NYU-Led Team Cracks Feynman's Reverse Sprinkler Problem, Ruling Out Rival Theories With Custom 'Silly Sprinklers'

Overview

A team led by mathematicians at New York University has produced what they describe as the experimental answer to Feynman’s Sprinkler Problem, a fluid-dynamics puzzle that asks how a sprinkler behaves when water is drawn into it rather than sprayed out. Using an array of custom-built “silly sprinklers” — the loop- and spiral-shaped lawn toys that fling water in unpredictable patterns — the researchers found that a single mechanism, the momentum carried by flowing water, explains the rotation of sprinklers running both forward and in reverse, according to New York University. The findings were published in the Proceedings of the National Academy of Sciences on July 13, 2026, according to EurekAlert!.

What We Know

The reverse-sprinkler question asks what happens when a sprinkler runs backward, with water flowing into its arms instead of spraying outward: does it spin, and if so, which way? According to EurekAlert!, the question was “made famous in the 1980s by physicist Richard Feynman’s failed experimental attempts to resolve it.” A separate, older explanation for how ordinary sprinklers turn was “put forth in the 1880s by physicist Ernst Mach,” who argued that “fluid swirls in one direction and the sprinkler in the other,” according to New York University.

The NYU-led team, headed by Leif Ristroph, an associate professor at NYU’s Courant Institute School of Mathematics, Computing, and Data Science, first investigated the problem in 2024 using a conventional S-shaped sprinkler. That earlier work found that “a reverse sprinkler rotates much more slowly than does a conventional one — about 50 times slower — even though the mechanisms are fundamentally similar,” according to New York University. But that study left open the possibility that more complex designs — “such as the silly sprinklers that spread water through differently curved and loopy tubes — might yield a different answer,” and it “was not able to disprove other leading theories,” per the same release.

To close those gaps, the researchers built multiple silly sprinklers with varying contours and tested each one in both forward and reverse modes, according to Phys.org. They “measured the sprinklers’ rotational motions, the flows outside and inside the devices, and the torque or twisting force,” according to New York University.

The results ruled out both rival theories. Mach’s swirl-based explanation “could not account for reverse rotations and torques” observed across the new tests, while Feynman’s own hypothesis — which centered on “water flows occurring at the very outside of the sprinklers’ arms” — also failed, since experiments showed “the outer portions of the arms and the flows there had no effect on the sprinkler motions and torques,” according to New York University. Instead, the team found “strong support” for its own momentum flux theory, which it “generalized and found to apply equally well for both reverse and forward modes and for all the differently shaped sprinklers,” per the same source.

According to New York University, a conventional forward sprinkler works “like a rotating version of a rocket powered by water jetting out of the arms,” while a reverse sprinkler acts as an “inside-out rocket,” with jets shooting inside the chamber. The rotation in reverse mode arises because “the two internal jets collide, but they do not meet exactly head-on—a subtle effect that produces forces that rotate the sprinkler in reverse,” according to Phys.org.

Ristroph summarized the result: “By showing that momentum flux is the answer to Feynman’s Sprinkler Problem, our findings address a long-standing open problem in flow physics,” according to New York University. Co-author Brennan Sprinkle, an assistant professor at the Colorado School of Mines, pointed to potential engineering payoffs: “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,” he said, according to New York University.

The study’s other authors are NYU graduate students Jesse Smith and Mingxuan Zuo and NYU undergraduate Will Kuhlke, according to ScienceDaily. The work was supported by National Science Foundation grants DMS-2407787 and DMS-2407788, according to EurekAlert!.

What We Don’t Know

The press materials describe torque and flow measurements made across several sprinkler geometries but do not disclose the underlying numerical torque values or the precise angle by which the internal jets miss meeting head-on. The full PNAS paper, which could contain those figures, was not accessible for direct review at publication time. It is also not stated whether the team’s silly-sprinkler results changed the 50-times-slower rotation ratio established in the 2024 study of the conventional sprinkler, or whether that ratio held across the newly tested designs as well.

Analysis

The study’s practical framing — pointing toward turbines and other energy-conversion devices — suggests the researchers see the work as more than a revisit of a decades-old curiosity. By testing a family of differently shaped sprinklers rather than a single design, the team was able to distinguish a universal mechanism (momentum flux) from an explanation that might have applied only to one geometry, addressing the core limitation that had left the 2024 study inconclusive against rival theories.