Pressure in Flow Work (u + Pv)

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SUMMARY

The pressure used in flow work calculations is the pressure of the fluid within the system, not the external pressure, due to the need for pressure continuity at the boundary of the control volume. In closed systems, the external pressure aligns with the gas pressure at the piston face, but during irreversible deformation, the pressure within the cylinder can be non-uniform. This results in an average pressure that does not equal the pressure at the piston face, emphasizing the importance of using fluid pressure for accurate flow work calculations.

PREREQUISITES
  • Understanding of fluid mechanics principles
  • Knowledge of pressure concepts in closed systems
  • Familiarity with control volume analysis
  • Basic concepts of irreversible deformation in gases
NEXT STEPS
  • Research the principles of pressure continuity in fluid mechanics
  • Study the effects of irreversible deformation on gas pressure
  • Learn about control volume analysis techniques
  • Examine case studies involving flow work calculations in closed systems
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Engineers, physicists, and students studying fluid mechanics or thermodynamics, particularly those interested in flow work and pressure dynamics in closed systems.

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Why is the pressure used in flow work the pressure of the fluid? If the fluid was say at 10kPa and the external pressure was at 0Pa, why don't we use the 0Pa in our calculations for flow work, since it's the external pressure that's the resistance? Or is it not possible to have this difference at all in fluid and external pressure?
 
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The two pressures have to match at the boundary of the control volume. Pressure is continuous.

In a closed system, the external pressure always matches the gas pressure at the piston face. It is just that, for an irreversible deformation, the pressure in the cylinder is not uniform and the average pressure in the cylinder is not equal to the pressure at the piston face.
 

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