Ebook
Incompressible Flow, 4th EditionISBN: 9781118415733
912 pages
July 2013

Description
The most teachable book on incompressible flow— now fully revised, updated, and expanded
Incompressible Flow, Fourth Edition is the updated and revised edition of Ronald Panton's classic text. It continues a respected tradition of providing the most comprehensive coverage of the subject in an exceptionally clear, unified, and carefully paced introduction to advanced concepts in fluid mechanics. Beginning with basic principles, this Fourth Edition patiently develops the math and physics leading to major theories. Throughout, the book provides a unified presentation of physics, mathematics, and engineering applications, liberally supplemented with helpful exercises and example problems.
Revised to reflect students' ready access to mathematical computer programs that have advanced features and are easy to use, Incompressible Flow, Fourth Edition includes:
 Several more exact solutions of the NavierStokes equations
 Classicstyle Fortran programs for the Hiemenz flow, the PsiOmega method for entrance flow, and the laminar boundary layer program, all revised into MATLAB
 A new discussion of the global vorticity boundary restriction
 A revised vorticity dynamics chapter with new examples, including the ring line vortex and the FraenkelNorbury vortex solutions
 A discussion of the different behaviors that occur in subsonic and supersonic steady flows
 Additional emphasis on composite asymptotic expansions
Incompressible Flow, Fourth Edition is the ideal coursebook for classes in fluid dynamics offered in mechanical, aerospace, and chemical engineering programs.
Table of Contents
Preface xi
Preface to the Third Edition xiii
Preface to the Second Edition xv
Preface to the First Edition xvii
1 Continuum Mechanics 1
1.1 Continuum Assumption 3
1.2 Fundamental Concepts, Definitions, and Laws 3
1.3 Space and Time 5
1.4 Density, Velocity, and Internal Energy 7
1.5 Interface between Phases 10
1.6 Conclusions 12
Problems 13
2 Thermodynamics 15
2.1 Systems, Properties, and Processes 15
2.2 Independent Variables 16
2.3 Temperature and Entropy 16
2.4 Fundamental Equations of Thermodynamics 18
2.5 Euler’s Equation for Homogenous Functions 19
2.6 Gibbs–Duhem Equation 20
2.7 Intensive Forms of Basic Equations 20
2.8 Dimensions of Temperature and Entropy 21
2.9 Working Equations 21
2.10 Ideal Gas 22
2.11 Incompressible Substance 25
2.12 Compressible Liquids 26
2.13 Conclusions 26
Problems 26
3 Vector Calculus and Index Notation 28
3.1 Index Notation Rules and Coordinate Rotation 29
3.2 Definition of Vectors and Tensors 32
3.3 Special Symbols and Isotropic Tensors 33
3.4 Direction Cosines and the Laws of Cosines 34
3.5 Algebra with Vectors 35
3.6 Symmetric and Antisymmetric Tensors 37
3.7 Algebra with Tensors 38
3.8 Vector CrossProduct 41
*3.9 Alternative Definitions of Vectors 42
*3.10 Principal Axes and Values 44
3.11 Derivative Operations on Vector Fields 45
3.12 Integral Formulas of Gauss and Stokes 48
3.13 Leibnitz’s Theorem 51
3.14 Conclusions 52
Problems 53
4 Kinematics of Local Fluid Motion 54
4.1 Lagrangian Viewpoint 54
4.2 Eulerian Viewpoint 57
