Mathematicians Finally Solved Feynman's 'Reverse Sprinkler' Problem (arstechnica.com) 58
Jennifer Ouellette reports via Ars Technica: 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." [...]
Enter Leif Ristroph and colleagues, who built their own custom sprinkler that incorporated ultra-low-friction rotary bearings so their device could spin freely. They immersed their sprinkler in water and used a special apparatus to either pump water in or pull it out at carefully controlled flow rates. Particularly key to the experiment was the fact that their custom sprinkler let the team observe and measure how water flowed inside, outside, and through the device. Adding dyes and microparticles to the water and illuminating them with lasers helped capture the flows on high-speed video. They ran their experiments for several hours at a time, the better to precisely map the fluid-flow patterns.
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.
Enter Leif Ristroph and colleagues, who built their own custom sprinkler that incorporated ultra-low-friction rotary bearings so their device could spin freely. They immersed their sprinkler in water and used a special apparatus to either pump water in or pull it out at carefully controlled flow rates. Particularly key to the experiment was the fact that their custom sprinkler let the team observe and measure how water flowed inside, outside, and through the device. Adding dyes and microparticles to the water and illuminating them with lasers helped capture the flows on high-speed video. They ran their experiments for several hours at a time, the better to precisely map the fluid-flow patterns.
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.
Re:Whistle suckers. (Score:5, Insightful)
It's advanced applied mathematics and physics.
There are hundreds of "who gives a fuck" cases throughout history which proved to save many lives afterwards. PAP screening always comes to mind (OK, that's medicine, still valid, though).
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There's always "something else" that this person or another prioritizes over another "something else".
You want funds to go to that thing, I want funds to go to the other thing, which we deem more practical, or more important or whatever, then we realize all of a sudden that my country or yours are shit in the world in terms of advanced research in several categories, and then we both scream "Y U NOT DONE SOMEHTING???"
Careful what you wish for, it might come true, but not in the way you envisioned.
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If you had that insight as a 4th grader, you must have been an exceptional child.
The physics underpinning the reverse sprinkler is the same principle that makes pop pop boats [wikipedia.org] work: intuition would have you deduce that pop pop boats should remain stationary, yet they move forward. It took me a long time as an adult to wrap my head around that.
Re: Physicists are exictied that physics works... (Score:4, Insightful)
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You're correct. The poster above you, who claims an obvious and inescapable result, is ignorant of the physics involved (which is why it makes a compelling problem in the first place, and is why it entered the collection of stories about/around/by Feynman).
Re: Physicists are exictied that physics works... (Score:1)
How does an opposite action lead to anything other than an opposite reaction?
I mean, that was the eventual result.
Re: Physicists are exictied that physics works.. (Score:2)
Reversing the flow through a sprinkler does not reverse the physics, I guess this is the part you're missing? Fully reversed, it would look like a video of a sprinkler played in reverse. That's not what reversing the flow through a sprinkler does unless you have spaghetti-like strands of water to feed back through the nozzles.
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When "action" and "reaction" aren't well-defined, or even sensible. For example, during preacceleration of a charged particle (the Abraham-Lorentz force).
And in the case in question, where entropy is generated.
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To reverse entropy you need to reverse probability, not time. Antimatter looks just like matter traveling backward in time, and of course its entropy increases. That is to say, the effect of reversing time is that entropy still increases but matter and antimatter switch places. And if you were to rewind time you wouldn't see any laws of physics being violated (they're time symmetric) but you'd see very improbable outcomes.
Considering there's 100 quadrillion atoms in a speck of dust, you can round that impro
Reversible process (Score:2)
The ejection of water past the sprinkler nozzles is not a reversible process, dude.
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My understanding of this problem was that it was a hypothetical problem assuming that it was possible, like those perfectly spherical frictionless cars.
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Most would assume the sprinkler moved in reverse because it FEELS correct.
The physicists found out WHY it does that.
Re:Physicists are exictied that physics works.... (Score:4, Informative)
The physicists found out WHY it does that
The physicists did in no way confirm the common-sense idea most people have about this problem,. Most would assume the sprinkler moves in reverse when the flow of water is reversed (opposite action = opposite reaction). But physicists argued that the sprinkler would in fact stand still with all forces cancelling out... if you reduce the problem to simple laminar flows of water and the forces they exert on the sprinkler. According to TFA, Feynman even confirmed this in an experiment.
What they did find is that there is a tiny additional force to be accounted for (resulting from vortices inside the sprinkler). The effect is very subtle and is only visible when you suck high volumes of water into a sprinkler on low-friction bearings. In real-life situations (and Feynman's experiment), the sprinkler does not rotate.
