Richard Feynman got this one wrong — or at least couldn’t get far enough to find out. As a Princeton graduate student in the early 1940s, he pressurized a glass carboy to run a sprinkler backward, sucking water in instead of spraying it out, and the apparatus exploded before yielding a definitive result. He never got the answer. Neither did anyone else who tried for the next eight decades.

That streak ended this week. A team of mathematicians at NYU’s Courant Institute School of Mathematics, Computing, and Data Science, with a collaborator at Colorado School of Mines, has published a comprehensive experimental resolution in the Proceedings of the National Academy of Sciences: angular momentum carried by fluid jets — what the team calls “momentum flux” — governs sprinkler rotation in both forward and reverse modes, across every arm geometry tested. Arm shape, it turns out, is the key variable engineers need to control.

The instrument that finally cracked the case was a children’s lawn toy.

Why Reversing the Flow Doesn’t Reverse the Physics

Before getting to what the team found, it helps to understand why this problem stayed open for 143 years. It isn’t because the question is exotic — it’s because fluid dynamics has a property that makes intuition fail in exactly this kind of situation.

Leif Ristroph, an associate professor at NYU’s Courant Institute and the paper’s senior author, put it plainly: “You can blow out a candle but you can’t suck it out. When you blow out a fluid through an orifice at a high enough flow rate, it forms a concentrated jet…When you reverse the system and pull in fluid at the same flow rate, the flow does not reverse — it pulls in fluid from all directions. That comes from the irreversibility of the Navier-Stokes equation.”

That irreversibility is the root of the puzzle. Running a sprinkler in reverse is not simply running a movie of a forward sprinkler backward. The physics are categorically different in the two directions, and so the question of which way the device spins — and why — could not be resolved by theory alone. It required precision experiments with the right apparatus. And for decades, the right apparatus didn’t exist.

Problem History: Mach Asked First, Feynman Made It Famous

Ernst Mach posed the question first, in the third chapter of his 1883 textbook The Science of Mechanics, where he reported the device showed “no distinct rotation.” When Feynman encountered the problem at Princeton in the early 1940s, he apparently did so without knowing Mach had been there, and his failed experiment became the source of one of the more colorful anecdotes in his 1985 memoir, Surely You’re Joking, Mr. Feynman! The problem took his name largely by convention; Feynman himself objected to it, pointing back to Mach.

What followed were decades of contradictory experiments, conflicting theoretical treatments, and passionate disagreements in the pages of the American Journal of Physics. Two main camps formed around rival theories: one attributed rotation to the direction that fluid swirled (Mach’s swirl theory); another focused on flows at the outer portions of the sprinkler arms (Feynman’s outer-flow theory, developed by researchers following up on his famous study). Neither theory fully accounted for what experimenters observed.

The 2024 Baseline: A First Precision Answer

In January 2024, Ristroph and colleagues published the first precision experiments to confirm that a reverse sprinkler does in fact rotate — and in the opposite direction from a conventional one — under suction. That study, in Physical Review Letters, found that the reverse sprinkler rotates roughly 50 times more slowly than a conventional one under comparable flow conditions.

The mechanism the 2024 team proposed was what they termed momentum flux. A conventional forward sprinkler acts like a rotating rocket: water jets out of the arms, carrying angular momentum away from the device, and the device spins in the opposite direction in response. A reverse sprinkler acts as an “inside-out rocket”: as water is sucked inward, incoming jets converge inside the central hub of the device. Those jets don’t meet exactly head-on — a subtle geometric asymmetry — and the slight off-axis collision produces a small net torque that rotates the device in reverse.

But the 2024 study examined only conventional S-shaped sprinklers, leaving open the question of whether more complicated arm geometries would yield different behavior. It also hadn’t fully ruled out the rival theories.

Enter the Silly Sprinklers

For the new PNAS study, the team built its own set of custom sprinklers modeled on the looping, twisting forms of children’s lawn toys — “silly sprinklers,” whose irregular curves served as deliberate experimental variables. By testing multiple geometries in both forward and reverse modes, the researchers could isolate which physical effects actually determined rotation and torque, and which had no effect.

Each device was tested in both modes: water sprayed outward (forward) and water sucked inward (reverse). The team simultaneously measured rotational motion, the flows both outside and inside the devices, and the torque when sprinklers were held stationary.

The results put Mach’s swirl theory and Feynman’s outer-flow theory to a direct test — and eliminated both.

Two Rival Theories Ruled Out

Mach’s swirl theory predicted that the direction of fluid swirl determined the sprinkler’s rotation direction. The experiments showed the theory could not account for the reverse rotations and torques observed across the differently shaped devices.

Feynman’s outer-flow theory centered on water flows occurring at the very outside of the sprinkler arms as the operative mechanism. The experiments showed the outer portions of the arms and the flows there had no effect on sprinkler motion or torque.

Momentum flux, by contrast, held across every geometry and both flow directions. Ristroph told Physics World: “If you measure the angular momentum flux from any one of these designs it’s quantitatively one-to-one with the torque on the solid [in the forward case].” The beautiful thing, he added, is that the same principle works in reverse — the difference is where you look. In reverse, the relevant jets are pointing inward at the hub, not outward at the arm tips.

What Controls the 50× Speed Gap

The dramatic difference in rotation speed between the two modes — the reverse sprinkler spinning roughly 50 times slower than the forward one — follows directly from the geometry of the jet interactions.

In forward mode, outward jets deliver strong, well-directed thrust — clean rocket-like propulsion. In reverse mode, incoming jets converge in the hub and collide at a slight off-axis angle. That subtle misalignment generates the decisive torque in the reverse direction, but the torque is far weaker than the clean outward push, because the convergence from all directions dilutes the angular momentum that any one jet contributes. The arm shapes can control how the jets form and collide — changing the geometry changes the torque.

