Fluids Under Pressure

This contributed volume is based on talks given at the August 2016 summer school “Fluids Under Pressure,” held in Prague as part of the “Prague-Sum” series. Written by experts in their respective fields, chapters explore the complex role that pressure plays in physics, mathematical modeling, and fluid flow analysis. Specific topics covered include: Oceanic and atmospheric dynamics Incompressible flows Viscous compressible flows Well-posedness of the Navier-Stokes equations Weak solutions to the Navier-Stokes equations Fluids Under Pressure will be a valuable resource for graduate students and researchers studying fluid flow dynamics.

It is possible to "stretch" a liquid and, when suitably prepared, liquids are capable of sustaining substantial levels of tension, often for significant periods of time. These negative pressure states are metastable but can last for days - long enough for substantial experimental investigation. This volume is a review of recent and current research into the behaviour of liquids under negative pressure. Part I deals with the thermodynamics of stretched liquids. Part II discusses the physical and chemical behaviour of liquids under negative pressure. Part III contains papers on the effect of negative pressure on the solidification of a liquid. Part IV is devoted to stretched helium and Part V discusses cavitation in various stretched liquids. Part VI deals with the effect of foreign substances on cavitation.

This book addresses graduate students and researchers wishing to better understand the liquid and supercritical fluid states of matter, presenting a single cohesive treatment of the liquid and supercritical fluid states using the gas-like and solid-like approaches. Bringing this information together into one comprehensive text, this book outlines how our understanding of the liquid and supercritical fluid states is applied and explores the use of supercritical fluids in daily life and in research, for example in power generation, and their existence in planetary interiors. Presents a single coherent treatment of the key knowledge about the liquid and supercritical fluid states Provides comprehensive survey of key fluid properties from the latest experiments and applies our theoretical knowledge to understand the behaviour of these real fluids Explores the consequences of recent advances in the field on our understanding in industry, nature, and in interdisciplinary research, including planetary science

APlusPhysics: Your Guide to Regents Physics Essentials is a clear and concise roadmap to the entire New York State Regents Physics curriculum, preparing students for success in their high school physics class as well as review for high marks on the Regents Physics Exam. Topics covered include pre-requisite math and trigonometry; kinematics; forces; Newton's Laws of Motion, circular motion and gravity; impulse and momentum; work, energy, and power; electrostatics; electric circuits; magnetism; waves; optics; and modern physics. Featuring more than five hundred questions from past Regents exams with worked out solutions and detailed illustrations, this book is integrated with the APlusPhysics.com website, which includes online question and answer forums, videos, animations, and supplemental problems to help you master Regents Physics essentials. "The best physics books are the ones kids will actually read." Advance Praise for APlusPhysics Regents Physics Essentials: "Very well written... simple, clear engaging and accessible. You hit a grand slam with this review book." -- Anthony, NY Regents Physics Teacher. "Does a great job giving students what they need to know. The value provided is amazing." -- Tom, NY Regents Physics Teacher. "This was tremendous preparation for my physics test. I love the detailed problem solutions." -- Jenny, NY Regents Physics Student. "Regents Physics Essentials has all the information you could ever need and is much easier to understand than many other textbooks... it is an excellent review tool and is truly written for students." -- Cat, NY Regents Physics Student

This book is an undertaking of a pioneering work of uniting three vast fields of interfacial phenomena, rheology and fluid mechanics within the framework of solid-liquid two phase flow. No wonder, much finer books will be written in the future as the visionary aims of many nations in combining molecular chemistry, biology, transport and interfacial phenomena for the fundamental understanding of processes and capabilities of new materials will be achieved. Solid-liquid systems where solid particles with a wide range of physical properties, sizes ranging from nano- to macro- scale and concentrations varying from very dilute to highly concentrated, are suspended in liquids of different rheological behavior flowing in various regimes are taken up in this book. Interactions among solid particles in molecular scale are extended to aggregations in the macro scale and related to settling, flow and rheological behavior of the suspensions in a coherent, sequential manner. The classical concept of solid particles is extended to include nanoparticles, colloids, microorganisms and cellular materials. The flow of these systems is investigated under pressure, electrical, magnetic and chemical driving forces in channels ranging from macro-scale pipes to micro channels. Complementary separation and mixing processes are also taken under consideration with micro- and macro-scale counterparts. - Up-to-date including emerging technologies- Coherent, sequential approach- Wide scope: microorganisms, nanoparticles, polymer solutions, minerals, wastewater sludge, etc- All flow conditions, settling and non-settling particles, non-Newtonian flow, etc- Processes accompanying conveying in channels, such as sedimentation, separation, mixing

ELEMENTARY FLUID MECHANICS BY JOHN K. VENNARD Assistant Professor of Fluid Mechanics New York University. PREFACE: Fluid mechanics is the study under all possible conditions of rest and motion. Its approaches analytical, rational, and mathematical rather than empirical it concerns itself with those basic principles which lead to the solution of numerous diversified problems, and it seeks results which are widely applicable to similar fluid situations and not limited to isolated special cases. Fluid mechanics recognizes no arbitrary boundaries between fields of engineering knowledge but attempts to solve all fluid problems, irrespective of their occurrence or of the characteristics of the fluids involved. This textbook is intended primarily for the beginner who knows the principles of mathematics and mechanics but has had no previous experience with fluid phenomena. The abilities of the average beginner and the tremendous scope of fluid mechanics appear to be in conflict, and the former obviously determine limits beyond which it is not feasible to go these practical limits represent the boundaries of the subject which I have chosen to call elementary fluid mechanics. The apparent conflict between scope of subject and beginner f s ability is only along mathematical lines, however, and the physical ideas of fluid mechanics are well within the reach of the beginner in the field. Holding to the belief that physical concepts are the sine qua non of mechanics, I have sacrificed mathematical rigor and detail in developing physical pictures and in many cases have stated general laws only without numerous exceptions and limitations in order to convey basic ideas such oversimplification is necessary in introducing a new subject to the beginner. Like other courses in mechanics, fluid mechanics must include disciplinary features as well as factual information the beginner must follow theoretical developments, develop imagination in visualizing physical phenomena, and be forced to think his way through problems of theory and application. The text attempts to attain these objectives in the following ways omission of subsidiary conclusions is designed to encourage the student to come to some conclusions by himself application of bare principles to specific problems should develop ingenuity illustrative problems are included to assist in overcoming numerical difficulties and many numerical problems for the student to solve are intended not only to develop ingenuity but to show practical applications as well. Presentation of the subject begins with a discussion of fundamentals, physical properties and fluid statics. Frictionless flow is then discussed to bring out the applications of the principles of conservation of mass and energy, and of impulse-momentum law, to fluid motion. The principles of similarity and dimensional analysis are next taken up so that these principles may be used as tools in later developments. Frictional processes are discussed in a semi-quantitative fashion, and the text proceeds to pipe and open-channel flow. A chapter is devoted to the principles and apparatus for fluid measurements, and the text ends with an elementary treatment of flow about immersed objects.

