Study of hydraulic jump in a sloping channel with abrupt drop

Abstract

Hydraulic jump is a phenomenon well known to hydraulic engineers as a useful means of dissipating excess energy and prevent scour below overflow spillways, chutes and sluices. In situations where the downstream depth is larger than the sequent depth for a normal jump, a drop in the channel floor may be used to ensure a jump. If this type of jump occurs in a sloping condition the analysis of the phenomenon becomes very complex due to the inclusion of so many parameters related to sudden drop and channel slope. A hydraulic model investigation is conducted to evaluate the characteristics of hydraulic jump in a sloping channel with abrupt drop in this present study. The basic equation is based on the application of the one dimensional momentum equation and continuity equation. The results of the experimental study were used to evaluate a developed prediction equation for computing sequent depth ratio in a sloping channel with abrupt drop whose format is similar to the well-known Belanger equation for classical jump with modification of Froude number. The modified Froude number term contains three additional parameters, two of them incorporate the effect of Froude number and the third one represents for describing the effect of drop height. A 12.19 m (40 ft) long tilting flume has been used to carry out the investigations. Several contraction geometries were inserted in the channel to reduce the height of the supercritical flow upstream of the drop section. Three drop heights of 2 cm, 4.5 cm, and 6 cm were maintained together with three different channel slopes (0.0042, 0.0083 and 0.0125). The initial depth, sequent depth, velocity etc. were measured with different combinations of drop height and channel slope. From the entire test runs three desired parameters k1, k2 and k3 were calculated and then these three were calibrated with the experimental data to relate these factors with some known variables like drop height, channel slope and inflow Froude number. With the aid of these factors, modified inflow Froude number will be calculated to get the desired form of Belanger’s format prediction model.