The Bernoulli principle from the perspective of statistical mechanics

In summary, the Bernoulli principle from the perspective of statistical mechanics states that the sum of the kinetic energy and potential energy per unit volume of a fluid remains constant in a fluid flow. It is related to statistical mechanics through the concept of energy conservation and can be applied in various real-life situations, but its limitations include idealized, steady flow conditions and neglecting factors such as turbulence and viscosity.
  • #1
mfduqued
9
0
Hi community,

I have a question about the Bernoulli principle. From statistical mechanics the pressure in the ideal gas is independent of velocity.

But in the case of the flow of an ideal gas in a channel, the pressure depends on the velocity.

Where can I clarify this misunderstanding?

Thanks for your time, and any suggestion
 
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  • #2
mfduqued said:
From statistical mechanics the pressure in the ideal gas is independent of velocity.
Under what circumstances does SM derive this statement of independency ?
 

1. What is the Bernoulli principle from the perspective of statistical mechanics?

The Bernoulli principle from the perspective of statistical mechanics states that in a fluid flow, the sum of the kinetic energy and potential energy per unit volume of the fluid remains constant, and any changes in one form of energy will result in an opposite change in the other form of energy.

2. How is the Bernoulli principle related to statistical mechanics?

The Bernoulli principle is related to statistical mechanics because it is based on the concept of energy conservation, which is a fundamental principle in statistical mechanics. The Bernoulli principle can be derived from the statistical mechanics equation for energy conservation.

3. What are the assumptions made in using the Bernoulli principle in statistical mechanics?

The assumptions made in using the Bernoulli principle in statistical mechanics include: the fluid is incompressible, the flow is steady, and there are no external forces acting on the fluid.

4. How is the Bernoulli principle applied in real-life situations?

The Bernoulli principle is applied in various real-life situations, such as in aviation (lift force on an airplane wing), in hydrodynamics (flow through pipes and channels), and in weather patterns (movement of air masses).

5. What are the limitations of the Bernoulli principle in statistical mechanics?

The Bernoulli principle in statistical mechanics is limited in its application to idealized, steady flow situations. It does not take into account factors such as turbulence, compressibility, and viscosity, which can significantly affect the fluid flow and potentially invalidate the assumptions made in using the principle.

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