The Feynman Sprinkler: Which Way Does a Sucking Sprinkler Turn?

The puzzle: run the sprinkler backward

A rotary lawn sprinkler is a hub with two or four curved arms, each ending in a nozzle that points tangentially. Water forced up the central stem shoots out sideways, and the whole assembly spins in the direction opposite the jets. Now imagine dunking that sprinkler in a pool and connecting the stem to a pump running the other way, so that water is drawn into the nozzles and out through the stem. The flow is reversed at every point. Does the sprinkler now spin the opposite way? Stay still? Spin the same way as before?

The question was first written down by the physicist and philosopher Ernst Mach in his 1883 treatise The Science of Mechanics, where he described a reaction wheel and remarked that sucking air in produced “no distinct rotation.” It became folklore at Princeton around 1940 through Richard Feynman and John Wheeler, and Feynman later immortalized it in Surely You’re Joking, Mr. Feynman!. What makes it a genuine puzzle is that two perfectly reasonable momentum arguments give opposite answers — a warning sign that a naive symmetry is hiding real fluid mechanics.

Why a normal sprinkler spins backward

The forward case is unambiguous, and it is nothing but the rocket principle. Water leaves each nozzle at speed v with volume flow rate Q, carrying momentum flux ρQv per nozzle (ρ is the water density). By Newton’s third law, the nozzle feels an equal and opposite reaction force ρQv directed backward along the arm. Acting tangentially at radius R, that force produces a torque

• τ = ρQvR = ρAv²R, where A is the nozzle area (since Q = Av).

The exit speed follows from Bernoulli/Torricelli, v = √(2ΔP/ρ) for a supply overpressure ΔP, so the torque scales with the driving pressure. This is exactly the rocket-equation logic: expel mass one way, recoil the other. The crucial feature is that the ejected water leaves as a collimated jet — a narrow, directed beam that carries its angular momentum ρQvR away from the sprinkler and never returns. Because that angular momentum is exported continuously, the reaction torque is steady and the sprinkler spins indefinitely.

The naive arguments — and why they conflict

Reverse the flow and intuition splits in two:

• “Reverse everything” argument: every velocity flips sign, so the momentum flux flips sign, so the torque flips sign, so the sprinkler should spin the opposite way — toward the incoming water.
• “Momentum delivered” argument: the incoming stream carries momentum into the sprinkler. When that water is captured and turned to flow down the central axis, it dumps its momentum onto the sprinkler in the reverse direction. That delivered momentum cancels the intake reaction, so there is no net torque and the sprinkler stays put.

Both cannot be right. The resolution is that time-reversing a viscous, momentum-carrying flow is not a symmetry of the equations of motion. The Navier–Stokes equations are not time-reversible in the presence of viscosity, and even the inviscid picture is not spatially mirror-symmetric between the two cases. Physically: a jet stays narrow and directed, but a sink pulls fluid in from all directions at once. Blowing and sucking are geometrically different, so the reversed problem is a genuinely new one, not the old one played in rewind.

The steady-state answer: zero net torque

The clean way to settle the ideal case is a control-volume angular-momentum balance. Draw a large imaginary surface around the whole sprinkler. In steady state the angular momentum stored inside is constant, so the torque on the sprinkler equals minus the net flux of angular momentum across that surface.

• For the ejector, fluid leaves through the tangential jets, exporting angular momentum ρQvR about the axis. Nonzero flux → nonzero, persistent torque.
• For the sucker, the picture flips in a decisive way. Far from each nozzle the intake behaves like an ideal point sink: fluid streams in nearly radially, from every direction, carrying essentially zero net angular momentum about the axis. The fluid that reaches the center then exits along the stem, whose moment arm about the rotation axis is zero. Inflow carries no angular momentum, outflow leaves on the axis — so the net angular-momentum flux is ≈ 0, and the steady torque is ≈ 0.

