HYDRAULIC JUMP CHARACTERISTICS FOR DIFFERENT OPEN CHANNEL AND STILLING BASIN LAYOUTS

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1 International Journal of Civil Engineering and Technolog (IJCIET) Volume 7, Issue, March-April 6, pp. 9 3, Article ID: IJCIET_7 5 Available online at Journal Impact Factor (6): 9.78 (Calculated b GISI) ISSN Print: and ISSN Online: IAEME Publication HYDRAULIC JUMP CHARACTERISTICS FOR DIFFERENT OPEN CHANNEL AND STILLING BASIN LAYOUTS Mahmoud Ali R. Eltoukh Civil Engineering Department, Shoubra Facult of Engineering, Benha Universit, Egpt ABSTRACT Hdraulic jump is considered as the best wa for dissipating energ present in moving water downstream of hdraulic structures. This paper conducted laborator experiments to investigate the hdraulic jump characteristics variations for different rectangular open channel laouts. In this paper, the used open channel laouts were five bed slopes of.75,.349,.54,.699, and.875, and a sill with three different heights was placed along a model of the stilling basin at three different longitudinal distances. The characteristics of the hdraulic jump, which was formed downstream vertical gate, were measured for variable discharges. Results of experiments show that, the hdraulic jump ratios, jump length and initial depth ratio, L j /, jump length and sequent depth ratio, L j /, jump depths ratio, /, -, and relative energ loss and initial energ ratio, DE/E increase with initial Froude's number for different bed slopes. On the other hand, results show that, the sill has significant effect on the energ dissipation. A new equation was developed to design stilling basin, i.e. the sill height, H, and the longitudinal distance, L B. Ke words: Rectangular Channel; Hdraulic Jump; Energ Dissipation; Bed Slope. Cite this Article: Mahmoud Ali R. Eltoukh. Hdraulic Jump Characteristics For Different Open Channel and Stilling Basin Laouts, International Journal of Civil Engineering and Technolog, 7(), 6, pp

2 Hdraulic Jump Characteristics For Different Open Channel and Stilling Basin Laouts List of Smbols F Initial Froude's number [ ] g Gravitational of acceleration [m/s ] Initial depth [m] Sequent depth [m] S Channel bed slope [ ] L j Length of jump [m] H Sill height [m] L B The sill longitudinal distance downstream the gate [m]. INTRODUCTION Water kinetic energ downstream the vertical gate must be dissipated to prevent scouring of downstream river bed, which ma result in failure of downstream structures. Chern [] applied the model of smoothed particle hdrodnamics (SPH) for investigating the hdraulic jump characteristics in various corrugated beds. It was found that, the dissipated energ on sinusoidal beds is more than that on other beds. The analsis of results shows that, using corrugated beds increases the energ dissipation of hdraulic jump in open channels. It was deduced that, the SPH model is used for studing the variation of the effect of the hdraulic jump characteristics with using corrugated beds. Kordi [], studied the transitional expanding hdraulic jump. The results show that, the sequent depth, for the classical jumps is bigger than required sequent depth to form an expanding jump. The expanding hdraulic jump length was found to be.5 times of that corresponding of the free jump. The forming classical hdraulic jump in a horizontal bed, and wide rectangular open channel with a smooth bed has been studied extensivel, [3,4,5, and 6]. Hager [7] analzed the hdraulic jump theoreticall and experimentall. Hughes [8] studied the Hughes [8] studied the characteristics of hdraulic jump in horizontal rectangular open channel with artificiall roughened beds and smooth side walls. Also, it was found that, both the hdraulic jump length, and the sequent depth are reduced due to boundar roughness. The observed reductions were related to both the bed roughness degree and the initial Froude's number. The observed hdraulic jump characteristics were consistent with the theor. The proposed approximation equation for the theoretical hdraulic jump was found to be compared with the observed hdraulic jump characteristics. Afzal [9] investigated the stream-wise flow structure of turbulent hdraulic jump, which was taken placed over a rectangular channel rough bed. It was found that, the hdraulic jump over a rough bed can be deduced using classical theor of the smooth bed hdraulic jump, using the effective upstream Froude's number instead of the Froude's number. Abdel-Azim [] studied the effect of both negative and positive bed slopes on the hdraulic jump. The analsis of results showed that, both the initial Froude's number and the bottom slope have major effects on the depth ratio of the hdraulic jump while the initial depth ratio has minor effect on the depth ratio of the hdraulic jump. Chan-Deng [], and Smith [] Studied the hdraulic jump in an slopped rectangular contracted channel. The developed theoretical equations for the sequent depth and sequent area ratios for hdraulic jumps in the contraction taking into consideration the effects of bottom slope and the contracting width. Beirami [3] studied the hdraulic jumps in inclined bed channels. It was showed that, the negative bed slope reduces the sequent depth ratio, while the positive bed slope increases the sequent depth ratio. Gandhi [4] studied the supercritical flow 9

3 Mahmoud Ali R. Eltoukh characteristics in rectangular channel. Neveen [5] investigated effect of channel bed slope on the hdraulic jump characteristics. Small bed slopes was used for that purpose, (.7,.4,.54,.8, and.). Alikhani et al. [6] studied the hdraulic jump which is formed in stilling basin having vertical end sill. Experiments used model with /3 scale for stilling basin and a dam spillwa to deduce the forced hdraulic jump design criteria for single continuous sill, which was set up at the stilling basin end. The height of the end sill and its longitudinal distance downstream the vertical gate was established to reduce basin and jump lengths. Debabeche and Achour [7] studied the hdraulic jump formed through a triangular channel and the effect of a continuous sill on its characteristics. The purpose of this paper is to investigate the characteristics of hdraulic jump, that was formed downstream vertical gate in rectangular open channel. Bigger bed slope values than that in the pervious work were used for this purpose. Also, a new equation was developed for stilling basin design.. THEORY The theor here is built on the principle of momentum, i.e. the rate of change of momentum between the beginning and the end of the hdraulic jump must equal to the total force exerted on the moving water mass within the jump. Also, the dimensional analsis theor was used. The following functional relationship between the paper variables is used to characterize the hdraulic jump which was taken placed downstream vertical gate and the sill height and position in a rectangular channel, Fig. (). f, V, L, S, g,,, H,, j L B () Figure () Hdraulic jump with sill Where; is the initial depth, V is the initial velocit, is the hdraulic jump sequent depth (which was considered as the flow depth just downstream the sill), L j is the hdraulic jump length, S is the bed slope, g is the gravitational acceleration, is water densit, is water viscosit, H is the sill height, and L B is the stilling basin length. For open channel with horizontal bed (S = ) and turbulent flow, the effect of Renolds number is neglected, and the dimensionless groups ma be written as: For a classical hdraulic jump, the sequent depth ratio is given b Belanger [8] Equation, as: 9

4 Hdraulic Jump Characteristics For Different Open Channel and Stilling Basin Laouts The hdraulic jump sequent depth ratio on sloped bed is given b the Chen-Feng Li [9] equation, as: Where; 8F / cos 4C (4) C V V tan / V the water volume with the jump V 3. THE EXPERIMENTAL WORK Laborator experiments were carried out in a recirculation self contained tilting glass sided flume in the Hdraulics Laborator of Shoubra Facult of Engineering, Benha Universit. The dimensions of the flume are.5 m long, 9 cm width and 3 cm height. A control valve was used to regulate the discharge. A screw jack which, located at the upstream end of the flume is used to adjust the flume bed slope. The flume bed slope was directl determined b using a slope indicator, and the flume was rotated freel about a hinged pivot. The tail-water surface depth was regulated b a downstream adjustable gate. The sidewalls along the entire length of the flume are made of glass with metal-frames, to make visual investigations of the flow patterns is allow. The flume horizontal bed was made of steel and it is provided with a PVC pipe to drain the water from the flume. An electric centrifugal pump was used fed water into the flume from an external water source. The water discharged into the flume through two pumps with different discharges. A series of experimental runs at different values of discharge were carried out and the formed hdraulic jump downstream the flume sluice gate. For each experimental run the initial depth, sequent depth, and the hdraulic jump length, L j were measured. The gate opening was changed through the experiments. This paper used five positive bed slopes, S.75,.349,.54,.699, and.875. The flow discharge was measured b using a pre-calibrated orifice meter. The flow depth was measured using a point gauge with accurac of ±. mm, Fig. (). 4. RESULTS AND DISCUSSION First of all, the used flume was calibrated, where five runs were conducted for horizontal flume bed. It was found that, the obtained results are convenient with Belanger's equation. Results of the experimental runs were carried out to stud the different characteristics of the hdraulic jump such as sequent depth ratio, /, jump height, and relative length of the jump, L j /, relative energ loss, E L / E with Froude's number for different bed slopes. Also, other runs were conducted for designing the stilling basin. 93

5 Mahmoud Ali R. Eltoukh 4. The Sequent Depth Ratio, / Experimental runs were carried out to stud the relationship between the hdraulic jump sequent depth ratio, / and Froude's number, F and bed slopes, S, Fig. (3). This figure shows that, the sequent depth ratio, / increases as the Frounde's number F and the channel bed slope S, increase. This information is useful for designing a hdraulic structure of a stilling basin. For example; increasing 96% in F S results in 46% increasing in the sequent depth ratio. The following formula was fitted, and it ma be used in estimating the value of the sequent depth ratio for given initial Froude's number, F and channel bed slope, S; F S.898F S.3 R The Hdraulic Jump Height, ( ) The effect of the initial Froude's number, F and the channel bed slope, S on the hdraulic jump height, was investigated in this section. Fig. (4) shows that, the hdraulic jump height has directl proportional relationship with each initial Froude's number and the channel bed slope. For example; increasing of F S b 96%, results in 37% increasing in the hdraulic jump height. A fitted formula was estimated to calculate the jump height for given Froude's number, F and bed slope, S; F S.94F S 3.93 R (6) (5) Figure () Schematic laout of experimental setup 94