4.3 Substantial Derivative 59
4.4 Decomposition of Motion 60
4.5 Elementary Motions in a Linear Shear Flow 64
*4.6 Proof of Vorticity Characteristics 66
*4.7 RateofStrain Characteristics 68
4.8 Rate of Expansion 69
*4.9 Streamline Coordinates 70
4.10 Conclusions 72
Problems 72
5 Basic Laws 74
5.1 Continuity Equation 74
5.2 Momentum Equation 78
5.3 Surface Forces 79
*5.4 Stress Tensor Derivation 79
5.5 Interpretation of the Stress Tensor Components 81
5.6 Pressure and Viscous Stress Tensor 83
5.7 Differential Momentum Equation 84
*5.8 Moment of Momentum, Angular Momentum, and Symmetry of Tij 89
5.9 Energy Equation 90
5.10 Mechanical and Thermal Energy Equations 92
5.11 Energy Equation with Temperature as the Dependent Variable 94
5.12 Second Law of Thermodynamics 94
5.13 Integral Form of the Continuity Equation 95
5.14 Integral Form of the Momentum Equation 97
*5.15 Momentum Equation for a Deformable Particle of Variable Mass 100
*5.16 Integral Form of the Energy Equation 103
5.17 Integral Mechanical Energy Equation 104
5.18 Jump Equations at Interfaces 106
5.19 Conclusions 108
Problems 108
6 Newtonian Fluids and the Navier–Stokes Equations 111
6.1 Newton’s Viscosity Law 111
6.2 Molecular Model of Viscous Effects 114
6.3 NonNewtonian Liquids 118
*6.4 Wall Boundary Conditions; The NoSlip Condition 120
6.5 Fourier’s Heat Conduction Law 123
6.6 Navier–Stokes Equations 125
6.7 Conclusions 125
Problems 126
7 Some Incompressible Flow Patterns 127
7.1 PressureDriven Flow in a Slot 127
7.2 Mechanical Energy, Head Loss, and Bernoulli Equation 132
7.3 Plane Couette Flow 136
7.4 PressureDriven Flow in a Slot with a Moving Wall 138
7.5 Double Falling Film on a Wall 139
7.6 Outer Solution for Rotary Viscous Coupling 142
7.7 The Rayleigh Problem 143
7.8 Conclusions 148
Problems 148
8 Dimensional Analysis 150
8.1 Measurement, Dimensions, and Scale Change Ratios 150
8.2 Physical Variables and Functions 153
8.3 Pi Theorem and Its Applications 155
8.4 Pump or Blower Analysis: Use of Extra Assumptions 159
8.5 Number of Primary Dimensions 163
*8.6 Proof of Bridgman’s Equation 165
*8.7 Proof of the Pi Theorem 167
8.8 Dynamic Similarity and Scaling Laws 170
8.9 Similarity with Geometric Distortion 171
8.10 Nondimensional Formulation of Physical Problems 174
8.11 Conclusions 179
Problems 180
9 Compressible Flow 182
9.1 Compressible Couette Flow: Adiabatic Wall 182
9.2 Flow with Power Law Transport Properties 186
9.3 Inviscid Compressible Waves: Speed of Sound 187
9.4 Steady Compressible Flow 194
9.5 Conclusions 197
Problems 197
10 Incompressible Flow 198
10.1 Characterization 198
10.2 Incompressible Flow as LowMachNumber Flow with Adiabatic Walls 199
10.3 Nondimensional Problem Statement 201
10.4 Characteristics of Incompressible Flow 205
10.5 Splitting the Pressure into Kinetic and Hydrostatic Parts 207
*10.6 Mathematical Aspects of the Limit Process M2 → 0 210
*10.7 Invariance of Incompressible Flow Equations under Unsteady Motion 211
*10.8 LowMachNumber Flows with ConstantTemperature Walls 213
*10.9 Energy Equation Paradox 216
10.10 Conclusions 218
Problems 219
11 Some Solutions of the Navier–Stokes Equations 220
