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Introduction to Fluid Mechanics by Philip J. Pritchard and John C. Leylegian



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Fox and McDonald’s Introduction to Fluid Mechanics Eighth Edition written by Philip J. Pritchard , Manhattan College. With special contributions from: John C. Leylegian , Manhattan College. This book is intended to help undergraduate engineering students learn the fundamentals of fluid mechanics. It was developed for use in a first course on fluid mechanics, either one or two semesters/terms. While the principles of this course has been well established for many years, fluid mechanics education has envolved and improved.


Fox and McDonald’s Introduction to Fluid Mechanics Eighth Edition written by Philip J. Pritchard cover the following topics.


  • 1 INTRODUCTION
    1.1 Note to Students 3
    1.2 Scope of Fluid Mechanics 4
    1.3 Definition of a Fluid 4
    1.4 Basic Equations 5
    1.5 Methods of Analysis 6
    System and Control Volume 7
    Differential versus Integral Approach 8
    Methods of Description 9
    1.6 Dimensions and Units 11
    Systems of Dimensions 11
    Systems of Units 11
    Preferred Systems of Units 13
    Dimensional Consistency and “Engineering” Equations 14
    1.7 Analysis of Experimental Error 15
    1.8 Summary 16
    Problems 17

  • 2 FUNDAMENTAL CONCEPTS
    2.1 Fluid as a Continuum 21
    2.2 Velocity Field 23
    One-, Two-, and Three-Dimensional Flows 24
    Timelines, Pathlines, Streaklines, and Streamlines 25
    2.3 Stress Field 29
    2.4 Viscosity 31
    Newtonian Fluid 32
    Non-Newtonian Fluids 34
    2.5 Surface Tension 36
    2.6 Description and Classification of Fluid Motions 38
    Viscous and Inviscid Flows 38
    Laminar and Turbulent Flows 41
    Compressible and Incompressible Flows 42
    Internal and External Flows 43
    2.7 Summary and Useful Equations 44
    References 46
    Problems 46

  • 3 FLUID STATICS
    3.1 The Basic Equation of Fluid Statics 56
    3.2 The Standard Atmosphere 60
    3.3 Pressure Variation in a Static Fluid 61
    Incompressible Liquids: Manometers 61
    Gases 66
    3.4 Hydraulic Systems 69
    3.5 Hydrostatic Force on Submerged Surfaces 69
    Hydrostatic Force on a Plane Submerged Surface 69
    Hydrostatic Force on a Curved Submerged Surface 76
    *3.6 Buoyancy and Stability 80
    3.7 Fluids in Rigid-Body Motion (on the Web) W-1
    3.8 Summary and Useful Equations 83
    References 84
    Problems 84

  • 4 BASIC EQUATIONS IN INTEGRAL FORM FOR A CONTROL VOLUME
    4.1 Basic Laws for a System 98
    Conservation of Mass 98
    Newton’s Second Law 98
    The Angular-Momentum Principle 99
    The First Law of Thermodynamics 99
    The Second Law of Thermodynamics 99
    4.2 Relation of System Derivatives to the Control Volume Formulation 100
    Derivation 101
    Physical Interpretation 103
    4.3 Conservation of Mass 104 Special Cases 105
    4.4 Momentum Equation for Inertial Control Volume 110
    *Differential Control Volume Analysis 122
    Control Volume Moving with Constant Velocity 126
    4.5 Momentum Equation for Control Volume with Rectilinear Acceleration 128
    4.6 Momentum Equation for Control Volume with Arbitrary Acceleration (on the Web) W-6
    *4.7 The Angular-Momentum Principle 135
    Equation for Fixed Control Volume 135
    Equation for Rotating Control Volume (on the Web) W-11
    4.8 The First Law of Thermodynamics 139
    Rate of Work Done by a Control Volume 140
    Control Volume Equation 142
    4.9 The Second Law of Thermodynamics 146
    4.10 Summary and Useful Equations 147
    Problems 149

