THE HYDRAULIC JUMP IN RADIALLY SPREADING FLOW - A NEW MODEL AND NEW EXPERIMENTAL-DATA

A new model for the hydraulic jump in radially spreading flow is prese nted. The equation of motion for a liquid annulus spreading out under the influence of hydrostatic pressure gradient and frictional drag is developed. The resulting nonlinear differential equation for the liqui d depth, h(r), is solved by computer simulation. The jump is assumed t o begin when the laminar flow is engulfed by the underlying boundary l ayer liquid, as suggested recently in the literature. This complicated mixing process is crudely modeled by a drag term which slows the flow and initiates a positive feedback mechanism culminating at a new crit ical depth, beyond which the depth increases asymptotically to a final value. The model predicts a new relationship between the laminar flow depth just before the jump and the final depth. An experimental appar atus was built to make detailed measurements of the depth h(r), both i n the region before the jump and beyond the jump. The theoretical pred ictions were compared to the experimental data, and gave surprisingly good agreement by suitable adjustment of the two parameters k and C of the model. The parameter k determines the growth rate of the boundary layer thickness, and C determines the drag force. The results suggest that the usual textbook assumption of zero momentum loss across the j ump is not appropriate for this type of hydraulic jump. The case of a hydraulic jump in the absence of gravity is considered also and a much different behavior is predicted, which could be tested by experiment in a microgravity environment. (C) 1996 American Association of Physic s Teachers.