This is precisely the “momentum-delivered” conclusion, now made rigorous: the momentum the water brings in is handed back to the sprinkler as the flow is decelerated and redirected inside the hub. Several careful analyses reached the same verdict, including A. T. Forrester’s 1986 paper in the American Journal of Physics (“Inverse sprinklers: A lesson in the use of a conservation principle”). An ideal, inviscid sucking sprinkler does not undergo steady rotation. The only motion is a brief transient twitch when the flow is switched on or off, as the internal flow field is established or torn down.

Why real sprinklers creep toward the source

“Ideal” is doing a lot of work above. Real water has viscosity, real arms are curved tubes, and the incoming stream does not fill them uniformly. Three effects break the perfect cancellation, and all of them push the same way — a slow rotation toward the incoming water, opposite to the ejector’s sense:

• Transients. During spin-up and spin-down the flow field is unsteady, so the time-derivative term in the angular-momentum balance is nonzero. This gives a real but temporary kick toward the source, which is what most casual demonstrations see.
• Internal jetting. Water entering a nozzle and rounding the bend of the S-arm does not spread across the tube; it hugs the inside of the curve and forms a fast internal jet that strikes the far tube wall. That impingement exerts a small steady torque the momentum bookkeeping at the outer boundary misses.
• Viscous losses. Friction along the walls dissipates part of the incoming momentum before it can perfectly cancel the intake reaction, leaving a small residual.

The Reynolds number of a working sprinkler is high — for v ~ 3 m/s in a 1 cm tube, Re ≈ vd/ν ~ 3×10⁴ — high enough to tempt an inviscid analysis, yet the boundary layers and internal jets that viscosity organizes are exactly what generate the residual torque. The net effect is tiny: the reverse sprinkler turns in the same sense predicted by the “reverse everything” camp, but vastly more slowly than a forward sprinkler under the same pressure.

How we know: from an exploding carboy to precision physics

Feynman’s own attempt was a fiasco. In the Princeton cyclotron laboratory he sealed an S-tube inside a large glass carboy (a bulbous water bottle) and connected the top to the lab’s compressed-air line, so that air pressure would force water to flow into the tube and out the stem. As he cranked the pressure up looking for rotation, the bottle exploded, spraying glass and water across the room — and he was banned from the lab. Accounts note the tube gave a small twitch at first, consistent with a transient, before the experiment ended in flying glass.

Controlled experiments came later. R. E. Berg and M. R. Collier (University of Maryland, Am. J. Phys. 57, 654, 1989) built a low-friction apparatus and measured a small, definite rotation of the sucking sprinkler toward the intake, opposite to the ejecting case. The most precise word to date came in 2024, when Leif Ristroph’s group at NYU’s Applied Mathematics Laboratory published a study in Physical Review Letters using an ultra-low-friction, water-immersed sprinkler and dye visualization. They confirmed a steady reverse rotation — roughly 50 times slower than the forward sprinkler at matched flow — and traced it to the internal, off-center jets that form inside the bent arms as fluid is drawn in and turned. The century-old “paradox” thus resolves into a hierarchy: ideal theory gives zero steady torque; real viscosity and internal flow give a small, genuine, and now-measured rotation toward the source. The enduring lesson is Feynman’s own: an “obvious” fluid argument is worth exactly nothing until you account for the geometry of jets and sinks and the irreversibility that viscosity smuggles in.

Ejecting (normal) vs. sucking (reverse) sprinkler — why reversing the flow does not simply reverse the result.

Property	Ejecting (normal)	Sucking (ideal, inviscid)	Sucking (real)
Boundary flow geometry	Collimated jet — directed momentum	Isotropic sink — pulls from all sides	Sink plus internal wall-jets
Net steady torque	τ = ρQvR ≠ 0	≈ 0	Small but nonzero
Rotation direction	Away from the jets	None (no steady spin)	Toward the incoming water
Relative rotation rate	1× (baseline)	0	~1/50×
Angular momentum fate	Carried away forever	Cancels inside the hub	Mostly cancels; residue from internal jets
Character	Steady, persistent	Only a start/stop twitch	Slow steady spin + transient kick