Sprinkla: Reverse Sprinkler
Mechanics, Chaos & Fluids arc, page 97 of 193. Back to The Pixelated Physics Universe
Who they are
Sprinkla spins on one toe, arms bent like a lawn sprinkler. Run her backwards, sucking water in, and she still turns.
Sprinkla is a character of the Mechanics, Chaos & Fluids arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
A sprinkler that sprays water spins because of the jets' reaction. Run it in reverse underwater, sucking water in, and it turns the other way, unsteadily and about 40 times slower than forward at the same flow rate. The curved arms fling the inflow outward, so the two jets meeting in the hub miss head-on and push it round. Mach posed it in 1883, Feynman popularised it, and it was settled experimentally in 2024 by K. Wang, B. Sprinkle, M. Zuo and L. Ristroph (Phys. Rev. Lett. 132, 044003).
$$ \begin{gathered} \tau = \rho\,Q\,v\,r \qquad \text{(forward, held still)} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $\tau$ | stall torque on the sprinkler held fixed | N·m |
| $\rho$ | fluid density | kg/m³ |
| $Q$ | total volume flow rate | m³/s |
| $v$ | jet exit speed (jets tangential) | m/s |
| $r$ | arm radius, axis to nozzle | m |
Honest caveat: The torque formula is an ideal, tangential-jet idealisation.
Sources
- Wang, Sprinkle, Zuo & Ristroph (2024) Centripetal Fluid Rotation Drives Reverse Rotation of Feynman's Sprinkler, Phys. Rev. Lett. 132, 044003
- Jenkins (2004) An elementary treatment of the reverse sprinkler, Am. J. Phys. 72, 1276
- NYU News (2024) Physicists solve the puzzle of Feynman's reverse sprinkler
Crossovers
Sprinkla meets Navia ($1M Fluid Problem). Sprinkla's reverse sprinkler only turns slowly, in a subtle way that experiments settled recently. Navia guards a deeper question about the same Navier–Stokes equations: whether smooth 3D solutions always stay smooth. That is still unsolved.
Sprinkla meets Flagella (Corkscrew Escape). Sprinkla's sprinkler lives at high Reynolds number, where inertia and jets matter. Flagella lives at a Reynolds number of about 10⁻⁵, where inertia is negligible and only a non-reciprocal stroke like a corkscrew can swim.
Wear the lore
Concept keywords: Reverse Sprinkler, Sprinkla, Mechanics, Chaos & Fluids, physics lore, Pixelated Physics