Re: [Phys-l] question about Bernoulli

["LaMontagne, Bob" <RLAMONT@providence.edu>]

If we choose an axis, say z, parallel to the two pipes of different diameter, then constant E definitely shows that an increased vz must be accompanied by a decreased vx and vy leading to lower pressure along the walls of the pipes. But to make this package complete, the question becomes why the collisions would favor an enhanced v2z in the smaller pipe? The molecules are not aware they have entered a region of smaller cross sectional area.

Bob at PC

> -----Original Message-----
> From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
> bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker
> Sent: Tuesday, November 23, 2010 11:22 AM
> To: Forum for Physics Educators
> Subject: Re: [Phys-l] question about Bernoulli
>
>
> > and by what mechanism was it reduced?
>
> Particle/particle collisions.
>
> Each collision can be visualized in terms of points on a sphere
> in six-dimensional phase space.  Ignoring the mass for simplicity,
> we have:
>   v1x^2 + v1y^2 + v1z^2 + v2x^2 + v2y^2 + v2z^2 = E = constant
>
> Each collision will cause the system to random-walk on the
> sphere.  If every collision were one-dimensional (i.e. zero
> impact parameter) we would not have a random walk, but since
> the impact parameters are random we do.  The energy will soon
> be distributed over all the accessible states.
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