  • 5 INTRODUCTION TO DIFFERENTIAL ANALYSIS OF FLUID MOTION
    5.1 Conservation of Mass 172
    Rectangular Coordinate System 173
    Cylindrical Coordinate System 177
    *5.2 Stream Function for Two-Dimensional Incompressible Flow 180
    5.3 Motion of a Fluid Particle (Kinematics) 184
    Fluid Translation: Acceleration of a Fluid Particle in a Velocity Field 185
    Fluid Rotation 190
    Fluid Deformation 194
    5.4 Momentum Equation 197
    Forces Acting on a Fluid Particle 198
    Differential Momentum Equation 199
    Newtonian Fluid: NavierStokes Equations 199
    *5.5 Introduction to Computational Fluid Dynamics 208
    The Need for CFD 208
    Applications of CFD 209
    Some Basic CFDNumerical Methods Using a Spreadsheet 210
    The Strategy of CFD 215
    Discretization Using the Finite-Difference Method 216
    Assembly of Discrete System and Application of Boundary Conditions 217
    Solution of Discrete System 218
    Grid Convergence 219
    Dealing with Nonlinearity 220
    Direct and Iterative Solvers 221
    Iterative Convergence 222
    Concluding Remarks 223
    5.6 Summary and Useful Equations 224
    References 226
    Problems 226

  • 6 INCOMPRESSIBLE INVISCID FLOW
    6.1 Momentum Equation for Frictionless Flow: Euler’s Equation 237
    6.2 Euler’s Equations in Streamline Coordinates 238
    6.3 Bernoulli Equation—Integration of Euler’s Equation Along a Streamline for Steady Flow 241
    *Derivation Using Streamline Coordinates 241
    *Derivation Using Rectangular Coordinates 242
    Static, Stagnation, and Dynamic Pressures 244
    Applications 247
    Cautions on Use of the Bernoulli Equation 252
    6.4 The Bernoulli Equation Interpreted as an Energy Equation 253
    6.5 Energy Grade Line and Hydraulic Grade Line 257
    *6.6 Unsteady Bernoulli Equation: Integration of Euler’s Equation Along a Streamline (on the Web) W-16
    *6.7 Irrotational Flow 259
    Bernoulli Equation Applied to Irrotational Flow 260
    Velocity Potential 261
    Stream Function and Velocity Potential for Two-Dimensional, Irrotational, Incompressible Flow:
    Laplace’s Equation 262
    Elementary Plane Flows 264
    Superposition of Elementary Plane Flows 267
    6.8 Summary and Useful Equations 276
    References 279
    Problems 279

  • 7 DIMENSIONAL ANALYSIS AND SIMILITUDE
    7.1 Nondimensionalizing the Basic Differential Equations 292
    7.2 Nature of Dimensional Analysis 294
    7.3 Buckingham Pi Theorem 296
    7.4 Determining the Π Groups 297
    7.5 Significant Dimensionless Groups in Fluid Mechanics 303
    7.6 Flow Similarity and Model Studies 305
    Incomplete Similarity 308
    Scaling with Multiple Dependent Parameters 314
    Comments on Model Testing 317
    7.7 Summary and Useful Equations 318
    References 319
    Problems 320

