Student solution available in interactive e-text
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
References 14
Chapter 2 Fundamental Concepts 15
2.1 Fluid as a Continuum 16
2.2 Velocity Field 17
One-, Two-, and Three-Dimensional Flows 18
Timelines, Pathlines, Streaklines, and Streamlines 19
2.3 Stress Field 23
2.4 Viscosity 25
Newtonian Fluid 26
Non-Newtonian Fluids 28
2.5 Surface Tension 29
2.6 Description and Classification of Fluid Motions 30
Viscous and Inviscid Flows 32
Laminar and Turbulent Flows 34
Compressible and Incompressible Flows 34
Internal and External Flows 35
2.7 Summary and Useful Equations 36
References 37
Chapter 3 Fluid Statics 38
3.1 The Basic Equation of Fluid Statics 39
3.2 The Standard Atmosphere 42
3.3 Pressure Variation in a Static Fluid 43
Incompressible Liquids: Manometers 43
Gases 48
3.4 Hydrostatic Force on Submerged Surfaces 50
Hydrostatic Force on a Plane Submerged Surface 50
Hydrostatic Force on a Curved Submerged Surface 57
3.5 Buoyancy and Stability 60
3.6 Fluids in Rigid-Body Motion 63
3.7 Summary and Useful Equations 68
References 69
Chapter 4 Basic Equations In Integral Form For a Control Volume 70
4.1 Basic Laws for a System 71
Conservation of Mass 71
Newton’s Second Law 72
The Angular-Momentum Principle 72
The First Law of Thermodynamics 72
The Second Law of Thermodynamics 73
4.2 Relation of System Derivatives to the Control Volume Formulation 73
Derivation 74
Physical Interpretation 76
4.3 Conservation of Mass 77
Special Cases 78
4.4 Momentum Equation for Inertial Control Volume 82
Differential Control Volume Analysis 93
Control Volume Moving with Constant Velocity 97
4.5 Momentum Equation for Control Volume with Rectilinear Acceleration 99
4.6 Momentum Equation for Control Volume with Arbitrary Acceleration 105
4.7 The Angular-Momentum Principle 110
Equation for Fixed Control Volume 110
Equation for Rotating Control Volume 114
4.8 The First and Second Laws of Thermodynamics 118
Rate of Work Done by a Control Volume 119
Control Volume Equation 121
4.9 Summary and Useful Equations 125
Chapter 5 Introduction to Differential Analysis of Fluid Motion 128
5.1 Conservation of Mass 129
Rectangular Coordinate System 129
Cylindrical Coordinate System 133
5.2 Stream Function for Two-Dimensional Incompressible Flow 135
5.3 Motion of a Fluid Particle (Kinematics) 137
Fluid Translation: Acceleration of a Fluid Particle in a Velocity Field 138
Fluid Rotation 144
Fluid Deformation 147
5.4 Momentum Equation 151
Forces Acting on a Fluid Particle 151
Differential Momentum Equation 152
Newtonian Fluid: Navier–Stokes Equations 152
5.5 Summary and Useful Equations 160
References 161
Chapter 6 Incompressible Inviscid Flow 162
6.1 Momentum Equation for Frictionless Flow: Euler’s Equation 163
6.2 Bernoulli Equation: Integration of Euler’s Equation Along a Streamline for Steady Flow 167
Derivation Using Streamline Coordinates 167
Derivation Using Rectangular Coordinates 168
Static, Stagnation, and Dynamic Pressures 169
Applications 171
Cautions on Use of the Bernoulli Equation 176
6.3 The Bernoulli Equation Interpreted as an Energy Equation 177
6.4 Energy Grade Line and Hydraulic Grade Line 181
6.5 Unsteady Bernoulli Equation: Integration of Euler’s Equation Along a Streamline 183
6.6 Irrotational Flow 185
Bernoulli Equation Applied to Irrotational Flow 185
Velocity Potential 186
Stream Function and Velocity Potential for Two-Dimensional, Irrotational, Incompressible Flow: Laplace’s Equation 187
Elementary Plane Flows 189
Superposition of Elementary Plane Flows 191
6.7 Summary and Useful Equations 200
References 201
Chapter 7 Dimensional Analysis and Similitude 202
7.1 Nondimensionalizing the Basic Differential Equations 204
7.2 Buckingham Pi Theorem 206
7.3 Significant Dimensionless Groups in Fluid Mechanics 212
7.4 Flow Similarity and Model Studies 214
Incomplete Similarity 216
Scaling with Multiple Dependent Parameters 221
Comments on Model Testing 224
7.5 Summary and Useful Equations 225
References 226
Chapter 8 Internal Incompressible Viscous Flow 227
8.1 Internal Flow Characteristics 228
Laminar versus Turbulent Flow 228
The Entrance Region 229
Part A. Fully Developed Laminar Flow 230
8.2 Fully Developed Laminar Flow Between Infinite Parallel Plates 230
Both Plates Stationary 230
Upper Plate Moving with Constant Speed, U 236
8.3 Fully Developed Laminar Flow in a Pipe 241
Part B. Flow In Pipes and Ducts 245
8.4 Shear Stress Distribution in Fully Developed Pipe Flow 246
8.5 Turbulent Velocity Profiles in Fully Developed Pipe Flow 247
8.6 Energy Considerations in Pipe Flow 251
Kinetic Energy Coefficient 252
Head Loss 252
8.7 Calculation of Head Loss 253
