• Sprinkla Reverse Sprinkler pixel-art physics T-shirt, white tee, front view

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Sprinkla

The Reverse Sprinkler Physics

\[\tau = \rho\,Q\,v\,r \qquad \text{(forward, held still)}\]
$29.99 USD
$29.99 USD
Promoção Esgotado
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Size guide S–5XL · inches

Sprinkla spins on one toe, arms bent like a lawn sprinkler. Run her backwards, sucking water in, and she still turns.

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.

τ = ρ Q v r (forward, held still)

  • τ: stall torque (N·m)
  • ρ: fluid density (kg/m³)
  • Q: volume flow rate (m³/s)
  • v: jet exit speed (m/s)
  • r: arm radius (m)

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).

Honest caveat: The torque formula is an ideal, tangential-jet idealisation.

On the shirt

Front: Sprinkla, the pixel-art character, with the title. Back: the forward torque, the reverse-rotation result, the hub-jet explanation and the 2024 paper. Printed on a unisex tee.

Shipping calculated at checkout by destinationMade to order, ships in 2–5 business days

Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

Para ter uma escala: o tamanho M tem 20 in (50.80 cm) de largura, cerca de 3.143 × 1034 comprimentos de Planck (lP = 1.616255 × 10−35 m). Uma fita métrica é mais rápida.

Measurements in inches, ±1.5 in tolerance.

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Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Spray water out of my arms and I spin: every jet pushes back on me, and holding me still takes a torque of ρQvr.

Now run me backwards, underwater, sucking water in. People argued for over a century about what I would do. Ernst Mach asked in 1883; Richard Feynman made it famous. In 2024 a team at New York University finally measured it: I still turn, the other way, unsteadily and roughly forty to fifty times slower than forward at the same flow.

The reason is in my hub. My curved arms fling the incoming water outward, so the two inflowing jets meet off-centre instead of head-on, and they nudge me round. The simple torque formula is an idealisation with perfectly tangential jets; the reverse motion needed the experiment.

Equations

\[\tau = \rho\,Q\,v\,r \qquad \text{(forward, held still)}\]
SymbolMeaningUnit
\(\tau\) stall torque on the sprinkler held fixed \(\mathrm{N·m}\)
\(\rho\) fluid density \(\mathrm{kg/m³}\)
\(Q\) total volume flow rate \(\mathrm{m³/s}\)
\(v\) jet exit speed (jets tangential) \(\mathrm{m/s}\)
\(r\) arm radius, axis to nozzle \(\mathrm{m}\)

Sources

  1. Wang, Sprinkle, Zuo & Ristroph (2024) Centripetal Fluid Rotation Drives Reverse Rotation of Feynman's Sprinkler, Phys. Rev. Lett. 132, 044003
  2. Jenkins (2004) An elementary treatment of the reverse sprinkler, Am. J. Phys. 72, 1276
  3. NYU News (2024) Physicists solve the puzzle of Feynman's reverse sprinkler

Field notes

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