This is a very good question. The first thing that you would think
about in this problem is that the pressure of the air around us is
"pushing" on the top of the water and forcing it to come out, this
however, is not correct. When you consider the air pressure, you must
consider it everywhere. So although the air is pushing on the water
from the top, it is also pushing equally on the water that is coming
out of the hole, and the air pressure cancels. What is causing the
water to fall out is gravity. There are two ways to consider this. 1.)
In terms of potential energy and, 2.) In terms of internal pressure of
the water (which is what i think you are wondering about).
1.) All systems want to go to the lowest energy state. In a
cylinder filled with water the center of mass of the water is exactly
in the middle of how much water there is. The center of mass want to
drop as low as it can, much like how a ball will drop if you just let
go of it. The distance the center of mass of the water is raised above
the hole in the container is the "potential energy" of the water. as
the center of mass drops the "potential energy" get changes into
"kinetic energy" of the water leaking out of the side. This is called
Torcelli's law. mathematically is looks like:
g*h = (1/2)V^2 ,
g = 9.81 meters/(sec)^2
h = height of center of mass above exit hole
V = velocity of the exiting water in meters/sec
solving this equation:
V = (2*g*h)^.5
2.) The second way of thinking about is to think of the water in
the cylinder (or whatever shape it is) as bunch of VERY thin "slices"
of water (like a stack of pringles chips except flat). Each slice is
being pulled on by the force of gravity. This force is spread over the
area of the slice which gives a pressure. If we start at the top, the
first slice has the air pressure acting on it. The second slice has the
air and the first slice putting pressure on it. The third has air, the
first and second. And so on. Notice how as you go deeper, each
layer has more layers above to support, so it much have a higher
pressure. The pressure P at a given depth is given by this formula:
P = Po + R*g*d
P = pressure you are measuring
Po = air pressure. (=101325 Pascal =101325 kg/meter/sec^2)
R = density of fluid. (=1000 kilograms/meter^3 for water)
d = the depth from the surface of the water in meters.
(published on 10/22/2007)