Major Losses: Friction Factor 253
Minor Losses 258
Pumps, Fans, and Blowers in Fluid Systems 262
Noncircular Ducts 262
8.8 Solution of Pipe Flow Problems 263
Single-Path Systems 264
Multiple-Path Systems 276
Part C. Flow Measurement 279
8.9 Restriction Flow Meters for Internal Flows 279
The Orifice Plate 282
The Flow Nozzle 286
The Venturi 286
The Laminar Flow Element 287
Linear Flow Meters 288
Traversing Methods 289
8.10 Summary and Useful Equations 290
References 292
Chapter 9 External Incompressible Viscous Flow 293
Part A. Boundary Layers 295
9.1 The Boundary Layer Concept 295
9.2 Laminar Flat Plate Boundary Layer: Exact Solution 299
9.3 Momentum Integral Equation 302
9.4 Use of the Momentum Integral Equation for Flow with Zero Pressure Gradient 306
Laminar Flow 307
Turbulent Flow 311
9.5 Pressure Gradients in Boundary Layer Flow 314
Part B. Fluid Flow About Immersed Bodies 316
9.6 Drag 316
Pure Friction Drag: Flow over a Flat Plate Parallel to the Flow 317
Pure Pressure Drag: Flow over a Flat Plate Normal to the Flow 320
Friction and Pressure Drag: Flow over a Sphere and Cylinder 320
Streamlining 326
9.7 Lift 328
9.8 Summary and Useful Equations 340
References 342
Chapter 10 Fluid Machinery 343
10.1 Introduction and Classification of Fluid Machines 344
Machines for Doing Work on a Fluid 344
Machines for Extracting Work (Power) from a Fluid 346
Scope of Coverage 348
10.2 Turbomachinery Analysis 348
The Angular Momentum Principle: The Euler Turbomachine Equation 348
Velocity Diagrams 350
Performance—Hydraulic Power 352
Dimensional Analysis and Specific Speed 353
10.3 Pumps, Fans, and Blowers 358
Application of Euler Turbomachine Equation to Centrifugal Pumps 358
Application of the Euler Equation to Axial Flow Pumps and Fans 359
Performance Characteristics 362
Similarity Rules 367
Cavitation and Net Positive Suction Head 371
Pump Selection: Applications to Fluid Systems 374
Blowers and Fans 380
10.4 Positive Displacement Pumps 384
10.5 Hydraulic Turbines 387
Hydraulic Turbine Theory 387
Performance Characteristics for Hydraulic Turbines 389
10.6 Propellers and Wind Turbines 395
Propellers 395
Wind Turbines 400
10.7 Compressible Flow Turbomachines 406
Application of the Energy Equation to a Compressible Flow Machine 406
Compressors 407
Compressible-Flow Turbines 410
10.8 Summary and Useful Equations 410
References 412
Chapter 11 Flow In Open Channels 414
11.1 Basic Concepts and Definitions 416
Simplifying Assumptions 416
Channel Geometry 418
Speed of Surface Waves and the Froude Number 419
11.2 Energy Equation for Open-Channel Flows 423
Specific Energy 425
Critical Depth: Minimum Specific Energy 426
11.3 Localized Effect of Area Change (Frictionless Flow) 431
Flow over a Bump 431
11.4 The Hydraulic Jump 435
Depth Increase Across a Hydraulic Jump 438
Head Loss Across a Hydraulic Jump 439
11.5 Steady Uniform Flow 441
The Manning Equation for Uniform Flow 443
Energy Equation for Uniform Flow 448
Optimum Channel Cross Section 450
11.6 Flow with Gradually Varying Depth 451
Calculation of Surface Profiles 452
11.7 Discharge Measurement Using Weirs 455
Suppressed Rectangular Weir 455
Contracted Rectangular Weirs 456
Triangular Weir 456
Broad-Crested Weir 457
11.8 Summary and Useful Equations 458
References 459
Chapter 12 Introduction to Compressible Flow 460
12.1 Review of Thermodynamics 461
12.2 Propagation of Sound Waves 467
Speed of Sound 467
Types of Flow—The Mach Cone 471
12.3 Reference State: Local Isentropic Stagnation Properties 473
Local Isentropic Stagnation Properties for the Flow of an Ideal Gas 474
12.4 Critical Conditions 480
12.5 Basic Equations for One-Dimensional Compressible Flow 480
Continuity Equation 481
Momentum Equation 481
First Law of Thermodynamics 481
Second Law of Thermodynamics 482
Equation of State 483
12.6 Isentropic Flow of an Ideal Gas: Area Variation 483
Subsonic Flow, M <1 485
Supersonic Flow, M >1 486
Sonic Flow, M =1 486
Reference Stagnation and Critical Conditions for Isentropic Flow of an Ideal Gas 487
Isentropic Flow in a Converging Nozzle 492
Isentropic Flow in a Converging-Diverging Nozzle 496
12.7 Normal Shocks 501
Basic Equations for a Normal Shock 501
Normal-Shock Flow Functions for One-Dimensional Flow of an Ideal Gas 503
12.8 Supersonic Channel Flow with Shocks 507
12.9 Summary and Useful Equations 509
References 511
Problems P-1
Appendix A Fluid Property Data A-1
Appendix B Videos For Fluid Mechanics A-13
Appendix C Selected Performance Curves For Pumps and Fans A-15
Appendix D Flow Functions For Computation of Compressible Flow A-26
Appendix E Analysis of Experimental Uncertainty A-29
Appendix F Introduction to Computational Fluid Dynamics A-35
Index I-1
