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Re: .Bernoulli and curve balls.



On Sat, 28 Sep 1996 13:13:13 -0800 (PST) John Mallinckrodt said:
I think I see what you are saying. The air on the left side is forced to
go faster than that on the right and it "looks like" Bernoulli.
However, to "Be" Bernoulli the energy to go faster has to come from within
the fluid. Here, I believe the energy comes from the ball. If you don't
reduce the random energy of the air molecules they still bang on the ball
just as hard and just as much as before so the pressure does not change. The
additional velocity component is simply superimposed on the random motions of t
he air molecules. Does barometric pressure drop when the wind blows? Will
a barometer give a lower reading if you turn on a fan? Somehow we have to
get rid of the idea that Bernoulli said faster moving fluids exert lower
pressure. He said this happens if the extra speed comes at the expense of the
random motions that produce the pressure. Otherwise all bets are off!

Without ANY desire whatsoever to get involved in the discussion of whether
or not Bernoulli's principle has anything valid to say in this context, I
believe this is where you go wrong. It may well be the case that the
airstream velocity relative to the surface of the ball is higher on the
right, but that would be irrelevant to the Bernoulli-based explanation.
What matters in such explanations is the increase or decrease of the flow
velocity of the air relative to its velocity as it approaches the ball,
i.e., in the frame in which the ball is motionless. (See the usual
Bernoulli-based explanation of lift from a wing, for example.)

In the frame of the ball, viscous coupling with the surface of the ball
impedes the air on the right more than it does on the left (and may even
increase the flow on the left if the ball is spinning fast enough.)
Therefore the "slow air" is on the right and the ball is pushed to the
left. Of course it is worth pointing out that viscosity is incompatible
with a Bernoulli based explanation. Hmm...

Just to further confuse matters ...

If we look at the process from the frame of the undisturbed air, the
velocity IS higher on the right and the ball seemingly should be pushed to
the left. (Of course by this same reasoning an airplane wing should
produce a downward "lift.")

It seems to me that I heard somewhere that velocities are frame-dependent;
isn't it just a little peculiar, then, to say "pressure is high where the
velocity is low" and vice versa? I guess this is just one more reason
why I generally prefer momentum transfer as an explanation for lift and
drag phenomena.

John
----------------------------------------------------------------
A. John Mallinckrodt email: mallinckrodt@csupomona.edu
Professor of Physics voice: 909-869-4054
Cal Poly Pomona fax: 909-869-5090
Pomona, CA 91768 office: Building 8, Room 223
web: http://www.sci.csupomona.edu/~mallinckrodt/