Re: Bernoulli and viscosity

[Brian Whatcott <betwys@DIRECTVINTERNET.COM>]

At 08:03 AM 12/12/02, Wolfgang Rueckner, you wrote:
> Your suggestions below (except for the moon test) are actually
> standard demos we perform for classes.
>
> (1)  A tall bucket full of water has two openings at the bottom with
> standard plumbing elbows inserted into the openings so that the water
> squirts up.  One of the two elbows is "pinched off" so that the
> opening is very small.  The students are asked to predict which one
> squirts higher.  They predict the pinched off opening.  According to
> Torricelli's law (derived from Bernoulli's), the velocity of efflux
> should be the same and, indeed, they DO squirt to the same height.
> They should also squirt as high as the water level in the bucket, but
> not quite because of frictional losses.
>
> (2)  Punch a small hole in the side of a plastic cup near the bottom.
> Fill it with water and of course it squirts out.  Drop the cup from
> an appreciable height (so students have time to observe -- use a
> ladder) into a waste basket and show that the velocity of efflux is
> zero -- no water comes out of the hole.  g is zero in the reference
> frame of the falling cup.
>
> (3)  I later follow up on (1) above when discussing Poiseuille's law.
> The experimental result of (1) is quite counterintuitive to the
> students because they have experience in pinching off a hose and
> having the water squirt higher.  Thus another bucket full of water
> has two small "hoses" (small diameter rubber tubing) coming out of
> the bottom.  The hoses are of equal length and I.D.  Both squirt
> water to the same height when aimed upward.  But if the end of one is
> pinched to make the opening smaller, it squirts much higher (more
> than a factor of 10).
>
> Wolfgang

There is an attractive rationalization which can be applied to the water,
which squirts to a higher level than its head would suggest. It goes like this.

In supposing that a vertical water leak will (nearly) reach the water surface
level, we suppose that the air pressure at the surface, and at the exit are
equal.

If a venturi is arranged to accelerate the water in the jet, this can be
visualized
as reducing the pressure in that region. So we might expect not so much a
height multiplier, but rather a height increase controled by the water head,
but augmented by the extra head represented by the reduced pressure
at the venturi.
You will recall the delightfully simple (and messy) water venturi vacuum pump,
which can easily reach 20 inches Hg. That *could* represent an extra
13.6 X 20 inches of water height.  (22 feet)


Brian Whatcott
  Altus OK                      Eureka!