Relaxation time approximation and ideal hydrodynamics

In summary, relaxation time approximation is a theoretical approach used in hydrodynamics to simplify the equations of motion for a fluid. It is often used in ideal hydrodynamics and has limitations such as assuming quick local equilibrium and neglecting turbulence and non-Newtonian behavior. However, it is commonly used in practical applications, particularly in the study of fluid dynamics and the modeling of processes such as heat and mass transfer. It is most accurate for simple Newtonian fluids and not applicable to complex fluids with non-Newtonian behavior.
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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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unfortunetly there is nothing more
 

FAQ: Relaxation time approximation and ideal hydrodynamics

What is relaxation time approximation in hydrodynamics?

Relaxation time approximation is a theoretical approach used in hydrodynamics to simplify the equations of motion for a fluid. It assumes that the fluid reaches a state of local equilibrium after a short period of time, and that the dynamics of the fluid can be described using a single relaxation time parameter.

How does relaxation time approximation relate to ideal hydrodynamics?

Relaxation time approximation is often used in ideal hydrodynamics, which assumes that the fluid is inviscid and incompressible. This simplification allows for easier calculation of the fluid's behavior and is applicable in situations where the fluid's viscosity and compressibility are negligible.

What are the limitations of relaxation time approximation in hydrodynamics?

While relaxation time approximation is a useful tool in simplifying the equations of motion in hydrodynamics, it is not always accurate. It assumes that the fluid reaches a state of local equilibrium quickly, which may not always be the case in real-world scenarios. Additionally, it does not take into account the effects of turbulence or non-Newtonian behavior.

How is relaxation time approximation used in practical applications?

Relaxation time approximation is commonly used in the study of fluid dynamics, particularly in the modeling and simulation of fluids in engineering and environmental systems. It is also used in the development of models for processes such as heat transfer, mass transfer, and chemical reactions in fluids.

Can relaxation time approximation be applied to all types of fluids?

No, relaxation time approximation is most applicable to simple fluids with Newtonian behavior, such as water or air. It is not accurate for complex fluids such as polymers or suspensions, which exhibit non-Newtonian behavior. In these cases, more advanced models must be used to accurately describe the fluid's behavior.

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