Researchers Solve Feynman’s Reverse Sprinkler Puzzle with Silly Sprinklers

Researchers at New York University’s Courant Institute have solved the longstanding reverse sprinkler problem through experiments with unique designs of silly sprinklers. Their findings, published recently in the Proceedings of the National Academy of Sciences, reveal how these amusing devices can help unravel complex fluid dynamics.

Understanding the Reverse Sprinkler Problem

The reverse sprinkler problem, popularized by physicist Richard Feynman, has intrigued scientists since the 1940s. It originates from a thought experiment by Ernst Mach in his 1883 textbook, The Science of Mechanics. Mach suggested that a reverse sprinkler, which draws water in instead of spraying it out, would not rotate due to the opposing forces acting on it. Feynman later conducted experiments that showed slight rotation but left the debate open.

Feynman noted, “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.” This ambiguity spurred ongoing research into the mechanics behind sprinklers.

Innovative Experiments with Silly Sprinklers

In 2024, a team led by applied mathematician Leif Ristroph at NYU constructed a custom silly sprinkler featuring ultra-low-friction rotary bearings. The team pumped water in and out at controlled rates to observe the flow patterns. Their experiments revealed that the reverse sprinkler rotates at a speed 50 times slower than a traditional sprinkler, operating on similar principles.

Ristroph described the reverse sprinkler’s behavior as an “inside-out rocket,” where internal jets collide to create reverse rotation. This contrasts with a forward sprinkler, which functions more like a rotating rocket, with jets shooting outward.

Implications for Fluid Dynamics and Engineering

The findings from Ristroph et al. not only support their momentum flux theory but also challenge both Mach’s and Feynman’s hypotheses. The team’s experiments extended beyond traditional designs, testing various arm shapes to understand how they influence fluid flow and torque generation.

• Reverse sprinkler rotates 50 times slower than a regular sprinkler.
• Uses ultra-low-friction rotary bearings for free spinning.
• Experiments involved controlled water flow rates.
• Findings challenge previous theories by Mach and Feynman.

The research provides valuable insights that could guide future engineering advancements, particularly in designing devices like turbines, which rely on fluid dynamics.