Geometry controls momentum flux in the sprinkler problem

Hydro- and aero-mechanical devices convert fluid flows into useful motions, force, and power. The operating principles can involve subtle and poorly understood physics, as epitomized by open questions about systems that aspirate flows through curving tubular arms. Since its introduction by Mach and popularization by Feynman, the so-called reverse sprinkler problem has evoked many competing theories and fluid mechanical effects that have not to date been distinguished by experiments. Here we conduct a series of experiments that directly report on the motions, torques, and flows for devices whose geometries are tailored to disambiguate the leading hypotheses. Our observations run counter to several ideas, such as those based on the total angular momentum of the fluid and others focusing on the flow and pressure distributions at the outer portions of the arms. The measurements instead reveal strong correlations between the sense of torque/rotation and the fluid momentum fluxing into the device. These results suggest an operating principle for the reverse sprinkler involving isotropic input of fluid from the far field and swirl-up in the arms that generates angular momentum, a residual portion of which is injected inside and drives rotation. The mass-to-momentum flux conversion is governed by the geometry of the curving arms. The physics learned here is fundamental to flow-structure interaction problems and may inform applications for harvesting and transforming flow energy.