Fluid Mechanics

CHAPTER 1 INTRODUCTION 1 1.1 Introduction to Fluid Mechanics 2 Note to Students 2 Scope of Fluid Mechanics 3 Definition of a Fluid 3 1.2 Basic Equations 4 1.3 Methods of Analysis 5 System and Control Volume 6 Differential versus Integral Approach 7 Methods of Description 7 1.4 Dimensions and Units 9 Systems of Dimensions 9 Systems of Units 10 Preferred Systems of Units 11 Dimensional Consistency and Engineering Equations 11 1.5 Analysis of Experimental Error 13 1.6 Summary 14 Problems 14 CHAPTER 2 FUNDAMENTAL CONCEPTS 17 2.1 Fluid as a Continuum 18 2.2 Velocity Field 19 One-, Two-, and Three-Dimensional Flows 20 Timelines, Pathlines, Streaklines, and Streamlines 21 2.3 Stress Field 25 2.4 Viscosity 27 Newtonian Fluid 28 Non-Newtonian Fluids 30 2.5 Surface Tension 31 2.6 Description and Classification of Fluid Motions 34 Viscous and Inviscid Flows 34 Laminar and Turbulent Flows 36 Compressible and Incompressible Flows 37 Internal and External Flows 38 2.7 Summary and Useful Equations 39 References 40 Problems 40 CHAPTER 3 FLUID STATICS 46 3.1 The Basic Equation of Fluid Statics 47 3.2 The Standard Atmosphere 50 3.3 Pressure Variation in a Static Fluid 51 Incompressible Liquids: Manometers 51 Gases 56 3.4 Hydrostatic Force on Submerged Surfaces 58 Hydrostatic Force on a Plane Submerged Surface 58 Hydrostatic Force on a Curved Submerged Surface 65 3.5 Buoyancy and Stability 68 3.6 Fluids in Rigid-Body Motion (on the Web) 71 3.7 Summary and Useful Equations 71 References 72 Problems 72 CHAPTER 4 BASIC EQUATIONS IN INTEGRAL FORM FOR A CONTROL VOLUME 82 4.1 Basic Laws for a System 84 Conservation of Mass 84 Newton s Second Law 84 The Angular-Momentum Principle 84 The First Law of Thermodynamics 85 The Second Law of Thermodynamics 85 4.2 Relation of System Derivatives to the Control Volume Formulation 85 Derivation 86 Physical Interpretation 88 4.3 Conservation of Mass 89 Special Cases 90 4.4 Momentum Equation for Inertial Control Volume 94 Differential Control Volume Analysis 105 Control Volume Moving with Constant Velocity 109 4.5 Momentum Equation for Control Volume with Rectilinear Acceleration 111 4.6 Momentum Equation for Control Volume with Arbitrary Acceleration (on the Web) 117 4.7 The Angular-Momentum Principle 117 Equation for Fixed Control Volume 117 4.8 The First and Second Laws of Thermodynamics 121 Rate of Work Done by a Control Volume 122 Control Volume Equation 123 4.9 Summary and Useful Equations 128 Problems 129 CHAPTER 5 INTRODUCTION TO DIFFERENTIAL ANALYSIS OF FLUID MOTION 146 5.1 Conservation of Mass 147 Rectangular Coordinate System 147 Cylindrical Coordinate System 151 *5.2 Stream Function for Two-Dimensional Incompressible Flow 153 5.3 Motion of a Fluid Particle (Kinematics) 155 Fluid Translation: Acceleration of a Fluid Particle in a Velocity Field 156 Fluid Rotation 162 Fluid Deformation 165 5.4 Momentum Equation 169 Forces Acting on a Fluid Particle 169 Differential Momentum Equation 170 Newtonian Fluid: Navier Stokes Equations 170 *5.5 Introduction to Computational Fluid Dynamics 178 The Need for CFD 178 Applications of CFD 179 Some Basic CFD/Numerical Methods Using a Spreadsheet 180 The Strategy of CFD 184 Discretization Using the Finite-Difference Method 185 Assembly of Discrete System and Application of Boundary Conditions 186 Solution of Discrete System 187 Grid Convergence 187 Dealing with Nonlinearity 188 Direct and Iterative Solvers 189 Iterative Convergence 190 Concluding Remarks 191 5.6 Summary and Useful Equations 192 References 194 Problems 194 CHAPTER 6 INCOMPRESSIBLE INVISCID FLOW 200 6.1 Momentum Equation for Frictionless Flow: Euler s Equation 201 