The long-running mystery of the Feynman Sprinkler

Richard Feynman left the world many legacies, including multiple books on physics, the atomic bomb, and some stellar bongo solos. He also left the world the mystery of the Feynman Sprinkler — proving that science doesn't have to be impressive to be frustrating.

To be fair, Feynman didn't want it to be called the Feynman Sprinkler. The idea for the sprinkler, and its first working model, were made by Ernst Mach, an earlier physicist. Mach had seen the typical water sprinkler, a pinwheel affair that moved because it squirted out water. He wondered what would happen if, instead of squirting water out, the sprinkler was put in an aquarium full of water and made to suck water in.


Feynman wondered the same, and even wrote, in one of his books, that he'd made a working model of the reverse sprinkler. After a point, Feynman claimed, the entire thing exploded. He declined to explain either the physics behind the sprinkler or what happened in the lab before his experiment blew up. Instead, he left the behavior of a reverse sprinkler to tease future generations. People decided, en masse, that if he was going to vex them, they were going to vex him right back, and so the problem bears his name despite his wishes.

Standing Still

Mach made a working model of the sprinkler himself, and found that the sprinkler stayed still in the water. For many years, other physicists agreed. That may seem counter-intuitive — most people believe that the sprinkler will just go "backwards" — but consider the arguments made for the standstill. Mach himself made a good one; think about blowing air out through a straw. The air moves out in one directed stream. It goes one way and you (or the sprinkler) goes another. When you're sucking air into a straw, however, you aren't pulling in a column of air, but air from everywhere around the end of the straw. The pulling isn't as directed as the pushing.


Other physicists have put it another way. Yes, pulling inwards on the water should move the sprinkler —the water goes one way, and the sprinkler goes another, and momentum is conserved. But what happens when that water hits that first bend inside the sprinkler? When the water hits that bend it's pushing against the sprinkler. That should knock the sprinkler back as much as it was being pulled forward. So the reverse sprinkler shouldn't be going in reverse, it should be standing still.


Moving Backwards

That's not quite how it worked out. Scientists kept tinkering with the sprinkler, possibly encouraged by Feynman's compatriots. Various people who worked with Feynman at Princeton spilled the beans that, before the explosion, there was the slightest tremor of the sprinkler "backwards" — into the water it was sucking. People worked on the friction of the various sprinkler components, and the sucking speed and when they got it just right. When the sprinkler blows out water it moves in one direction, and when it sucks it in, it moves in the opposite direction.


How does this happen? It's true that the liquid being pulled into the sprinkler will hit the bend in the sprinkler tubing. That should stop the sprinkler once again, but only if the water has the same momentum it had when it was first being pulled into the tube. If the water loses momentum between the mouth of the tube and the bend, the sprinkler will get an overall kick from the water. Water doesn't flow perfectly. It undergoes turbulence, even inside the sprinkler tube. The turbulence of the water itself will dissipate some of the energy the water had when it got sucked into the tube, and when it hits the bend, it will push the sprinkler back with just a little less force than it imparted to the sprinkler when it got sucked in. Because there is less force knocking the sprinkler back than there is pulling the sprinkler forward, the reverse sprinkler will slowly pick up speed.

Top Image: Alegri.

[Via An Elementary Treatment of the Reverse Sprinkler, The Feynman Inverse Sprinkler Problem]


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