Fluid Mechanics (Dover Books on Physics)

Description

"The mixture of prose, mathematics, and beautiful illustrations is particularly well chosen." — American Scientist This monumental text by a noted authority in the field is specially designed to provide an orderly structured introduction to fluid mechanics, a field all too often seen by students as an amorphous mass of disparate equations instead of the coherent body of theory and application it should be. In addition, the book will help upgrade students' mathematical skills as they learn the fundamentals of fluid mechanics. The text presents a unified method of analysis that poses fluid mechanics problems in precise mathematical language without becoming stiff or unnecessarily rigorous. This method involves three steps: First, the text carefully defines each problem so the student knows what is given and what is missing. Second, each chapter treats the physical aspects of the problems so the student can visualize how things work in the real world. Third, the text represents the physical model by appropriate mathematical symbols and operators, collects these into equations, and then solves them. The result is a superb learning and teaching process that covers everything the engineer needs to know — nature of fluids, hydrostatics, differential and integral equations, dimensional analysis, viscous flows, and other topics — while allowing students to see each element in its relation to the whole. Each chapter contains numerous examples incorporating problem-solving techniques, demonstrations to illustrate topical material, study questions, boxed equations of significant results, appropriate references to supplementary materials and other study aids. Over 760 illustrations enhance the text. This volume will be an indispensable reference and resource for any student of fluid mechanics or practicing engineer. Front Matter Table of Contents Prefaces Preface to the Dover Edition Preface to the First Edition 1. Format and Fundamentals 1.1 Introduction: A Survey of Fluid Mechanics 1.2 Format of This Text 1.2.1 The Subject of Fluid Mechanics 1.2.2 The Structure of Fluid Mechanics 1.3 Fundamental Quantities, Units 1.3.1 Le Systéme International, SI System 1.3.2 The USCS System 1.3.3 Two other Systems of Units 1.3.4 Secondary Dimensions 1.4 Fundamental Idealizations 1.5 Fundamental Coordinates 1.6 Fundamental Kinematic Field 1.6.1 Absolute Velocity 1.6.2 Relative Velocity 1.6.3 Absolute Acceleration Field 1.6.4 Relative Acceleration Field 1.7 Fundamental Descriptions: Lagrange versus Euler Description 1.7.1 Lagrangian Description 1.7.2 Eulerian Description 1.7.3 Substantive Derivative D/Dt: The Stokes Derivative 1.7.3.1 The Acceleration in the Eulerian Description References Study Questions Problems 2. Description of Fluids 2.1 Introduction 2.2 What is a Fluid? 2.2.1 Concerning Water 2.3 Classification of Fluid Flows 2.3.1 Gases versus Liquids 2.3.2 Continuum versus Discrete Fluids 2.3.3 Perfect versus Real Fluids 2.3.4 Newtonian versus Non-Newtonian Fluids 2.3.5 Compressible and Incompressible Fluids 2.3.6 Steady and Unsteady Fluid Flows 2.3.7 One, Two, and Three-Dimensional Flows 2.3.8 Rotational versus Irrotational Flow 2.4 Properties of Fluids 2.4.1 Mass, M 2.4.2 Density, rho 2.4.3 Specific Weight, gamma 2.4.4 Specific Gravity, S 2.4.5 Pressure, p 2.4.6 Bulk Modulus of Elasticity, K 2.4.7 Absolute or Dynamic Viscosity, mu 2.4.8 Kinematic Viscosity, v 2.4.9 Surface Tension, sigma 2.4.10 Capillary Rise or Depression, h References Study Questions Problems 3. Aerohydrostatics 3.1 Hydrostatics 3.1.1 Manometers 3.1.2 Barometer 3.1.3 U-Tube Manometer 3.1.4 Inclined Manometer 3.2 Uniform Acceleration 3.3 Aerostatics 3.3.1 Halley's Law 3.3.2 Logarithmic