Effect of roughness on sequent depth in hydraulic jumps over rough bed

Hydraulic jump is an important phenomenon in open channel flows such as rivers and spillways. Hydraulic jump is mainly used for kinetic energy dissipation at the downstream side of a spillway with the assist of baffle blocks. It has been demonstrated that corrugated or rough beds show considerably more energy dissipation than smooth beds. The experimental research evaluating the effect of crushed stones on the hydraulic jump is presented in this paper. Five different-size sets of crushed stones were used. Results show that the effect of rough bed does not increase after a certain height of crushed stone is reached.

Effect of roughness on sequent depth in hydraulic jumps over rough bed

Introduction
Hydraulic jump is a phenomenon that is used for the purpose of dissipating energy in most hydraulic structures.Hydraulic jump occurs at the position of the flow where the transition from supercritical flow to subcritical flow occurs.The jump formed in a smooth bed, wide and horizontal rectangular channel is known as the classical jump.This classical jump has been studied extensively by many researchers (Hager [1], Rajaratnam [2]).Gravity is the driving force behind the flow through open channels.Hence, it stands to reason that the ratio of inertial forces to gravitational forces will play a major role in the openchannel flow analysis.Following the convention of using the first power law of velocity, we define the dimensionless number, i.e. the Froude No.If y 1 is the supercritical stream depth, y 2 the depth of subcritical stream, and F r1 the Froude number for supercritical stream, then the sequent depth ratio of a hydraulic jump can be given by the Belanger momentum equation [3] as folows in (1): (1) where: F r -Froude number F r1 -Froude number for the incoming flow y 1 -upstream flow depth y 2 -tail water depth.
The investigations by many researchers have shown that if the bed over which the jump is formed is rough, the tail water depth y 2 , required to form the jump will be considerably less than the sequent depth y 2 [4,5].Many researchers documented that the jump length is also reduced notably.This led to an idea that the length of the jump can be reduced using roughness on the bed which will eventually lead to the reduction of length of the apron used to control hydraulic jump in hydraulic structures.The main concern with hydraulic jump on rough bed is that the roughness on the upstream will be subjected to cavitation.Further studies by Ead et al. [3] led to the conclusion that the effect of cavitation can be reduced by keeping the level of the crest of the roughness at the same level of the bed such that no portion will be protruding over the bed level.Further, several researchers Carollo, Ferro and Pampalone [6], Ead and Rajaratnam [3], Ghorbani and Bazaz [7]) presented the effect of "shape of the roughness", for which triangular, trapezoidal, and semi-circular strips made of wood, plastic etc. were introduced to the bed for roughness.In this study, the effect of roughness on sequent depth of hydraulic jump is studied for different roughness elements.Hence an experimental investigation was conducted on hydraulic jump over rough bed, and the results are presented here with an aim that this idea will prove useful for further investigations in this field.

