Re: [Phys-l] question about Bernoulli

[John Mallinckrodt <ajm@csupomona.edu>]

I would again suggest (as I did a few days ago in more detail) that, for situations observing a generalized Bernoulli's law (which applies to steady, nonviscous, *compressible*, streamline fluid flow and encompasses so-called "incompressible" flow):

1. In the frame of the fluid, the molecular velocity distribution is isotropic.  Any anisotropy is a simple and direct result of working (as one must) in *the* frame (for non"boring" cases†) in which the flow is "steady."

2. The pressure reduction in high velocity areas is mostly a direct result of lower density (less "squeezing") and only partially a result of smaller average velocities (due to the temperature reduction that accompanies the barotropic density reduction)

3. The role of velocity/temperature changes becomes negligible as one goes to the "incompressible" limit.  In that limit, the (close to negligible) density reduction is almost entirely responsible for the pressure reduction.

† For "boring" cases such as the one John Denker described, the question is moot since there are no velocity/pressure/density/temperature changes along a streamline.

I could be wrong about all of the above, but I believe I made at least a compelling case for it and I've seen nobody dispute--or even comment on, for that matter--my analysis.

John Mallinckrodt
Cal Poly Pomona

On Nov 23, 2010, at 10:15 AM, LaMontagne, Bob wrote:

> 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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