Feynman sprinkler

Feynman sprinkler. A thought experiment in fluid dynamics and classical mechanics concerning the motion of a submerged, self-propelled sprinkler. The puzzle, popularized by physicist Richard Feynman, asks whether such a device rotates when it sucks in fluid instead of expelling it, reversing its normal operation. This deceptively simple question probes fundamental principles of conservation of momentum and the nature of reaction forces in fluids, leading to extensive debate and experimental study.

Description and history

The core problem involves an S-shaped or T-shaped sprinkler submerged in a tank of water. Normally, when ejecting fluid through its bent arms, Newton's third law causes a reactive torque, spinning the sprinkler in the opposite direction. The historical puzzle, which predates Richard Feynman, questions the behavior when the flow is reversed, acting as a "sucking" or "inhalation" sprinkler. Feynman famously encountered this problem as a student at Princeton University and attempted an informal experiment in the cyclotron laboratory. The puzzle's lineage is often traced to discussions among physicists like Ernest Lawrence and John Archibald Wheeler, though similar questions appear in earlier hydrodynamics literature. The enduring mystery lies in predicting the direction of rotation, or if any occurs, when the device intakes fluid.

Physics and fluid dynamics

Analyzing the sprinkler requires applying the laws of conservation of momentum to a control volume surrounding the device. For the standard ejecting sprinkler, the analysis is straightforward: expelled fluid carries momentum away, and the equal and opposite reaction on the sprinkler arms provides torque, as described by Leonhard Euler's equations for machinery. The reverse case is subtler because inflowing water must change direction inside the apparatus. Key physical considerations include the role of internal pressure gradients, the acceleration of fluid entering the curved arms, and the resultant forces on the internal walls of the tubing. Some theoretical approaches, invoking the Bernoulli equation and Navier–Stokes equations, suggest a small inward-directed force at the nozzle entrance, potentially causing a weak rotation opposite to the ejecting case. However, other models accounting for full viscous effects and entry conditions predict no net torque.

Experimental investigations

Several researchers have constructed apparatuses to test the phenomenon empirically. An early notable experiment was conducted by C. V. Boys in the late 19th century, with inconclusive results due to experimental friction. In the 1980s, a team at the University of Maryland, College Park, including Mark D. Weitz and others, performed a careful study using a sensitive sprinkler in a large water tank. Their results, published in the American Journal of Physics, indicated a small but measurable rotation in the same direction as the standard ejecting sprinkler when sucking, contradicting some theoretical predictions. Later experiments by Jearl Walker for Scientific American and others at the Massachusetts Institute of Technology have confirmed this result, attributing it to complex fluid entry dynamics and asymmetric cavitation effects near the intake nozzles, which can alter the local momentum balance.

Related problems and variants

The Feynman sprinkler is conceptually linked to several classic problems in mechanics. It is a hydrodynamic analog of the Hero's engine, an early reaction turbine described by Hero of Alexandria. In aerospace engineering, the principle relates to the operation of jet engines and rocket engines, where thrust generation depends on momentum exchange. A related inverse problem is the Borda mouthpiece, which analyzes loss in fluid momentum. In electromagnetism, an analogous puzzle involves the forces on a solenoid when current is switched on or off, tying to conservation laws for field momentum. Variants of the sprinkler problem include analyzing its behavior in a compressible flow like air or with non-Newtonian fluids.

In popular culture

The sprinkler problem has transcended academic circles to become a staple of physics folklore. It is frequently recounted in biographies of Richard Feynman, such as Surely You're Joking, Mr. Feynman!, highlighting his playful and hands-on approach to science. The puzzle appears in educational media, including episodes of the television show NOVA and demonstrations by the Royal Institution. It is a common topic in online physics forums and video series like Veritasium, often used to illustrate the counterintuitive nature of fluid mechanics and the scientific method's reliance on experimental evidence over pure reasoning.

Category:Fluid dynamics Category:Thought experiments Category:Physics problems