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DETERMINING the LOCATION of HYDRAULIC JUMP by MODEL TEST and HEC-2 FLOW ROUTING/ a Thesis Presented to the Faculty of the Fritz

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DETERMINING the LOCATION of HYDRAULIC JUMP by MODEL TEST and HEC-2 FLOW ROUTING/ a Thesis Presented to the Faculty of the Fritz L-DETERMINING THE LOCATION OF HYDRAULIC JUMP BY MODEL TEST AND HEC-2 FLOW ROUTING/ A Thesis Presented to The Faculty of the Fritz J. and Dolores H. Russ College of Engineering and Technology Ohio University In Partial Fulment of the Requirement for the Degree Master of Science by Chen-Feng Li, 4 August, 1995 ACKNOWLEDGEMENTS The author gratefdly acknowledges the hanicial support fiom my family, advisor Dr. Chang (Civil Engineering Dept., Ohio University) and Feng Chia University (Taiwan). The author would like to thank the Civil Engineering Department for the help they provided by supplying the various equipment used for my studies. The author also wants to thank those who have helped in my thesis writing. TABLE OF CONTENTS TABLE OF CONTENTS ................................iv LIST OF TABLES ...................................vii LIST OF FIGURES .................................. viii LIST OF SYMBOLS ..................................xii I. INTRODUCTION .................................. 1 I. 1 Background of Study .......................... 1 1.2 Purpose of Study ............................ 2 1.3 Buckingham PI Theorem and Dynamic Simulation ........... 2 1.4 Experiments and Requirements ..................... 3 I .5 The FUTURE Development of the Study ................ 4 I1 . SELECTED LITERATURE REVIEW ..................... 6 11 . 1 Theoretical Development of Hydraulic Jump .............. 6 II.2 Studies of Hydraulic Jump ....................... 6 LI.3 Channel Slope and Hydraulic Jump ................... 8 v 11.4 Length and Location of Hydraulic Jump .................11 II.5 Force and Hydraulic Jump ........................14 II.6 Hydraulic Structures and Hydraulic Jump ................16 II.6.1 Hydraulic Jump in A Stilling Basin ...............17 II.6.2 Sluice Gate and Hydraulic Jump ................17 11.6.3 Sill and Hydraulic Jump ....................19 11.7 Computer Simulation ofHydraulic Jump Surface Profiles ........24 m . METHODOLOGY AND EXPERIMENTS ...................31 III . 1 Flow Conditions and Hydraulic Jump ..................31 III .1.1 Flow Conditions ........................31 III . 1.2 Basic Concepts of Hydraulic Jump ...............33 III. 2 Basic Theory of this Study ........................34 111 .2.1 Dimensional analysis ......................35 III.2.2 Application of Dimensional Analysis ..............35 III .3 Experiments of Hydraulic Jumps .....................37 III.4 Dynamic Simulation ...........................40 III .5 Determination of Prototype Sequent Depths ...............44 III.5.1 Sequent Depths and Direct Model Conversion .........44 III .5.2 Sequent Depths and the Belanger Equation ...........45 III.6 HEC-2 Flow Routing and Hydraulic Jump ...............46 III.7 Determining the Location of Hydraulic Jump ..............48 vi 111 .7.1 Location of Jump Heels ....................49 III.7.2 Location of Jump Toes..................... 50 IV . RESULTS AND DISCUSSIONS .......................58 IV . 1 Experimental Results for Jump Length ..................58 IV.2 Gravity and Friction Effects on Hydraulic Jump .............60 IV.3 L,N, Versus F, ............................64 IV.4 Jump Height and Froude Number ....................64 IV .5 Ratio of Water Depth. and Froude Number ...............65 V . CONCLUSIONS ............................... 104 VI . BIBLIOGRAPHY ..............................107 VII . APPENDIX ................................. 112 LIST OF TABLES 1. Table 2- 1: Relationship of the hydraulic Quantities for D- and B-jumps . 27 2. Table 4- 1: Experimental measurements and related estimation for 8 = 1" . 66 3. Table 4-2: Experimental measurements and related estimation for 8 = 2" , . ,67 4. Table 4-3: Experimental measurements and related estimation for 8 = 3". 68 5. Table 4-4: Experimental measurements and related estimation for 8 = 4". 69 6. Table 4-5: Experimental measurements and related estimation for 8 = 5". 70 7. Table 4-6: Comparison of sequent depths estimated by the Belanger equation and model test for channel bed slope = 1" . 7 1 8. Table 4-7: Comparison of sequent depths estimated by the Belanger equation and model test for channel bed slope = 2" . 7 1 9. Table 4-8: Comparison of sequent depths estimated by the Belanger equation and model test for channel bed slope = 3" . 72 10. Table 4-9: Comparison of sequent depths estimated by the Belanger equation and model test for channel bed slope = 4" . 72 Comparison of sequent depths estimated by the Belanger equation and model test for channel bed slope = 5" . 