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Re: [Phys-l] question about Bernoulli



On Nov 23, 2010, at 3:17 PM, John Denker wrote:

On 11/23/2010 02:52 PM, John Mallinckrodt wrote:

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."

Any anisotropy? Even if the velocity distribution is isotropic,
the acceleration is likely to be anisotropic. The laws of physics
include acceleration terms.

I don't understand your point here.

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)

Direct result? You can't have one without the other, so there
is no logical basis for deciding which is the "cause" and which
is the "result". Maybe you can decide on metaphysical grounds,
in which case I'm not interested.
http://www.av8n.com/physics/causation.htm

Fine. My point isn't really about "causation." I'm perfectly happy to say "The pressure reduction in high velocity areas is directly related to the density reductions and the associated temperature reduction. The density reduction accounts for the bulk of the pressure 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.

Again, assigning "responsibility" for a "result" has no basis
in physics. The velocity increase and the pressure decrease
and the density decrease go hand-in-hand and that's all the
laws of physics say about it ... and that's all that needs to
be said about it.

Again, fine. My point is primarily that I don't believe that the pressure reduction for "incompressible" fluids can be understood very well in terms of a kinetic theory model that bases the pressure on the collision rate and the momenta of the particles. When you squeeze a liquid, you are very slightly decreasing the average distance between molecules that *really* don't want to get closer together.

John Mallinckrodt
Cal Poly Pomona