Following the advice of Richard Feynman, I always try to conceptualize
physical phenomena using as many different models as I can. When it comes
to the Bernoulli principle, I have a problem with the average particle
motion model. Perhaps someone can correct my conceptual error.
My conceptual model is as follows: Imagine a straight pipe becoming
constricted along the positive x-direction. As the fluid moves in this
positive x-direction, the average particle velocity must increase slightly
in the positive x-direction by an amount equal to the velocity of the flow,
and since all collisions are elastic, there must be a corresponding
decrease in the other directions. Most of a given particle's velocity is
thermal, of course, and thus quite large compared to the flow velocity and
in a mostly random direction. The decrease in velocity in the y- and
z-directions means softer collisions with the pipe wall and thus lower
pressure. Hence the Bernoulli principle.
While all this seems quite logical, I fail to see the mechanism whereby the
pipe wall at the constriction enhances the average velocity in the positive
x-direction. In fact, the angle of the constriction would tend to
*decrease* the average velocity in the positive x-direction. For example,
imagine a particle with only a positive x-velocity approaching the
constriction very close to the pipe wall. It collides with the wall and
converts part of its energy into y- and/or z-velocity, thereby decreasing
the positive x-velocity. Particles with velocities normal to the pipe wall
before the constriction also decrease their positive x-velocity through
collisions with the wall at the constriction. Moreover, though the
collisions among the particles themselves serves to maintain the constant
density because collisions are more frequent when the density is larger,
those collisions cannot add momentum in the positive x-direction.
Clearly there is a flaw in my conceptualization. The question is: where?
Richard Blade
Richard Blade
13631 E. Marina Dr. #302
Aurora, CO 80014
303-283-9670
Permanent email: rblade@uccs.edu
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