Study of hydraulic jump in abruptly expanded sloping channel

Abstract

Hydraulic jump primarily serves as an energy dissipator to dissipate excess energy of flowing water downstream of hydraulic structures, such as spillways and sluice gates. Considering its immense practical utility in hydraulic engineering and allied fields, this phenomenon has. given a considerable attention by the researchers for the last 180 years. During the last four decades, the hydraulic jump in a channel with a lateral expansion was found to be interesting. This type of jump is of practical importance in dissipating excess energy downstream of spillways, weirs etc., when tail water depth is inadequate to give a good 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 expansion and channel slope. The sequent depth ratio of a hydraulic jump in an abrupt expansion of a sloping channel is considered 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 present experimental study were used to evaluate a developed prediction equation for computing sequent depth ratio in an expanding channel whose format is similar to the well-known Belanger equation for classical jump with modification of Froude number. The modified Froude number term contains two additional parameters, one of them incorporates the effect of sudden expansion and the second one represents for describing the effect of channel slope. This theoretically-based equation is easy and simple to apply in design of enlarged stilling basin compared to other approaches. Experiments were conducted in the Hydraulics and River Engineering Laboratory of BUET. A 70 ft long tilting flume has been used to carry out the investigations. Several contraction geometries were inserted in the channel to reduce the width of the super critical flow upstream of the expansion section. Downstream width was kept constant and four expansion ratios of 0.5, 0.6, 0.7 and 0.8 were maintained together with three different channel slopes (0.0042, 0.0089 and 0.0131). The initial depth, sequent depth, velocity etc. were measured with different combinations of expansion ratio and channel slope. From the entire test runs two desired parameters k, and k2 were calculated and then these two were calibrated with the experimental data to relate these factors with some known variables like expansion ratio, 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.