Feynman sprinkler

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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 ("Hero engine") 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 physicist Richard Feynman, who mentions it in his bestselling memoirs Surely You're Joking, Mr. Feynman! The problem did not originate with Feynman, nor did he publish a solution to it.

History[edit]

Illustration 153a from Ernst Mach's Mechanik (1883). When the hollow rubber ball is squeezed, air flows in the direction of the short arrows and the wheel turns in the direction of the long arrow. When the rubber ball is released, the direction of the flow of the air is reversed but Mach observed "no distinct rotation" of the device.

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.[1] There, Mach argued that the device shows "no distinct rotation."[2] In the early 1940s (and apparently without awareness of the earlier discussion by Mach), 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, became intrigued by the problem and eventually 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.[3] 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.[4] 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.”[5] 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.[6]

In 2005, physicist Edward C. Creutz (who was in charge of the Princeton cyclotron at the time of the incident) 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,

There was a little tremor, as [Feynman] called it, and the sprinkler head rapidly moved back to its original position and stayed there. The water flow continued with the sprinkler stationary. We adjusted the pressure to increase the water flow, about five separate times, and the sprinkler did not move, although water was flowing freely through it in the backwards direction [...] The carboy then exploded, due to the internal pressure. A janitor then appeared and helped me clean up the shattered glass and mop up the water. I don't know what [Feynman] had expected to happen, but my vague thoughts of a time reversal phenomenon were as shattered as the carboy.[7]

Solution[edit]

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 and experimental treatments of this problem have claimed (as did Mach and Gleick) that a sprinkler will not turn when made to suck in the surrounding fluid. It is now understood, however, that an ideal reverse sprinkler (i.e., one which can turn without friction and is surrounded by an ideal fluid) will indeed accelerate "backwards" towards the incoming fluid as the suction is being switched on, and will come to a stop as the suction is switched off.[8][9] The ideal reverse sprinkler will not experience any torque in its steady state. This behavior 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.[8]

Most experimental setups fail to detect any turning of the reverse sprinkler because the transient torque is not large enough to overcome the friction of the sprinkler's bearing. The increased friction prevents the sprinkler from actually turning "backwards", although it is being (weakly) pushed in that direction. On the other hand, experiments with very low-friction bearings do find a small torque on the reverse sprinkler even in its steady state.[10] This is now understood to be a consequence of the viscosity of the fluid being sucked into the sprinkler, which leads to the dissipation of some of the energy of the incoming fluid and diffuses some of its angular momentum to the surrounding tank. This torque, induced by the viscosity, causes the reverse sprinkler to turn weakly towards the incoming fluid (i.e., in the direction contrary to the motion of a regular sprinkler expelling water).[8][11]

The smallness of the torque on a reverse sprinkler is closely analogous to the propulsion of the so-called "pop pop boat," a toy boat that moves forward as it alternately expels and then sucks in water through a pipe connected to a small internal tank heated by a candle.[11]

References[edit]

  1. ^ Ernst Mach, Die Mechanik in Ihrer Entwicklung Historisch-Kritisch Dargerstellt, (Leipzig: Brockhaus, 1883). Available in English as The Science of Mechanics: A Critical and Historical Account of its Development, (Chicago: Open Court, 1919), 4th ed., pp. 299-301.
  2. ^ Ernst Mach, The Science of Mechanics: A Critical and Historical Account of its Development, (Chicago: Open Court, 1919), 4th ed., p. 301.
  3. ^ Richard P. Feynman, Perfectly Reasonable Deviations From the Beaten Track: The Letters of Richard P. Feynman, ed. Michelle Feynman, (New York: Basic Books, 2006), pp. 209-211. ISBN 0-465-02371-1
  4. ^ Richard P. Feynman, Surely You're Joking, Mr. Feynman!, (Norton, New York, NY, 1985), pp. 63-65.
  5. ^ John A. Wheeler (1989). "The young Feynman". Physics Today 42 (2): 24–28. Bibcode:1989PhT....42b..24W. doi:10.1063/1.881189. 
  6. ^ James Gleick, Genius: The Life and Science of Richard Feynman (New York: Pantheon, 1992), pp. 106-108.
  7. ^ Edward C. Creutz (2005). "Feynman’s reverse sprinkler". American Journal of Physics 73 (3): 198. Bibcode:2005AmJPh..73..198C. doi:10.1119/1.1842733. 
  8. ^ a b c Alejandro Jenkins (2004). "An elementary treatment of the reverse sprinkler". American Journal of Physics 72 (10): 1276–1282. arXiv:physics/0312087. Bibcode:2004AmJPh..72.1276J. doi:10.1119/1.1761063. 
  9. ^ James B. Calvert, "Turbines," University of Denver. Retrieved April 5, 2006.
  10. ^ D3-22: Inverse Sprinkler - Metal Model, The University of Maryland Department of Physics, retrieved June 29, 2011
  11. ^ a b Alejandro Jenkins (2011). "Sprinkler head revisited: momentum, forces, and flows in Machian propulsion". European Journal of Physics 32 (5): 1213–1226. arXiv:0908.3190. Bibcode:2011EJPh...32.1213J. doi:10.1088/0143-0807/32/5/009. 

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