Physicists Crack the ‘Feynman Sprinkler’ Mystery After Decades of Debate

Scientists have claimed to have finally provided a detailed solution to what is arguably the most famous lawn-care-related puzzle in physics.

Commonly known as the Feynman sprinkler problem, the riddle is named after the legendary 20th-century physicist Richard Feynman, who famously struggled to solve it despite not being the original person to pose the question.

The conundrum asks: if a standard lawn sprinkler is submerged underwater and its flow is reversed so that water is sucked into its arms instead of being sprayed out, will the device rotate in its original direction, spin in the opposite direction, or remain stationary?

A research team led by Leif Ristroph, an experimental physicist and applied mathematician at New York University, believes they have finally cracked the case. “I am confident we’ve provided the experimental answer to the Feynman sprinkler problem,” Dr. Ristroph stated.

Their findings are detailed in a recent paper published in the Proceedings of the National Academy of Sciences.

“This Feynman problem, as put by Feynman — this is solved,” remarked Detlef Lohse, a professor at the University of Twente in the Netherlands, who was not involved in the study.

To grasp the complexity of the reverse submerged sprinkler, one must first look at a standard S-shaped garden sprinkler. As it rotates, water flows up through the center and out through nozzles at the ends of the curved arms, creating thrust that spins the device. The physics governing this motion—essentially behaving like a water-powered rocket—is well-understood and uncontroversial.

However, reversing the flow transforms the problem into a much more complex challenge.

Despite the equations governing the water and the sprinkler being identical, a simple answer has eluded scientists for decades. Physicists have been debating the issue since Austrian physicist Ernst Mach first described it in 1883.

In his memoir, “Surely You’re Joking, Mr. Feynman,” Feynman noted that the topic was a frequent point of contention among graduate students during his time at Princeton University in the 1940s.

Feynman presented competing arguments for how the reverse sprinkler might spin in either direction, but he never reached a definitive conclusion. He did mention his attempt to settle the matter through experimentation, which ended in disaster: “Suddenly the whole thing just blew glass and water in all directions throughout the laboratory,” Feynman recounted.

Dr. Ristroph turned his attention to the mystery approximately five years ago. “I was searching around for some good unsolved hard problems, and this one really caught my eye, just because it has such an infamous history,” he said.

One of Ristroph’s collaborators was Brennan Sprinkle, then a postdoctoral researcher at NYU. “Leif said something very polite,” Dr. Sprinkle recalled. “A polite version of ‘Hey, you’ve got a kind of funny name — check out this experiment I got running.’”

Upon visiting the lab, Dr. Sprinkle was immediately intrigued by both the coincidence of his name and the scientific intrigue. “My first reaction was, yeah, this would be funny,” he said. “And then my second reaction was, ‘Oh, actually, this is a deeply nonintuitive problem that is very cool.’”

Theoreticians had long offered conflicting predictions regarding the rotation, and previous experiments—even those more stable than Feynman’s—had failed to yield conclusive results.

Following rigorous testing, Dr. Ristroph and his NYU colleagues reported two years ago that they had discovered the answer: a submerged sprinkler sucking in water rotates in the opposite direction of a standard spraying sprinkler.

The rotation is significantly slower, moving at roughly one-fortieth the speed of a typical sprinkler.

The researchers also identified the mechanism behind this reverse rotation. The bends in the sprinkler arms create a force that shifts the two incoming jets of water.

“If you’re a car and you’re turning right, you will feel a force, an inertial force, going in the opposite direction,” Dr. Sprinkle explained.

In the fluid medium, this force prevents the jets from colliding head-on, instead creating a twisting force that drives the sprinkler’s rotation.

The discovery has faced some skepticism.

“I have never received so much hate mail,” Dr. Ristroph admitted.

Because fluid dynamics are notoriously complex, critics questioned whether a single experimental configuration could represent the general rule.

To address this, a new series of experiments detailed in Monday’s paper tested various “silly sprinkler” shapes to see if different configurations altered the spin direction.

For instance, they tested Feynman’s theory that suction at the ends of the arms would dictate the direction. They added a second bend to each arm, facing the opposite direction, to see if it would change the outcome.

“It does nothing like it, just didn’t matter,” Dr. Ristroph noted. The modified sprinklers rotated in the same direction as the simple S-shape. Other variations yielded similar results. The primary factor was the amount of bending near the pivot, which determines the offset of the incoming jets.

“The alternative ideas are ‘pretty definitively wrong from what we found,’” Dr. Ristroph said, expressing renewed confidence in their 2024 findings.

While reverse-spinning submerged sprinklers have little practical utility, the research provides vital insights into how solid objects interact with fluid flows.

This knowledge could eventually be applied to advanced engineering, such as designing systems to harvest energy from wind or ocean waves.

Dr. Ristroph noted that the problem isn’t entirely settled, as no one has yet produced a computer simulation that accurately maps how water exerts pressure on the sprinkler. The complexity arises from the high internal pressures and the constant motion of all elements.

This remains the current focus of Dr. Sprinkle, now a professor of applied mathematics and statistics at the Colorado School of Mines.

“It just winds up being a pretty numerically challenging setup,” Dr. Sprinkle concluded.

Source link