Re: Bernoulli Principle, 2nd try

[Gary Turner <turner@MORNINGSIDE.EDU>]

Just some ramblings from a fool with time on his hands having just
finished grading finals!   Yeah!  Take it for what it's worth, I'm not
really thinking well right now.

The example of a train in a long tunnel is not a good example of the BP.
This really is a bulk motion - to someone standing next to the train, they
would feel a high pressure surge as the train approached, then a low
pressure as the train passes.  There really is a low density in the wake
of the train, but it gradually returns to normal.  A more visible example
of this is to watch the water level near the bow of a large boat, it rises
in front of the boat then falls below the normal water level nextto the
boat before gradually coming back up.

That said, the experiment would be valid outside the tunnel.  A similar
experiment would involve two opposing fluid flows without the train wall
separating them.  With viscosity, fluid would be "ripped" out of both
fluid streams, creating a boundary layer of eddy currents.  To an observer
in either fluid, they would observe fluid being ripped out of their
stream, just as the smoke gets pulled out of the window.  That fluid will
mix and much of it be returned to the original fluid stream further back -
the passengers in the car behind will pick up the smoke from the car in
front, just very much diluted.

So maybe that effect is viscous, but that doesn't help to explain the
Bernolli Principle, which relies on non-viscous fluids.

[Aside - I've not tried the golf-ball demo, does it work on a horizontal
flow, or does the flow have to be inclined at some angle?]

As has already been discussed, the aspirator and sheet of paper tricks can
also be attributed to viscous effects.  If you didn't hold on to those
sheets of paper, they would blow away with the fluid stream!  Aerofoils
rely on a ram pressure, not on Bernoulli, so where does Bernoulli play a
part?

There may also be a problem with the assumptions when considered at a
molecular level.  If you have purely laminar flow, there is no room for
perpendicular velocity components in the flow field.  If you have non-
viscous flow, there are no boundary layers otside the main flow field to
house those perpendicular components, so where do the wall-fluid
collisions come from in the first place?  If they aren't there, what is to
stop a fluid in an adjacent static reservoir from being bumped into the
laminar flow by the non-laminar motion behind it?

Does this bumping demonstrate a pressure difference?  Well not really,
because now we are at the molecular level, where macroscopic variables
such as pressure and temperature are poorly defined.  Pressure is really
only well-defined in a macroscopic context; trying to find a real
molecular description for what is really a theoretical macroscopic
phenomenon may not be possible.

Has anyone verified BP using a laminar flow of superfluid?





On Wed, 2 Jul 2003 15:14:09 +0300, pvalev <pvalev@BAS.BG> wrote:

> --- Tucker Hiatt <thiatt@USFCA.EDU> wrote:
>
> > 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!
>
>
> I think the answer to this conundrum may be the solution to
> Bernoulli's problem as well. By friction, the lateral walls
> of the train push air molecules in the direction of
> movement and so leave an area depleted of air molecules,
> with lower air pressure, behind them.
> Something similar must happen when there is a flow parallel to
> the submarine wall.
>
> Pentcho