Here is a surprisingly efficient and extremely simple pump for transporting clean drinking water from one place to another. The diagrams below show how to move water in the horizontal direction, but the pump may also be designed to move water from a low elevation to a high elevation. (It can pump water up a hill.)
The rotating arms of this pump are probably driven by electric motors. An inexpensive micro-computer keeps the arms synchronized so that each arm is always 120 degrees out of phase with its neighbors. (It should be easy to superimpose a clock synchronizing pulse onto the power lines that go alongside the hose to feed the electric motors. In this case, each microcomputer that controls each motor operates independently, and there’s no need for the micro-computers to communicate with one another.) Though I can’t prove it mathematically, I think the efficiency of this pump will be quite good. Generation of turbulence in the water should be about as low as it could be. And besides this, what other losses are present in the system? The heat that is generated by the motors will not be more than with any other kind of pump, and the friction with the hose is low because the hose is supported by pulley wheels.
Here’s a sequence of images that show the motion of the hose in detail. If the arms rotate with clockwise polarity, then water will be transported from right to left:
Variations on this idea may include a long belt that mechanically links the rotating arms together. (This is probably not a very good idea, but it might be a good choice if a completely mechanical wind pumping system is desired.) Also, PVC pipe may replace the hose. In this case a PVC segment is connected to its neighbors with a flexible joint (like or short piece of hose), or else the diameter of the end of its neighbor pipe is large enough for the end of the PVC segment in question to extend to a point inside of the end of the neighbor pipe.
The diagrams show the arms rotating in the plane of the hose or pipe, but they may rotate in the orthogonal plane instead. In this case they mimick the motion of the High Efficiency Helical Liquid Pump. But maybe the best way to move the hose is to use a crankshaft with a “piston rod” that has a fixed connection to the hose: