The influence of surface tension on the circular hydraulic jump

Abstract

We present the results of a combined theoretical and experimental investigation of the influence of surface tension $\sigma$ on the laminar circular hydraulic jump. An expression is deduced for the magnitude of the radial curvature force per unit length along a circular jump, $F_c\,{=}\,{-}\sigma ( s - \uDelta R )/R_j$, where $R_j$ is the jump radius, and $s$ and $\uDelta R$ are, respectively, the arclength along the jump surface and radial distance between the nearest points at the nose and tail of the jump at which the surface is horizontal. This curvature force is dynamically significant when $2\sigma/(\rho g R_j \uDelta H)$ becomes appreciable, where $\uDelta H$ is the jump height, $\rho$ the fluid density and $g$ the acceleration due to gravity. The theory of viscous hydraulic jumps (Watson 1964) is extended through inclusion of the curvature force, and yields a new prediction for the radius of circular hydraulic jumps. Our experimental investigation demonstrates that the surface tension correction is generally small in laboratory settings, but appreciable for jumps of small radius and height.