11.1 PressureDriven Flow in Tubes of Various Cross Sections: Elliptical Tube 221
11.2 Flow in a Rectangular Tube 224
11.3 Asymptotic Suction Flow 227
11.4 Stokes’s Oscillating Plate 228
11.5 Wall under an Oscillating Free Stream 231
*11.6 Transient for a Stokes Oscillating Plate 234
11.7 Flow in a Slot with a Steady and Oscillating Pressure Gradient 236
11.8 Decay of an Ideal Line Vortex (Oseen Vortex) 241
11.9 Plane Stagnation Point Flow (Hiemenz Flow) 245
11.10 Burgers Vortex 251
11.11 Composite Solution for the Rotary Viscous Coupling 253
11.12 Von Karman Viscous Pump 257
11.13 Conclusions 262
Problems 263
12 Streamfunctions and the Velocity Potential 266
12.1 Streamlines 266
12.2 Streamfunction for Plane Flows 269
12.3 Flow in a Slot with Porous Walls 272
*12.4 Streamlines and Streamsurfaces for a ThreeDimensional Flow 274
*12.5 Vector Potential and the E2 Operator 277
12.6 Stokes’s Streamfunction for Axisymmetric Flow 282
12.7 Velocity Potential and the Unsteady Bernoulli Equation 283
12.8 Flow Caused by a Sphere with Variable Radius 284
12.9 Conclusions 286
Problems 287
13 Vorticity Dynamics 289
13.1 Vorticity 289
13.2 Kinematic Results Concerning Vorticity 290
13.3 Vorticity Equation 292
13.4 Vorticity Diffusion 293
13.5 Vorticity Intensification by Straining Vortex Lines 295
13.6 Production of Vorticity at Walls 296
13.7 Typical Vorticity Distributions 300
13.8 Development of Vorticity Distributions 300
13.9 Helmholtz’s Laws for Inviscid Flow 306
13.10 Kelvin’s Theorem 307
13.11 Vortex Definitions 308
13.12 Inviscid Motion of Point Vortices 310
13.13 Circular Line Vortex 312
13.14 Fraenkel–Norbury Vortex Rings 314
13.15 Hill’s Spherical Vortex 314
13.16 Breaking and Reconnection of Vortex Lines 317
13.17 Vortex Breakdown 317
13.18 Conclusions 323
Problems 324
14 Flows at Moderate Reynolds Numbers 326
14.1 Some Unusual Flow Patterns 327
14.2 Entrance Flows 330
14.3 Entrance Flow into a Cascade of Plates: Computer Solution by the Streamfunction–Vorticity Method 331
14.4 Entrance Flow into a Cascade of Plates: Pressure Solution 341
14.5 Entrance Flow into a Cascade of Plates: Results 342
14.6 Flow Around a Circular Cylinder 346
14.7 Jeffrey–Hamel Flow in a Wedge 362
14.8 Limiting Case for Re → 0; Stokes Flow 367
14.9 Limiting Case for Re→−∞ 368
14.10 Conclusions 372
Problems 372
15 Asymptotic Analysis Methods 374
15.1 Oscillation of a Gas Bubble in a Liquid 374
15.2 Order Symbols, Gauge Functions, and Asymptotic Expansions 377
15.3 Inviscid Flow over a Wavy Wall 380
15.4 Nonuniform Expansions: Friedrich’s Problem 384
15.5 Matching Process: Van Dyke’s Rule 386
15.6 Composite Expansions 391
15.7 Characteristics of Overlap Regions and Common Parts 393
15.8 Composite Expansions and Data Analysis 399
15.9 Lagerstrom’s Problems 403
15.10 Conclusions 406
Problems 407
16 Characteristics of HighReynoldsNumber Flows 409
16.1 Physical Motivation 409
16.2 Inviscid Main Flows: Euler Equations 411
16.3 Pressure Changes in Steady Flows: Bernoulli Equations 414
16.4 Boundary Layers 418
16.5 Conclusions 428
Problems 428
17 Kinematic Decomposition of Flow Fields 429
*17.1 General Approach 429
*17.2 Helmholtz’s Decomposition; Biot–Savart Law 430
