In graduate school, my advisor introduced us to a particularly vexing fluid dynamical thought experiment known as the Feynman sprinkler. After observing an S-shaped sprinkler that rotated when water shot out its arms, physicist Richard Feynman wondered what would happen if the device were placed in a tank of water with the flow reversed. If the sprinkler was sucking in water, would it rotate and, if so, in what direction?
This seemingly simple question has confounded physicists ever since, in part because you can make believable arguments for multiple different results. Attempts to build the apparatus experimentally produced differing results, too — often due to variables that don’t appear in the thought experiment, like friction in the sprinkler’s bearing. But, at long last, a group posits they have the final answer to the problem.
They cleverly built their sprinkler so that it floats in its tank, with the addition or removal of water from the sprinkler controlled by a second siphon-connected tank. With no solid-solid contacts, the sprinkler can rotate with very little friction.
The team found that sucking water into the sprinkler does, indeed, reverse the sprinkler’s rotation, but it’s not a simple reversal of the forward sprinkler’s flow. To see why, check out the video above, which visualizes flow inside the sprinkler during suction. For clarity, the device is held fixed in place during flow visualization. Notice that the two arms of the sprinkler sit directly opposite one another in the hub. Thus, you’d expect their two jets to collide and form counter-rotating vortices along a vertical axis. But the vortex pairs are offset from the centerline.
This asymmetry takes place because the velocity profiles of flow across the hub inlets are skewed. Instead of the largest velocity occurring on the centerline of the inlet, each occurs slightly to one side. So when the jets collide, they do so off-center and impart a torque to the sprinkler. The reason for the skewed profiles at the inlets lies further upstream in the curved arms of the sprinkler. Centrifugal force from turning the corner leaves a mark on the flow, leading, ultimately, to the skewed velocity profiles, offset jets, and spinning sprinkler. (Image and research credit: K. Wang et al.; via APS Physics)