This photograph shows the jet-like flows of water emitted by the forward sprinkler, as visualized using dye and false colored. Credit: NYU’s Applied Mathematics Laboratory

Quirky backyard sprinklers helped scientists solve a decades-old mystery about how flowing water makes objects spin.

Every summer, lawns across the country come alive with “silly sprinklers,” colorful devices with looping and spiraling tubes that send water spraying in unexpected patterns. Although they may look like simple backyard toys, mathematicians have now used their unusual shapes to help solve a physics puzzle that has remained unsettled for decades.

Solving Feynman’s Sprinkler Problem

The mystery is known as Feynman’s Sprinkler Problem. It asks what happens when a sprinkler operates in reverse, drawing water into its arms instead of spraying it outward. By experimenting with specially built sprinklers in a variety of shapes, researchers reached a clear conclusion. Their results also reveal more broadly how moving fluids apply force and cause objects to rotate.

“This work provides the experimental answer for Feynman’s Sprinkler Problem by showing, across several sprinkler types, how the angular momentum of water flows drives sprinklers’ rotation,” explains Leif Ristroph, an associate professor at New York University’s Courant Institute School of Mathematics, Computing, and Data Science and the senior author of the paper, which appears in the journal Proceedings of the National Academy of Sciences.

The researchers emphasize that the findings do more than settle a famous question in physics.

“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,” notes Brennan Sprinkle, an assistant professor at Colorado School of Mines and one of the paper’s co-authors.

This photo captures the flows coming into the reverse sprinkler, as visualized using particles and false colored. Credit: NYU’s Applied Mathematics Laboratory

Why Reverse Sprinklers Are So Strange

The team first reported its work on Feynman’s Sprinkler Problem in 2024. The question became widely known during the 1980s after physicist Richard Feynman described his own unsuccessful attempts to test it experimentally.

In that earlier research, the scientists discovered that a reverse sprinkler turns about 50 times more slowly than a standard sprinkler, even though both operate through closely related physical processes.

A normal sprinkler behaves much like a rotating rocket. Water shoots from the arms and pushes the device in the opposite direction. A reverse sprinkler, however, functions like an “inside-out rocket.” Water enters through its arms and forms jets inside the central chamber where the arms connect.

The team found that these two inward moving jets collide without meeting perfectly head on. That slight imbalance produces forces that cause the sprinkler to rotate in reverse.

Ristroph, Sprinkle, and their colleagues called this explanation the momentum flux theory because it describes how the momentum carried by swirling water moves through the sprinkler and generates rotation.

The sprinkler designs studied, with the observed rotation direction in the forward (red arrow) and reverse (blue) modes. Credit: NYU’s Applied Mathematics Laboratory

Testing Sprinklers With Loops and Curves

The 2024 experiments focused only on standard sprinklers with S shaped arms. That left open an important question. Sprinklers with more complicated loops, curves, and winding tubes might behave differently.

The earlier work also had not completely ruled out other major explanations that scientists had proposed over the years.

For the new study, the researchers designed and built their own collection of silly sprinklers with a wide range of contours. They tested each device in both forward and reverse operation. In forward mode, the sprinkler sprayed water outward in the usual way. In reverse mode, it pulled water inward.

These varied designs allowed the team to track how each sprinkler rotated, observe water movement inside and outside the device, and measure the torque or twisting force produced when the sprinkler was prevented from turning.

Competing Physics Theories Put to the Test

The scientists compared their momentum flux explanation with two other theories that had long been considered possible solutions.

One theory, proposed by physicist Ernst Mach during the 1880s, suggested that the fluid swirls in one direction while the sprinkler turns in the opposite direction. However, this idea could not explain the reverse rotations and torque measured during the new experiments.

Another explanation, associated with Feynman and later researchers, focused on water moving around the outer ends of the sprinkler arms. The new tests showed that neither the outer portions of the arms nor the flows surrounding them affected the sprinkler’s motion or torque.

The results instead strongly supported the momentum flux theory. The researchers expanded the theory and demonstrated that it accurately describes both forward and reverse operation across every sprinkler shape they tested.

Their experiments also revealed that changing the shape of the arms can alter and control the water jets. That ability could prove valuable when designing practical devices that rely on fluid flow.

“By showing that momentum flux is the answer to Feynman’s Sprinkler Problem, our findings address a long-standing open problem in flow physics and provide useful knowledge about how these devices work and their effectiveness,” concludes Ristroph.

Reference: “Geometry controls momentum flux in the sprinkler problem” by Jesse Etan Smith, Mingxuan Zuo, Will Kuhlke, Brennan Sprinkle and Leif Ristroph, 13 July 2026, Proceedings of the National Academy of Sciences.
DOI: 10.1073/pnas.2537479123

The paper’s other authors were NYU graduate students Jesse Smith and Mingxuan Zuo, as well as Will Kuhlke, an NYU undergraduate.

The work was supported by grants from the National Science Foundation (DMS-2407787 and DMS-2407788).

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