Study on the sequent depth ratio of hydraulic jump in abruptly expanding channel

Abstract

A hydraulic jump occurs when a supercritical flow has to change into subcritical flow. Although researchers have investigated the transition from supercritical to subcritical /low for nearly 180 years, the hydraulic jump within a lateral expansion was found to be of interest during the last four decades. This type of jump is of practical application in dissipating energy downstream of spillways, weirs, etc. Downstream of the spillway of a dam there can be an abruptly expanding rectangular stilling basin. The determination of sequent depth in such basin is one of the main problems faced by the field engineers who monitor the performance of the design. The sequent depth ratio of hydraulic jump in an abruptly expanding. rectangular and horizontal channel is considered in the present study. The basic principle of the formulation is based on the application of the one-dimensional momentum equation and the 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 abrupt expansion and the second one describes the position of jump upstream of the expansion. This theoretically based equation is easy and simple to apply in design of enlarged stilling basin compared to other approaches. Experiments have been conducted at the Hydraulics and River Engineering Laboratory of BUET. A tilting flume having a 40-ft(l2.2 m) overall length, a I-ft (0.3048 m) depth and I-It(0.3048 m) width has been used to carry out the investigations. Several contraction geometries were inserted in the channel to reduce the width of the supercritical flow upstream of the expansion section. The downstream width was kept constant and three expansion ratios of 0.50. 0.667 and 0.833 were maintained. The Froude numbers were varied at four different gate openings (3.6 cm, 4.75 cm, 6.15 cm and 7.3 cm) and four di llerent toe positions. The initial depth, the sequent depth and the flow velocity were measured. There were 171 runs performed in the present study. The relationships obtained for predicting the sequent depth ratio have been compared to the present experimental data. It reveals that the present form of the parameters of developed equation have been found reasonable for computing sequent depth ratio in the expanding channel.