Relaxation time approximation and ideal hydrodynamics

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SUMMARY

The discussion focuses on the approximation of relaxation time and the application of ideal hydrodynamics in solving related homework problems. The participant utilized a linear deviation model, expressing the function as f = f_0 + C, to address the first question. For the second part, they applied the ideal gas equation to derive partial derivatives concerning time for density, velocity, and temperature but encountered difficulties in reaching a conclusive answer.

PREREQUISITES
  • Understanding of linear functions in mathematical modeling
  • Familiarity with the ideal gas equation
  • Knowledge of partial derivatives in calculus
  • Basic principles of hydrodynamics
NEXT STEPS
  • Study the derivation of partial derivatives in fluid dynamics
  • Explore advanced applications of the ideal gas law in hydrodynamics
  • Research linear approximation techniques in mathematical physics
  • Review case studies on relaxation time in fluid systems
USEFUL FOR

Students in physics or engineering disciplines, particularly those focusing on fluid dynamics and thermodynamics, will benefit from this discussion.

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Homework Statement



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Homework Equations



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The Attempt at a Solution



since the deviation from f_0 to f is linear
then we can write f=f_0 + C where C is some constant
this should be enough to prove the first question (i think so)
for the second part i used the ideal gas equation to drive the partial derivatives with respect to time for density, velocity and temperature
but i couldn't able to get the answer[/B]
 

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