Elementary Classical Hydrodynamics
The Commonwealth and International Library: Mathematics Division
Published on 22. October 2013
232 pages
978-1-4831-6550-9 (ISBN)
Description
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.
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Content
Preface1. Fundamental Principles 1.1. Introduction 1.2. Basic Concepts and Quantities 1.3. The Equation of Continuity 1.4. Velocity and Acceleration 1.5. The Equation of Motion 1.6. Hydrostatics 1.7. Direct Use of the Equations of Hydrodynamics2. Some General Theorems 2.1. Bernoulli's Equation 2.2. The Analysis of Fluid Motion 2.3. Flow, Circulation and Vorticity3. Potential Flows 3.1. Velocity Potential and the Uniqueness Theorem 3.2. Multiply Connected Regions 3.3. Kinetic Energy and Kelvin's Theorem 3.4. Impulse and Momentum 3.5. Sources, Sinks and Doublets 3.6. The Drag Force and Lift on a Moving Body in Uniform Incompressible Fluid 3.7. Stokes' Stream Function4. Two-Dimensional Fluid Motion 4.1. The Stream Function and Velocity Potential 4.2. Circular Harmonics 4.3. Conjugate Functions 4.4. The Circle Theorem and Images 4.5. The Theorem of Blasius 4.6. The Kinetic Energy 4.7. Moving Boundaries 4.8. Vortex Motion 4.9. The Use of Conformal Transformations 4.10. Uniqueness Theorems5. Waves in Liquids 5.1. Fundamental Concepts 5.2. Tidal Waves 5.3. Surface Waves6. Compressible Fluids-Sound Waves 6.1. Sound waves 6.2. Some Important Features of Compressible FlowsAppendix: Integrals with Moving BoundariesBibliographyAnswers to the ExercisesIndex
