Feynman Sprinkler: Eppur si muove

Abstract

This paper reexamines five recent analyses and experimental studies of the reverse sprinkler problem and identifies conceptual limitations they share. Jenkins, Rueckner, Beals, Wang et al., and Smith et al. all focus primarily on internal flow dynamics, ignoring the pressure gradients, currents, and pressure forces in the surrounding fluid. This paper argues that these external effects, together with incomplete absorption of angular momentum by the sprinkler arm, are the primary sources of the observed torque, both ultimately driven by the ambient pressure surrounding the sprinkler. The former is supported by Rueckner's straight-arm experiment; the latter is consistent with the comprehensive experimental results of Smith et al., for which the present paper provides the first theoretical explanation. A generalization of Jenkins's momentum-transfer argument is presented, clarifying why internal flow alone cannot drive the observed backward rotation — a conclusion that holds even when the assumptions of the generalized argument are relaxed in light of the experimental findings of Wang et al. A simplified estimate of the lift force at the nozzle entrance illustrates the scale of the external flow effect. The paper includes reflections on the conceptual difficulties that have shaped previous analyses.