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Re: Bernoulli Principle



At 03:57 PM 6/25/2003 -0400, Wolfgang, you wrote:
/snip/The Bernoulli Principle (or rather equation) is obtained from
conservation of energy applied to the fluid.
/snip/
-- can one make an argument about what the
pressure difference ought to be from a molecular motion point of
view? And I'm not talking about a detailed kinetic theory of gases
derivation but rather a plausible argument that could be used in an
introductory physics course.

Looking forward to your thoughts -- Wolfgang


I accept the justice of John Denker's warning about plausibility
arguments in aerodynamics soon miring one in fallacy.

And here is a living example :-)
Suppose there is a sphere filled with air at 1 atm out of which a
small tube opens on an evacuated space. A molecule has a small chance
of heading into the tube, where, lacking collisions, it will proceed
at its natural velocity. Depending on its entry angle, it may impact
the walls of the tube, where a reflection exchanges momentum
to provide some wall pressure, which decreases with distance into the tube
due to the goemetry of the structure.
Consider another fine tube connected to a second closed sphere.
If the sphere is initially evacuated, on would expect a low pressure flow
to generate an increasing pressure at the sphere.

If one connects two spheres with a narrow passage, the pressurized sphere can
transmit mass to the other sphere, suggesting a plausible (?)
high/ low/ high pressure and low/high/low velocity profile.

The foregoing has the twin vices of
1) offering a gedanken where fools rush in.
2) The complexity of a particle velocity/collision model
is here grotesquely foreshortened.

But you asked, so this is my straw man.

Brian Whatcott Altus OK