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71. Suck or Spout:

The Sprinkler Paradox

The Question:

Sprinklers are S-shaped gardening devices, mounted horizontally on a pipe, through which water is guided and spouted out. The nice thing is that as soon as the water is turned on, the device starts turning in counter-clockwise direction, and keeps turning, thus watering the entire flower bed.[1]

The motion derives from the recoil of the water: as the water is pushed out the nozzle, conservation of momentum requires that there be a counteracting backward momentum. That is what pushes the device into the counter-clockwise rotation.It is the same recoil that you feel when holding a shower hose in your hand and turn on the faucet. If you don’t hold it tightly, it will jump backwards out of your hand.

Now, if such an S-shaped device is supended in a tub filled with water, and it sucks in water, rather than spouting it out, will the device rotate in the other (clockwise) direction?

The Paradox:

No…Yes…

It depends on whom you ask.

Some physicists argue on theoretical grounds that the sucking device should not move at all. But others have demonstrated in experiments that it does rotate, and indeed in the clockwise direction. On YouTube, one can find video clips which show that such S-shaped devices both do, and do not rotate in the clockwise direction when they suck water in.

So, what goes?

Background:

The device that sucks water in, instead of spouting it out, is often called a Feynman Sprinkler, even though the Nobel Prize winner Richard Feynman did not invent it. In fact, he objected to it being called the Feynman Sprinkler even though he made it notorious in one of his books. I will honor the famous physicist by not naming it after him.

It was the Austrian physicist and philosopher Ernst Mach who wrote about the phenomenon in 1883 in “Die Mechanik in ihrer Entwickelung” (The development of mechanics).[2] One would think, he wrote, that when the contraption sucks in water, the opposite rotation should arise than when spouting. “But this does not happen, in general.”

Sixty years later, Feynman, then still a student, devised an experiment tpgtheer with his colleagues, to test the phenomenon experimentally. They submerged an S-shaped device into a glass container filled with water, and let it suck in the water. As Mach had predicted, apart from an initial tremble, the sucking device did not budge. But the brilliant Princeton students apparently did not believe it and increased the flow of water by raising the pressure…until the glass container exploded. And that was the end of it. Feynman never explained why nothing happened and what he had actually expected.

Dénouement:

The confusion arises because one would think that sucking and spouting are symmetric phenomena. However, sucking is not spouting, played backwards.

When the device spouts, Mach explained, a narrow jet of water is directed into the air in front of it. The recoil of this jet is what pushes the S-shaped device in the counter-clockwise direction. It’s all because of the Law of the Conservation of Momentum. The law indicates that the spouting water goes one way and, in order to conserve momentum, the sprinkler goes the other. This forces the S-shaped spouting sprinkler to rotate clockwise.

But when the device sucks water in, it is not a thin column of water that enters the spout. The water comes from all directions. Hence, there is no jet to produce a recoil and there is no clockwise rotation when the S-shaped device sucks the water in.

To illustrate this, one can perform an experiment at home. Stand in front of a fan: your hair is blown backwards in the jet of air. Now go and stand behind the fan. Your hair does not blow at all. In fact, you feel practically nothing. The air that is sucked from behind the ventilator to the front comes from all directions behind the fan, and is only then channeled into a column in front.

Does the law of the conservation of momentum not hold in this case? Does the incoming water not go one way and the sprinkler the other? The explanation is that the incoming water, now a focused column, hits the bend of the S-shaped sprinkler and pushes against the sprinkler, thus countracting the tendency to rotate; the sprinkler remains at a standstill.

Clear enough, so why is there any disagreement? Even Ernst Mach seems to have been aware that some might not agree, as evidenced by his careful wording. The reverse rotation that one may expect does not happen “in general”, he wrote, and added that “as a rule” there is no noticeable rotation. Was he aware of a problem?

In fact, some experiments do show movement, indeed clockwise rotation. But that is due to other factors. The incoming water creates vortices inside the sprinkler and thus dissipates energy. By the time the column of water hits the bend, it has lost some of its momentum. Thus, the counteracting force is a tiny bit weaker than the tendency to clockwise-rotate. And this is why some experiments do show clockwise rotation.

Technical supplement:

Since there were enough technical detail above, there will be no technical supplement here.

© George Szpiro, 2019

[1] If the device is Z-shaped, it will rotate in clockwise direction but for simplicity we only consider S-shaped ones here.

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