Comment on the inverse sprinkler problem

Sprinkler head revisited: momentum, forces, and flows in Machian propulsion

“…Conservation of momentum provides the simplest and most reliable theoretical tool for understanding Machian propulsion. In the context of the reverse sprinkler problem, this argument was first made clearly in print in 1987, in a brief letter by Alton K. Schultz (a geophysicist) [13]. Schultz's argument is as follows: as water flows out of a regular sprinkler, it carries away with it an ever increasing quantity of angular momentum about the sprinkler's pivot.…”

“…The reverse sprinkler is not, of course, technologically useful, but as a teaching tool it might be valuable for demonstrating the use of global conservation laws in fluid mechanics and, perhaps, even the fallibility of great physicists (such as Mach and Feynman) when faced with what looks like an elementary question. 13 For a theoretical physicist, perhaps the most compelling way to explain Machian propulsion is as a variation on the global conservation of momentum argument made in [17] to derive "d'Alembert's paradox." 14 Confusion has perhaps also been sustained by the fact that, in much of the world, the university physics curriculum no longer includes any serious instruction in fluid mechanics.…”

An elementary treatment of the reverse sprinkler

“…A. K. Schultz 9 argues that, at each instant, the water flowing into the reverse sprinkler's intake carries a constant angular momentum around the sprinkler pivot, and if the sprinkler could turn without any resistance (either from the friction of the pivot or the viscosity of the fluid) this angular momentum would be counterbalanced by the angular momentum that the sprinkler picked up as the water flow was being switched on. As the fluid flow is switched off, such an ideal sprinkler would then lose its angular momentum and come to a halt.…”

“…17 An exchange on the issue of conservation of angular momentum between A. K. Shultz and Forrester appeared shortly thereafter. 9,18 The following year L. Hsu, a high school student, published an experimental analysis which found no rotation of the reverse sprinkler and questioned (quite sensibly) Forrester's claim that pushing the water out of the bottle was not equivalent to sucking it out. 19 E. R. Lindgren also published an experimental result that supported the claim that the reverse sprinkler did not turn.…”

“…The most detailed and pertinent work on the subject, both theoretical and experimental, was published by Berg, Collier, and Ferrell, who claimed that the reverse sprinkler turns toward the incoming water. 24,25 Guided by Schultz's arguments about conservation of angular momentum, 9 the authors offered a somewhat convoluted statement of the correct observation that the sprinkler picks up a bit of angular momentum before reaching a steady state of zero torque once the water is flowing steadily into the sprinkler. When the water stops flowing, the sprinkler comes to a halt.…”