Feynman sprinkler

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
Irrigation sprinkler
Irrigation sprinklers are sprinklers used on farms, golf courses, and yards, to provide water to vegetation and plants in the event of drought. They may also be used for recreation, as a cooling system, or to keep down the amount of airborne dust....

-like device which is submerged in a tank and made to suck in the surrounding fluid
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....

. The question of how such a device would turn was the subject of an intense and remarkably long-lived debate.

A regular sprinkler has nozzle
Nozzle
A nozzle is a device designed to control the direction or characteristics of a fluid flow as it exits an enclosed chamber or pipe via an orifice....

s arranged at angles on a freely rotating wheel such that when water is pumped out of them, the resulting jets
Jet (fluid)
A jet is an efflux of fluid that is projected into a surrounding medium, usually from some kind of a nozzle, aperture or orifice. Jets can travel long distances without dissipating...

 cause the wheel to rotate; both a Catherine wheel
Catherine wheel (firework)
The Catherine wheel is a type of firework consisting of a powder-filled spiral tube, or an angled rocket mounted with a pin through its centre...

 and the aeolipile
Aeolipile
An aeolipile , also known as a Hero engine, is a rocket style jet engine which spins when heated. In the 1st century AD, Hero of Alexandria described the device, and many sources give him the credit for its invention.The aeolipile Hero described is considered to be the first recorded steam engine...

 ("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
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

 Richard Feynman
Richard Feynman
Richard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...

, who mentions it in his popular autobiographical
Autobiography
An autobiography is a book about the life of a person, written by that person.-Origin of the term:...

 book Surely You're Joking, Mr. Feynman!
Surely You're Joking, Mr. Feynman!
"Surely You're Joking, Mr. Feynman!": Adventures of a Curious Character is an edited collection of reminiscences by the Nobel Prize-winning physicist Richard Feynman. The book, released in 1985, covers a variety of instances in Feynman's life...

. 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 Ch. III, sec. III of Ernst Mach
Ernst Mach
Ernst Mach was an Austrian physicist and philosopher, noted for his contributions to physics such as the Mach number and the study of shock waves...

's textbook The Science of Mechanics, first published in 1883. There, Mach argued that the device shows "no distinct rotation." 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
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....

, generating a lively debate. Richard Feynman, at the time a young graduate student at Princeton, became intrigued by the problem and eventually built a make-shift experiment within the facilities of the university's cyclotron
Cyclotron
In technology, a cyclotron is a type of particle accelerator. In physics, the cyclotron frequency or gyrofrequency is the frequency of a charged particle moving perpendicularly to the direction of a uniform magnetic field, i.e. a magnetic field of constant magnitude and direction...

 laboratory. The experiment ended with the explosion of the glass container (a "carboy
Carboy
A carboy is a rigid container with a typical capacity of 5 to 15 gallons . Carboys are primarily used for transporting fluids, often water or chemicals.They are also used for in-home fermentation of beverages, often wine.-Brewing:...

") that he was using as part of his setup.

In 1966, Feynman turned down an offer from the editor of Physics Teacher
The Physics Teacher
The Physics Teacher is a peer-reviewed journal published by the American Association of Physics Teachers and includes papers on physics research, papers on the history and philosophy of physics, papers on applied physics, papers curriculum developments, papers on pedagogy, papers on instructional...

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
John Archibald Wheeler
John Archibald Wheeler was an American theoretical physicist who was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr in explaining the basic principles behind nuclear fission...

, 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
James Gleick
James Gleick is an American author, journalist, and biographer, whose books explore the cultural ramifications of science and technology...

'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, 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,

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
T-symmetry
T Symmetry is the symmetry of physical laws under a time reversal transformation: T: t \mapsto -t.Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics.Time asymmetries...

." 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
Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...

 and is surrounded by an ideal fluid) will accelerate
Angular acceleration
Angular acceleration is the rate of change of angular velocity over time. In SI units, it is measured in radians per second squared , and is usually denoted by the Greek letter alpha .- Mathematical definition :...

 towards the incoming fluid as the suction is being switched on, and come to a stop as the suction is switched off. The ideal reverse sprinkler will not experience any torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....

 in its steady state
Steady state
A system in a steady state has numerous properties that are unchanging in time. This implies that for any property p of the system, the partial derivative with respect to time is zero:...

. This behavior may be understood in terms of conservation of angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...

: 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.

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. On the other hand, experiments with very low-friction bearings find a small torque on the reverse sprinkler even in its steady state. This is now understood to be a consequence of the viscosity
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher 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).

The smallness of the torque on a reverse sprinkler is closely analogous to the propulsion of the so-called "pop pop boat
Pop pop boat
A pop-pop boat is a toy with a very simple heat engine without moving parts, powered by a candle or oil burner. The name comes from the noise the boats make. Other names are putt-putt boat, crazy boat, flash-steamer, hot-air-boat, pulsating water engine 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.

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