*17.3 Line Vortex and Vortex Sheet 431
*17.4 Complex Lamellar Decomposition 434
*17.5 Conclusions 437
*Problems 437
18 Ideal Flows in a Plane 438
18.1 Problem Formulation for Plane Ideal Flows 439
18.2 Simple Plane Flows 442
18.3 Line Source and Line Vortex 445
18.4 Flow over a Nose or a Cliff 447
18.5 Doublets 453
18.6 Cylinder in a Stream 456
18.7 Cylinder with Circulation in a Uniform Stream 457
18.8 Lift and Drag on TwoDimensional Shapes 460
18.9 Magnus Effect 462
18.10 Conformal Transformations 464
18.11 Joukowski Transformation: Airfoil Geometry 468
18.12 Kutta Condition 473
18.13 Flow over a Joukowski Airfoil: Airfoil Lift 475
18.14 Numerical Method for Airfoils 482
18.15 Actual Airfoils 484
*18.16 Schwarz–Christoffel Transformation 487
*18.17 Diffuser or Contraction Flow 489
*18.18 Gravity Waves in Liquids 494
18.19 Conclusions 499
Problems 499
19 ThreeDimensional Ideal Flows 502
19.1 General Equations and Characteristics of ThreeDimensional Ideal Flows 502
19.2 Swirling Flow Turned into an Annulus 504
19.3 Flow over a Weir 505
19.4 Point Source 507
19.5 Rankine Nose Shape 508
19.6 Experiments on the Nose Drag of Slender Shapes 510
19.7 Flow from a Doublet 513
19.8 Flow over a Sphere 515
19.9 Work to Move a Body in a Still Fluid 516
19.10 Wake Drag of Bodies 518
*19.11 Induced Drag: Drag due to Lift 519
*19.12 Lifting Line Theory 524
19.13 Winglets 525
*19.14 Added Mass of Accelerating Bodies 526
19.15 Conclusions 531
Problems 531
20 Boundary Layers 533
20.1 Blasius Flow over a Flat Plate 533
20.2 Displacement Thickness 538
20.3 Von K´arm´an Momentum Integral 540
20.4 Von K´arm´an–Pohlhausen Approximate Method 541
20.5 Falkner–Skan Similarity Solutions 543
20.6 Arbitrary TwoDimensinoal Layers: Crank–Nicolson Difference Method 547
*20.7 Vertical Velocity 556
20.8 Joukowski Airfoil Boundary Layer 558
20.9 Boundary Layer on a Bridge Piling 563
20.10 Boundary Layers Beginning at Infinity 564
20.11 Plane Boundary Layer Separation 570
20.12 Axisymmteric Boundary Layers 573
20.13 Jets 576
20.14 Far Wake of Nonlifting Bodies 579
20.15 Free Shear Layers 582
20.16 Unsteady and Erupting Boundary Layers 584
*20.17 Entrance Flow into a Cascade, Parabolized Navier–Stokes Equations 587
*20.18 ThreeDimensional Boundary Layers 589
*20.19 Boundary Layer with a Constant Transverse Pressure Gradient 593
*20.20 Howarth’s Stagnation Point 598
*20.21 ThreeDimensional Separation Patterns 600
20.22 Conclusions 603
Problems 605
21 Flow at Low Reynolds Numbers 607
21.1 General Relations for Re → 0: Stokes’s Equations 607
21.2 Global Equations for Stokes Flow 611
21.3 Streamfunction for Plane and Axisymmetric Flows 613
21.4 Local Flows, Moffatt Vortices 616
21.5 Plane Internal Flows 623
21.6 Flows between Rotating Cylinders 628
21.7 Flows in Tubes, Nozzles, Orifices, and Cones 631
21.8 Sphere in a Uniform Stream 636
21.9 Composite Expansion for Flow over a Sphere 641
21.10 Stokes Flow near a Circular Cylinder 642
*21.11 Axisymmetric Particles 644
*21.12 Oseen’s Equations 646
*21.13 Interference Effects 647
21.14 Conclusions 648
Problems 649
22 Lubrication Approximation 650
22.1 Basic Characteristics: Channel Flow 650
