Help with compressible flow problems

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SUMMARY

The discussion focuses on calculating the pressure increment required to isentropically compress air and water at 1 atm and 20°C to 50% of their volume. The isentropic bulk modulus for water is specified as 2.24 x 109 N/m2, while air is treated as an ideal gas with a specific heat ratio (γ) of 1.4. The user attempts to apply the equation P2/P1 = (V1/V2)γ and calculates P2 as 383.9 Pa. The user expresses confusion regarding the derivation of the equation and seeks additional resources for practice.

PREREQUISITES
  • Understanding of isentropic processes in thermodynamics
  • Familiarity with the ideal gas law and specific heat ratios
  • Knowledge of bulk modulus and its application in fluid mechanics
  • Basic algebra and manipulation of equations
NEXT STEPS
  • Study the derivation of the isentropic process equations in thermodynamics
  • Learn about the application of the bulk modulus in compressible flow problems
  • Practice problems involving ideal gas behavior and specific heat ratios
  • Explore resources on fluid mechanics and compressible flow analysis
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Students studying thermodynamics, engineers working with fluid mechanics, and anyone seeking to understand compressible flow problems in practical applications.

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Homework Statement



Calculate the pressure increment required to isentropically compress air and water at 1 atm and 20°C to 50% of their volume. The isentropic bulk modulus for water at 20°C is 2.24 109 N/m2, and air can be considered an ideal gas with γ =1.4 .

Homework Equations



\frac{P2}{P1}=\frac{V1}{V2}γ=\frac{T2}{T1}\frac{γ}{γ-1}

The Attempt at a Solution


\frac{P2}{1013.25Pa}=(0.5)1.4=383.9 Pa

I am reading ahead on the lecture notes which literally just show me how to derive the equation i provided so I have no clue at all what I'm doing would appreciate any pointers/ resources to get more practice on these types of questions :)
 
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