Centrifugal Flows Drive Reverse Rotation of Feynman’s Sprinkler

The issue of reversibility in hydromechanical sprinklers that auto-rotate while ejecting fluid from S-shaped tubes raises fundamental questions that remain unresolved. Here, we report on precision experiments that reveal robust and persistent reverse rotation under suction and a model that accounts for the observed motions. We implement an ultralow friction bearing in an apparatus that allows for free rotation under ejection and suction for a range of flow rates and arbitrarily long times. Flow measurements reveal a rocketlike mechanism shared by the reverse and forward modes that involves angular momentum flux, whose subtle manifestation in the reverse case stems from centrifugal effects for flows in curved conduits. These findings answer Feynman’s long-standing question by providing quantitatively accurate explanations of both modes, and they suggest further inquiries into flux-based force generation and the roles of geometry and Reynolds number.

Figure 1

Experimental setups. (a) Cut-away schematic of the floating sprinkler, which consists of tubular arms connected to a cylindrical hub. Capillary interactions with a siphon tube and outer ring center the sprinkler and allow it to rotate freely. (b) Flow control apparatus (not to scale) operating in suction mode. A siphon draws water through the sprinkler at rate $Q$, and a valve allows for impulsive start-up. Overflows maintain the levels in the main and side tanks. (c) Flow imaging with a laser sheet illumination of particle-laden water. A camera captures photos and videos in the regions of interest.

Figure 2

Rotational dynamics in forward and reverse and across flow rates. (a) Instantaneous angular velocity $\mathrm{\Omega }(t)$ for expulsion (red) and suction (blue) for flow of volumetric rate $|Q|=2.0{\mathrm{cm}}^3/\mathrm{s}$ initiated at $t=0$. The gray curves are repeated trails. (b) Long-time average or terminal velocity $\overline{\mathrm{\Omega }}$ versus flux $Q$ or Reynolds number Re for experiments (dots) and a model (squares). (c) Model prediction for torque ${\tau }_{FT}$ due to angular momentum flux. Inset: dimensionless torque coefficient $C_T$ versus Re. In all plots, bars on experimental data represent standard deviations and are suppressed when smaller than the symbol. Bars on model data are propagated from measured fluctuations in the particle image velocimetry (PIV) flow data.

Figure 3

Flow visualizations in the forward (F) and reverse (R) modes. All scale bars are 1 cm and flow rates $|Q|=1{\mathrm{cm}}^3/\mathrm{s}$. (a) Streakline photograph using fluorescein dye. (b) Pathline image of the emitted jet taken at a moment when the outlet moves downward. (c) Pathlines of the suction flow near an upward moving outlet in reverse mode. (d) The jets inside the hub undergo a glancing collision and form four vortices.

Figure 4

Flow field measurements near the internal orifice for the reverse sprinkler. (a) Flow profiles along several transects for $\mathrm{Re}=300$ extracted from video via particle image velocimetry (PIV). (b) Profiles $V(x)$ across the inner orifice and for varying Reynolds and Dean numbers (color bar), with temporal fluctuations ($\pm 1$ standard deviation) represented by colored bands. (c) Profiles normalized by their maximum values.