It seems to me the description given by Cliff Parker's student has some
merit.
The traditional Bernoulli derivation of conservation of energy in a
flowing fluid as it passes through wider or narrower tubing always
seemed okay to me, but I wanted something more to help me understand
aspirators or other types of applications in which an additional fluid
is involved in addition to the fluid flowing in the primary stream. 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,
and it was not clear what would happen to the Bernoulli equations as air
entered the fast-moving water stream. That is, how does Bernoulli treat
the additional material sucked into the stream? I also wondered how to
calculate the design of an aspirator from Bernoulli equations.
Furthermore, I got confused when I dismantled commercial aspirators and
found the suction port does not enter the water stream at the narrowest
part. Rather, the pumping port is placed after the water stream begins
to widen back out. Does this make sense from a pure Bernoulli
viewpoint? I would think Bernoulli alone would have us place the
pumping port at the narrowest portion where we would calculute the water
pressure is the lowest. As a college student I struggled with this and
never got a satisfactory answer.
These things became more clear in graduate school when I began to do a
lot of vacuum work with various kinds of vacuum pumps, most notably
"ejector" pumps, but also diffusion, and turbomolecular pumps. The
ejector pump is essentially an aspirator working at lower pressure than
your typical chem-lab water aspirator, and using an oil-vapor stream as
the pumping fluid. In the book "Vacuum Technology" by Andrew Guthrie,
he says "ejector pumps... depend for their pumping action on entrainment
of gas by viscous drag and by diffusion of gas into the vapor at the
boundary of a dense vapor stream." Speaking of the standard chem-lab
aspirator Guthrie says, "The water jet pump (or aspirator) is a form of
ejector pump... A stream of water flows through the jet tube and into a
suitable choke tube. [The jet tube is the narrow part. The choke tube
is the wider tube the jet squirts into.] At the entrance to [the choke
tube] the jet from the nozzle drags along the surrounding air. As it
enters the mouth of the choke tube, air forms a sheath around the jet.
As the jet diverges, the air sheath grows thinner, becomes entangled in
the jet, and is carried out with the water."
[Guthrie is describing a diagram. The portions in square brackets are
my words to explain what Guthrie is talking about.]
Notice that Guthrie (a physicist) does not mention Bernoulli at all in
the description of these pumps. I find his description of an aspirator
much more satisfactory than saying "it works by the Bernoulli
principle." Indeed, in my mind I don't think aspirators work by the
Bernoulli principle at all, even though it's usually taught that way.
Ejector, diffusion, and turbomolecular pumps all work by imparting a
momentum (to the molecules we want to pump) in the direction we want the
molecules to go.
When Clifford Parker described his student's response as "The air stream
is blowing the air particles from around the top of the ball away..."
this sounded to me like a description of the ejector process.
I think Bernoulli is fine for describing incompressible fluids flowing
in pipes. Textbooks warn that Bernoulli's equation is useful for
qualitative descriptions, but Bernoulli can be grossly inaccurate
compared to actual experiments. I think this is because we extend
Bernoulli way past the boundaries for which it is valid. To be valid we
need incompressible fluid, we need zero viscosity, and we need
steady-state streamlined flow. In something like an aspirator (or in
other demonstrations involving things like air) we do not have an
incompressible fluid, we do have viscosity, we do have turbulence.
Take, for example, the case of blowing a stream of air through two
pieces of paper originally separated by a couple centimeters, and
watching the two sheets come closer together. This is usually described
as a Bernoulli effect. I find it easier to describe it as an ejector
pump. The stream of air collides with, imparts momentum to, entrains,
drags along by viscous forces, the air between the sheets. This ejector
pumping action continues as long as the stream flows. This lowers the
pressure between the sheets and the ambient pressure outside the sheets
pushes the sheets inward until the pressure of the inside stream and the
various other forces on and within the paper matches the ambient air
pressure. I don't see any need to bring Bernoulli into the discussion.
Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton College
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu