Elementary Fluid Mechanics

This textbook provides a clear and concise introduction to both theory and application of fluid dynamics. It has a wide scope, frequent references to experiments, and numerous exercises (with hints and answers).

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 textbook describes the fundamental OC physicalOCO aspects of fluid flows for beginners of fluid mechanics in physics, mathematics and engineering, from the point of view of modern physics. It also emphasizes the dynamical aspects of fluid motions rather than the static aspects, illustrating vortex motions, waves, geophysical flows, chaos and turbulence. Beginning with the fundamental concepts of the nature of flows and the properties of fluids, the book presents fundamental conservation equations of mass, momentum and energy, and the equations of motion for both inviscid and viscous fluids. In addition to the fundamentals, this book also covers water waves and sound waves, vortex motions, geophysical flows, nonlinear instability, chaos, and turbulence. Furthermore, it includes the chapters on superfluids and the gauge theory of fluid flows. The material in the book emerged from the lecture notes for an intensive course on Elementary Fluid Mechanics for both undergraduate and postgraduate students of theoretical physics given in 2003 and 2004 at the Nankai Institute of Mathematics (Tianjin) in China. Hence, each chapter may be presented separately as a single lecture."

' This textbook describes the fundamental “physical” aspects of fluid flows for beginners of fluid mechanics in physics, mathematics and engineering, from the point of view of modern physics. It also emphasizes the dynamical aspects of fluid motions rather than the static aspects, illustrating vortex motions, waves, geophysical flows, chaos and turbulence. Beginning with the fundamental concepts of the nature of flows and the properties of fluids, the book presents fundamental conservation equations of mass, momentum and energy, and the equations of motion for both inviscid and viscous fluids. In addition to the fundamentals, this book also covers water waves and sound waves, vortex motions, geophysical flows, nonlinear instability, chaos, and turbulence. Furthermore, it includes the chapters on superfluids and the gauge theory of fluid flows. The material in the book emerged from the lecture notes for an intensive course on Elementary Fluid Mechanics for both undergraduate and postgraduate students of theoretical physics given in 2003 and 2004 at the Nankai Institute of Mathematics (Tianjin) in China. Hence, each chapter may be presented separately as a single lecture. Contents:FlowsFluidsFundamental Equations of Ideal FluidsViscous FluidsFlows of Ideal FluidsWater Waves and Sound WavesVortex MotionsGeophysical FlowsInstability and ChaosTurbulenceSuperfluid and Quantized CirculationGauge Theory of Ideal Fluid FlowsAppendices:Vector AnalysisVelocity Potential, Stream FunctionIdeal Fluid and Ideal GasCurvilinear Reference Frames: Differential OperatorsFirst Three Structure FunctionsLagrangians Readership: Undergraduate and postgraduate students in physics, mathematics, and engineering as well as scientists and engineers who are not specialists in fluid mechanics. Keywords:Elementary Fluid Mechanics;Physical Fluid Mechanics;Waves;Vortex Motions;Chaos;Turbulence;Geophysical Fluid Flows;Gauge Theory of Fluid FlowsKey Features:Textbook with a new and modern approachIncludes concise and compact presentations of important new areas in fluid mechanics from the viewpoint of physics, such as flows in rotating frames, stratified flows, recent results of the Earth Simulator, Lorenz chaotic system, fully developed turbulence, and the gauge theory of fluid flowsReviews: “The author is to be commended for introducing a chapter on the gauge theory of fluid mechanics, which is quite scarce in fluid mechanics books … the book can serve as an excellent introduction for graduate students in applied mathematics and physics who are interested in pursuing research in specific areas of fluid mechanics … One of the strengths of the book is its culmination in a detailed solution to all the problems.” Choice “This book contains an excellent basic presentation of theory, applications, and methods of solutions for various problems of classical and modern fluid dynamics.” Zentralblatt MATH '

This book gives an overview of classical topics in fluid dynamics, focusing on the kinematics and dynamics of incompressible inviscid and Newtonian viscous fluids, but also including some material on compressible flow. The topics are chosen to illustrate the mathematical methods of classical fluid dynamics. The book is intended to prepare the reader for more advanced topics of current research interest.

Suitable for both a first or second course in fluid mechanics at the graduate or advanced undergraduate level, this book presents the study of how fluids behave and interact under various forces and in various applied situations - whether in the liquid or gaseous state or both.

Elementary Classical Hydrodynamics deals with the fundamental principles of elementary classical hydrodynamics, with emphasis on the mechanics of inviscid fluids. Topics covered by this book include direct use of the equations of hydrodynamics, potential flows, two-dimensional fluid motion, waves in liquids, and compressible flows. Some general theorems such as Bernoulli's equation are also considered. This book is comprised of six chapters and begins by introducing the reader to the fundamental principles of fluid hydrodynamics, with emphasis on ways of studying the motion of a fluid. Basic concepts and quantities such as viscosity, density, and pressure, are considered, along with hydrostatics and the equation of motion. The discussion then turns to Bernoulli's equation, the motion of a small element of fluid, velocity potential, and the kinetic energy of a uniform incompressible fluid. The chapters that follow explore two-dimensional fluid motion; a uniform inviscid, incompressible liquid having a free surface and upon which the only body force acting is uniform gravity; and a compressible gas with undisturbed uniform pressure and density, paying particular attention to the propagation and reflection of sound waves. This book is intended as an elementary introduction to the mechanics of inviscid fluids for first and second year undergraduates.