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Feynman’s Reverse Sprinkler

Why Sucking Water In Is Not Just Running a Sprinkler Backward

Big Question: When water enters a curved sprinkler instead of leaving it, where is angular momentum created, transported and transferred to the device?

Quick Answer

In a forward sprinkler, water is accelerated and expelled tangentially, carrying angular momentum away. The sprinkler receives the opposite torque.

In a reverse sprinkler, water approaches the arm openings from the surrounding bath and is drawn into curved tubes. Precision experiments published in 2024 showed a persistent reverse rotation, much weaker than the forward case, and connected it to angular-momentum flux generated as inward flow curves through the arms. A 2026 Proceedings of the National Academy of Sciences study then tested many sprinkler geometries and found that torque and rotation track the momentum flux entering the device. The outer flow and several older proposed explanations did not control the motion; arm geometry controlled how incoming mass was converted into angular momentum flux.

The current evidence therefore supports a unified momentum-flux picture for both forward and reverse sprinklers, while explaining why their speeds and flow structures are not symmetric.

PNAS — Geometry Controls Momentum Flux in the Sprinkler Problem →

What You Will Learn

• Why ordinary sprinklers rotate.
• Why reversing flow does not create a simple time-reversed problem.
• What momentum flux means in an open system.
• What angular momentum flux means.
• Why curved internal geometry matters.
• How suction can generate weak reverse rotation.
• Why transient torque and steady torque must be distinguished.
• What the 2024 experiments added.
• What the 2026 geometry experiments ruled out.
• Why outer-arm forces are not the controlling explanation in the newer evidence.
• How conservation laws identify required torque without guessing from pressure arrows.
• How this reasoning transfers to pumps, turbines and fluid-driven machines.

Part 1 — The Naive Model: Just Reverse the Arrows

A tempting argument says:

1. Forward sprinkler pushes water one way.
2. Water pushes sprinkler the other way.
3. Reverse the water flow.
4. Therefore reverse the force exactly.

The conclusion can happen to match the observed reverse direction, but the reasoning is incomplete because fluid flow through a real device is not obtained by simply changing every velocity sign.

Viscosity, turbulence, inlet geometry, pressure fields, mixing and free-stream capture all make the reverse flow structurally different.

Part 2 — Start With the Forward Sprinkler

Water enters the hub and is driven through curved arms. By the time it exits, it has tangential velocity relative to the sprinkler axis.

That outgoing water carries angular momentum.

To create that angular momentum, the sprinkler must exert torque on the water. The water exerts the opposite torque on the sprinkler.

sprinkler torque is tied to the rate at which angular momentum crosses the control boundary.

Part 3 — Momentum Flux Is an Open-System Idea

For a closed object, we often write force as the rate of change of its momentum.

For a control volume with fluid continuously entering and leaving, momentum is also transported across the boundary by flowing mass.

The momentum balance must therefore include momentum flux: mass-flow rate multiplied by velocity, integrated over the inlets and outlets.

For rotation, the corresponding quantity is angular momentum flux.

Part 4 — Why Suction Is Geometrically Different

In reverse operation, water far from each opening does not arrive as a narrow pre-formed jet aimed perfectly into the tube.

It is drawn from a surrounding region and converges toward the inlet. Once inside, the flow must turn through the curved arm.

The curved conduit changes the direction of the velocity field and produces pressure and inertial effects associated with the bend.

Part 5 — The 2024 Precision Experiment

Earlier reverse-sprinkler experiments had reported contradictory outcomes: transient motion, no steady rotation, reverse rotation and geometry-dependent behaviour.

One major difficulty was friction. A reverse torque can be so weak that an ordinary bearing hides it.

In 2024, Wang, Sprinkle, Zuo and Ristroph used an ultralow-friction floating apparatus and long-duration experiments. They observed robust persistent reverse rotation under suction and measured the internal flow field.

Their model connected the reverse torque to angular momentum flux generated by curved inward flow, with centrifugal effects playing a central role in the curved conduits.

Physical Review Letters — Centrifugal Flows Drive Reverse Rotation of Feynman’s Sprinkler →

Part 6 — Why the Reverse Sprinkler Is Much Slower

The forward sprinkler deliberately ejects focused jets with strong tangential momentum.

The reverse sprinkler draws water inward from a broad surrounding region. Much of the fluid arrives with little organised angular momentum and only acquires swirl as it is redirected by the curved arms.

The resulting net angular-momentum flux is therefore much smaller, so the reverse torque and steady rotation are much weaker.

Part 7 — The 2026 Geometry Test

A good model should survive changes in geometry—not merely fit one sprinkler.

In 2026, Smith, Zuo, Kuhlke, Sprinkle and Ristroph built multiple modified sprinklers designed to separate competing explanations. Some changed the outer arm portions; others altered how the internal curved channels guided the fluid.

The key result was that the sense of torque and rotation correlated strongly with the momentum flux entering or leaving the device. The outer portions of the arms and surrounding outer flow did not determine the effect.

The authors concluded that the geometry of the curving arms controls how mass flow is converted into angular momentum flux. The study was published online July 13, 2026 and in the July 28, 2026 issue of PNAS.

Part 8 — Why This Strengthens the Model

A single experiment can support several stories at once.

Changing geometry selectively is more discriminating. If a theory says the outside flow causes torque, altering the outside section should strongly change the result. If it does not, that hypothesis loses support.

By contrast, changing the internal flow geometry changed the relevant momentum flux and torque as the momentum-flux model predicted.

good experiments do not merely reproduce an effect; they force rival mechanisms to make different predictions.

Part 9 — The Outer Pressure Argument Is Not Enough

Older explanations often focused on pressure forces near the inlet openings or on forces exerted by water outside the arms.

Pressure is certainly part of fluid mechanics and contributes locally to momentum balance. But the 2026 experiments found that modifying external portions did not control the observed torque.

The more robust description is global: track the angular momentum carried by the fluid through the device and how geometry creates that flux.

Part 10 — Angular Momentum Is Conserved, but the Sprinkler Is Not Isolated

It is easy to ask, “If water starts with zero angular momentum far away, how can it enter the sprinkler with angular momentum?”

The answer is that the curved arms exert forces on the water while redirecting it. Those forces create angular momentum in the fluid relative to the sprinkler axis. The water exerts an equal and opposite torque on the solid structure.

Angular momentum is conserved for the full interacting system, but it is continuously exchanged between fluid, sprinkler and external supports or pumping apparatus.

Part 11 — Why “Time Reversal” Is a Dangerous Shortcut

The equations of ideal inviscid mechanics can have time-reversal symmetries under special conditions.

A real sprinkler is an open, driven, dissipative fluid system. Suction does not reconstruct the exact microscopic velocity field of the previous ejection process in reverse.

Jet breakup, mixing, viscous boundary layers and the geometry of fluid capture all make the two operations physically distinct.

Part 12 — Transient and Steady Rotation Are Different Questions

Starting or stopping suction can produce transient pressure and momentum changes that twist a hose or sprinkler briefly.

That is not the same as a persistent steady torque after the flow settles.

Many historical disagreements became difficult to compare because experiments differed in bearing friction, run duration, geometry and whether they measured transient or steady behaviour.

Part 13 — The Failed Model → The Better Model

Naive model	Why it fails	Better model
Reverse the flow, reverse every force exactly.	Inlet flow is not the microscopic time reverse of jet ejection.	Measure the actual velocity field and momentum flux.
Pressure at the opening alone determines torque.	Geometry tests show outer-flow explanations are not sufficient.	Use a global angular-momentum balance.
If the reverse torque is tiny, it must be zero.	Bearing friction can hide weak steady motion.	Use ultralow-friction apparatus and long runs.
One sprinkler geometry proves the mechanism.	Several rival models can fit one shape.	Change geometry to force competing predictions apart.

Part 14 — Follow One Packet of Water

1. Water begins in the surrounding bath with little organised swirl relative to the sprinkler.
2. Suction draws it toward an inlet.
3. The fluid enters the curved arm.
4. The wall redirects the velocity vector.
5. The curved flow develops angular momentum relative to the central axis.
6. Pressure and wall forces supply the required change in momentum.
7. The fluid transports angular momentum toward the hub.
8. A residual angular-momentum flux enters the device interior.
9. The equal-and-opposite torque acts on the sprinkler.
10. The sprinkler rotates weakly in the reverse sense until drag balances the driving torque.

How Do We Know?

• Use ultralow-friction bearings or floating supports.
• Measure steady angular speed for long periods.
• Visualise internal and external flow with tracer particles or dye.
• Measure velocity fields and calculate angular-momentum flux.
• Change only outer-arm geometry to test external-flow hypotheses.
• Change internal curvature to test momentum-flux predictions.
• Compare forward and reverse modes at controlled flow rates.
• Measure torque directly rather than inferring it only from rotation.

