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. //

Mach proposed that there would be no rotation with a reverse sprinkler: the reaction force on the nozzle as it sucks in water pulls the nozzle counter-clockwise, while the water flowing into the inside of the nozzle pushes it clockwise. The two forces cancel each other out in this steady-state scenario. Feynman’s own experiment showed a slight tremor when pressure was first applied to pump water through the nozzle, and then the sprinkler returned to its original position and remained still.

But others suggested that if the friction was low enough and the inflow rate high enough, a reverse sprinkler will start to turn in the opposite direction of an ordinary sprinkler, thanks to the formation of a vortex inside.