This is an introductory fluid mechanics text, intended for the first Fluid Mechanics course required of all engineers. The goal of this book is to modernise the teaching of fluid mechanics by encouraging students to visualise and simulate flow processes. The book also introduces students to the capabilities of computational fluid dynamics (CFD) techniques, the most important new approach to the study of fluids. Fluid mechanics is traditionally one of the most difficult topics in the curriculum for ME students: this text aims to overcome those learning difficulties through visualisation of the key concepts.Contents: 1. Fundamental Concepts 1.1 Introduction 1.2 Gases. Liquids and Solids 1.3 Methods of Description 1.4 Dimensions and Unit Sytems 1.5 Problem Solving 2. Fluid Properties 2.1 Introduction 2.2 Mass, Weight and Density 2.3 Pressure 2.4 Temperature and Other Thermal Properties 2.5 The Perfect Gas Law 2.6 Bulk Compressibility Modules 2.7 Viscosity 2.8 Surface Tension 2.9 Fluid Energy 3. Case Studies in Fluid Mechanics 3.1 Introduction 3.2 Common Dimensionless Groups 3.3 Case Studies 4. Fluid Forces 4.1 Introduction 4.2 Classification of Fluid Forces 4.3 The Orgins of Body and Surface Forces 4.4 Body Forces 4.5 Surface Forces 4.6 Stress in a Fluid 4.7 Forces Balance in a Fluid 5. Fluid Statics 5.1 Introduction 5.2 Hydrostatic Stress 5.3 Hydrostatic Equation 5.4 Hydrostatic Pressure Distribution 5.5 Hydrostatic Force 5.6 Hydrostatic Moment 5.7 Resultant Force and Point of Application 5.8 Buoyancy and Archimedes 5.9 Equilibrium and Stability of Immerseed Bodies 6. The Velocity Field and Fluid Transport 6.1 Introduction 6.2 The Fluid Velocity Field 6.3 Fluid Acceleration 6.4 The Substantial Derivative 6.5 Classification of Flows 6.6 No-Slip, No-Penetration Boundary Condition 6.7 Fluid Transport 6.8 Average Velocity and Flowrate 7. Control Volume Analysis 7.1 Introduction 7.2 Basic Concepts: System and Control Volume 7.3 System and Control Volume Analysis 7.4 Reynolds Transport Theorem for a System 7.5 Reynolds Transport Theorem for a Control Volume 7.6 Control Volume Analysis 8. Flow of an Invicid Fluid: The Bernoulli Equation 8.1 Introduction 8.2 Friction Flow along a Streamline 8.3 Bernoulli Equation 8.4 Static, Dynamic, Stagnation and Total Pressure 8.5 Applications of the Bernoulli Equation 8.6 Relationship to the Energy Equation 9. Dimensional Analysis and Similitude 9.1 Introduction 9.2 Buckingham PI Theorem 9.3 Repeating Variables Method 9.4 Similitude and Model Development 9.5 Correlation of Experimental Data 9.6 Application to Case Studies 10. Elements of Flow Visualisation and Flow Structure 10.1 Introduction 10.2 Lagrangian Kinematics 10.3 The Eulerian-Langrangian Connection 10.4 Material Lines, Surfaces and Volumes 10.5 Pathlines and Streaklines 10.6 Streamlines and Streamtubes 10.7 Motion and Deformation 10.8 Velocity 10.9 Rate of Rotation 10.10 Rate of Expansion 10.11 Rate of Shear Deformation 11. Governing Equations of Fluid Dynamics 11.1 Introduction 11.2 Continuity Equation 11.3 Momentum Equation 11.4 Constitutive Model for a Newtonian Fluid 11.5 Navier-Stokes Equations 11.6 Euler Equations 11.7 Energy Equation 11.8 Discussion 12. Analysis of Incompressive Flow 12.1 Introduction 12.2 Steady Viscous Flow 12.3 Unsteady Viscous Flow 12.4 Turbulent 12.5 Inviscid Irrotational Flow 13. Flow in Pipes and Ducts 13.1 Introduction 13.2 Steady Fully Developed Flow in a Pipe or Duct 13.3 Analysis of Flow in Single Path Pipe and Duct Systems 13.4 Analysis of Flow in Multiple Path Pipe and Duct Systems 13.5 Elements of Pipe and Duct Systems Design 14. External Flow 14.1 Introduction 14.2 Boundary Layers: Basic Concepts 14.3 Drag: Basic Concepts 14.4 Drag Coefficients 14.5 Life and Drag of Airfoils 15. Open Channel Flow 15.1 Introduction 15.2 Basic Concepts in Open Channel Flow 15.3 The Importance of the Froude Number 15.4 Energy Conservation in Open Channel Flow 15.5 Flow in a Channel with Uniform Depth 15.6 Flow in a Channel with Gradually-Varying Depth 15.7 Flow Under a Sluice Gate 15.8 Flow over a Weir