# Hydraulic Modeling

ISBN: 978-1-118-94619-0
608 pages
April 2016

## Description

Water. Except for air, it is the most important ingredient to all life on Earth. It surrounds us every day. We are literally bathed in it, we cook our food with it, and we need a steady stream of it in our bodies every single day just to survive. But water, and the study of it, is one of the most important and unheralded branches of engineering, affecting every other aspect of engineering in almost every industry. We harness its power for energy, we inject massive blasts of it into the earth to extract oil, gas, and minerals, and we use it in nearly every single industrial application, including food processing, refining, manufacturing, and waste disposal, just to name a few.

Hyraulic modeling is, essentially, the understanding and prediction of fluid flow and its applications in industrial, municipal, and environmental settings, whether in a creekbed, locked in the pores of rocks deep in the earth, or in the ocean.  Mathematical models, which started out with mechanical pencils and drafting tables originally, have been increasingly relied upon over the last few decades, due to the invention, growth, and refinement of computers. Physical modeling, however, is still practiced in laboratories, and it is the intersection of physical and mathematical modeling of fluid flow that is most successful in creating models that are safer, less costly, and are better for the environment.

Hydraulic Modeling introduces and explores this incredibly important science, from the most basic tenets to valuable real-world applications that are used in industry today. It is the only volume on the market to offer a thorough coverage of the subject without adding lots of useless fluff or inapplicable appendices. It is a must-have for any engineer, scientist, or student working with hydraulic modeling, as a daily reference or a textbook.

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Introduction 1

1 Fundamentals of Modeling 5

1.1 Modeling as the Method of Cognition 5

1.2 Hydraulic and Numerical Modeling 8

1.3 Dimensions of Quantity 14

1.4 Conditions of Similarity 22

1.5 About the Newton’s Law of Similarity 27

2 The Mathematical Models of Fluid Motion 31

2.1 Preliminary Remarks 31

2.2 Conditions of Mass and Momentum Conservation 33

2.3 Non-Viscous Fluid 36

2.4 Viscous Fluid 39

2.5 Turbulence 46

2.6 Boundary Conditions 67

2.7 Averaging on Space and Time 78

2.8 Numerical Modeling 89

3 Approximate Similarity of Hydraulic Phenomenon 101

3.1 Inconsistency of Similarity Criterion 101

3.2 Approximate Similarity and Distorted Model 103

3.3 Self-Similarity 104

3.4 Finding of Approximate Similarity Conditions With Application of Dimension Theory 111

3.5 Phenomenon Characterization and Criterions Combination 117

4 Pressure Flows 121

4.1 Uniform Stream 121

4.2 Non-Uniform Flow 153

4.3 Non-Stationary Flow 169

5 Open Flow in Hard Channel 183

5.1 Specific Character of Open Flows. Role of Froude and Euler Criterions 183

5.2 Self-Similarity of Open Flows in Reynolds Criterion. Turbulence Characteristics 192

5.3 Simulation of Flow Plan for Channel Flow 203

5.5 Pressure Model of Open Flow 232

6 Multi-Component Flows 249

6.1 General View 249

6.2 Transfer of Solids by Fluids 251

6.3 Gas Involvement from the Free Surface 263

6.4 Structure of Gas-Fluid Flows 272

7 Flow in the Deformable Channel 279

7.1 Features of Riverbed Deformations Modeling 279

7.2 Local Erosion in the Cohesionless Ground 281

7.3 Local Erosions in Solid and Rocky Grounds 291

7.4 Alluvial River-Bed Planned Deformations 300

7.5 The Ratio of the River-Bed Averaged Characteristics in Nature and on the Model 310

7.6 Determining of Planned Deformations on the Pressure Model 317

7.7 “Hybrid” Modeling of River-Bed Deformations 321

7.8 Flow in the Channel with Grassy Vegetation 328

8 Heat and Mass Transfer and Phase Transitions 343

8.1 Heat Transfer in the Equipment Elements 343

8.2 Transport Processes in the Fluid 352

8.3 Heat Transfer in the Water Reservoirs-Coolers 376

8.4 Phase Transformations 388

8.5 Cavitation 391

9.2 Pressure Pulsations at the Points of Border Flow 414

9.3 Jet Impact 472

9.4 Vibrations 482

9.5 Hydroelasticity 495

9.6 Complex Modeling of Hydrodynamic Loads 504

9.6.1 Pressure Pulsations at the Point of Water Fight Against Measurements in Nature and Model 505

9.6.2 The Pulsation Pressure in the Head Spillway Measurement in Nature and Model 532

9.6.3 Complex Modeling of Stress Under Hydrodynamic Loads 548

Conclusion 557

References 559

Appendix 579

Index 589

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## Author Information

Victor M. Lyatkher, PhD, is a professor, engineer, and inventor..  He was educated in Moscow and Leningrad, and has developed and patented numerous processes and machines. These deal mainly with renewable energy sources such as tidal power, water turbines, and vertical axis wind turbines. He developed a new method to forecast long-term variations in the Caspian Sea level, and designed a new kind of low head turbine. Mr. Lyatkher has worked for over thirty years in the wind and hydro-power industry. He has received several prizes and awards for his accomplishments, including the Prize of the Council of Ministers of the USSR, the Award of the Indian Society of Earthquake Technology, and five medals of the All Union USSR Exhibition, gold, silver and bronze.He has published numerous books (in russian) on the subject of renewable energy, and was the original inventor of helical turbine, patented in the USSR in 1983.

Alexander M.  Proudovsky, PhD, graduated from the Moscow Engineering and Construction Institute in 1955, received his PhD in 1976 and became Doctor of Technical Sciences in 2000. A renowned expert in the field of hydraulic and hydrothermal modeling of hydraulic structures and nuclear power facilities and a member of the International Association for Hydraulic research since 1974, he has written over 200 articles and 2 books on modeling, both in collaboration with Victor Lyatkher.

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