CHAPTER 1 INTRODUCTION /11.1 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
CHAPTER 2 FUNDAMENTAL CONCEPTS /20
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
CHAPTER 3 FLUID STATICS /55
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
CHAPTER 4 BASIC EQUATIONS IN INTEGRAL FORM FOR A CONTROL VOLUME /96
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
CHAPTER 5 INTRODUCTION TO DIFFERENTIAL ANALYSIS OF FLUID MOTION /171
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 CFD/Numerical 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
CHAPTER 6 INCOMPRESSIBLE INVISCID FLOW /235
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
CHAPTER 7 DIMENSIONAL ANALYSIS AND SIMILITUDE /290
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
CHAPTER 8 INTERNAL INCOMPRESSIBLE VISCOUS FLOW /328
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
CHAPTER 9 EXTERNAL INCOMPRESSIBLE VISCOUS FLOW /421
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
CHAPTER 10 FLUID MACHINERY /492
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
CHAPTER 11 FLOW IN OPEN CHANNELS /600
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
CHAPTER 12 INTRODUCTION TO COMPRESSIBLE FLOW /657
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
CHAPTER 13 COMPRESSIBLE FLOW /689
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
APPENDIX B EQUATIONS OF MOTION IN CYLINDRICAL COORDINATES /798
APPENDIX C VIDEOS FOR FLUID MECHANICS /800
APPENDIX D SELECTED PERFORMANCE CURVES FOR PUMPS AND FANS /803
APPENDIX E FLOW FUNCTIONS FOR COMPUTATION OF COMPRESSIBLE FLOW /818
APPENDIX F ANALYSIS OF EXPERIMENTAL UNCERTAINTY /829
APPENDIX G SI UNITS, PREFIXES, AND CONVERSION FACTORS /836
APPENDIX H A BRIEF REVIEW OF MICROSOFT EXCEL (ON THE WEB) /W-33
Answers to Selected Problems /838
Index /867