Mathematicians finally solved Feynman’s “reverse sprinkler” problem
Light-scattering microparticles reveal the flow pattern for the reverse (sucking) mode of a sprinkler, showing vortices and complex flow patterns forming inside the central chamber. Credit: K. Wang et al., 2024 Light-scattering microparticles reveal the flow pattern for the reverse (sucking) mode of a sprinkler, showing vortices and complex flow patterns forming inside the central chamber. Credit: K. Wang et al., 2024 A typical lawn sprinkler features various nozzles arranged at angles on a rotating wheel; when water is pumped in, they release jets that cause the wheel to rotate. But what would happen if the water were sucked into the sprinkler instead? In which direction would the wheel turn then, or would it even turn at all? That's the essence of the "reverse sprinkler" problem that physicists like Richard Feynman, among others, have grappled with since the 1940s. Now, applied mathematicians at New York University think they've cracked the conundrum, per a recent paper published in the journal Physical Review Letters-and the answer challenges conventional wisdom on the matter.
Our study solves the problem by combining precision lab experiments with mathematical modeling that explains how a reverse sprinkler operates," said co-author Leif Ristroph of NYU's Courant Institute. We found that the reverse sprinkler spins in the reverse' or opposite direction when taking in water as it does when ejecting it, and the cause is subtle and surprising."
Ristroph's lab frequently addresses these kinds of colorful real-world puzzles. For instance, back in 2018, Ristroph and colleagues fine-tuned the recipe for the perfect bubble based on experiments with soapy thin films. (You want a circular wand with a 1.5-inch perimeter, and you should gently blow at a consistent 6.9 cm/s.) In 2021, the Ristroph lab looked into the formation processes underlying so-called "stone forests" common in certain regions of China and Madagascar. These pointed rock formations, like the famed Stone Forest in China's Yunnan Province, are the result of solids dissolving into liquids in the presence of gravity, which produces natural convective flows.