February 28, 2024

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Finally, mathematicians have solved Feynman's “reverse sprinkler” problem.

Finally, mathematicians have solved Feynman's “reverse sprinkler” problem.

Microscopic light-scattering particles reveal the reverse-mode (absorption) flow pattern of the spray, illustrating the vortices and complex flow patterns that form within the central chamber. Credit: K. Wang et al., 2024

A typical lawn sprinkler features different nozzles arranged at angles on a rotating wheel; When water is pumped, it releases jets that cause the wheel to spin. But what would happen if the water was sucked into the sprinkler instead? In which direction will the wheel turn then, or will it turn at all? This is the essence”Reverse spraying“A problem that physicists like Richard Feynman, among others, have faced since the 1940s. Now, applied mathematicians at New York University believe they have solved the puzzle, according to Recent paper Published in the journal Physical Review Letters, the answer challenges conventional wisdom on the subject.

“Our study solves the problem by combining careful laboratory experiments with mathematical modeling that explains how backflow sprinklers work.” said co-author Lev Ristrov From the Courant Institute at New York University. “We found that the reverse sprinkler rotates in the opposite or opposite direction when drawing in water as it does when removing it, and the reason is subtle and surprising.”

Ristrov's lab frequently tackles these kinds of colorful real-world puzzles. For example, in 2018, Ristrov and colleagues Finely tuned The perfect bubble recipe is based on experiments with thin films made of soap. (You want a circular wand that is 1.5 inches in circumference, and should blow gently at a constant speed of 6.9 cm/sec.) I searched in The formation processes underlying so-called “stone forests” are common in certain regions of China and Madagascar. These pointy rock formations, like the famous ones Stone forest In Yunnan Province, China, it is the result of solids melting into liquids in the presence of gravity, resulting in natural convective flows.

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In 2021, his lab He built a working Tesla valveAccording to the inventor's design, the flow of water through the valve is measured in both directions at different pressures. They found that the water flows about twice as slowly in the non-preferred direction. In 2022 Ristrov studied Very complex aerodynamics What makes a good kite, specifically what is needed for smooth flight. They found that the aerodynamics of a kite differ significantly from conventional aircraft, which rely on ailerons to generate lift.

رسم توضيحي لـ أ "Reaction wheel" From a book <em>Mechanics</em> By Ernst Mach (1883).” src=”https://cdn.arstechnica.net/wp-content/uploads/2024/02/feynman7-640×692.jpg” width=”640″ height=”692″ srcset=”https http://cdn.arstechnica.net/wp-content/uploads/2024/02/feynman7.jpg 2x”/></a><figcaption class=
Zoom in / Illustration of the “reaction wheel” by Ernst Mach mechanical (1883).

Public domain

The backscatter problem is associated with Feynman because he popularized the concept, but it actually dates back to a chapter in Ernst Mach's 1883 textbook Mechanics (Die Mechanik in Ihrer Entwicklung Historisch-Kritisch Dargerstellt). Mach's thought experiment remained in relative obscurity until a group of physicists at Princeton University began discussing the issue in the 1940s.

Feynman was a graduate student there at the time, and he threw himself into the debate with great enthusiasm, even devising an experiment in the cyclotron laboratory to test his hypothesis. (In true Feynman fashion, this experiment culminated in the device's glass carriage exploding due to the high internal pressure.)

One might think that a reverse sprinkler would work just like a regular sprinkler, only run backwards, so to speak. But the physics turns out to be more complicated. “The answer is quite obvious at first glance,” Feynman wrote. You must be joking, Mr. Feynman (1985). “The problem is that some people might think it's quite obvious [that the rotation would be] One way, and someone else might think it's quite obvious the other way.

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