73 LIST OF FIGURES Figure 2- 1: Types of the hydraulic jumps in the horizontal channels (Open-Channel Hydraulics, Chow, 1959). .28 Figure 2-2: Types of the hydraulic jumps in the sloping channels (By Rajaratnam, N., et al., 1974) . .29 Figure 2-3 : Classification of the jump in sloping channels. .30 Figure 3-1: The characteristics of different flow conditions. .51 Figure 3-2: The illustration of a rectangular flow cross section . .52 Figure 3-3: The E-q curve . .53 Figure 3-4: Forces acting on the jump formed in the horizontal channel . .54 Figure 3-51 Model of the channel. .55 Figure 3-6: Channel section profiles . .56 Figure 3-7: The energy profile of water flow . .57 Figure 4- 1: The relationship between initial Froude No. (F,) and the ratio of jump length (Lj) to the sequent depth of water (y,) for lochannel slope. .74 Figure 4-2: The relationship between initial Froude No. (F,) and the ratio ofjump length (Lj) to the sequent depth of water (y,) for 2" channel slope . .75 Figure 4-3: The relationship between initial Froude No. (F,) and the ratio of jump length (Lj) to the sequent depth of water (y,) for 3" channel slope . .76 Figure 4-4: The relationship between initial Froude No. (F,) and the ratio of jump length (Lj) to the sequent depth of water (y,) for 4" channel slope . .77 Figure 4-5: The relationship between initial Froude No. (F,) and the ratio of jump length (Lj) to the sequent depth of water (y,) for 5" channel slope ................. .78 Figure 4-6: The relationships between initial Froude No. (F,) and the ratio of jump length (L,) to the sequent depth of water (y,) for loto 5" channel slope ...............79 Figure 4-7: Forces acting on the jump formed in a sloping channel ......80 Figure 4-8: The relationship between the initial Froude No. (F,) and the prototype 's sequent depth of the water (y,,) for lochannel slope ...................... .81 Figure 4-9: The relationship between the initial Froude No. (F,) and the prototype 's sequent depth of the water (y,,) for lochannel slope ...................... .82 Figure 4- 10: The relationship between the initial Froude No. (F,) and the prototype 's sequent depth of the water (y,,) for lochannel slope ...................... .83 Figure 4- 11: The relationship between the initial Froude No. (F,) and the protowe 's sequent deptb of the water (y,,) for lochannel slope .......................84 Figure 4-12: The relationship between the initial Froude No. (F,) and the prototype 's sequent depth of the water (y,,) for lochannel slope ...................... .85 Figure 4- 13: The relationship between the initial Froude No. (F,) and the ratio of jump length (L,) to the initial depth (y,) of water for lochannel slope ................ Figure 4- 24: The relationship between the initial Froude No. (F,) and the ratio ofjump length (L,)to the initial depth (y,) of the water for 2"channel slope ................... .87 Figure 4- 15: The relationship between the initial Froude No. (F,) and the ratio ofjump length (L,) to the initial depth (y,) of water for 3" channel slope ...................88 Figure 4- 16: The relationship between the initial Froude No. (F,) and the ratio ofjump length (L,) to the initial depth (y,) of water for 4" channel slope ................... .89 Figure 4- 17: The relationship between the initial Froude No. (F,) and the ratio of jump length (Lj) to the initial depth (y,) of water for 5" channel slope .................. .90 Figure 4- 18: The relationships between the initial Froude No. (F,) and the ratio of jump length (Lj) to the initial depth (y,) of water for loto 5" channel slopes. ...............9 1 Figure 4- 19: The relationship between the initial Froude No. (F,) and the ratio of the jump height (y2-y,) for lochannel slope ...................... .92 Figure 4-20: The relationship between the initial Froude No. (F,) and the ratio of the jump height (y2-y,) for 2" channel slope .......................93 Figure 4-2 1: The relationship between the initial Froude No. (F,) and the ratio of the jump height (y2-y,) for 3" channel slope ...................... .94 Figure 4-22: The relationship between the initial Froude No. (F,) and the ratio of the jump height (y2-y,) for 4" channel slope ...................... .95 Figure 4-23: The relationship between the initial Froude No. (F,) and the ratio of the jump height (y2-y,) for 5" channel slope ...................... .96 Figure 4-24: The relationships between the initial Froude No. (F,) and the ratio of the jump height (y,-y,) for loto 5" channel slope. ....................97 Figure 4-25: The relationship between the initial Froude No. (F,) and the ratio of sequent depth to the initial depth of water for lo of channel slope ......................98 Figure 4-26: The relationship between the initial Froude No. (F,) and the ratio of sequent depth to the initial depth of water for 2" of channel slope ..................... .99 37. Figure 4-27: The relationship between the initial Froude No. (F,) and the ratio of sequent depth to the initial depth of water for 3" of channel
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