A pressure vessel is fitted with an inlet pipe and an outlet pipe, both pipes being equipped with non-return valves. The outlet pipe takes its feed from the bottom of the pressure vessel. Inside the vessel is a reactor core fuelled with suitably enriched uranium.
When the vessel is empty the reactor core is unmoderated and subcritical. The vessel is filled with water through the inlet pipe and this permeates the reactor core and provides a moderator, allowing the core to go critical and a chain reaction to start. The heat from the reaction boils the water and the pressure of the steam expels the water through the outlet pipe. With no water in the core the chain reaction halts, heat ceases to be produced, and the steam inside the pressure vessel condenses. This creates a partial vacuum, drawing in more water, and the cycle repeats.
Being nuclear-powered the pump can run for a very long time on one charge of fuel, and with the only moving parts being the non-return valves, which can be made suitably robust, it should be essentially maintenance-free and can be used to power all sorts of things like perpetual fountains or what have you. Of course the fountain will gradually get so radioactive that you can't get within a hundred yards of the bloody thing but hey, if it's nuclear-powered you can make it big enough that you get the best view from a distance.
See also: Nuclear Dogshit Vaporiser - another application of the same principle.