  • 8 INTERNAL INCOMPRESSIBLE VISCOUS FLOW
    8.1 Introduction 330
    Laminar versus Turbulent Flow 330
    The Entrance Region 331
    PART A. FULLY DEVELOPED LAMINAR FLOW 332
    8.2 Fully Developed Laminar Flow between Infinite Parallel Plates 332
    Both Plates Stationary 332
    Upper Plate Moving with Constant Speed, U 338
    8.3 Fully Developed Laminar Flow in a Pipe 344
    PART B. FLOW IN PIPES AND DUCTS 348
    8.4 Shear Stress Distribution in Fully Developed Pipe Flow 349
    8.5 Turbulent Velocity Profiles in Fully Developed Pipe Flow 351
    8.6 Energy Considerations in Pipe Flow 353
    Kinetic Energy Coefficient 355
    Head Loss 355
    8.7 Calculation of Head Loss 357
    Major Losses: Friction Factor 357
    Minor Losses 361
    Pumps, Fans, and Blowers in Fluid Systems 367
    Noncircular Ducts 368
    8.8 Solution of Pipe Flow Problems 369
    Single-Path Systems 370
    *Multiple-Path Systems 383
    PART C. FLOW MEASUREMENT 387
    8.9 Direct Methods 387
    8.10 Restriction Flow Meters for Internal Flows 387
    The Orifice Plate 391
    The Flow Nozzle 391
    The Venturi 393
    The Laminar Flow Element 394
    8.11 Linear Flow Meters 397
    8.12 Traversing Methods 399
    8.13 Summary and Useful Equations 400
    References 402
    Problems 403

  • 9 EXTERNAL INCOMPRESSIBLE VISCOUS FLOW
    PART A. BOUNDARY LAYERS 423
    9.1 The Boundary-Layer Concept 423
    9.2 Boundary-Layer Thicknesses 425
    9.3 Laminar Flat-Plate Boundary Layer: Exact Solution (on the Web) W-19
    9.4 Momentum Integral Equation 428
    9.5 Use of the Momentum Integral Equation for Flow with Zero Pressure Gradient 433
    Laminar Flow 434
    Turbulent Flow 439
    Summary of Results for Boundary-Layer Flow with Zero Pressure Gradient 441
    9.6 Pressure Gradients in Boundary-Layer Flow 442
    PART B. FLUID FLOW ABOUT IMMERSED BODIES 445
    9.7 Drag 445
    Pure Friction Drag: Flow over a Flat Plate Parallel to the Flow 446
    Pure Pressure Drag: Flow over a Flat Plate Normal to the Flow 450
    Friction and Pressure Drag: Flow over a Sphere and Cylinder 450
    Streamlining 456
    9.8 Lift 459
    9.9 Summary and Useful Equations 474
    References 477
    Problems 478

  • 10 FLUID MACHINERY
    10.1 Introduction and Classification of Fluid Machines 494
    Machines for Doing Work on a Fluid 494
    Machines for Extracting Work (Power) from a Fluid 496
    Scope of Coverage 498
    10.2 Turbomachinery Analysis 499
    The Angular-Momentum Principle: The Euler Turbomachine Equation 499
    Velocity Diagrams 501
    Performance: Hydraulic Power 504
    Dimensional Analysis and Specific Speed 505
    10.3 Pumps, Fans, and Blowers 510
    Application of Euler Turbomachine Equation to Centrifugal Pumps 510
    Application of the Euler Equation to Axial Flow Pumps and Fans 512
    Performance Characteristics 516
    Similarity Rules 522
    Cavitation and Net Positive Suction Head 526
    Pump Selection: Applications to Fluid Systems 529
    Blowers and Fans 541
    10.4 Positive Displacement Pumps 548
    10.5 Hydraulic Turbines 552
    Hydraulic Turbine Theory 552
    Performance Characteristics for Hydraulic Turbines 554
    Sizing Hydraulic Turbines for Fluid Systems 558
    10.6 Propellers and Wind-Power Machines 562
    Propellers 563
    Wind-Power Machines 571
    10.7 Compressible Flow Turbomachines 581
    Application of the Energy Equation to a Compressible Flow Machine 581
    Compressors 582
    Compressible-Flow Turbines 586
    10.8 Summary and Useful Equations 586
    References 589
    Problems 591