6.2 Bernoulli Equation: Integration of Euler s Equation Along a Streamline for Steady Flow 204 Derivation Using Streamline Coordinates 204 Derivation Using Rectangular Coordinates 205 Static, Stagnation, and Dynamic Pressures 207 Applications 209 Cautions on Use of the Bernoulli Equation 214 6.3 The Bernoulli Equation Interpreted as an Energy Equation 215 6.4 Energy Grade Line and Hydraulic Grade Line 219 6.5 Unsteady Bernoulli Equation: Integration of Euler s Equation Along a Streamline (on the Web) 221 *6.6 Irrotational Flow 221 Bernoulli Equation Applied to Irrotational Flow 221 Velocity Potential 222 Stream Function and Velocity Potential for Two-Dimensional, Irrotational, Incompressible Flow: Laplace s Equation 223 Elementary Plane Flows 225 Superposition of Elementary Plane Flows 227 6.7 Summary and Useful Equations 236 References 237 Problems 238 CHAPTER 7 DIMENSIONAL ANALYSIS AND SIMILITUDE 245 7.1 Nondimensionalizing the Basic Differential Equations 246 7.2 Nature of Dimensional Analysis 247 7.3 Buckingham Pi Theorem 249 7.4 Significant Dimensionless Groups in Fluid Mechanics 255 7.5 Flow Similarity and Model Studies 257 Incomplete Similarity 259 Scaling with Multiple Dependent Parameters 264 Comments on Model Testing 267 7.6 Summary and Useful Equations 268 References 269 Problems 269 CHAPTER 8 INTERNAL INCOMPRESSIBLE VISCOUS FLOW 275 8.1 Internal Flow Characteristics 276 Laminar versus Turbulent Flow 276 The Entrance Region 277 PART A. FULLY DEVELOPED LAMINAR FLOW 277 8.2 Fully Developed Laminar Flow Between Infinite Parallel Plates 277 Both Plates Stationary 278 Upper Plate Moving with Constant Speed, U 283 8.3 Fully Developed Laminar Flow in a Pipe 288 PART B. FLOW IN PIPES AND DUCTS 292 8.4 Shear Stress Distribution in Fully Developed Pipe Flow 293 8.5 Turbulent Velocity Profiles in Fully Developed Pipe Flow 294 8.6 Energy Considerations in Pipe Flow 297 Kinetic Energy Coefficient 298 Head Loss 298 8.7 Calculation of Head Loss 299 Major Losses: Friction Factor 299 Minor Losses 303 Pumps, Fans, and Blowers in Fluid Systems 308 Noncircular Ducts 309 8.8 Solution of Pipe Flow Problems 309 Single-Path Systems 310 Multiple-Path Systems 322 PART C. FLOW MEASUREMENT 326 8.9 Restriction Flow Meters for Internal Flows 326 The Orifice Plate 329 The Flow Nozzle 330 The Venturi 332 The Laminar Flow Element 332 Linear Flow Meters 335 Traversing Methods 336 8.10 Summary and Useful Equations 337 References 340 Problems 341 CHAPTER 9 EXTERNAL INCOMPRESSIBLE VISCOUS FLOW 352 PART A. BOUNDARY LAYERS 354 9.1 The Boundary-Layer Concept 354 9.2 Laminar Flat-Plate Boundary Layer: Exact Solution (on the Web) 358 9.3 Momentum Integral Equation 358 9.4 Use of the Momentum Integral Equation for Flow with Zero Pressure Gradient 362 Laminar Flow 363 Turbulent Flow 367 Summary of Results for Boundary-Layer Flow with Zero Pressure Gradient 370 9.5 Pressure Gradients in Boundary-Layer Flow 370 PART B. FLUID FLOW ABOUT IMMERSED BODIES 373 9.6 Drag 373 Pure Friction Drag: Flow over a Flat Plate Parallel to the Flow 374 Pure Pressure Drag: Flow over a Flat Plate Normal to the Flow 377 Friction and Pressure Drag: Flow over a Sphere and Cylinder 377 Streamlining 383 9.7 Lift 385 9.8 Summary and Useful Equations 399 References 401 Problems 402 CHAPTER 10 FLUID MACHINERY 412 10.1 Introduction and Classification of Fluid Machines 413 Machines for Doing Work on a Fluid 413 Machines for Extracting Work (Power) from a Fluid 415 Scope of Coverage 417 10.2 Turbomachinery Analysis 417 The Angular-Momentum Principle: The Euler Turbomachine Equation 417 Velocity Diagrams 419 Performance Hydraulic Power 422 Dimensional Analysis and