We discuss the reverse sprinkler problem: How does a sprinkler turn when submerged and made to suck in water? We propose a solution that requires only a knowledge of mechanics and fluid dynamics at the introductory university level. We argue that as the flow of water starts, the sprinkler briefly experiences a torque that would make it turn toward the incoming water, while as the flow of water ceases it briefly experiences a torque in the opposite direction. No torque is expected when water is flowing steadily into it unless dissipative effects, such as viscosity, are considered. Dissipative effects result in a small torque that would cause the sprinkler arm to accelerate toward the steadily incoming water. Our conclusions are discussed in light of an analysis of forces, conservation of angular momentum, and the experimental results reported by others. We review the conflicting published treatments of this problem, some of which have been incorrect and many of which have introduced complications that obscure the basic physics involved.
Topics
Fluid dynamics
REFERENCES
1.
R. P. Feynman, Surely You’re Joking, Mr. Feynman (Norton, New York, 1985), pp. 63–65.
2.
Reference 1, p. 63.
3.
It has not been possible to identify the book to which Feynman was referring. As we shall discuss, the matter is treated in Ernst Mach’s Mechanik, first published in 1883 (Ref. 10). Yet this book is not a “hydrodynamics book” and the reverse sprinkler is presented as an example, not a problem. In Ref. 21, J. A. Wheeler suggests that the problem occurred to them while discussing a different question in the undergraduate mechanics course that Wheeler was teaching and for which Feynman was the grader.
4.
Reference 1, p. 65.
5.
In the literature it is more usual to see this problem identified as the “Feynman inverse sprinkler.” Because the problem did not originate with Feynman and Feynman never published an answer to the problem, we have preferred not to attach his name to the sprinkler. Furthermore, even though it is a pedantic point, a query of the Oxford English Dictionary suggests that “reverse” (opposite or contrary in character, order, or succession) is a more appropriate description than “inverse” (turned up-side down) for a sprinkler that sucks water.
6.
This observation might seem trivial, but its consequences can be counterintuitive. The Zapruder film of the 1963 assassination of U.S. president J. F. Kennedy shows Kennedy’s head snapping backward after the fatal shot, even though the official theory of the assassination asserts that the shot was fired from behind Kennedy by gunman L. H. Oswald. For several decades, conspiracy theorists have seized on this element of the Zapruder film as evidence that the fatal shot could not have been fired by Oswald and must have come instead from in front of the president’s motorcade. In 1976, L. W. Alvarez published an analysis of the Zapruder film in which he explained that the jet of brain tissue that emerged from president’s exit wound might easily have thrown his head in the direction opposite to that of the incoming bullet. Alvarez demonstrated this to his satisfaction both theoretically and experimentally, the latter by firing at a melon and photographing it as it moved in the direction opposite to what one would naively have expected (Ref. 7).
7.
L. W.
Alvarez
, “A physicist examines the Kennedy assassination film
,” Am. J. Phys.
44
, 813
–827
(1976
).8.
Two interesting problems for an introductory university-level physics course suggest themselves. One is to show that the center of mass of the bullets-and-ship system will not move in the horizontal direction regardless of the firing rate, as one expects from momentum conservation. Another would be to analyze this problem in light of Einstein’s relativity of simultaneity.
9.
A. K.
Schultz
, “Comment on the inverse sprinkler problem
,” Am. J. Phys.
55
, 488
(1987
).10.
E. Mach, Die Mechanik in Ihrer Entwicklung Historisch-Kritisch Dargerstellt (1883). First published in English in 1893 as The Science of Mechanics: A Critical and Historical Account of its Development (Open Court, La Salle, IL, 1960), 6th ed., pp. 388–390.
11.
Reference 10, p. 390.
12.
In Ref. 23, P. Hewitt proposes a physical setup identical to the one shown in Fig. 8(b), and observes that the device turns in opposite directions depending on whether the fluid pours out of or into it. Hewitt’s discussion seems to ignore the important difference between such a setup and the reverse sprinkler.
13.
Reference 10, p. v.
14.
P.
Kirkpatrick
, “A neglected lesson from the Cartesian diver
,” Am. J. Phys.
10
, 160
(1942
).15.
H. S.
Belson
, “ ‘Empty’ Hero’s engine
,” Am. J. Phys.
