A Feynman sprinkler, also referred to as a Feynman inverse sprinkler or as a reverse sprinkler, is a sprinkler-like device which is submerged in a tank and made to suck in the surrounding fluid. The question of how such a device would turn was the subject of an intense and remarkably long-lived debate. A regular sprinkler has nozzles arranged at angles on a freely rotating wheel such that when water is pumped out of them, the resulting jets cause the wheel to rotate; both a Catherine wheel and the aeolipile work on the same principle. A "reverse" or "inverse" sprinkler would operate by aspirating the surrounding fluid instead. The problem is now commonly associated with theoretical physicistRichard Feynman, who mentions it in his bestsellingmemoirsSurely You're Joking, Mr. Feynman! The problem did not originate with Feynman, nor did he publish a solution to it.
History
The first documented treatment of the problem is in chapter III, section III of Ernst Mach's textbook The Science of Mechanics, first published in 1883. There, Mach reported that the device showed "no distinct rotation." In the early 1940s, the problem began to circulate among members of the physics department at Princeton University, generating a lively debate. Richard Feynman, at the time a young graduate student at Princeton, built a makeshift experiment within the facilities of the university's cyclotron laboratory. The experiment ended with the explosion of the glass carboy that he was using as part of his setup. In 1966, Feynman turned down an offer from the editor of Physics Teacher to discuss the problem in print and objected to it being called "Feynman's problem," pointing instead to the discussion of it in Mach's textbook. The sprinkler problem attracted a great deal of attention after the incident was mentioned in Surely You're Joking, Mr. Feynman!, a book of autobiographical reminiscences published in 1985. Feynman neither explained his understanding of the relevant physics, nor did he describe the results of the experiment. In an article written shortly after Feynman's death in 1988, John Wheeler, who had been his doctoral advisor at Princeton, revealed that the experiment at the cyclotron had shown “a little tremor as the pressure was first applied but as the flow continued there was no reaction.” The sprinkler incident is also discussed in James Gleick's biography of Feynman, Genius, published in 1992, where Gleick claims that a sprinkler will not turn at all if made to suck in fluid. In 2005, physicistEdward Creutz revealed in print that he had assisted Feynman in setting up his experiment and that, when pressure was applied to force water out of the carboy through the sprinkler head,
Solution
The behavior of the reverse sprinkler is qualitatively quite distinct from that of the ordinary sprinkler, and one does not behave like the other "played backwards." Most of the published theoretical treatments of this problem have concluded that the ideal reverse sprinkler will not experience any torque in its steady state. This may be understood in terms of conservation of angular momentum: in its steady state, the amount of angular momentum carried by the incoming fluid is constant, which implies that there is no torque on the sprinkler itself. There are two counterbalancing forces: the pressure differential pushing on the back of the nozzle, and the inflowing water impacting on the opposite side. Many experiments, going back to Mach, find no rotation of the reverse sprinkler. However, in setups with sufficiently low friction and high rate of inflow, the reverse sprinkler has been seen to turn weakly in the opposite sense to the conventional sprinkler, even in its steady state. Such behavior could be explained by the diffusion of momentum in a non-ideal flow. However, careful observations of the actual behavior of experimental setups show that this turning is associated with the formation of a vortex inside the body of the sprinkler. An analysis of the actual distribution of forces and pressure in a non-ideal reverse sprinkler provides the theoretical basis to explain this:
