Hysteresis of the Hydraulic Jump Controlled by Sill in a Rectangular Channel

Abstract

A theoretical approach is proposed to compute the hysteresis of a controlled hydraulic jump by a broad-crested sill in a rectangular channel, when the inflow is generated by a gate and a standard spillway with an abrupt slope. The attention is focused on the calculation of both the maximum and minimum inflow Froude numbers compatible with the formation of the hydraulic jump in the energy dissipator stilling basin. When the inflow is generated by a gate, the theoretical development shows that the inflow Froude number is linked to the relative sill height by a cubic equation which can be solved using trigonometric functions. When the inflow is generated by a standard spillway with an abrupt slope, the inflow Froude number and relative sill are well-defined by an involutive function