What happens when lawn sprinklers suck in water? Physicists answer that quirky question

Jets and vortices in the sprinkler make it twirl in the opposite way from when it spews water

Jets of water extend out of an s-shaped sprinkler in a tank of liquid

Conservation of momentum explains the movements of an S-shaped sprinkler, which spins counterclockwise as it expels streams of water (visualized with green dye) when submerged in a tank of water. Physicists want to understand what happens when the sprinkler sucks water in instead.

Applied Math Lab/NYU

Physicists are fascinated with heady puzzles, from the nature of space and time to how the universe came to be. But spinning lawn sprinklers? Yes, that too.

A new experiment provides an answer to a quirky physics quandary popularized by physicist Richard Feynman in the 1980s. The puzzle centers on a style of sprinkler that works by squirting water out the ends of an S-shaped tube. The sprinkler spins away from the escaping water due to conservation of angular momentum. That much is straightforward.

But what happens if you stick the sprinkler in a tank of water and have it suck the water in? The question seems simple. But complex fluid flows and subtleties of momentum conservation have led different physicists to argue that it should either spin in the opposite direction as it does when operated normally, or not move at all. Different experiments likewise clashed.

So applied mathematician Leif Ristroph and colleagues gave it a whirl. “It ended up being one of the hardest problems our lab has ever worked on,” says Ristroph, of New York University. The team performed experiments with a painstakingly crafted transparent sprinkler, alongside mathematical calculations that backed up their measurements. The device floats in a tank of water to reduce friction, an effect that confounded earlier experiments. When run in reverse, the sprinkler indeed spins the opposite way, the researchers report in a paper accepted to Physical Review Letters. Further experimentation revealed why.

Whereas the normal sprinkler spews jets of water outward, in the reverse operation, jets form within the sprinkler itself. These jets stir up vortices, observed using lasers to illuminate microparticles added to the water. Importantly, the jets and their vortices aren’t symmetrical. When the jets collide in the sprinkler’s middle, they continue at an angle, suggesting they made a glancing collision, rather than hitting head-on.

This high-speed video shows fluid moving inside a sprinkler as it sucks in water (made visible by laser-illuminated microparticles). As the water enters the sprinkler, two jets form and collide at glancing angles, forming four asymmetric vortices. In this part of the study, the sprinkler was fixed in place, rather than being allowed to rotate. But when released, the jets’ momentum sends the sprinkler spinning in the opposite direction of a normal sprinkler that spews water out, solving a longstanding physics puzzle.

That’s because, even though the arms of the sprinkler are perfectly aligned, the internal jets aren’t. The trip through the curved arms displaces the flow of water in each jet. That asymmetry sets the sprinkler rotating backward to conserve angular momentum.

The sprinkler puzzle’s solution just demanded a spritz of insight.

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