dynamics
  • Knowledge of centripetal acceleration
  • Familiarity with thermodynamic concepts
NEXT STEPS
  • Study the effects of centripetal acceleration on fluid pressure in rotating systems
  • Learn about the application of the ideal gas law in varying pressure conditions
  • Explore fluid dynamics in rotating reference frames
  • Review thermodynamic principles related to constant temperature processes
USEFUL FOR

Students in physics or engineering, particularly those studying fluid dynamics, thermodynamics, or rotational mechanics, will benefit from this discussion.

SonOfOle
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Homework Statement


A space station consists of a large cylinder of radius R_0 filled with air. The cylinder spins about its symmetry axis at an angular velocity of \Omega providing a centripetal acceleration of g at the rim of the cylinder (at R_0).

If the temperature is constant inside the station, what is the ratio of the air pressure P_c at the center of the cylinder to the air pressure at the rim P_r? (Treat the air as an ideal gas with each gas particle having a mass of m.


Homework Equations


PV=NRT...


The Attempt at a Solution


This is beyond where I know what to start with. Could someone point me in a good direction? (or know of a place online or in textbooks that I could look up how to approach problems like this?)

Thanks,
 
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Take a look at question one in this page. There's a solution in PDF and PS formats (Czech language).

http://fykos.troja.mff.cuni.cz/index.php?id=2&serie=5&volume=21&lang=en&"
 
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