Re: [Phys-l] question about Bernoulli

[William Robertson <wrobert9@ix.netcom.com>]

Maybe people misunderstand what I'm looking for. The conversation  
below gets halfway there. My comments interspersed.

Bill



On Nov 23, 2010, at 9:22 AM, John Denker wrote:

> On 11/23/2010 08:27 AM, LaMontagne, Bob wrote:
>
> > the component of velocity of the molecules perpendicular to the
> > pipe walls - was it reduced?
>
> Yes.

This is a major step. Certainly if the component of velocity of the  
molecules perpendicular to the pipe walls is reduced, that would  
explain a lower pressure. Any lay person paying attention could  
understand that. It makes sense because if all we concentrate on in  
the Bernoulli equation is pressure and velocity, we must assume that  
height and density are constant.
> > and by what mechanism was it reduced?
>
> Particle/particle collisions.

Particle-particle collisions cause this. Great. Is it possible to look  
at what happens to molecules, as an aggregate, as they enter a  
constriction? Is there some mechanism, non-mathematical, that explains  
why the component of velocity of these molecules perpendicular to the  
walls is reduced? It's not a question about individual molecules, but  
a question about what happens to all of them, in a statistical sense.  
We can look at individual collisions among molecules and between  
molecules and a constricting container, subject to a pressure  
difference, that might result in the molecules as a whole in the  
narrow part of the container having a reduced velocity component  
perpendicular to the walls.

I understand the energy arguments. I understand that pressure  
gradients must result in differences in velocity. I understand that  
there must be a pressure difference for the acceleration of the  
molecules, which absolutely means the pressure is lower in one part of  
the flow. Just hoping for a picture of what's happening to these  
molecules, individually and/or collectively, that results in a lesser  
perpendicular velocity component in the are of flow where they're  
moving faster. And here I'm assuming that a lower perpendicular  
velocity component is the answer. In my original post, I stated  
various explanations for Bernoulli, two at least that included a  
change in density (in one case locally and in one case globally). I  
would love to be able to rule out the density argument, at least, but  
that's why I'm asking everyone here to look at it.


> 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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