22.2 Flow in a Channel with a Porous Wall 653
22.3 Reynolds Equation for Bearing Theory 655
22.4 Slipper Pad Bearing 657
22.5 SqueezeFilm Lubrication: Viscous Adhesion 659
22.6 Journal Bearing 660
22.7 HeleShaw Flow 664
22.8 Conclusions 667
Problems 668
23 Surface Tension Effects 669
23.1 Interface Concepts and Laws 669
23.2 Statics: Plane Interfaces 676
23.3 Statics: Cylindrical Interfaces 679
23.4 Statics: Attached Bubbles and Drops 681
23.5 ConstantTension Flows: Bubble in an Infinite Stream 683
23.6 ConstantTension Flows: Capillary Waves 686
23.7 Moving Contact Lines 688
23.8 ConstantTension Flows: Coating Flows 691
23.9 Marangoni Flows 695
23.10 Conclusions 703
Problems 705
24 Introduction to Microflows 706
24.1 Molecules 706
24.2 Continuum Description 708
24.3 Compressible Flow in Long Channels 709
24.4 Simple Solutions with Slip 712
24.5 Gases 715
24.6 Couette Flow in Gases 719
24.7 Poiseuille Flow in Gases 722
24.8 Gas Flow over a Sphere 726
24.9 Liquid Flows in Tubes and Channels 728
24.10 Liquid Flows near Walls; Slip Boundaries 730
24.11 Conclusions 735
25 Stability and Transition 737
25.1 Linear Stability and Normal Modes as Perturbations 738
25.2 Kelvin–Helmholtz Inviscid Shear Layer Instability 739
25.3 Stability Problems for Nearly Parallel Viscous Flows 744
25.4 Orr–Sommerfeld Equation 746
25.5 Invsicid Stability of Nearly Parallel Flows 747
25.6 Viscous Stability of Nearly Parallel Flows 749
25.7 Experiments on Blasius Boundary Layers 752
25.8 Transition, Secondary, Instability, and Bypass 756
25.9 Spatially Developing Open Flows 759
25.10 Transition in Free Shear Flows 759
25.11 Poiseuille and Plane Couette Flows 761
25.12 Inviscid Instability of Flows with Curved Streamlines 763
25.13 Taylor Instability of Couette Flow 765
25.14 Stability of Regions of Concentrated Vorticity 767
25.15 Other Instabilities: Taylor, Curved, Pipe, Capillary Jets, and Gortler 769
25.16 Conclusions 771
26 Turbulent Flows 772
26.1 Types of Turbulent Flows 772
26.2 Characteristics of Turbulent Flows 773
26.3 Reynolds Decomposition 776
26.4 Reynolds Stress 777
*26.5 Correlation of Fluctuations 780
*26.6 Mean and Turbulent Kinetic Energy 782
*26.7 Energy Cascade: Kolmogorov Scales and Taylor Microscale 784
26.8 Wall Turbulence: Channel Flow Analysis 789
26.9 Channel and Pipe Flow Experiments 797
26.10 Boundary Layers 800
26.11 Wall Turbulence: Fluctuations 804
26.12 Turbulent Structures 811
26.13 Free Turbulence: Plane Shear Layers 817
26.14 Free Turbulence: Turbulent Jet 822
26.15 Bifurcating and Blooming Jets 824
26.16 Conclusions 825
A Properties of Fluids 827
B Differential Operations in Cylindrical and Spherical Coordinates 828
C Basic Equations in Rectangular, Cylindrical, and Spherical Coordinates 833
D Streamfunction Relations in Rectangular, Cylindrical, and Spherical Coordinates 838
E Matlab R Stagnation Point Solver 842
F Matlab R Program for Cascade Entrance 844
G Matlab R Boundary Layer Program 847
References 851
Index 869
Author Information
RONALD L. PANTON is the J. H. Herring Centennial Professor Emeritus in the Department of Mechanical Engineering at The University of Texas at Austin.