how to design a scheme to lift water using piping system?

Answer 1

With only pipes, no motors or whatever, you are only going to be able to use a siphon system, which will only allow you to lift the water if the eventual destination of the water is BELOW the start point. A siphon won't lift water from the bottom of a well to the top, but in can lift water from one reservoir, over a wall, to a tank below or something like that.

Also, bear in mind that suction of any kind can only raise water about 33 feet. After that, the weight of the water in the pipe will be too much for the suction. That's why the pump for a well is located at the bottom of a well, so it pushes the water up rather than pulling the water out from the top. For this reason, a siphon can't work if it has to lift more than 33 feet.

There is another possibility - a pump based on a fluidyne Stirling engine. Here's a link or two, you should be able to find more:
http://www.fieldlines.com/story/2004/12/9/41413/0938
http://www.maxpie.de/Fluidyne.htm (in German, but has great pitures)

Answer 2

All you need to do is have the air pressure at the top of the piping system lower than the pressure at the bottom, e.g. vacuum at the top has minimum '0' to negative atmosheric pressure, while the bottom still has at least '1' atmosphere of pressure, thus, up comes the water...