  • 11 FLOW IN OPEN CHANNELS
    11.1 Basic Concepts and Definitions 603
    Simplifying Assumptions 604
    Channel Geometry 605
    Speed of Surface Waves and the Froude Number 606
    11.2 Energy Equation for Open-Channel Flows 610
    Specific Energy 613
    Critical Depth: Minimum Specific Energy 616
    11.3 Localized Effect of Area Change (Frictionless Flow) 619
    Flow over a Bump 620
    11.4 The Hydraulic Jump 625
    Depth Increase Across a Hydraulic Jump 627
    Head Loss Across a Hydraulic Jump 628
    11.5 Steady Uniform Flow 631
    The Manning Equation for Uniform Flow 633
    Energy Equation for Uniform Flow 639
    Optimum Channel Cross Section 640
    11.6 Flow with Gradually Varying Depth 641
    Calculation of Surface Profiles 643
    11.7 Discharge Measurement Using Weirs 646
    Suppressed Rectangular Weir 646
    Contracted Rectangular Weirs 647
    Triangular Weir 648
    Broad-Crested Weir 648
    11.8 Summary and Useful Equations 650
    References 652
    Problems 653

  • 12 INTRODUCTION TO COMPRESSIBLE FLOW
    12.1 Review of Thermodynamics 659
    12.2 Propagation of Sound Waves 665
    Speed of Sound 665
    Types of Flow—The Mach Cone 670
    12.3 Reference State: Local Isentropic Stagnation Properties 673
    Local Isentropic Stagnation Properties for the Flow of an Ideal Gas 674
    12.4 Critical Conditions 681
    12.5 Summary and Useful Equations 681
    References 683
    Problems 683

  • 13 COMPRESSIBLE FLOW
    13.1 Basic Equations for One-Dimensional Compressible Flow 691
    13.2 Isentropic Flow of an Ideal Gas: Area Variation 694
    Subsonic Flow, M , 1 697
    Supersonic Flow, M . 1 697
    Sonic Flow, M 5 1 698
    Reference Stagnation and Critical Conditions for Isentropic Flow of an Ideal Gas 699
    Isentropic Flow in a Converging Nozzle 704
    Isentropic Flow in a Converging-Diverging Nozzle 709
    13.3 Normal Shocks 715
    Basic Equations for a Normal Shock 716
    Fanno and Rayleigh Interpretation of Normal Shock 718
    Normal-Shock Flow Functions for One-Dimensional Flow of an Ideal Gas 719
    13.4 Supersonic Channel Flow with Shocks 724
    Flow in a Converging-Diverging Nozzle 724
    Supersonic Diffuser (on the Web) W-24
    Supersonic Wind Tunnel Operation (on the Web) W-25
    Supersonic Flow with Friction in a Constant-Area Channel (on the Web) W-26
    Supersonic Flow with Heat Addition in a Constant-Area Channel (on the Web) W-26
    13.5 Flow in a Constant-Area Duct with Friction 727
    Basic Equations for Adiabatic Flow 727
    Adiabatic Flow: The Fanno Line 728
    Fanno-Line Flow Functions for One-Dimensional Flow of an Ideal Gas 732
    Isothermal Flow (on the Web) W-29
    13.6 Frictionless Flow in a Constant-Area Duct with Heat Exchange 740
    Basic Equations for Flow with Heat Exchange 740
    The Rayleigh Line 741
    Rayleigh-Line Flow Functions for One-Dimensional Flow of an Ideal Gas 746
    13.7 Oblique Shocks and Expansion Waves 750
    Oblique Shocks 750
    Isentropic Expansion Waves 759
    13.8 Summary and Useful Equations 768
    References 771
    Problems 772

  • APPENDIX
    A FLUID PROPERTY DATA 785
    B EQUATIONS OF MOTION IN CYLINDRICAL COORDINATES 798
    C VIDEOS FOR FLUID MECHANICS 800
    D SELECTED PERFORMANCE CURVES FOR PUMPS AND FANS 803
    E FLOW FUNCTIONS FOR COMPUTATION OF COMPRESSIBLE FLOW 818
    F ANALYSIS OF EXPERIMENTAL UNCERTAINTY 829
    G SI UNITS, PREFIXES, AND CONVERSION FACTORS 836
    H A BRIEF REVIEW OF MICROSOFT EXCEL (ON THE WEB) W-33

  • Answers to Selected Problems

  • Index

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