On 06/30/2003 07:30 PM, Chuck Britton wrote:
> I have wondered how a zero-viscosity liquid would behave as it
> traveled through tubes of differing sizes.
...
> Viscosity seems to be a requirement for these pumping schemes
It is not a requirement. You can build an aspirator
that works fine, independent of viscosity.
> and is verboten with a Bernoulli explanation.
It is not verboten. Just irrelevant. In the
limit of smallish viscosity, it is a small
correction, so there are pedagogical reasons
for not bothering with it.
> He4 could be cooled enough to make virtually all of it be at zero
> viscosity. Would the faster flow in the narrow channel still be able
> to 'entrain' the liquid in the middle side-tube - indicating a lower
> pressure in the narrow tube? If 'entrainment' requires viscosity AND
> if this He4 experiment DID show lower pressure with the higher
> velocity, how would we describe it in terms of molecular kinetics.
>
> Well, Feynmann tells us that there ARE no discrete atoms of helium in
> this situation - 'just' a macroscopic wavefunction.
True, the superfluid is just one big wavefunction,
not discrete atoms -- but the spirit of the question
is still good: just re-ask the question in terms of
a classical fluid under conditions of huge Reynolds
number (i.e. negligible viscosity relative to other
relevant things).
The negligible-viscosity aspirator would pump fluid
just fine. Whether it would "entrain" the second
fluid is a separate question. It might or might not,
depending on details. Your typical perfume atomizer
is not just a pump; it is also expected to actually
atomize the perfume, which involves lots of mixing
and typically exploits the Coanda effect. That in
turn involves turbulence which is affected by
viscosity. Actually the less viscosity the better,
as long as it is not strictly zero.
> I wonder if any
> measurements like this have been done???]
They have.
A good starting point is Putterman _Superfluid Hydrodynamics_.
Or google.
For that matter, airplanes operate with very high
Reynolds number (millions) so this regime is quite
well understood.