Re: Bernoulli and viscosity

[John Mallinckrodt <ajm@CSUPOMONA.EDU>]

John Denker wrote:

> Check out The Feynman Lectures on Physics volume II section 40-3.
> For an unadorned bullet-hole in a tank Feynman says "we are not able
> to calculate" the efflux (even in the absence of significant
> viscosity). If anybody can show me a simple solution to this problem
> I'm going to be verrrrrrry impressed.
>
> Even in the absence of viscosity, it's tricky to get the energy
> balance _and_ the momentum balance right. The typical naive approach
> is to overlook one or the other -- resulting in a plausible but
> quite wrong answer.

Feynman's discussion is worth taking a look at, but IMO it's wrong to
suggest that the classic--and simple--Bernoulli-only analysis has no
merit.

That analysis predicts a range of 2[h*H]^1/2 where h is the depth of
the hole and H is its height above the surface on to which the stream
plays.  The demos I've seen reproduce this result reasonably well as
long as the hole is not too small.  In fact, I just took an orange
juice carton, punched a ragged hole about half a cm in diameter in
the side about half way along the ~18 cm length, and got a range of
~16 cm.  That seems close enough to me for a kitchen validation.

--
John Mallinckrodt        mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm