The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Chapter 1 Basic Principles Chapter 2 Specific Energy Chapter 3 Momentum Chapter 4 Uniform Flow Chapter 5 Gradually Varied Flow Chapter 6 Hydraulic Structures Chapter 7 Governing Equations of Unsteady Flow Chapter 8 Numerical Solution of the Unsteady Flow Equations Chapter 9 Simplified Methods of Flow Routing Chapter 10 Flow in Alluvial Channels

Open Channel Hydraulics

Numerical Methods for Scientists and Engineers

random data analysis and measurement procedures is available in our digital library an online access to it is set as public so you can get it instantly. Our book servers spans in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the random data analysis and measurement procedures is universally compatible with any devices to read.

Random Data Analysis And Measurement Procedures

By trapping sediment in reservoirs, dams interrupt the continuity of sediment transport through rivers, resulting in loss of reservoir storage and reduced usable life, and depriving downstream reaches of sediments essential for channel form and aquatic habitats. With the acceleration of new dam construction globally, these impacts are increasingly widespread. There are proven techniques to pass sediment through or around reservoirs, to preserve reservoir capacity and to minimize downstream impacts, but they are not applied in many situations where they would be effective. This paper summarizes collective experience from five continents in managing reservoir sediments and mitigating downstream sediment starvation. Where geometry is favorable it is often possible to bypass sediment around the reservoir, which avoids reservoir sedimentation and supplies sediment to downstream reaches with rates and timing similar to pre-dam conditions. Sluicing (or drawdown routing) permits sediment to be transported through the reservoir rapidly to avoid sedimentation during high flows; it requires relatively large capacity outlets. Drawdown flushing involves scouring and re-suspending sediment deposited in the reservoir and transporting it downstream through low-level gates in the dam; it works best in narrow reservoirs with steep longitudinal gradients and with flow velocities maintained above the threshold to transport sediment. Turbidity currents can often be vented through the dam, with the advantage that the reservoir need not be drawn down to pass sediment. In planning dams, we recommend that these sediment management approaches be utilized where possible to sustain reservoir capacity and minimize environmental impacts of dams.

/pdf/sustainable-sediment-management-in-reservoirs-and-regulated-14momatd77.pdf

Sustainable sediment management in reservoirs and regulated rivers: Experiences from five continents

In high velocity water flows, large quantities of air bubbles are entrained at the free-surfaces. Practical applications are found in Chemical, Civil, Environmental, Mechanical, Mining and Nuclear Engineering. Air-water flows are observed in small-scale as well as large-scale flow situations. E.g., thin circular jets used as mixing devices in chemical plants (Qw ~ 0.001 L/s, diameter ~ 1 mm), and spillway flows (Qw > 10,000 m3/s, flow thickness over 10 m). In each case, however, the interactions between the entrained air bubbles and the turbulence field are significant. This monograph investigates the "air bubble entrainment in free-surface turbulent shear flows". It develops an analysis of the air entrainment processes in free-surface flows. The air-water flows are investigated as homogeneous mixtures with variable density. The variations of fluid density result from the non-uniform air bubble distributions and the turbulent diffusion process. Several types of air-water free-surface flows are studied : plunging jet flows (Part II), open channel flows (Part III), and turbulent water jets discharging into air (Part IV). Each configuration can be characterised as a high-velocity free-surface flow with turbulent shear layer and large air bubble content. Experimental observations confirm the conceptual idea that the air-water mixture behaves as a homogeneous compressible fluid. The monograph presents numerous and recent experimental investigations with mean velocities up to 57 m/s and mean air contents up to 70%. The analysis of experimental studies provides new information on the air-water flow field : air bubble distributions, air-water velocity profiles, air bubble sizes and bubble-turbulence interactions. The results show a strong similarity between all the flow patterns. In each case the distributions of air concentration (i.e. void fraction) can be approximated by a simple advective diffusion theory. New analysis is developed for each flow configuration and compared successfully with model and prototype data. The velocity distributions in air-water flows have the same shape as for monophase flows. However the presence of air bubbles modifies some turbulence characteristics while the turbulence controls the mechanism of bubble breakup. The book presents new useful information for design engineers and research-and-development scientists who need a better understanding of the fluid mechanics of air-water flows. Both qualitative and quantitative information are provided. In some cases the limits of our knowledge are pointed out. The book consists of five parts. Part I introduces the topic and its relevance, develops a dimensional analysis and discusses the air-water gas transfer process. In each subsequent part, the distributions of air content and air-water velocity are described. The results are grouped as : plunging jet flows (Part II), open channel flows (Part III) and high-velocity water jets discharging into the atmosphere (Part IV). In Part V, an analogy between the various types of air-water flows is developed. In the appendices, tables of physical and chemical properties of fluids are provided in appendix A. The report presents results expressed in SI Units. A table of unit conversions is given in appendix B. Estimates of bubble rise velocity are discussed in appendix C. Appendix D develops sound celerity calculations in two-phase flows. Appendices E, G, H and I present complete calculations of the air bubble diffusion process. Boundary layer characteristics and jet trajectory calculations are detailed in appendices F and J respectively. Appendix K defines bubble size distribution characteristic parameters. Observations by LEONARDO DA VINCI are recounted in appendix L. 'Errare Humanum Est'. Appendix M presents a correction form. Readers who find an error or mistake are welcome to record the error on the page and to send a copy to the author. At the beginning of the book, the reader will find the table of contents, a list of symbols, a glossary and an album of colourful photographs of 'white waters'.

Air Bubble Entrainment in Free-Surface Turbulent Shear Flows

The stepped channel design have been used for more than 3,500 years (chapter 2). A significant number of dams were built with overflow stepped spillways during the 19th century and early 20th century, before the design technique became outdated with the progresses in hydraulic jump stilling basin design. Recent advances in technology (e.g. RCC, polymer-coated gabion wire) have triggered a regain in interest for the stepped design, although much expertise had been lost in the past 80 years. The steps increase significantly the rate of energy dissipation taking place along the chute and reduce the size of the required downstream energy dissipation basin. Stepped cascades are used also in water treatment plants to enhance the air-water transfer of atmospheric gases (e.g. oxygen, nitrogen) and of volatile organic components (VOC). Research on stepped spillway hydraulics has been active between 1980 and 2000. For the period 1985-2000, the international database Science Citation Index® lists over sixteen journal papers and twenty-six discussions and closures on stepped chute hydraulics, all but two published between 1990 and 2000. A 1985 paper (SORENSEN, Jl Hyd Engrg) was cited seventeen times during the period; two papers published in 1994 (CHANSON, Jl of Hyd Res, No. 2 and 3) were cited fourteen and eleven times respectively (Ref.: Science Citation Index). The international database Global Books in Print® lists one book (CHANSON 1995, Pergamon). In 1998, Professor OHTSU and Dr YASUDA organised a workshop on the hydraulic characteristics of stepped channel flows in Tokyo, attended by over seventy participants. In 2000, Professors MINOR and HAGER organised an international workshop on hydraulics of stepped spillways in Zurich. The workshop attracted over forty participants from Europe, North America, Iran, and Australia; the sponsorship of the American Society of Civil Engineers (ASCE), International Association for Hydraulic Engineering and Research (IAHR) and Swiss national committee on large dams demonstrated the importance of the event. This book presents the state of the art in stepped chute hydraulics. It is based upon the research expertise of the writer, his professional experience as an expert-consultant, and his experience in teaching stepped spillway hydraulics to undergraduate students, postgraduate research students and professionals since 1982 (Fig. i). Results from more than forty five laboratory studies and four prototype investigations were re-analysed and compared. The book provides a new understanding of stepped channel hydraulics, and it is aimed at both the research and professional community. In the introduction (chapter 1), the basic concepts of stepped channels and stepped chute flows are described. A clear distinction is made between the main flow regimes (nappe flow, transition and skimming flow). A chapter presents the historical progress of stepped channels and spillways from the Antiquity up to today (chapter 2). Then the monograph reviews the hydraulic characteristics of stepped channel flows. Three different flow regimes may take place depending upon the flow conditions and chute geometry: nappe flow regime for small discharges, transition flow and skimming flow regime. The hydraulics of each flow regime is described in chapters 3, 4 and 5. The effects of flow aeration and air bubble entrainment are discussed. The gas transfer processes taking place above stepped chute are described : e.g., aeration, re-oxygenation, stripping, de-nitrification (chapter 6). Later practical examples of hydraulic design are presented : e.g. stepped fountains, stepped weirs, gabion stepped spillways, earth dam spillways with precast concrete blocks, roller compacted concrete (RCC) weirs, debris dams (chapter 7). The writer presents further a critical review of accidents and failures with stepped channels, highlighting that the hydrodynamic forces on the step faces are much larger than on smooth chute inverts (chapter 8). Wave phenomena and instabilities are reviewed and discussed in a separate section (chapter 9). In the last chapter (summary and conclusions, chapter 10), he summarises the key issues and he answers explicitly basic questions. At the beginning of the book, the reader will find the table of contents, a list of symbols and a glossary of technical terms and names. He will find also an index at the end of the book. After the conclusion (chapter 10), a detailed list of references is presented. It is followed by a list of physical and chemical properties of fluids (appendix I), The book presents results expressed in SI Units. A table of unit conversions is given in appendix II. Several appendices detail particular calculations : nappe trajectory at a drop structure (appendix III), bubble rise velocity calculations (appendix IV), modelling form drag and flow resistance in skimming flows (appendix V), void fraction distributions in chute flows (appendix VI), chute calculations in skimming flow (appendix VII), modelling air-water gas transfer in skimming flows (appendix VIII). Appendix IX presents a correction form. Readers who find an error or mistake are welcome to record the error on the page and to send a copy to the author. Corrections and updates will be posted on the Internet at : {http://www.uq.edu.au/~e2hchans/reprints/book4.htm} Lastly relevant Internet resources are listed below.

https://espace.library.uq.edu.au/view/UQ:109112/Book4_Ref.pdf

Hydraulics of Stepped Chutes and Spillways

The book is an introduction to the hydraulics of open channel flows. The material is designed for undergraduate students in Civil, Environmental and Hydraulic Engineering. It will be assumed that the students have had an introductory course in fluid mechanics and that they are familiar with the basic principles of fluid mechanics : continuity, momentum, energy and Bernoulli principles. The book will first develop the basic principles of fluid mechanics with applications to open channels. Open channel flow calculations are more complicated than pipe flow calculations because the location of the free-surface is often unknown 'a priori' (i.e. beforehand). Later the students are introduced to the basic concepts of sediment transport and hydraulic modelling (physical and numerical models). At the end of the course, the design of hydraulic structures is introduced. The book is designed to bring a basic understanding of the hydraulics of rivers, waterways and man-made canals (e.g. Plates a-1 to a-13) to the reader. The lecture material is divided into four parts of increasing complexity : - Part I : Introduction to the basic principles. Application of the fundamental fluid mechanics principles to open channels. Emphasis on the application of the Bernoulli principle and Momentum equation to open channel flows. - Part II : Introduction to sediment transport in open channels. Basic definitions followed by simple applications. Occurrence of sediment motion in open channels. Calculations of sediment transport rate. Interactions between the sediment motion and the fluid motion. - Part III : Modelling open channel flows. Physical modelling of open channel flows. Numerical modelling of open channel flows. Physical modelling : application of the basic principles of similitude and dimensional analysis to open channels. Numerical modelling : numerical integration of the energy equation; one-dimensional flow modelling. - Part IV : Introduction to the design of hydraulic structures for the storage and conveyance of water. Hydraulic design of dams, weirs and spillways. Design of drops and cascades. Hydraulic design of culverts : standard box culverts and minimum energy loss culvert. Basic introduction to professional design of hydraulic structures. Application of the basic principles to real design situations. Analysis of complete systems. Applications, tutorials and exercises are grouped into four categories : applications within the main text to illustrate the basic lecture material, exercises for each chapter within each section, revision exercises using knowledge gained in several chapters within one section, and major assignments (i.e. problems) involving expertise gained in several sections : e.g., typically section I and one or two other sections. In the lecture material, complete and detailed solutions of the applications are given. Numerical solutions of some exercises, revision exercises and problems are available on the Internet (Publisher's site : http://www.arnoldpublishers.com/). A suggestion/correction form is placed at the end of the book. Comments, suggestions and critic are welcome and they will be helpful to improve the quality of the book. Readers who find an error or mistake are welcome to record the error on the page and to send a copy to the author. "Errare Humanum Est" .

https://espace.library.uq.edu.au/view/UQ:108443/n97_REFER.pdf

The Hydraulics of Open Channel Flow: An Introduction

English Preface The book is an introduction to the hydraulics of open channel flows. The material is designed for undergraduate students in Civil, Environmental and Hydraulic Engineering. It will be assumed that the students have had an introductory course in fluid mechanics and that they are familiar with the basic principles of fluid mechanics : continuity, momentum, energy and Bernoulli principles. The book will first develop the basic principles of fluid mechanics with applications to open channels. Open channel flow calculations are more complicated than pipe flow calculations because the location of the free-surface is often unknown 'a priori' (i.e. beforehand). Later the students are introduced to the basic concepts of sediment transport and hydraulic modelling (physical and numerical models). At the end of the course, the design of hydraulic structures is introduced. The book is designed to bring a basic understanding of the hydraulics of rivers, waterways and man-made canals (e.g. Plates a-1 to a-13) to the reader. The lecture material is divided into four parts of increasing complexity : - Part I : Introduction to the basic principles. Application of the fundamental fluid mechanics principles to open channels. Emphasis on the application of the Bernoulli principle and Momentum equation to open channel flows. - Part II : Introduction to sediment transport in open channels. Basic definitions followed by simple applications. Occurrence of sediment motion in open channels. Calculations of sediment transport rate. Interactions between the sediment motion and the fluid motion. - Part III : Modelling open channel flows. Physical modelling of open channel flows. Numerical modelling of open channel flows. Physical modelling : application of the basic principles of similitude and dimensional analysis to open channels. Numerical modelling : numerical integration of the energy equation; one-dimensional flow modelling. - Part IV : Introduction to the design of hydraulic structures for the storage and conveyance of water. Hydraulic design of dams, weirs and spillways. Design of drops and cascades. Hydraulic design of culverts : standard box culverts and minimum energy loss culvert. Basic introduction to professional design of hydraulic structures. Application of the basic principles to real design situations. Analysis of complete systems. Applications, tutorials and exercises are grouped into four categories : applications within the main text to illustrate the basic lecture material, exercises for each chapter within each section, revision exercises using knowledge gained in several chapters within one section, and major assignments (i.e. problems) involving expertise gained in several sections : e.g., typically section I and one or two other sections. In the lecture material, complete and detailed solutions of the applications are given. Numerical solutions of some exercises, revision exercises and problems are available on the Internet (Publisher's site : http://www.arnoldpublishers.com/). A suggestion/correction form is placed at the end of the book. Comments, suggestions and critic are welcome and they will be helpful to improve the quality of the book. Readers who find an error or mistake are welcome to record the error on the page and to send a copy to the author. "Errare Humanum Est" ( ).

https://espace.library.uq.edu.au/view/UQ:108445/n97_REFER.pdf

The hydraulics of open channel flow

A physical model is a scaled representation of a hydraulic flow situation. Both the boundary conditions (e.g. channel bed, sidewalls), the upstream flow conditions and the
 flow field must be scaled in an appropriate manner (Fig. 14.1). Physical hydraulic models are commonly used during design stages to optimize a structure and to ensure a safe operation of
 the structure. They have an important further role to assist non-engineering people during the `decision-making' process. A hydraulic model may help the decision-makers to visualize and to
 picture the flow field, before selecting a `suitable' design. In civil engineering applications, a physical hydraulic model is usually a smaller- size representation of the prototype (i.e.
 the full-scale structure) (e.g. Fig. 14.2). Other applications of model studies (e.g. water treatment plant, flotation column) may require the use of models larger than the prototype. In
 any case the model is investigated in a laboratory under controlled conditions.

https://espace.library.uq.edu.au/view/UQ:9400/chap14.pdf

Hubert Chanson

Papers

Air Bubble Entrainment in Free-Surface Turbulent Shear Flows

Hydraulics of Stepped Chutes and Spillways

The Hydraulics of Open Channel Flow: An Introduction

The hydraulics of open channel flow

The Hydraulics of Open Channel Flow: An Introduction. Physical Modelling of Hydraulics