At 3:57 PM -0400 6/25/03, Wolfgang Rueckner wrote:
>>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.
On 06/30/2003 02:36 AM, Tucker Hiatt wrote:
> ... I am disappointed
> that the answer seems, so far, to be "No; no one (on PHYS-L) *can*
> explain Bernoulli's Principle from a molecular point of view."
I regret that some people are disappointed, but I
really don't think that the molecular point of view
is the right way to approach Bernoulli's principle.
Particles do not have pressure. Pressure is a
property of the fluid, not of the particles that
make up the fluid. It is an emergent property.
Similarly the fluid velocity that appears in
Bernoulli's principle is a property of the fluid,
not of the individual particles (although it is
of course distantly related thereto).
Since Bernoulli's principle speaks of pressure,
and particles don't have pressure, asking for
Bernoulli's principle in terms of particles is
virtually guaranteed to lead to disappointment.
For a general discussion of emergent properties,
see Hofstadter _Gödel, Escher, Bach_.
Trying to explain emergent properties in ultra-
reductionist terms is a losing strategy. Can
one atom feel pain? Can two atoms feel pain?
Conclude by pseudo-induction that no finite
number of atoms can feel pain. Thence conclude
that people cannot feel pain.
===============================
On 06/30/2003 08:00 AM, cliff parker wrote:
>
> CONSERVATION OF ENERGY!
I love using conservation of energy, but alas it is
not a good answer to the question at hand.
1) Bernoulli's principle is equivalent to conservation
of mechanical energy (to first order) in the special
case where the fluid density is nearly constant -- but
the notion of constant fluid density is inconsistent
with the particle viewpoint.
> The particles are generally moving randomly
> in any fluid.
That depends on what you mean by "generally" and
"randomly". There is of course lots of randomness,
but since we are talking about a flowing fluid, there
is some very important non-randomness also.
> The kinetic energy of the particles is distributed
> evenly in all directions.
That's not true. For a flowing fluid, there will
be more KE associated with the X-motion than with
the Y-motion or Z-motion. This is crucial.
> 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.
Again, not true. In normal flight, the pressure on
the top of the wing is not the same as the pressure
on the bottom of the wing. Crucially not the same.
> 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.
Moving in "one particular direction" is neither necessary
nor sufficient for there to be a difference in kinetic
energy.
> 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.
It may be cool, but it demonstrates neither Bernoulli's
principle nor conservation of energy. The energy-density
of the jet from the shop-vac is radically different from
the energy-density of the ambient air.
This is most likely a demonstration of the Coanda effect,
i.e. curvature-enhanced turbulent mixing, which has
essentially nothing to do with how wings work.
> 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.
That's not the correct physics.
Saying we are "blowing the air particles from around the
top" is tantamount to saying we have lower density on
top. That's just not true.
===============================
It's bad luck to prove things that aren't true.
Before you go proving your own version of Bernoulli's
principle, consider the case of acoustical resonance
in a pipe that is open at both ends. At the center
there will be zero velocity (by symmetry) but there
will be pressure excursions.
======================================
On 06/30/2003 01:01 PM, Edmiston, Mike wrote:
>
> For example, in a water-driven air aspirator, it always seemed okay
> to me that the water pressure in the narrow region could be lower
> than the pressure in the wider region before the restriction, but it
> was not clear the water pressure would be be lower than astmospheric
> pressure
That's because you're smart. From the given
description there is no grounds for concluding
that the pressure in the throat will be lower
than ambient.
To make a sound argument, you need to work
backwards from the outlet side of the aspirator.
If (and only if) you tell me that the outlet
discharges to ambient, then we can work back
and conclude that the pressure in the throat
is less than ambient. (Guess what happens if
you put your thumb over the outlet or otherwise
pressurize the outlet!)
> the pumping port is placed after the water stream begins
> to widen back out.
Viscosity may be part of the explanation for this.
Also they may be trying to cultivate some Coanda
effect.