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Feynman's Reverse Sprinkler SOLVED 2024

A 140-year physics puzzle: if a sprinkler spins when water shoots out, what happens when it sucks water in?

Forward Mode
Water ejects → Sprinkler spins counter-clockwise

Physics State

Angular Velocity 12.5 rad/s
Flow Direction Outward
Torque Source Reaction force
Speed Ratio ~50× faster
1.0×
1.0×

The 140-Year Mystery

A lawn sprinkler works by reaction: water shoots out the curved arms, and by Newton's third law, the sprinkler spins in the opposite direction. Simple enough. But what happens if you reverse the flow—sucking water into the sprinkler instead of ejecting it? Does it spin the same way? The opposite way? Not at all?

The Question: Ernst Mach first posed this puzzle in the 1880s. Richard Feynman famously worked on it at Princeton in the 1940s (and allegedly exploded a container while experimenting). Despite over a century of attempts, the answer remained disputed until January 2024.

Why It's Hard

At first glance, you might think symmetry demands the sprinkler spin backward when sucking—after all, the flow is reversed. But the physics isn't symmetric. When water exits, it carries momentum away from the nozzles, creating clear reaction torque. When water enters, the momentum change happens more subtly, as the incoming flow must turn and accelerate through the curved arms.

Feynman himself wrote: "The problem is subtle. When the sprinkler is submerged and water flows in, there is no clear argument that it should or shouldn't turn." Textbooks disagreed. Experiments gave conflicting results. Some said no rotation; others saw forward rotation; still others saw reverse rotation.

The 2024 Solution

In January 2024, Leif Ristroph's team at NYU's Courant Institute finally settled the question with careful experiments and analysis, published in Physical Review Letters.

The Answer: The reverse sprinkler does rotate—in the opposite direction from forward mode—but much more slowly, roughly 50 times slower than the forward sprinkler at the same flow rate.

The Mechanism: Centrifugal Jets

The key insight is that the incoming water jets don't collide head-on inside the sprinkler's central chamber. Instead, they slam together at a slight angle, creating an asymmetric flow pattern that generates torque.

More specifically, when water flows through the curved arms during suction, centrifugal effects cause the flow to "hug" the outer walls of the curved conduits. This creates an asymmetric angular momentum flux that, surprisingly, produces a weak net torque in the reverse direction.

Forward: τ = ρQ²r/A (strong reaction force)
Reverse: τ ≈ centrifugal asymmetry effects (much weaker)

Why Forward Is Faster

In forward mode, there's a clear rocket-like mechanism: water exits at high velocity, and the sprinkler feels the reaction force directly. The torque scales with the square of the flow rate and the arm length.

In reverse mode, the torque comes from subtle internal flow effects—not a direct reaction to exiting momentum. The water must change direction multiple times, and the asymmetries that produce rotation are second-order effects. This explains the 50× speed difference.

Feynman's Experiment

Richard Feynman's attempt at Princeton is legendary—and possibly apocryphal in its dramatic details. He placed a sprinkler in a large carboy (glass bottle) and pressurized it to force water in. At some point, the container exploded, showering the lab with glass and water.

Whether the explosion happened as dramatically as the stories suggest, Feynman's conclusion was that the sprinkler barely moved when sucking in water. He was right about the effect being weak—the 2024 work confirms the motion is real but slow.

Why It Took 140 Years

The reverse sprinkler problem is a cautionary tale about how seemingly simple physics can hide deep complexity. The effects involved—curved flow paths, centrifugal forces, momentum flux in confined geometries—don't yield to simple intuition or back-of-envelope calculations.

Modern high-speed cameras, precise torque measurements, and computational fluid dynamics finally provided the tools to resolve what pen-and-paper physics could not.