The circular hydraulic jump; the influence of downstream flow on the jump radius

Abstract

In this study, we examine the consistency of a gravity-based predictive theory for a hydraulic jump, given by Kurihara [ Proceedings of the Report of the Research Institute for Fluid Engineering (Kyusyu Imperial University, 1946), Vol. 3, pp. 11–33]; Tani [J. Phys. Soc. Jpn. 4, 212–215 (1949)] with the phenomenological condition at the jump given by Rayleigh [Proc. R. Soc. London, Ser. A 90, 324–328 (1914)]; and Watson [J. Fluid Mech. 20, 481–499 (1964)] and show that in light of experimental evidence, the gravity-based predictive theory for the kitchen sink hydraulic jump is incompatible with the phenomenological condition, which must be valid. We also examine the solution to the downstream film and its potential influence on the hydraulic jump. We show that for all practical purposes, at normal flow conditions, the downstream liquid film remains flat and does not affect the jump, and the theory given by Bhagat et al. [J. Fluid Mech. 851, R5 (2018)] gives an excellent prediction of the jump radius. For high viscosity liquids, on a relatively large plate, the viscous dissipation in the downstream film could increase the jump height and, consequently, move the jump radius inward.