Law 3.4 Forces on Planar Bodies 3.4.1 Force on a Planar Body in a Horizontal Plane 3.4.2 Pressure Force on Inclined Planar Surfaces 3.5 Hydrostatic Forces on Curved Bodies 3.5.1 Horizontal and Vertical Components of a Pressure Force 3.6 Buoyant Forces on Submerged Bodies 3.7 Initial Stability of Floating and Submerged Ships 3.7.1 Relative Location of Reference Points 3.7.2 Initial Stability of a Surface Ship 3.7.3 Initial Stability for the Submerged Submarine 3.7.4 Methods of Improving Initial Stability Study Questions Problems 4. Differential Forms of Fluid Behavior 4.1 Introduction 4.2 General Property Balance 4.3 The Differential Form of the Conservation of Mass 4.4 The Differential Form of the Conservation of Linear Momentum 4.4.1 The Physics of the Problem 4.4.2 The Composition of Velocity 4.4.3 The Strain Rate Dyadic S 4.4.4 Geometric Interpretation of the Velocity Components 4.4.5 The Stress Dyadic, P 4.4.6 The Surface Forces, F_s 4.4.7 Vorticity, zeta 4.4.8 Cauchy's Equation of Motion 4.4.9 The Navier-Stokes Equations 4.4.10 The Gromeka-Lamb Form of the Navier-Stokes Equation 4.4.10.1 Beltrami Flow 4.4.11 Boundary Conditions 4.4.11.1 Kinematic Boundary Condition 4.4.11.2 Stress Boundary Condition 4.5 The Differential Form of the Conservation of Energy 4.5.1 Boundary Conditions for the Energy Equation 4.6 Air as an Incompressible and/or Inviscid Fluid References Study Questions Problems 5. Integrated Forms of Fluid Behavior 5.1 Introduction 5.2 The Integral Form of the Conservation of Mass 5.2.1 Incompressible Flow Form of the Continuity Equation 5.3 The Integral Form of the Conservation of Linear Momentum 5.3.1 Linear Momentum Equation for Inertial Control Volume 5.3.1.1 Simplified Steady State Forms 5.3.1.2 One-Dimensional Steady Flow Case 5.3.1.3 Free Jet Reaction 5.3.1.4 Free Jet Reaction with Moving Wall 5.3.1.5 Airfoil Forces in Plane Flow 5.3.2 Integral Form of the Linear Momentum Equation for a Noninertial Control Volume 5.3.2.1 Moving Vanes in Steady Nonaccelerating Flows 5.4 The Integral Form of the Conservation of Angular Momentum 5.4.1 Case 1: V_r = 0. Rigid Body Motion 5.4.2 Case 2: Inertial Frame of Reference 5.4.2.1 Moment of Momentum Equations Applied to Pumps and Turbines 5.4.2.2 An Application: Centrifugal Pumps and Their Characteristics 5.4.2.3 Pump Performance Analysis 5.4.2.4 Some Limiting Factors in Pump Operation 5.4.2.5 Combination of Pump and System 5.5 The Integral Form of the Conservation of Energy 5.5.1 Rate of Heat Transfer, _i Q_e 5.5.2 Fluid Power, _i W_e 5.5.2.1 Work due to Shear Stresses, W_st 5.5.2.2 Work due to Normal Stresses, W_sp 5.5.3 Integral Form of the Energy Equation 5.5.3.1 Steady State Form 5.5.3.2 One-Dimensional Form 5.5.4 The Steady Flow Energy Equation versus Bernoulli's Equation 5.5.5 Energy Grade Lines Study Questions Problems 6. Recapitulation 6.1 Summary 6.2 Special Forms of the Governing Equations 6.3 Problem-Solving Technique 6.4 Examples of Problem-Solving Technique 7. Dimensional Analysis and Similitude 7.1 Introduction 7.2 Dimensional Analysis 7.2.1 The Principle of Dimensional Homogeneity 7.3 Buckingham Pi Theorem 7.3.1 Applications of the Buckingham Pi Theorem 7.4 The Rayleigh Method 7.4.1 A Critique of the Two Methods 7.5 Dimensionless Parameters 7.5.1 Dimensionless Navier-Stokes Equation 7.5.2 Scaling Rules 7.5.3 Reynolds Number, R_L 7.5.4 Froude Number, F_r 7.5.5 Mach Number M and Cauchy Number C 7.5.6 Weber Number, W 7.5.7 Euler Number E, and the Pressure Coefficient C_p 7.6 Similitude 7.7 Similarity Solutions and Transformations 7.8 Geometric and Dynamic Similitude 7.9 Modeling 7.9.1 Reynolds Number Modeling 7.9.2 Froude Number Modeling 7.10 Drag 7.11 Lift 7.12 Vorticity Effect in Lift and Drag References Study Questions