24
, 413
–414
(1956
).16.
Proceedings of the National Science Foundation Conference on Instruction in Fluid Mechanics, 5–9 September 1960, Exp. 2.2, p. II-20.
17.
A. T.
Forrester
, “Inverse sprinklers: A lesson in the use of a conservation principle
,” Am. J. Phys.
54
, 798
–799
(1986
).18.
A. T.
Forrester
, “Comments on a letter by A. K. Schultz
,” Am. J. Phys.
55
, 488
–489
(1987
).19.
L.
Hsu
, “Two simple experiments and the resolution of the Feynman-Forrester conflict
,” Am. J. Phys.
56
, 307
–308
(1988
).20.
E. R.
Lindgren
, “The transport of momentum theorem
,” Am. J. Phys.
58
, 352
–357
(1990
).21.
J. A.
Wheeler
, “The young Feynman
,” Phys. Today
42
(2
), 24
–28
(1989
).22.
J. Gleick, Genius: The Life and Science of Richard Feynman (Pantheon, New York, 1992), pp. 106–108.
23.
24.
R. E.
Berg
and M. R.
Collier
, “The Feynman inverse sprinkler problem: A demonstration and quantitative analysis
,” Am. J. Phys.
57
, 654
–657
(1989
).25.
R. E.
Berg
, M. R.
Collier
, and R. A.
Ferrell
, “The Feynman inverse sprinkler problem: A detailed kinematic study
,” Am. J. Phys.
59
, 349
–355
(1991
).26.
There are other references in the literature to the reverse sprinkler. For a rather humorous exchange, see Refs. 28 and 29. Already in 1990 the American Journal of Physics had received so many conflicting analyses of the problem that the editor proposed “a moratorium on publications on Feynman’s sprinkler” (Ref. 30). In one of her 1996 columns for Parade Magazine, Marilyn vos Savant, who bills herself as having the highest recorded IQ, offered an account of Feynman’s experiment which, she claimed, settled that the reverse sprinkler does not move (Ref. 32). Vos Savant’s column emphasized the confusion of Feynman and others when faced with the problem, leading a reader to respond with a letter to his local newspaper in which he questioned the credibility of physicists who address matters more complicated than lawn sprinklers, such as the origin of the universe (Ref. 33).
27.
MIT Edgerton Center Corridor Lab: Feynman Sprinkler, 〈http://web.mit.edu/Edgerton/www/FeynmanSprinkler.html〉.
28.
M.
Kuzyk
, Letter to the editor, Phys. Today
42
(11
), 129
–130
(1989
).29.
R. E.
Berg
and M. R.
Collier
, “New device lets you un-water your lawn
,” Phys. Today
43
(7
), 13
(1990
).30.
31.
R. E. Berg et al., University of Maryland Physics Lecture Demonstration Facility, 〈http://www.physics.umd.edu/lecdem/services/demos/demosd3/d3-22.htm〉.
32.
M. vos Savant, “Ask Marilyn,” Parade Magazine, 6 October 1996.
33.
A. de Gruyter, “Big bang theorists can’t simulate water sprinkler reversal,” Houston Chronicle, 26 October 1996, p. A35.
34.
35.
R. S.
Mackay
, “Boat driven by thermal oscillations
,” Am. J. Phys.
26
, 583
–584
(1958
).36.
I.
Finnie
and R. L.
Curl
, “Physics in a toy boat
,” Am. J. Phys.
31
, 289
–293
(1963
).37.
R. E. Berg, private communication with J. M. Dlugosz and A. Jenkins (2004).
38.
In the late 1950s and early 1960s, there was some interest in the related physics problem of the so-called “putt-putt” (or “pop-pop”) boat, a fascinating toy boat that propels itself by heating (usually with a candle) an inner tank connected to a submerged double exhaust. Steam bubbles cause water to be alternately blown out of and sucked into the tank (Refs. 34,35,36). The ship moves forward, much like Mach described the “reaction wheel” turning vigorously in one direction as air was alternately blown out and sucked in.
39.
R. P. Feynman, Six Easy Pieces (Perseus Books, Cambridge, MA, 1994), p. xxi.
40.
L. Carroll, The Annotated Alice: The Definitive Edition, edited by M. Gardner (Norton, New York, 2000), p. 91.
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