Experimental setup and experimentation
The experiments were conducted in Hydraulics and Fluid Mechanics Laboratory of the Civil Engineering Department at Visvesvaraya National Institute of Technology, Nagpur, Maharashtra, India.The flume used for experimental work was rectangular and horizontal in nature with adjustable bed slope (Tilting Mechanism) having 0.6 m in bed width and 21 m in length as shown in Figure 1.A 30 HP pump of proper rating curve and standard make, drives the circulating mechanism to work efficiently for the flume.A perplex Effect of roughness on sequent depth in hydraulic jumps over rough bed glass sheet was fixed as side walls for visualization.For discharge, measurement was recorded using the electromagnetic flow meter connected to a 0.150 m diameter pipe.At the downstream end of the flume, the water was collected in a tank measuring 3m in width and 1 m in depth.For preventing instrumental error, calibration is necessary before every run of the experiment.Discharge is maintained for individual run.Kako bi se olakšalo formiranje skoka, uzvodni zasun žlijeba u svim The hydraulic jump was formed in this flume measuring 21 x 0.6 x 0.5 m in size, with Plexiglas sides.The rough bed was made using crushed stones.The selection of crushed stones was motivated by the fact that they are used as coarse aggregate in concrete during construction of the lined channels.These stones are locally available and can be broken as per the size required.An additional advantage of these stones is that they have a very high "degree angularity", and hence a rougher surface area can be exposed to the flow.Because of the high angularity their laying on the bed of the channel is also easy, as a high level of anchorage can be achieved.They were anchored to the bed of the flume in such a way that no portion of the crushed stones affected the upstream bed where the supercritical stream was formed.In such a way, the gap between individual stones acts as a depression on the bed.The arrangement created in this way formed the system of turbulent eddies that might increase the bed shear stresses [3].Five sets of crushed stones were used in the whole experimentation.Individual sets were made by sieving crushed stones in such a way that they passed through a higher sieve and were retained on a lower one.After the sieving process, the aggregates were systematically classified into different series.The details are given in Table 1.To facilitate jump formation, the upstream sluice gate of the flume was adjusted in all the experiments to generate a supercritical flow, and the rough bed was placed immediately after the upstream gate, Figure 4. Actual photograph of hydraulic jump is shown on figure 5.A total of 236 experimental readings were taken (for all five series).The upstream and downstream depth were measured over the top level of the rough bed which was taken as 28 mm for series A, 35.5 mm for series B, 45 mm for series C, 56.5 mm for series D, and 69 mm for series E, using a point gauge with the least count of 0.1 mm, Figure 6.The Froude number for the experiments mostly ranged from 3 to 10.The water was made to enter the flume under a sluice gate, which produces a uniform supercritical

Results and analysis
The supercritical and subcritical depths were measured at the sections as shown in Figure 4.The supercritical depth was measured just before the start of the jump, and the subcritical depth was measured at the end of the jump, which can be defined as the section beyond which the water surface is nearly horizontal.

Figure 7. Variation of sequent depth ratio with respect to Froude number
For every set, the variation of the sequent depth ratio with Froude number was compared to the readings from previous studies.The variation of the sequent depth ratio with respect to Froude number is shown for smooth bed in Figure 7.The variation shows a clear linear pattern.The pattern is almost the same as that of the Belanger's equation.The regression result obtained from the graph shows an R 2 value of 0.9672 for Figure 8 shows a comparison between variation of the sequent depth ratio with respect to Froude number in smooth bed and the Belanger's equation.Effect of roughness on sequent depth in hydraulic jumps over rough bed The results show a linear trend, and the regression result obtained for this is = 0.9093 • F r1 + 0.6397 with an R 2 value of 0.9269 and the Froude number values varying between 3 and 7.
The variation of the sequent depth ratio with Froude number for series B is shown in Figure 10.
The R 2 value obtained is 0.906 and the Froude number varies between 2 to 7. The variation of Sequent Depth ratio with Froude number for series C is shown in Figure 11.The R 2 value obtained is 0.9405 and the Froude number varies between 2.5 to 10.Here the trend is also linear.The variation of Sequent Depth ratio with Froude number for series D is shown in Figure 12.
The R 2 value obtained is 0.9463 and the Froude number varies between 2.5 to 9.5.The variation of Sequent Depth ratio with Froude number for series E is shown in Figure 13.In series E, the equation obtained by regression analysis is = 0.6611 • F r1 + 1.2384 (7)

Figure 1 .
Figure 1.Top view (plan) of experimental setup

Figure 8 .
Figure 8.Comparison between present study and Belanger's equation in smooth bed

Figure 9 .
Figure 9. Variation of sequent depth ratio with repect to Froude Number for Series A (25 to 31.5 mm)

Figure 10 .
Figure 10.Variation of sequent depth ratio with Froude number for series B (31.5 to 40 mm)

Figure 11 .
Figure 11.Variation of sequent depth ratio with Froude number for series C (40 to 50 mm)

Figure 12 .
Figure 12.Variation of sequent depth ratio with Froude number for series D (50 to 63 mm)

Figure 13 .
Figure 13.Variation of sequent depth ratio with Froude number for series E (63 to 75 mm)