What Took So Long?

The problem persisted partly because adequate experimental control was genuinely difficult to achieve — low-friction bearings, stable flow rates, and long run times all turned out to be necessary — and partly because the “silly sprinkler” approach of varying arm geometry was the methodological key that let the team isolate variables that a standard S-shaped arm could not distinguish.

There’s also something worth noting in how the resolution came about. It wasn’t a theoretical breakthrough or a computational simulation. It was careful, hands-on laboratory experimentation with custom-built physical devices — classical experimental physics applied to a problem that had outlasted many attempts at purely analytical resolution.

The Deeper Lesson: What Fluid Physics Won’t Let You Reverse

The Navier-Stokes irreversibility Ristroph described isn’t just a technical nuance about this particular experiment. It’s a foundational property of viscous fluid flow, and the Feynman Sprinkler is one of the simplest, most accessible ways to see it in action. A movie of a turbulent fluid flow played backward doesn’t look like a physically possible flow — the universe’s fluid dynamics don’t run in both temporal directions equivalently. The sprinkler problem is a tabletop demonstration of that asymmetry.

Engineering Implications: Arm Geometry as a Design Variable

Beyond resolving a historical puzzle, the momentum flux framework has direct engineering relevance. Brennan Sprinkle, assistant professor at Colorado School of Mines and co-author of the paper, said: “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.”

The angular momentum equation — the Euler turbomachine equation — is already the foundational design principle in turbomachinery: turbines, pumps, and compressors all work by controlling how much angular momentum fluid jets transfer to a rotor. The PNAS finding extends this to bidirectional-flow devices and adds a specific, experimentally validated insight: arm geometry controls the jet flow, and jet flow controls the torque. For engineers designing reversible pumped-hydro turbines, tidal energy converters, or other systems that must handle flow in both directions, that is a directly useful variable.

Earl Dowell, a mechanical engineer at Duke University, offered a more measured assessment in Physics World. He acknowledged the experiments were “carried out competently and the results presented in a well-organized manner,” but characterized the competing theories the team tested as “notional ideas based upon highly simplified concepts that tend to be favored by some physicists.” He noted that experts in fluid mechanics would typically approach the problem with “well-established computational models for the flow field and rigid body dynamics.” Ristroph has acknowledged as much: the team is now developing new fluid-dynamics simulations to model what the experiments revealed, opening the next phase of the research program.

“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,” Ristroph said in the press release.

The paper’s authors include NYU graduate students Jesse Smith and Mingxuan Zuo, NYU undergraduate Will Kuhlke, Sprinkle, and Ristroph. The research was supported by the National Science Foundation under grants DMS-2407787 and DMS-2407788.

The paper “Geometry Controls Momentum Flux in the Sprinkler Problem” was published July 13, 2026, in the Proceedings of the National Academy of Sciences (DOI: 10.1073/pnas.2537479123).

Frequently Asked QuestionsWhat is the Feynman Sprinkler Problem, and who actually came up with it?

The Feynman Sprinkler Problem asks what happens when you run a standard lawn sprinkler in reverse — sucking water in through the arms instead of spraying it out. Does it spin in the same direction as a normal sprinkler, the opposite direction, or not at all? The problem was first posed in 1883 by Austrian physicist Ernst Mach in his textbook The Science of Mechanics. It came to bear Feynman’s name after he described his failed attempt to test it experimentally — in a Princeton cyclotron laboratory in the early 1940s — in his popular 1985 memoir. Feynman himself objected to the attribution and pointed back to Mach.

What does “momentum flux” mean, and why is it the answer?

Momentum flux, in this context, refers to the angular momentum carried by fluid jets as they pass through the sprinkler device. In a forward sprinkler, water jets exit the arms carrying angular momentum outward, and the device rotates in the opposite direction — exactly like a rocket. In a reverse sprinkler, water jets form inside the hub as incoming flows converge from all directions. Those internal jets collide at a slight off-axis angle, generating a weak torque in the reverse direction. The NYU team’s experiments showed this principle holds for all the arm geometries they tested — overturning both Mach’s swirl theory and the outer-flow explanation historically attributed to Feynman.

Why does the reverse sprinkler spin so much more slowly than a forward sprinkler?

Because the outward jets of a forward sprinkler deliver strong, well-directed thrust — clean momentum transfer in one direction. The reverse sprinkler’s inward jets converge from all directions and collide inside the hub at a subtle off-axis angle. That collision produces a torque, but a far weaker one, because the angular momentum arriving from all sides partially cancels before it reaches the hub. The NYU experiments found the reverse sprinkler rotates roughly 50 times more slowly than a forward sprinkler under comparable flow conditions.

Could understanding this actually make turbines more efficient — or is this more of a physics curiosity?

The finding has genuine engineering relevance, though the path from lab result to production hardware involves more steps. The angular momentum equation has been central to turbine and pump design for centuries — the Euler turbomachine equation is what makes it possible to design compressors, water turbines, and jet engines. What the PNAS paper adds is a validated experimental demonstration that arm geometry directly controls jet flow, and jet flow controls the torque in bidirectional-flow devices. Turbines that must operate efficiently in both directions — such as reversible pumped-hydro storage systems and tidal energy converters — could benefit from this kind of geometry-controlled torque optimization. Duke mechanical engineer Earl Dowell noted that computational fluid dynamics modeling would be needed to extend these findings to production engineering, and Ristroph’s team has said they are now developing those simulations.