We're not going to do your homework for you, but here are some things to think about.
The pressure of the water at the open bottom of the pipe is the
same as the pressure of the water in the swimming pool at that depth.
The change in water pressure from one depth to another is just
rho*g*(change in depth), where rho is the density of water (1 gram per
cubic centimeter, or 1000 kg per cubic meter, using MKS units). The
gravitational acceleration g is 9.81 meters/second^2, and h is measured
in meters. This gives pressures in Pascals.
The water pressure at the top of the swimming pool is 1
atmosphere, due to the air pressing down on the top. You can find how
far up in the tube the water can go because at some height in the tube
the pressure will be zero. Above this height there will be a vacuum in
the tube. Water is held up by pressure, and not "sucked up" by vacuum
(the vacuum exerts no force on the water).
Now this situation won't last. At the interface between water and
the space in the tube with vacuum, the water will evaporate very
quickly (and may even boil!). Eventually, the portion of the tube with
a vacuum in it will be full of water vapor. The pressure will be the
"vapor pressure of water" at the temperature this is all at. The water
will then settle down to a height below that originally calculated. If
you let this settle down over a long period of time, you will have
built a thermometer.
Tom J.
(published on 10/22/2007)
