Air Bladder Water Pump
Another simple device based on the premise that no two objects can occupy the same space. As you can see from the illustration the parts consist of a pvc pipe any length any diameter. A rubber bladder that when inflated exceeds the inner diameter of the pvc piping. This is more than you will need, but this gives a good margin to play with. A top cap that will hold bladder in place and holds the T bar air supply.
A simple valve in bottom of pvc piping, this need not be anything special.
A simple one could be a light piece of rubber cut in a circular shape and placed over an end cap with a reasonable size hole drilled in it.It could also be connected to bottom of badder and bottom of the end cap tubing, with a hinge so that it could be operated when the bladder expands and contracts.
A water outlet on the side of the PVC tubing and a reliable air pressure source. An air pipe of tubing made in a T shape this will be the means the air is supplied to rubber bladder.
The pipe section of tubing entering bladder would need to be of a smaller diameter that the rest . At the opposite end to air inlet a means would be needed to open and close air pressure supply.
This could be a simple rotary valve or electrical device operating by the unit itself. A much simpler solution could just be an air tap operated by hand when water is needed.
Experimental Version
A experimental version could be made by using a smaller diameter Pvc tubing a t piece inserted in middle to make an outlet and a bicycle tube. A bottom valve made as described previously.
Place the complete bicycle tube bent in half in the pvc piping so that air valve is at the top. Place the pipe pump in a water source and then using a bicycle hand pump inflate tube. You will need to find a way to deflate the tube. This will not need to be a problem if you use a continuous source of air and the t bar air inlet as previously described. If you are using a continuous source of air pressure such as an air compressor remove the rubber in valve stem of inner tube so that air can flow in both directions without hinderance.
Theory of Operation
Air at beginning is directed into rubber bladder by turning the air outlet tap to off position. The increasing pressure of bladder causes the bottom valve to be forced shut. The bladder continues to inflate and water is forced up the pipe until it exits out the outlet. When all water is expired. The air outlet tap is opened so that air escapes and pressure in bladder is decreased and the Bernouli effect takes place to cause the badder to be compress. This causes the bottom valve to be opened allowing more water to enter tube. The compressing of the bladder may also assist in drawing water into the piping if the water outlet is not too large or has a non return valve in it [ although it is not necessary to this design.]
I believe this device should work to any depth if air pressure can be maintained greater than water pressure depth.