6 Hdraulic Jump Characteristics For Different Open Channel and Stilling Basin Laouts 4 / F * S.5 Fig. (3) Determination of / b knowing intial Froude's number, F and bed slope, S F * S.5 Fig. (4) Hdraulic jump height, ( - ) variation with intail Froude's number, F and bed slopes 4.3 The Hdraulic Jump Length, L j Other experimental runs were carried out to investigate the variation of the hdraulic jump length with the initial Froude's number and bed slopes. Figs. (5 and 6) show the fitted relationship between each of the hdraulic jump length ratios, L j / and L j / with Froude's number and bed slope. Fig. (5) shows that, the Froude's number 95

7 Mahmoud Ali R. Eltoukh has linear relationship with L j /, and the bed slope has no effect on L j /. The linear relationship between F and L j / is; L j.39 F R.998 The hdraulic jump length ratio, L j / variations with the Froude's number and the bed slope are shown in Fig. (6). Also, the following equation ma be used for calculating L j / b known F and the channel bed slope, S; (7) L j X 5 F / S.4F / S R. 87 (8) 4.4 The Relative Energ Losses through Hdraulic Jump Length, E L / E Fig. (7) shows the relationship between the initial Froude's number F and the relative energ loss ( E L / E ) for different channel bed slopes. It was observed that, relative energ loss increases non-linear with the Froude's number. The bed slope L j / 4 3 s=.75 s=.349 s=.54 s=.699 s=.875 S = F Fig. (5) Variation of L j / with intial Froude's number for different bed slopes 96

8 Hdraulic Jump Characteristics For Different Open Channel and Stilling Basin Laouts L j / F / S.5 Fig. (6) Variation of L j / with the Intial Froude's Number and Bed Slope. Relative energ losses, E L /E Froude's number, F S=.75 S=.349 S=.54 S=.699 S=.875 Fig. (7) Relative energ losses relationship with Froude's number for different bed slopes Approximatel has no effect on the relative ener loss, E L / E. For example; Increasing of F b 59% result in E L / E increasing b 35%. From the fitted curve an equation ma be established and used directl for calculating E L / E b knowing the initial Froude's number. The equation is; 97

9 Mahmoud Ali R. Eltoukh E L E.99F.44 F.567 R.996 (9) 4.5 Design of Stilling Basin, H and LB Figs. (8 to ) demonstrate the ratio of sequent depth, / variation with the initial Froude's number F of the hdraulic jump formed due to the end sill for three ratio values for H / LB. The sequent depth ratio, / has an inversel relationship with the sill height ratio, H / LB comparing with the sequent depth ratios, / of the hdraulic jumps from Belengar Equation with the same conditions of flow. Figures show that the sequent depth ratio decreases as the sill height increases for a particular sill longitudinal length, L B. The results of this paper agree with the previous studies in proving that, the sill height, H and its position downstream the vertical gate, L B effect on the sequent depth ratio. Thus, the dimensions of the stilling basin, sill height, H and its location, L B, ma be designed. Through the analsis of the results of the experimental runs, a relationship between the effective dimensionless groups in Equation was fitted to be used for the designing of stilling basin. Fig. () shows the relationship between the initial Froude's number, F ratios of H / and L B /, which are considered the main / H/LB =.4 H/LB =.5 H/LB = Froude's number, F Fig. (8) Sequent depth ratio variation with sill height ratio, for L B = cm 98

10 Hdraulic Jump Characteristics For Different Open Channel and Stilling Basin Laouts / H/LB =.4 H/LB =.5 H/LB = Froude's number, F Fig. (9) Sequent depth variation with sill height ratio for L B = 5 cm / H/LB =.4 H/LB =.5 H/LB = Froude's number, F Fig. () Sequent depth raio variation with sill height ratio, for L B = cm 99

11 Mahmoud Ali R. Eltoukh 5 L B / F.(H/ ).5 Fig. () Sill height, H and stilling basin length L B estimation Figure Parameters to express the initial condition, sill geometr and stilling basin and respectivel. A fitted formula was estimated between these parameters. Fig. () and Equation enable the design of sill height, H and stilling basins, L B, once, the initial water depth and initial Froude's number, F are known. B selecting basin length of L B, the height of the sill, H can be calculated. The calculated sill height, H should be.645 checked to be less than/ 6 F, Hager [7]. L B.8 F H.8599 F / H 6.38 R.96 This ma require using several estimated values for L B. Based on previous studies, the initial value for stilling basin length L B was assumed as; LB 3 () 5 This assumption is because, for smaller values of L B than 3( - ), the hdraulic jump will take place downstream of the sill, but, for L B values larger than 5( - ), results in neglecting the effect of the sill. CONCLUSIONS The following conclusions are made based on this paper.. The results show, that hdraulic jump length ratio, L j / or L j / in terms of initial Froude's number, F, provide information to estimate hdraulic jump lengths at different channel bed slopes.. Furthermore, L j / has a linear relation with respect to F, while L j / does not. 3. Experimental results of this paper conclude that the sequent depth for a hdraulic jump estimation has to take the channel bed slope into account. 4. The hdraulic jump height, and the sequent depth ratio, / increases as the initial Froude's number and channel bed slope increase. 5. Equation and Fig. enable for Estimation of the sill height and basin length. () 3

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