A hydrostatic model of the Wirtz pump

The Wirtz pump is not only an excellent example of alternative technology, using as it does the kinetic energy of a stream to raise a proportion of its water, but its mathematical modelling also poses several intriguing problems. We give some history of the Wirtz pump and describe its operation. Taking a novel dynamical systems approach, we then derive a discrete mathematical model in the form of a mapping that describes its hydrostatic behaviour. Our model enables us to explain several aspects of the behaviour of the pump as well as to design one that gives approximately maximal, and maximally constant, output pressure.