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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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Forum for Physics Educators
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_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l