For decades, the peculiar behavior of reverse sprinklers—sprinklers that draw water inward rather than spraying it outward—has puzzled physicists and engineers alike. This enigmatic phenomenon, famously highlighted by Richard Feynman’s experiments, is finally being unraveled through a series of ingenious studies conducted by a team of mathematicians at New York University’s Courant Institute and collaborators. Their latest experimental work decisively answers the long-standing question: how and why do reverse sprinklers rotate?
In essence, conventional sprinklers expel water through curved arms, spinning like rotational rockets powered by outward jets. Reverse sprinklers, on the other hand, draw water inward, creating an “inside-out rocket” where water jets converge within the device rather than shooting outward. Prior to this study, the exact mechanics behind the subtle forces causing reverse sprinkler rotation remained elusive, complicated by fluid flow dynamics and torque analysis.
Leveraging custom-built sprinklers with diverse geometrical designs—reminiscent of the so-called “silly sprinklers” whose looping arms spray water in whimsical patterns—the researchers meticulously measured rotation rates, fluid flow patterns, and torques under both forward and reverse operating modes. This allowed for a comprehensive test of competing hypotheses in fluid mechanics that have vied to explain these motions for over a century.
The team found that the motion of sprinklers is governed predominantly by the angular momentum carried by the fluid jets, both in forward and reverse configurations. This “momentum flux theory” asserts that the swirling water’s angular momentum and ensuing colliding jets inside the sprinkler’s arms generate measurable rotational forces, controlling the device’s spin direction and speed. In contrast, classical theories dating back to Ernst Mach’s 19th-century ideas and Feynman’s interpretation—focusing on fluid swirl direction or external arm flows—failed to account for observed torques and rotation patterns in the new experimental data.
This breakthrough not only decodes a notorious physics paradox but also enriches our grasp of how fluid flows interact with mechanical structures, with far-reaching implications for engineering innovations. By controlling arm geometry, engineers could tailor fluid-induced forces with precision, optimizing the design of turbines and energy-harvesting devices that rely on similar flow-momentum interactions.
Moreover, the work reveals why reverse sprinklers rotate markedly slower—about 50 times less rapidly—than their conventional counterparts, as colliding internal water jets partially offset each other’s momentum while producing subtle but detectable torque. Such insights might steer future developments in efficient fluid machinery by harnessing the interplay of flow geometry and momentum flux.
By experimentally uniting theory, geometry, and flow dynamics, this study settles a physics riddle that has attracted curiosity since the mid-20th century. Most importantly, it lends a robust, generalized framework for understanding how diverse fluid-flow systems exert forces on contained mechanical structures, enabling advancements beyond the backyard sprinklers where it all began.
As the Courant Institute evolves into a comprehensive school uniting mathematics, computing, and data science, this research exemplifies the transformative power of interdisciplinary collaboration. Its findings, published in the prestigious Proceedings of the National Academy of Sciences, underscore how revisiting seemingly simple problems can unlock fundamental principles with wide-reaching technological impact.
Subject of Research: Fluid flow dynamics and their interaction with mechanical structures
Article Title: Geometry controls momentum flux in the sprinkler problem
News Publication Date: 13-Jul-2026
Web References: http://dx.doi.org/10.1073/pnas.2537479123
Image Credits: NYU’s Applied Mathematics Laboratory
Keywords
Fluid flow, momentum flux, reverse sprinkler, angular momentum, fluid dynamics, energy harvesting, classical mechanics
