- cross-posted to:
- science@beehaw.org
- cross-posted to:
- science@beehaw.org
We might not need to “unwater” our lawns, but results could help control fluid flows.
A typical lawn sprinkler features various nozzles arranged at angles on a rotating wheel; when water is pumped in, they release jets that cause the wheel to rotate. But what would happen if the water were sucked into the sprinkler instead? In which direction would the wheel turn then, or would it even turn at all? That’s the essence of the “reverse sprinkler” problem that physicists like Richard Feynman, among others, have grappled with since the 1940s. Now, applied mathematicians at New York University think they’ve cracked the conundrum, per a recent paper published in the journal Physical Review Letters—and the answer challenges conventional wisdom on the matter.
“Our study solves the problem by combining precision lab experiments with mathematical modeling that explains how a reverse sprinkler operates,” said co-author Leif Ristroph of NYU’s Courant Institute. “We found that the reverse sprinkler spins in the ‘reverse’ or opposite direction when taking in water as it does when ejecting it, and the cause is subtle and surprising.”
Ristroph’s lab frequently addresses these kinds of colorful real-world puzzles. For instance, back in 2018, Ristroph and colleagues fine-tuned the recipe for the perfect bubble based on experiments with soapy thin films. (You want a circular wand with a 1.5-inch perimeter, and you should gently blow at a consistent 6.9 cm/s.) In 2021, the Ristroph lab looked into the formation processes underlying so-called “stone forests” common in certain regions of China and Madagascar. These pointed rock formations, like the famed Stone Forest in China’s Yunnan Province, are the result of solids dissolving into liquids in the presence of gravity, which produces natural convective flows.
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Pretty neat! I guess I’m one of those naive folks who would have said that it’s obvious it goes in reverse. I also don’t see why this would be so hard to just test. Submerge a sprinkler, attach a pump to the hose, observe it moving in reverse as each arm sucks water up, right?
The big question then becomes: “is that behaviour inherent to all systems like this, or just this one?” Like, if you go to the store, buy a basic sprinkler, and then test it and it behaves exactly opposite to how you might expect it to. Or it does something completely unexpected, like phases into another dimension and starts pumping strawberry jam. Your next step shouldn’t be to say “Oh, weird, I guess that’s that.” You’d start knocking down variables. Is it the same with every sprinkler or just this one? Does the amount of suction applied affect it? If I replace the water with something else does the outcome change?"
If you’re doing research like this, you’re kind of expected to do the same sort of elaboration even if the result of a basic experiment conforms precisely to your hypothesis, because the question isn’t if any given sprinkler setup behaves in this way, it’s about whether this is a universal phenomenon across all similar setups. Because there’s an xkcd for everything, it’s this.
There is a difference between observing that the apple hit your head because of gravity and figuring out its number (and why), and how to potentially use it to further science in general.
I’m with you. As an engineer, I know a sprinkler works through the transition of potential energy (pressure) to kinetic energy (water jet) and the the law of momentum requires an opposite reaction to the ejected water. For the opposite you would still have the energy of the pump and the momentum of water which must change direction through the flow. OTOH, also as an engineer, I know that there are some effects we ignore or intentionally discount as being insignificant to “real world” applications. Depending on the application, 10% error may be more than close enough, or 0.1% might be. It’s rare that anything beyond the third significant digit affects something an engineer would care about, but physicists deal almost exclusively in those fine differences (having worked with them) and weird things really do happen.
Answer:
NYU’s Applied Mathematics Laboratory Ristroph et al. found that the reverse sprinkler rotates a good 50 times slower than a regular sprinkler, but it operates along similar mechanisms, which is surprising. “The regular or ‘forward’ sprinkler is similar to a rocket, since it propels itself by shooting out jets,” said Ristroph. “But the reverse sprinkler is mysterious since the water being sucked in doesn’t look at all like jets. We discovered that the secret is hidden inside the sprinkler, where there are indeed jets that explain the observed motions.”
A reverse sprinkler acts like an “inside-out rocket,” per Ristroph, and although the internal jets collide, they don’t do so head-on. “The jets aren’t directed exactly at the center because of distortion of the flow as it passes through the curved arm,” Ball wrote. “As the water flows around the bends in the arms, it is slung outward by centrifugal force, which gives rise to asymmetric flow profiles.” It’s admittedly a subtle effect, but their experimentally observed flow patterns are in excellent agreement with the group’s mathematical models.
