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The Feynman Sprinkler

August 18, 2013

It’s amazing how many of us understand the basics of quantum mechanics and general relativity, but still get tripped up by seemingly simple things. I’ve mentioned in the past that we’re still not entirely certain why a bicycle stays upright, which I think it pretty spectacular; we can put a man on the moon, but a bicycle thwarts us.

Recently I posted about a particularly nifty way to cool beer and I couldn’t be certain of the exact mechanism. Recently I had a good opportunity to use this method when I was having some knock-off beers with a bunch of physics PhD students, so I asked them to speculate on the mechanism too. It wasn’t immediately obvious to anybody there and even after the ensuing discussion, there still seemed to be some uncertainty. I think I’m pretty convinced now that it’s mainly evaporative cooling now though. (Although I’m yet to demonstrate this by experiment.)

So anyway, the point of this post wasn’t to talk about all that again. As a PhD student, Feynman and his fellow students found a problem in a hydrodynamics textbook that caused a bit of a stir. In fact after the students got nowhere with it, they took it to Feynman’s doctoral advisor, John Wheeler — who is a pretty damn big-shot himself — and even he didn’t have an answer for them. So what is it that thwarted some of the greatest minds of modern times? A sprinkler. A god-damn sprinkler.

"Physics is my bitch"

“Physics is my bitch”
Image credit: A. Jude

Imagine a simple sprinkler; so simple that it’s easier to show you a picture than to actually describe it.

The curly bits are rigid.

The curly bits are rigid.

Hopefully it is obvious that this will start spinning clockwise (as viewed from above) when we turn it on. What if some idiot neighbour kid decides to kick the sprinkler in the pool? Well obviously we go outside and beat that kid up for intervening with science. But what about the sprinkler? Will the sprinkler still keep rotating if it’s under water? Hopefully it is still obvious that the sprinkler will still keep rotating, just as before. This isn’t any different to having the sprinkler still above water but blowing air out instead; it will still propel itself around.

But now for the tricky part; the part that stumped the big-wigs. What if the direction of the water flow is reversed? Imagine that instead of blowing water out of the sprinkler, it sucked it in. If it helps, imagine that you stole the neighbour’s vacuum cleaner — apparently they had it coming — and you connected the vacuum to the sprinkler, where the hose goes in. We use the neighbour’s vacuum because the vacuum isn’t recovering from this. But the point is, the water is now flowing into the sprinkler instead of gushing out of it.

So which way does the reverse sprinkler rotate? Does it keep rotating the same way, or does it change direction? When the physicists discussed this, they all thought the answer was immediately obvious; half of them said it obviously goes the same way, while the other half said it changes direction.

One half: The ingoing water pushes the sprinkler arms in the direction that the water is flowing in, causing it to continue to rotate clockwise.

Other half: The entering water causes a suction effect where they water enters the sprinkler arms, causing it to rotate anticlockwise.

Since there was so much confusion, Feynman and his fellow students did the only reasonable thing they could do; they built a reverse sprinkler using equipment in a lab at Princeton. And like all good scientists, they conclusively established which way it would rotate and patted each other on the back for a job well done… Oh wait. No that’s not what happened at all! Excessive water pressure resulted in an explosion of water and shattered glassware.

It actually turns out that in most cases it doesn’t move at all. But in an ideal scenario (minimal friction) the sprinkler does start rotating in the opposite direction.

This reverse sprinkler is almost always attributed to Feynman now, despite his best efforts to tell people that he just found it in Ernst Mach’s textbook.

  1. Ben Farmer permalink

    I agree that it obviously has to reverse direction :p. The fluid that the sprinkler is immersed in starts out at rest and moves towards the tubes, so to conserve momentum locally something has to go in the opposite direction to the fluid!

    • Ben Farmer permalink

      Or more technically the water gets sucked in to the sprinkler due to lower static pressure along the open end of the tube, so the net force from the surrounding fluid on the arms has to be in that direction

      • I don’t think it’s that simple. The net force on the sprinkler arms is tiny compared to the force being applied by the vacuum. Early experiments concluded that it actually doesn’t move at all; at least that’s the conclusion in Mach’s book.

        Obviously an external force is acting on the water, whose momentum (tangent to the circle traced out by the ends of the sprinkler) is transferred to the sprinkler. This must make it go the same way as it did previously.

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