Text settings Story text Size Small Standard Large Width * Standard Wide Links Standard Orange * Subscribers only Learn more Minimize to nav Watering your lawn in the summer can be both pragmatic and fun with so-called “silly sprinklers,” designed to create amusing loops and spirals of water jets. And there’s some fascinating physics at work to boot. Researchers at New York University’s Courant Institute conducted a series of experiments with different silly sprinkler designs to find the answer to a longstanding problem in fluid dynamics, according to a new paper published in the Proceedings of the National Academy of Sciences.
As previously reported, the reverse sprinkler problem is associated with physicist Richard Feynman because he popularized the concept, but it actually dates back to a chapter in Ernst Mach’s 1883 textbook The Science of Mechanics (Die Mechanik in Ihrer Entwicklung Historisch-Kritisch Dargerstellt). Mach’s thought experiment languished in relative obscurity until a group of Princeton University physicists began debating the issue in the 1940s.
Feynman was a graduate student there at the time and threw himself into the debate with gusto, even devising an experiment in the cyclotron laboratory to test his hypothesis. One might intuit that a reverse sprinkler would work just like a regular sprinkler, merely played backward, so to speak. But the physics turns out to be more complicated. “The answer is perfectly clear at first sight,” Feynman wrote in Surely You’re Joking, Mr. Feynman (1985). “The trouble was, some guy would think it was perfectly clear [that the rotation would be] one way, and another guy would think it was perfectly clear the other way.”
Mach proposed that there would be no rotation with a reverse sprinkler: the reaction force on the nozzle as it sucks in water pulls the nozzle counter-clockwise, while the water flowing into the inside of the nozzle pushes it clockwise. The two forces cancel each other out in this steady-state scenario. Feynman’s own experiment showed a slight tremor when pressure was first applied to pump water through the nozzle, and then the sprinkler returned to its original position and remained still.
But others suggested that if the friction was low enough and the inflow rate high enough, a reverse sprinkler would start to turn in the opposite direction of an ordinary sprinkler, thanks to the formation of a vortex inside. Since Feynman’s efforts, experiments have been all over the place: some showed steady reverse rotation, some showed only transient rotation, and some produced unsteady rotation that changed direction or flowed in a direction determined by the contraption’s geometry.
In 2024, New York University applied mathematician Leif Ristroph and several colleagues built their own custom sprinkler that incorporated ultra-low-friction rotary bearings so their device could spin freely. They immersed their sprinkler in water and used a special apparatus to either pump water in or pull it out at carefully controlled flow rates. This let the team observe how water flowed inside, outside, and through the device. Adding dyes and microparticles to the water and illuminating them with lasers helped capture the flows on high-speed video. They ran their experiments for several hours at a time, the better to precisely map the fluid-flow patterns.
The team found that the reverse sprinkler rotates 50 times slower than a regular sprinkler, but it operates along similar mechanisms, which surprised them. Ristroph described the behavior as an “inside-out rocket,” where the internal jets shoot inside the chamber where the arms meet and collide—but they don’t collide head-on, which results in the forces that rotate the sprinkler in reverse. By contrast, a forward sprinkler is more like a rotating rocket, with jets shooting out of its arms.
The jet-like flows of water emitted by the forward sprinkler, as visualized using dye and false colored. NYU’s Applied Mathematics Laboratory The sprinkler designs, with the observed rotation direction in the forward (red arrow) and reverse (blue) modes. NYU’s Applied Mathematics Laboratory The sprinkler designs, with the observed rotation direction in the forward (red arrow) and reverse (blue) modes. NYU’s Applied Mathematics Laboratory The jet-like flows of water emitted by the forward sprinkler, as visualized using dye and false colored. NYU’s Applied Mathematics Laboratory The sprinkler designs, with the observed rotation direction in the forward (red arrow) and reverse (blue) modes. NYU’s Applied Mathematics Laboratory The 2024 experimentally observed flow patterns were in excellent agreement with the group’s mathematical models—which they dubbed the momentum flux theory. However, it didn’t definitively rule out competing theories. Also, the group only looked at sprinklers with S-shaped arms. So this latest paper builds on that earlier work by extending the experiments to silly sprinklers the team created themselves. Ristroph et al. tested them in both forward mode (where water sprays out) and reverse mode (where water is sucked in).
Their observations strongly supported Ristroph et al.’s momentum flux theory and were inconsistent with both Mach’s and Feynman’s hypotheses. They also found that the arm shape of a given sprinkler can control the jet flow, and the team devised specific guidelines for designing structures to control flow to produce torque and rotation. “Our findings provide a firmer understanding of how components respond to fluid flows—knowledge that can guide future engineering and technological advances for devices, such as turbines, that convert these flows into energy,” said co-author Brennan Sprinkle of the Colorado School of Mines.
Ristroph’s lab frequently addresses these kinds of colorful real-world puzzles. For instance, in 2018, Ristroph and colleagues fine-tuned the recipe for the perfect bubble based on experiments with soapy thin films. In 2021, the Ristroph lab looked into the formation processes underlying so-called “stone forests” common in certain regions of China and Madagascar. In 2021, his lab built a working Tesla valve, in accordance with the inventor’s design, and measured the flow of water through the valve in both directions at various pressures. And in 2022, Ristroph studied the surpassingly complex aerodynamics of what makes a good paper airplane—specifically what is needed for smooth gliding.
PNAS, 2026. DOI: 10.1073/pnas.2537479123 (About DOIs).
