Given a water column in a top closed, bottom open tube is the same
regardless of the diameter. That column is 408.33 inches at 14.7
atmospheric. If I invert say a 24 inch pipe 408.33 inches long full of
water the weight of the water will equal the air pressure pushing up
(6650 lbs). Question: Why then does water run out? Is it because the
vacuum created fills with water vapor thus equalizing system?

Hello 

You are correct in describing the pressure within the inverted tube at
atmospheric pressure - and in the absence of any perturbations within
the water, it would stay in the tube no matter the diameter (Note: a
tube of exactly 408.33" would have no vacuum when inverted). However,
small fluctuations in the distribution of water allow mixing of the
water and the air at the surface, this allows air to ascend past water
in the column which allows the water beneath the air to escape (ie
pour out the bottom).

There is a force which can counter this effect on a small scale -
surface tension.  Surface tension relates to the tendency of similar
molecules  in a liquid to stick together at the surface.  Surface
tension does not operate on large scales: the farther the molecules
are away from each other, the lower the attractive force between them.
Surface tension is the principle effect governing the size of
raindrops-to put the range in perspective.

So, if you could increase the surface tension of the water at the base
of the column, you could prevent the water from escaping. The simplest
way to achieve this in to use a smaller diameter pipe - or, if a
larger diameter pipe is used, the openings can be made plentiful and
small, which results in a smaller effective diameter at each of the
openings.  A demonstration of this can be found on the following page
(cheesecloth is used):
http://www.ac.wwu.edu/~vawter/PhysicsNet/QTMovies/PressureFluids/AirPressureOnColumofH2O.html

And a much longer explanation: 
http://www.branta.connectfree.co.uk/surface_tension.html

Two nice general descriptions of the physics behind this: 
http://ist-socrates.berkeley.edu/~chem1a/labmanual/expt6.htm
http://mars.jpl.nasa.gov/education/modules/water_activity4.pdf

Google search terms: inverted tube surface tension

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Request for Answer Clarification by 3rrotec-ga on 07 May 2003 05:17 PDT

Thanks for the answer! I'm having trouble reaching the 2nd url
(branta). Maybe typo? 3rrotec

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Clarification of Answer by synarchy-ga on 07 May 2003 06:38 PDT

Sorry about that - the 2nd link wound up with an 'l' at the end where
there should be none - the link again:
http://www.branta.connectfree.co.uk/surface_tension.htm

Thanks synarchy-ga! Good thorough answer and good links!

If it's a homework question, refer to a water phase diagram. 
http://www.sbu.ac.uk/water/phase.html  Also, it would depend on the
ambient temperature and pressure.  Perhaps the calculation was based
on incorrect assumptions of conditions.

If it's a practical problem, note that it no longer is an equilibrium
system.  If water can leave the column, it is likely air will push
into the column; especially one 2 feet wide.  Those air bubbles will
displace more water allowing more water to leave and pretty soon you
will have an empty pipe.

Hopefully a Researcher can provide you with a more complete answer.

Further illustration:

A full cup of water has a column height less than that which can be
supported by atmospheric pressure.  Place covered cup above your head.
 Look up.  Invert cup. Remove cover. Observe action of water.

Do the same with a straw.  Observe action of water.  Take finger off
top of straw.  Now what happens?

The cup is wide enough to allow air up the column.  The straw isn't. 
If you packed your 24 inch column with straws (even if just at the
bottom end), the result may be different.

You should have a look at Rayleigh-Taylor instability. They have
formalized the behavior of heavy fluid which sits on top of a lighter
fluid. The equilibrium state is not stable, and the light fluid pops
into the heavier one. The same goes for water on top of air.

for an overview have a look at:
http://cfa-www.harvard.edu/~dsmith/rayleigh-taylor.pdf