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Re: Physicists are exictied that physics works.... (Score:2)
Dunno if you've noticed, but "Chinese Made" no longer works to imply "poorly made" since close to EVERYTHING you can buy in the US is now Chinese Made, from a fair amount of Apple stuff to the Hoorbatgurk flashlight you bought on Amazon that broke upon unpacking it.
"Japanese Made" didn't mean "Crap" after a couple decades, and now barely appears at all, as the Japanese have most of their stuff made in China, too.
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Made in Japan tree pruning saws (Score:2)
The Japanese "tricut" blade tree pruning saw blades are top notch. I don't know how I got by without them.
Is a water jet really like a rocket? (Score:3)
A rocket works by expanding gas pushing back on the rocket as it tries to escape from the nozel. Water in a sprinkler or hose isn't expanding as it exits, its simply moving and any force it exerts in theory should be on whatever corners or curves it goes around before it gets to the exit. Or am I missing something?
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Technically the expansion gives it a benefit. But if your rocket literally weighed only a few grams and you expelled the fuel without igniting it out the back, yes it would also be propelled. This is the 3rd law of motion. The majority of the force in the sprinkler doesn't come from the fluid moving around a corner, it comes from the expelling of a significant mass.
Incidentally this is precisely why the suck vs blow in this case produced a 50x difference in resulting spin speed, the internal forces of fluid
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Newtons law assumes there is a reactive force. Where is the force on the pipe when water is simply moving through it? The reactive force should be back at the pump , not at the hose or pipe simply guiding the water.
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I've a got a fire hose you're welcome to use to test your theory with!
It really is like a rocket in my experience. I suspect it's for a similar reason as the rocket engine as well. The restriction of the nozzle as you'd find in a sprinkler or fire hose causes the water to speed up. It's a combination of the mass and speed that give specific impulse to the nozzle itself.
I would love to get the full explanation of the physics involved here.
Re: Is a water jet really like a rocket? (Score:2)
Yes I know it happens, what I dont understand is why. And you dont need a restricter for it to happen either, a normal hose will push back too.
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Except the hose isn't pushing the water out, its just guiding it. Any force should be exerted back at the pump.
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A rocket works by expanding gas pushing back on the rocket as it tries to escape from the nozzle
Incorrect.
A rocket works by expelling mass at high speed, exploiting Newton's third law of motion. The expansion effect you note is real and important, but it just serves to increase the speed at which the exhaust mass is expelled. It's a large efficiency enhancement to the basic underlying principle, not the basic principle.
What? (Score:2)
I thought one of those sprinklers spun because they contained an arm on a hinge that was impacted by the water jet, causing it to impart spin when in was pushed out and hit a stop. It then was pulled back by a spring and the process repeated.
Remove the arm and it is just a nozzle and would flop around like every other nozzle if it wasn't fixed to the ground.
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Maybe those were developed after Feynman was doing his own lawncare?
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Yes you're thinking of the common impact sprinkler (https://en.wikipedia.org/wiki/Impact_sprinkler). Feynman was referring to a different kind, which are still common for some applications: https://en.wikipedia.org/wiki/... [wikipedia.org]
Why? (Score:1)
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Never say "just" when you're talking about fluid dynamics.
Mod this up (Score:2)
Just sayin'.
I don't agree (Score:2)
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Though they say they found internal fluid dynamics were responsible for the spinning... I would very much like them to explain how they ruled out the effect you describe as a factor. (Maybe they did, I did not RTFA.)
WTF (Score:2)
Where does the water come from?
Guys guys guys (Score:2)
There's no way Feynman actually meant for you to BUILD a reverse sprinkler, right? It was a math problem wasn't it?
I mean just the summary is totally wild, that's great work though.
And you had to answer it (Score:2)
with equations and explaining your work in Caltech Freshman physics.
'Challenging conventional wisdom' (Score:2)
The math people finally proved what we have seen forever. Great, but can this be applied to anything to improve existing designs of anything else?
Internal pressure/flow (Score:2)
This is not really surprising. While the forward sprinkler operates on conservation of momentum (mass of water traveling along a velocity vector), the reverse system inflow suction draws water from all directions, canceling out most of that momentum effect.
However, flow inside the nozzles is (more or less) laminar. Giving it a defined velocity vector and momentum. Also, any change in direction creates additional velocity vectors which need to be resolved.
I would think that actual pressure distribution ins
False equivalence (Score:1)