Re: Bernoulli Principle, 2nd try

[Tucker Hiatt <thiatt@USFCA.EDU>]

Both Cliff Parker and John Barrer (and others) offered helpful
insights into the molecular/kinetic explanation of Bernoulli's
Principle (BP).  However, I don't think we yet have a proper view of
what's going on.

In describing a drop in fluid pressure with fluid speed, a "molecular
explanation" of BP must attribute that drop in pressure  either to
(1) a reduced mean molecular impact velocity (normal to the vessel
walls) or (2) a reduced frequency of those molecular impacts.  Is
there any other way to account for a drop in fluid pressure?

Of course, the standard energy arguments make sense, but they don't
appeal to a student's (or this teacher's!) "nuts & bolts"
understanding of the phenomenon.  Good students want to know this:
"Why do molecules push less forcefully on a wall when they flow
parallel to that wall?"  That seems to me to be a reasonable question.

And the answer seems clear *if* the fluid molecules acquire their
"parallel velocity" at the expense of their velocity perpendicular to
the walls.  But that is not what happens in most "Bernoulli
situations," is it?  For example, when the air from Cliff's shop vac
flows over the top of his suspended golf ball, that air gets its
parallel velocity from the shop vac.  There's no (obvious)
redirection of molecular velocity from "perpendicular to the golf
ball surface" to "parallel to the golf ball surface."  There's just
an addition to the parallel velocity.

In fact, doesn't this analysis point to a key problem with the
"energy conservation" explanation of BP?  In many cases where we have
to invoke BP to explain fluid pressure differences, the energy of
that fluid is not strictly conserved because the fluid does not
constitute a closed system.  In the case of the air flow over a golf
ball, the extra KE of the moving air does not come at the expense of
the internal energy density of the air; it comes from the shop vac
motor.

Finally, to throw gasoline on the fire, let me pose a gedanken
experiment that seems to identify another (related?) problem with the
BP as conventionally, conceptually understood.

Suppose a very long train moves through a very long, straight tunnel.
We conventionally invoke the BP to explain why smoke from a cigar in
the train's "smoking car" flows out the window into the air of the
tunnel.  We say the air pressure is lower outside the train because,
relative to the train, the tunnel's air is flowing past.  But what
about the smoke from a cigar at rest within the tunnel?  Shouldn't
that smoke flow into the window of the passing train?  After all, the
air pressure is lower inside the train because, relative to the
tunnel, the train's air is flowing past!

What this (no doubt flawed) thought experiment suggests is that the
BP violates the relativity principle.  Can Mr. Bernoulli define
"moving fluid" without invoking an absolute frame of reference?

Thanks for your attention to this vexing matter!

- Tucker


At 7:00 AM -0500 6/30/03, cliff parker wrote:
> I have not kept up with this thread previously so I don't know if my ideas
> have been discussed but I'll tell you a bit about the discussions that
> happen in my high school class.
>
> CONSERVATION OF ENERGY!  The particles are generally moving randomly in any
> fluid.  The kinetic energy of the particles is distributed evenly in all
> directions.  Therefore the pressure on any surface (wing, golf ball, etc.)
> will be the same on top as on bottom since particles are just as likely to
> crash into the top as the bottom.  If conditions arise which cause more
> particle to move in one particular direction than another there will be less
> kinetic energy available for the particles moving in other directions, in
> particular down onto the wing or one side or the other of the golf ball.
>
> When we discuss Bernoulli I always demonstrate by blowing air across the top
> of a golf ball with a shop vac.  The ball hovers without any obvious means
> of support.  Very cool demo.  One of my student last year described what was
> happening molecularly using similar ideas to the ones which I tried to
> describe above but stated more simply.  The air stream is blowing the air
> particles from around the top of the ball away so that they can not bump
> into the ball the way they would have before the shop was turned on.  The
> air particles below the ball are unaffected by the shop vac's air stream and
> therefore bump into the bottom of the ball just as they normally would.  I
> hope this helps.

At 6:55 AM -0700 6/30/03, John Barrer wrote:
> Here's a stab, but maybe not at molecular level.
> Pressure is energy per unit volume. If you think of
> the masses and springs model for substances (S,L, or G
> states), then increased static pressure results in the
> storage of energy in the "springs" (which for liquids
> have VERY high, but not infinite, values of k). Now
> imagine that compressed fluid moving in a pipe with no
> external force doing any work on it. When a
> constriction is encountered, the local velocity must
> rise b/c of cons of matter. Cons of energy then
> requires that the local static pressure (again, energy
> per unit volume) must fall, meaning that the springs
> relax a bit.
>
> Not exactly molecular, but reasonable based on two
> fundamental cons principles. Any help? John Barrere