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Bernoulli Principle



I believe there was some discussion about this question a year or two
ago, but I don't remember the details, so I will ask again --

The Bernoulli Principle (or rather equation) is obtained from
conservation of energy applied to the fluid. Epstein also makes a
plausible argument (in his Thinking Physics book) as to why the
faster moving fluid has a lower pressure than the slower moving fluid
from Newton's 2nd law -- imagine being in a tiny submarine moving
along with the slow moving fluid; as you move into the region where
the fluid is moving faster, you are accelerated in that direction and
therefore there must be a net force on the sub in that direction.
From this one can argue that there is a pressure difference (or
gradient) between the two regions and the pressure in the faster
moving fluid must be less than the slower fluid.

My question is this -- 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