Observation vs Inference

• Observation: low-friction reverse sprinklers can rotate persistently opposite the forward direction.
• Measurement: reverse rotation is much weaker than forward rotation.
• Measurement: torque correlates with fluid angular-momentum flux.
• Intervention: changing internal geometry changes momentum flux and torque as predicted.
• Inference: geometry-controlled momentum flux is the governing mechanism across tested forward and reverse sprinkler designs.
• Boundary: exact torque still depends on geometry, Reynolds number, losses and operating conditions; conservation laws do not remove the need to solve the flow.

Checkpoint Questions

1. Why does a forward sprinkler rotate?
2. What is momentum flux?
3. What is angular-momentum flux?
4. Why is suction not simply the exact time reverse of ejection?
5. Why was bearing friction a major experimental problem?
6. What did the 2024 experiments establish?
7. What did the 2026 geometry experiments add?
8. Why are changes to internal curvature scientifically useful?
9. Why must transient torque be separated from steady torque?
10. What conservation-law calculation should be done before choosing a local pressure explanation?

Answer Key

Open after attempting the questions

1. Outgoing water carries tangential angular momentum, so the sprinkler receives opposite torque.
2. The rate at which moving mass carries momentum through a boundary.
3. The rate at which flowing mass transports angular momentum through a boundary.
4. Real inward flow has different inlet geometry, dissipation, mixing and boundary layers.
5. The reverse torque is small and can be masked by mechanical drag.
6. Persistent weak reverse rotation and a curved-flow momentum-flux mechanism.
7. Multiple geometries showed that momentum flux, controlled by arm geometry, predicts the torque while several outer-flow explanations do not.
8. It changes how the entering fluid acquires angular momentum, producing discriminating predictions.
9. Startup impulses can exist even if the eventual steady torque differs.
10. A control-volume angular-momentum balance.

Primary Science Bridge

• moving water can push objects;
• changing direction requires force;
• curved tubes change fluid direction;
• friction can hide a small effect;
• reversing an action does not always reverse every detail of a system.

Secondary and JC Bridge

Core idea	Higher-resolution route
Newton’s laws	Open-system momentum balance
Rotation	Angular momentum and torque
Fluids	Momentum flux through control surfaces
Curved motion	Centrifugal/inertial flow effects
Experiments	Geometry-based hypothesis discrimination
Irreversibility	Viscous and open-flow time asymmetry

Unfamiliar Transfer Challenge

A curved duct draws air inward and causes its housing to rotate weakly. An engineer claims the torque comes from low pressure on the outside of the bend.

Design a discriminating test: modify the outside housing without changing internal flow geometry, then separately alter the internal curvature. Measure torque and angular-momentum flux in each case. The stronger model is the one whose causal variable tracks the intervention.

Deep Science Window — Angular-Momentum Control Volume

For a fixed control volume around the sprinkler, the net external torque equals the rate of change of angular momentum inside plus the net angular-momentum flux through the control surface. In steady state, the storage term can vanish while flux remains non-zero. That is why a continuously rotating fluid machine can experience steady torque even when the average amount of fluid inside is constant.

Deep Science Window — Why Geometry Is a Physical Variable

A conservation law constrains what must balance, but geometry determines how the flow satisfies that constraint. Curvature controls turning, pressure gradients and swirl generation. Two devices with identical mass flow rate can therefore exert different torques if their channels convert linear flow into angular momentum differently.

Evidence Boundaries

• Reverse flow ≠ exact time-reversed forward flow.
• Weak rotation ≠ zero torque.
• Pressure force ≠ complete mechanism without momentum accounting.
• 2024 curved-flow explanation ≠ endpoint of the evidence; 2026 geometry tests strengthen and generalise the momentum-flux picture.
• Conservation law ≠ detailed flow solution.
• One sprinkler design ≠ universal proof across all fluid machines.

Manual Summary — KNOW → CONNECT → EXPLAIN → APPLY → CHECK

KNOW: torque, momentum flux, angular momentum, control volume, curved flow, steady state.

CONNECT: arm geometry to fluid turning, turning to angular-momentum flux, and flux to opposite torque on the sprinkler.

EXPLAIN: why suction creates weak reverse rotation without being a simple reversed movie of forward operation.

APPLY: test another fluid-driven rotor using geometry changes and angular-momentum accounting.

CHECK: demand an actual flux measurement or discriminating geometry experiment before accepting a local-force cartoon.

Research Sources and Further Reading

• PNAS (2026) — Geometry Controls Momentum Flux in the Sprinkler Problem
• Physical Review Letters (2024) — Centrifugal Flows Drive Reverse Rotation of Feynman’s Sprinkler
• NYU Courant — 2026 Feynman Sprinkler Research Update