Problems 8. Flow Visualization 8.1 Introduction 8.2 Equation of a Streamline 8.3 Stream Function, psi 8.3.1 Cauchy-Riemann Conditions 8.3.2 Orthogonality of phi and psi 8.4 Visualization Techniques 8.4.1 Methods for Visualizing Flows of Liquids and Gases 8.4.1.1 Dyes 8.4.1.2 Smoke 8.4.1.3 Tufts 8.4.1.4 Small Particles 8.4.1.5 Optical Set-Ups References Study Questions Problems 9. Viscous Fluid Flows 9.1 Introduction 9.2 Rectilinear Flow between Parallel Plates 9.2.1 Temperature Distributions for Couette and Poiseuille Flows 9.2.1.1 Couette Flow Temperature Distribution 9.2.1.2 Poiseuille Flow Temperature Distribution 9.3 Suddenly Accelerated Flat Plate in a Viscous Fluid 9.4 Rotational Viscous Flows 9.4.1 Equations of Motion 9.4.2 Some Exact Solutions 9.4.2.1 Oseen's Solution 9.4.2.2 A Decaying Vortex References Study Questions Problems 10. Laminar Pipe Flow 10.1 Introduction 10.2 Description of the Physical Phenomenon 10.3 Equations of Motion for Laminar Flow in a Pipe 10.4 The Moody Diagram 10.4.1 Other Ways to Use the Moody Diagram 10.5 Minor Losses 10.5.1 Fittings and Obstructions 10.5.1.1 Loss Coefficient k for a Few Valves 10.5.2 Elbows, Tees, and Such 10.5.3 Sudden Contractions 10.5.4 Sudden Expansion 10.5.5 Gradual Expansion 10.6 Energy Equation for Real Fluid Flow in a Pipe 10.7 Examples of Pipe Flow 10.7.1 The Siphon 10.7.2 Pipes in Series 10.7.3 Flow in Parallel Pipes References Study Questions Problems 11. Turbulent Pipe Flow 11.1 Introduction 11.2 Detecting Turbulence 11.3 On the Origin of Turbulence 11.3.1 The Role of Vorticity in the Origin of Turbulence 11.4 Definitions of Various Velocity Terms 11.4.1 The Equations of Motion for Turbulent Flow 11.5 Zero-Equation Model for Fully Turbulent Flow 11.5.1 The Mixing Length Hypothesis MLH 11.5.2 Experimental Determination of Mixing Length 11.5.3 Advantages and Disadvantages of the MLH 11.6 Fully Turbulent Flow in a Pipe References Study Questions Problems 12. Potential Flow 12.1 Introduction 12.2 Laplace's Equation 12.2.1 Methods of Solving Laplace's Equation 12.3 The Complex Potential, Omega 12.4 The Complex Velocity, dOmega/dz 12.4.1 Stagnation Points 12.4.2 The Speed 12.5 Complex Potential for Fundamental Flows 12.5.1 Uniform Flow 12.5.2 Sources and Sinks 12.5.3 Vortex Motions 12.5.3.1 Circulation, Gamma 12.5.3.2 Complex Potential for an lrrotational Vortex 12.5.4 Doublet 12.6 Conservation of Circulation 12.7 Equation of the Body 12.8 Blasius' Theorem for Forces 12.9 Various Complex Potentials Omegaz and Corresponding Physical Flows 12.10 Combined Flows 12.10.1 Principle of Superposition 12.10.2 Flow about a Half-Body 12.10.3 Uniform Flow Past a Source and a Sink 12.10.4 Uniform Flow Past a Doublet: Flow Past a Cylinder 12.10.5 Uniform Flow Past a Cylinder with Circulation 12.11 Lift and Drag 12.11.1 The Phenomenon of Lift 12.11.2 The Phenomenon of Drag 12.11.3 Some Illustrative Projects on Lift and Drag 12.11.3.1 Purpose 12.12 Method of Images or a Way to Create Straight Boundaries 12.13 Potential and Stream Functions in Real Fluids 12.13.1 Compressible Fluids 12.13.2 Viscous Flows 12.13.3 Rotational Flows Being Ideal 12.14 Comparison of Potential Theory with Experiment References Study Questions Problems 13. Open-Channel Flow 13.1 Introduction 13.2 Steady Open-Channel Flow 13.2.1 Flow Classification 13.2.2 Uniform Open-Channel Flow 13.2.2.1 Evaluating the Chézy Coefficient C 13.2.2.2 Evaluating the Channel Geometry 13.2.2.3 The Most Efficient Channel Profile 13.2.3 Specific Energy 13.2.3.1 Specific Energy and Critical Depth for Free-Surface Flow in a Uniform Flat Bed Channel 13.3 Surge Waves and the Hydraulic Jump 13.3.1 Open-Channel Flow Past a Broad-Crested Weir 13.3.2 The Hydraulic Jump 13.4 Flows Past Sharp-Crested Weirs 13.5 