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HomeScienceDecades Old Physics Mystery – Feynman's Sprinkler Problem Finally Solved : ScienceAlert

Decades Old Physics Mystery – Feynman’s Sprinkler Problem Finally Solved : ScienceAlert

For generations, the summer heat has sent children running through the spiraling jets of water spewed out by old-fashioned S-shaped garden sprinklers.

But what would happen to the sprinkler if it were submerged and sucked in water? Would it rotate the same way as a normal sprinkler if the flow was reversed, driven by the force of the gushing water, or would it rotate in the opposite direction as the suction drives the rotation forward? Could he stay strangely still?

That’s the decades-old problematic question made famous by renowned mid-20th century physicist Richard Feynman and which has come to be known as Feynman’s sprinkler problem.

Now, a group of mathematicians believe they have finally solved it with a series of laboratory experiments backed by mathematical models.

They are certainly not the first to try it, but it helps that their predictions are validated with experimental results.

Panel of two images showing water flows illuminated by green lasers in two sprinkler configurations.
Water flows are expelled from a normal sprinkler (left) and collide in the internal chamber of a reverse sprinkler (right). (Wang et al., Medical Rev Lett2024)

In the early 1940s, Feynman was a graduate student at Princeton University who built an improvised experiment that, according to his colleagues, showed that the sprinkler remained stationary after a few small oscillations. Ernst Mach thought similarly in 1883, in the first documented reference to the problem.

Since then, experiments have produced conflicting results: some show that the sprinkler head rotates in reverse direction; others observed it changing direction erratically or moving only for a brief moment.

Kaizhe Wang, a doctoral student in physics at New York University, and his colleagues attributed these discrepancies to the geometry of past experimental setups and friction between the rotating shaft and the internal bearing, which possibly counteracted other forces.

So they built a new ultra-low-friction swivel bearing that allowed their custom-made reverse sprinkler to spin freely. The sprinkler had two arms made of curved tubes and a siphon at the top of the cylindrical tube to draw in water when the device was submerged in a tank full of water.

The device was also designed so that it could operate indefinitely, the pump drawing water from a reservoir into which the siphoned water flowed. This allowed the researchers to conduct their experiments for several hours, longer than previous experiments.

Three-part diagram showing the internal center of the sprinkler, its position in a tank filled with water with a pump and illuminated by a laser.
The experimental setup. (Wang et al., Medical Rev Lett2024)

The team also used colored dyes, laser scattering microparticles, and high-speed cameras to visualize and record sprinkler rotation and water flows, so they could compare their experimental results with their model results.

“We found that the reverse sprinkler rotates in the ‘reverse’ or opposite direction when it takes in water and when it expels it, and the cause is subtle and surprising,” explains Leif Ristroph, a mathematician at New York University and lead author of the study. .

Think of a regular sprinkler as a kind of rotating version of a rocket: the sprinkler head is pushed in the opposite direction of the outgoing water jets.

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Wang and his colleagues discovered that in their reverse sprinkler, the incoming water jets collide with each other in the internal chamber of the sprinkler, but are not exactly facing each other, generating torque to rotate the bucket.

The movement of the sprinkler bucket was not constant, but it rotated in the opposite direction, although 50 times slower than an outflow sprinkler. (In the video below, the device is prevented from rotating to improve the visualization of the flows.)

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“The degree of agreement between the experimental and model results is quite remarkable,” McGill University mechanical engineer Michael Païdoussis told Phillip Ball in Physics Magazine.

Other physicists agree that the experiments help clarify the mechanics of this fluid problem, which could have some practical applications.

Ristroph says the findings could be applied to engineering technologies to harvest energy from the flow of air or water, generating motion or forces.

“We now have a much better understanding of the situations in which fluid flow through structures can induce motion,” adds Brennan Sprinkle, a mathematician at the Colorado School of Mines and one of the paper’s co-authors.

The study has been published in Physical examination letters.

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