Physical Fluid Dynamics

PrefaceList of NotationChapter One Introduction and Mathematical Background 1.1 Introduction 1.2 Mathematical Background 1.3 Vector Calculus 1.4 Vector Integral Theorems 1.5 The Rheological Behavior of Fluids Problems BibliographyChapter Two The Physical Properties of Fluids 2.1 Intermolecular Forces 2.2 The Continuum Concept 2.3 Fluid Statics 2.4 Boundary Conditions Between Two Fluid Media 2.5 Fluid Motion 2.6 Transport Phenomena in Fluids 2.7 Scalar Intensities 2.8 Special Properties of Liquid Fluids 2.9 Special Properties of Gases 2.10 The Maxwell-Boltzmann Distribution 2.11 Fluid Flow Phenomena 2.12 Physical Similarity and Dimensional Analysis Problems BibliographyChapter Three Fluid Flow Kinematics 3.1 The Eulerian Equations 3.2 The Equation of Continuity (Conservation of Mass) 3.3 Streamline 3.4 Kinematics of Deformation 3.5 Circulation and Vorticity 3.6 Irrotational Motion and the Velocity Potential 3.7 Boundary Conditions for Ideal Fluids 3.8 Types of Potential Problems and Methods of Obtaining Solutions 3.9 Example of an Irrotational Flow System 3.10 Velocity Field with Nonzero Dilation and Vorticity 3.11 Sources and Sinks—Singularities in the Rate of Dilation Problems BibliographyChapter Four The Equations of Fluid Motion 4.1 Conservation of Momentum 4.2 Conservation of Energy—the Energy Equation 4.3 Equation of State 4.4 Diffusion Equation 4.5 Some Exact Solutions of the Navier-Stokes Equations 4.6 Unsteady Flow 4.7 Laminar Flow Near a Rotating Disk 4.8 Inviscid Incompressible Flows 4.9 Method of Singularities 4.10 Superposition of Flows 4.11 Drag and Lift for the Cylinder with Circulation 4.12 Solution by Change in Variable—Conformal Mapping Problems BibliographyChapter Five Vortex Dynamics 5.1 Vortices and Circulation 5.2 Kelvin's Circulation Theorem 5.3 Helmholtz Vortex Theorems 5.4 Origins of Circulation 5.5 Generation of a Vortex Ring by an Impulsive Pressure Acting over a Circular Area 5.6 Determination of the Velocity Field from a Given Vortex Field 5.7 Two Straight-Line Vortices and Their Motion 5.8 The Kármán Vortex Streets 5.9 Circular Vortex Filament—Vortex Rings 5.10 Viscous Compressible Vortex 5.11 Hydrodynamic-Electromagnetic Analogy Problems BibliographyChapter Six Vorticity and the Laminar Boundary Layer 6.1 Introduction 6.2 The Vorticity Equation 6.3 The Creation of Vorticity 6.4 A Point Source of Vorticity 6.5 Flow Past a Solid Body from Infinity 6.6 The Reynolds Number Effect 6.7 Equations of Motion 6.8 Exact Solutions of the Boundary Layer Equations 6.9 Approximate Methods of Solution of the Boundary Layer Equations 6.10 Steady Compressible Boundary Layers (in Two-Dimensional Flow) 6.11 Problem of Two-Dimensional Steady Compressible Flow 6.12 The General Case Problems BibliographyChapter Seven Slow Vicous Flow 7.1 Introduction 7.2 Stokes Flows 7.3 Two-Dimensional Flows 7.4 Three-Dimensional Stokes Flows 7.5 Criticism of Stokes's Solution 7.6 The Oseen Equations 7.7 Three-Dimensional Oseen Flows Problems BibliographyChapter Eight Unsteady Flows, Stability, and Turbulence 8.1 Introduction Part I Unsteady Flows 8.2 Simple Examples 8.3 Boundary Layer Flows with Outer Fluctuating Velocity (High Frequency) Part II Instability of Boundary Layer Flows 8.4 The Energy Equation for Disturbances in Parallel Flows 8.5 Stability of Parallel Flows 8.6 Stability of the Schlichting Jet 8.7 General Method of Solution in Inviscid Case 8.8 Stability at Finite Reynolds Numbers 8.9 Transition to Turbulent Flows Part III Turbulent Flows 8.10 The Equations of Mean Flow 8.11 Turbulent Boundary Layers 8.12 The Momentum Balance Equation 8.13 The Turbulent Jet 8.14 Flows Involving Solid Boundaries 8.15 Boundary Layer Flow along a Flat Plate 8.16 Summary Part IV Structure of Turbulence 8.17 The Microstructure of Turbulent Flow 8.18 The Velocity Correlation 8.19 Spectrum of Turbulence 8.20 Nonisotropic Turbulence Problems BibliographyChapter Nine Compressible Fluid Flow 9.1 Thermodynamics and Fluid Flow 9.2 Speed of Propagation of Sound Waves 9.3 One-Dimensional Compressible Flow 9.4 Basic Equations of Flow 9.5 Normal Shock Relations for a Perfect Gas 9.6 The Propagating Wave 9.7 Flow through a Constant-Area Tube with Heat Transfer 9.8 The Equation of the Rayleigh Line 9.9 The Fanno Line—Flow with Friction 9.10 Shock Waves 9.11 The Use of Shock Tubes for the Study of Kinetics in Chemical Physics Problems BibliographyChapter Ten Particle Fluid Dynamics 10.1 The Particle Continuum 10.2 Forces on a Rigid Spherical Particle in a Fluid 10.3 Viscosity of a Dilute Suspension of Small Particles 10.4 Macroscopic Continuum Description of Particle-Fluid Flow 10.5 Two-Dimensional Suspension Boundary Layer Equations 10.6 Laminar Mixing BibliographyChapter Eleven Hydrodynamics of Superfluids 11.1 Fountain Effect 11.2 Flow of Liquid Helium 11.3 Second Sound 11.4 Two-Fluid Model of He II 11.5 Critical Velocities 11.6 Quantized Vortices 11.7 Quantized Vortices and Critical Velocities 11.8 Jet Flow of Superfluid Helium 11.9 Reversible Hydrodynamic Equations 11.10 Irreversible Hydrodynamic Equations 11.11 Applications to Some Simple Flow Problems 11.12 Applications of the Gorter-Mellink Formulation to Flow Problems 11.13 Molecular Basis of the Hydrodynamic Theory 11.14 Concluding Remarks BibliographyAppendix Vector Operations and Identities A1 Vector Operations A2 Vector IdentitiesSubject Index