Linear Theory of Simple Harmonic Long-Crested Waves of Small Amplitude References Study Questions Problems 14. Boundary Layer Flows 14.1 Introduction 14.1.1 Reynolds' Experiment 14.2 The Boundary Layer Concept 14.3 Prandtl's Boundary Layer Equations 14.4 Blasius Solution for Laminar Boundary Layer Flow over a Flat Plate 14.5 Boundary Layer Thicknesses of Displacement and Momentum 14.6 Prandtl's Boundary Layer Theory from the Viewpoint of a Mathematician 14.6.1 Separation 14.6.2 On Prandtl's Boundary Layer Equations 14.7 Integral Momentum Principles 14.7.1 Momentum Principle for Boundary Layer Analysis 14.7.2 Method of Solution of the von Kármán-Pohlhausen Integral Momentum Equation 14.7.3 Laminar Boundary Layer Analysis on a Flat Plate 14.8 Mechanics of Boundary Layer Transition 14.8.1 The Nonlinear Region 14.8.1.1 Region of Instability to Small Wavy Disturbances 14.8.1.2 Region of Three-Dimensional Wave Amplification 14.8.1.3 Peak-Valley Development with Streamwise-Vortex System 14.8.1.4 Vorticity Concentration and Shear Layer Development 14.8.1.5 Breakdown 14.8.1.6 Turbulent-Spot Development 14.8.2 Salient Aspects of Transition 14.8.2.1 Transition in Pipe Flows 14.8.2.2 Transition in Flows over Bodies 14.8.3 Instability versus Transition 14.8.3.1 Determining the Position of the Instability Point for a Body 14.9 Turbulent Boundary Layers 14.9.1 The Inner Layer, 0 Less-Than or Equal to y/delta Less-Than or Equal to 0.2 14.9.1.1 Linear Sublayer, 0 Less-Than or Equal to u*y/v Less-Than or Equal to 3 14.9.1.2 Buffer Layer, 3 < u*y/v < 40 14.9.1.3 Logarithmic Law Region, 40 < u*y/v < 0.2 delta u*/v 14.9.2 The Outer Layer, 0.2 Less-Than or Equal to y/delta Less-Than or Equal to 1.0 14.9.2.1 The Viscous Superlayer 14.9.3 Fully Turbulent Boundary Layer Flow 14.10 Drag 14.10.1 Drag Coefficient of Automobiles 14.10.2 Effect of Thickness on the Drag of Symmetrical Bodies 14.10.3 The Effect of Shape on Drag 14.10.4 Effect of Roughness on the Drag of Airfoil Shapes 14.10.5 Aspects of Design for Minimum Drag 14.10.6 Applications 14.10.6.1 Drag on a Cylinder 14.10.6.2 Drag on a Sphere References Study Questions Problems 15. One-Dimensional Compressible Flow 15.1 Introduction 15.2 The Description of a Perfect Gas 15.3 The Second Law of Thermodynamics 15.4 Equations of a Process 15.5 The Compressible Flow Energy Equation 15.6 Problem Solution Technique in Applying the Energy Equation 15.6.1 Application of the I.F. Energy Equation for Compressible Flow 15.6.1.1 Nozzles and Diffusers 15.6.1.2 Compressors, Turbines, and Fans 15.6.1.3 Throttle 15.6.1.4 One-Dimensional Isentropic Pipe Flow 15.7 Normal Shock Waves 15.7.1 Mach Number Relationships for a Normal Shock 15.7.2 Mach Number Relationships for Stagnation Conditions in Isentropic Nozzles 15.7.3 Mass Rate through an Isentropic Nozzle 15.7.4 Location of a Normal Shock in a Nozzle 15.7.5 The Prandtl Relation 15.7.6 Thickness of the Normal Shock 15.8 Isothermal Gas Flow in a Pipe 15.9 Other Types of Shock Waves 15.10 Drag Coefficient C_D for Compressible Flow 15.10.1 Subsonic Compressible Drag Coefficients 15.10.2 Transonic and Supersonic Drag Coefficients 15.11 Closure References Study Questions Problems Answers to Selected Odd-Numbered Problems Dedication Index A B C D E F G H I J K L M N O P Q R S T U V W Z Appendices Appendix A: Complex Variables A.1 Complex Numbers A.2 de Moivre's Theorem A.3 Some Useful Definitions A.4 Regular Function A.5 Singular Points A.6 Taylor Series A.7 Laurent Series A.8 Cauchy-Goursat Theorem A.9 Cauchy's Integral Formula A.10 Residue A.11 Residue Theorem Appendix B: Vectors B.1 Vector Products B.2 Differentiation with Respect to a Scalar B.3 Formulas of Partial Differentiation B.4 Formulas of Integration Appendix C: Gas Tables