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The figure above is a schematic diagram of a rotating lawn sprinkler as seen from above. Water is injected into the central hub and squirted out the bent tubes as shown by the arrows. This causes the sprinkler to rotate in a clockwise direction as shown by the curved arrow at the top of the figure.

My question is as follows: Suppose the sprinkler were placed at the bottom of a pool and the hub were connected to a suction pump. This pump would then suck water in through the inlets in a direction opposite the arrows shown. In what direction would the sprinkler rotate, counter clockwise or clockwise? I believe that it would still be clockwise.

My argument is that as the water enters the tubes it has to make a right angle turn. This causes the water to transfer momentum to the tubes in a direction that causes the sprinkler to rotate clockwise. Does anyone have a counter-argument?

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This problem is usually called Feynman's Inverse Sprinkler, although the wikipedia article points out that it was first discussed by Ernst Mach and Feynman disliked it being attributed to him.

A solution was published by Alejandro Jenkins in the American Journal of Physics 72(10) 1276-82, republished in arXiv in May 2004 as An elementary Treatment of the Reverse Sprinkler. This examines various solutions which have been proposed, and results of experiments, and appears to be definitive.

Jenkins concludes that, in the steady state, if the liquid is ideal and has no viscosity, then the sprinkler does not turn either way. However, when the flow is increasing or decreasing there is a torque on the sprinkler - anticlockwise when the inward flow increases, clockwise when it decreases. When viscosity is taken into account, the sprinkler turns slowly towards the incoming liquid (anticlockwise in your diagram) even when the flow is steady. This torque is very small, and is often outweighed by friction in the bearings of the sprinkler.

The explanation is that the anticlockwise reaction force caused by the pressure difference of "sucking in" water, is exactly balanced by the clockwise momentum of the sucked-in water striking the walls of the sprinkler. You got the momentum transfer right, but missed the pressure difference effect.

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  • $\begingroup$ Yes, the sucking is not necessarily a time reversal of the spewing out, because when spewing out, the water can have a very different history from the water surrounding it. It could be at high pressure, for example. But when sucking in, it starts from the pressure of the surroundings, so that's important. I should have read the details more carefully. $\endgroup$
    – Ken G
    Commented Sep 25, 2016 at 4:05
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I think you are right, but the puzzle is included in one of Feynman's books, where he claims he brought it up to some well-known physicists and it created a bit of a stir. The argument for counterclockwise motion that Feynman suggested was based on Bernoulli's principle, as I recall, but I never found it convincing and I'm not sure he intended it seriously. He was something of a trickster, after all!

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  • $\begingroup$ Yes, Feynman's always a kick, highly recommended. $\endgroup$
    – Ken G
    Commented Sep 25, 2016 at 0:47
  • $\begingroup$ It is mentioned in the biography by James Gleick. Instead of using a suction pump Feynman compressed the water in a large jar which contained the sprinkler, to force the water backwards through the sprinkler... The glass jar exploded. He was fortunately out of the lab when it happened... Even geniuses have blindspots, it seems. $\endgroup$ Commented Sep 25, 2016 at 1:59

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