For decades scientists have been trying to solve Feynman’s Sprinkler Problem: How does a sprinkler running in reverse—in which the water flows into the device rather than out of it—work? Through a series of experiments, a team of mathematicians has figured out how flowing fluids exert forces and move structures, thereby revealing the answer to this long-standing mystery.
“Our study solves the problem by combining precision lab experiments with mathematical modeling that explains how a reverse sprinkler operates,” explains Leif Ristroph, an associate professor at New York University’s Courant Institute of Mathematical Sciences and the senior author of the paper, appears in the journal Physical Review Letters. “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.”
“The regular or ‘forward’ sprinkler is similar to a rocket, since it propels itself by shooting out jets,” adds Ristroph. “But the reverse sprinkler is mysterious since the water being sucked in doesn’t look at all like jets. We discovered that the secret is hidden inside the sprinkler, where there are indeed jets that explain the observed motions.”
The research answers one of the oldest and most difficult problems in the physics of fluids. And while Ristroph recognizes there is modest utility in understanding the workings of a reverse sprinkler—“There is no need to ‘unwater’ lawns,” he says—the findings teach us about the underlying physics and whether we can improve the methods needed to engineer devices that use flowing fluids to control motions and forces.
“We now have a much better understanding about situations in which fluid flow through structures can induce motion,” notes Brennan Sprinkle, an assistant professor at Colorado School of Mines and one of the paper’s co-authors. “We think these methods we used in our experiments will be useful for many practical applications involving devices that respond to flowing air or water.”
The Feynman sprinkler problem is typically framed as a thought experiment about a type of lawn sprinkler that spins when fluid, such as water, is expelled out of its S-shaped tubes or “arms.” The question asks what happens if fluid is sucked in through the arms: Does the device rotate, in what direction, and why?