Specific Speed 423 10.3 Pumps, Fans, and Blowers 428 Application of Euler Turbomachine Equation to Centrifugal Pumps 428 Application of the Euler Equation to Axial Flow Pumps and Fans 429 Performance Characteristics 432 Similarity Rules 437 Cavitation and Net Positive Suction Head 441 Pump Selection: Applications to Fluid Systems 444 Blowers and Fans 455 10.4 Positive Displacement Pumps 461 10.5 Hydraulic Turbines 464 Hydraulic Turbine Theory 464 Performance Characteristics for Hydraulic Turbines 466 Sizing Hydraulic Turbines for Fluid Systems 470 10.6 Propellers and Wind-Power Machines 474 Propellers 474 Wind-Power Machines 482 10.7 Compressible Flow Turbomachines 490 Application of the Energy Equation to a Compressible Flow Machine 490 Compressors 491 Compressible-Flow Turbines 495 10.8 Summary and Useful Equations 495 References 497 Problems 499 CHAPTER 11 FLOW IN OPEN CHANNELS 506 11.1 Basic Concepts and Definitions 508 Simplifying Assumptions 508 Channel Geometry 510 Speed of Surface Waves and the Froude Number 511 11.2 Energy Equation for Open-Channel Flows 515 Specific Energy 517 Critical Depth: Minimum Specific Energy 520 11.3 Localized Effect of Area Change (Frictionless Flow) 523 Flow over a Bump 523 11.4 The Hydraulic Jump 527 Depth Increase Across a Hydraulic Jump 530 Head Loss Across a Hydraulic Jump 531 11.5 Steady Uniform Flow 533 The Manning Equation for Uniform Flow 535 Energy Equation for Uniform Flow 540 Optimum Channel Cross Section 542 11.6 Flow with Gradually Varying Depth 543 Calculation of Surface Profiles 544 11.7 Discharge Measurement Using Weirs 547 Suppressed Rectangular Weir 547 Contracted Rectangular Weirs 548 Triangular Weir 548 Broad-Crested Weir 549 11.8 Summary and Useful Equations 550 References 551 Problems 552 CHAPTER 12 INTRODUCTION TO COMPRESSIBLE FLOW 555 12.1 Review of Thermodynamics 556 12.2 Propagation of Sound Waves 562 Speed of Sound 562 Types of Flow The Mach Cone 566 12.3 Reference State: Local Isentropic Stagnation Properties 569 Local Isentropic Stagnation Properties for the Flow of an Ideal Gas 570 12.4 Critical Conditions 576 12.5 Basic Equations for One-Dimensional Compressible Flow 576 Continuity Equation 576 Momentum Equation 577 First Law of Thermodynamics 577 Second Law of Thermodynamics 578 Equation of State 578 12.6 Isentropic Flow of an Ideal Gas: Area Variation 579 Subsonic Flow, M <1 581 Supersonic Flow, M >1 582 Sonic Flow, M =1 582 Reference Stagnation and Critical Conditions for Isentropic Flow of an Ideal Gas 583 Isentropic Flow in a Converging Nozzle 588 Isentropic Flow in a Converging-Diverging Nozzle 592 12.7 Normal Shocks 597 Basic Equations for a Normal Shock 598 Normal-Shock Flow Functions for One-Dimensional Flow of an Ideal Gas 600 12.8 Supersonic Channel Flow with Shocks 604 12.8 Supersonic Channel Flow with Shocks (continued, at www.wiley.com/college/fox) 606 12.9 Flow in a Constant Area Duct with Friction (www.wiley.com/college/fox) 606 12.10 Frictionless Flow in a Constant Area Duct with Heat Exchange (www.wiley.com/college/fox) 606 12.11 Oblique Shocks and Expansion Waves (www.wiley.com/college/fox) 606 12.12 Summary and Useful Equations 606 References 609 Problems 609 APPENDIX A FLUID PROPERTY DATA 613 APPENDIX B VIDEOS FOR FLUID MECHANICS 624 APPENDIX C SELECTED PERFORMANCE CURVES FOR PUMPS AND FANS 626 APPENDIX D FLOW FUNCTIONS FOR COMPUTATION OF COMPRESSIBLE FLOW 641 APPENDIX E ANALYSIS OF EXPERIMENTAL UNCERTAINTY 644 APPENDIX F ADDITIONAL COMPRESSIBLE FLOW FUNCTIONS (WWW.WILEY.COM/COLLEGE/FOX) WF-1 APPENDIX G A BRIEF REVIEW OF MICROSOFT EXCEL (WWW.WILEY.COM/COLLEGE/FOX) WG-1 Answers to Selected Problems 650 Index 660