Re: Bernoulli and viscosity

["John S. Denker" <jsd@MONMOUTH.COM>]

Robert Cohen wrote:

> The 2000-2001 Physics Olympiad preparation exam (mechanics) has a
> question in which water comes out of a bullet hole in a water tower.
>
> The solution...
>
> is a little overly complicated but essentially it calculates the
> difference in pressure

What means "overly" complicated?

Fluid dynamics is very complicated.

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.

I believe this problem is discussed in some detail
in Lamb, _Hydrodyamics_ but I can't cite chapter
and verse (my copy seems to have walked off).

The appearance of this problem on the test
probably reflects the ignorance of the test-makers
more than anything else.  No undergrad is going to
work it out from first principles in the time
alotted, so it is at best a check on whether
the student remembers reading about it.