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Incompressible flow
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English
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ISBN
047126122
9780471261223
9781118415733
9781118418451
9781118713075
9780471261223
9781118415733
9781118418451
9781118713075
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Table of Contents
From the Book - Regular Print - Third edition.
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 --
2 Thermodynamics 15 --
2.1 Systems, Properties, and Processes 15 --
2.2 Independent Variables 16 --
2.3 Temperature and Entropy 17 --
2.4 Fundamental Equations of Thermodynamics 18 --
2.5 Euler's Equation for Homogeneous 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 --
3 Vector Calculus and Index Notation 27 --
3.1 Index National Rules 28 --
3.2 Definition of Vectors and Tensors 30 --
3.3 Special Symbols and Isotropic Tensors 31 --
3.4 Direction Cosines and the Law of Cosines 32 --
3.5 Algebra with Vectors 33 --
3.6 Symmetric and Antisymmetric Tensors 35 --
3.7 Algebra with Tensors 37 --
3.8 Vector Cross-Product 38 --
3.9 Alternative Definitions of Vectors and Tensors 40 --
3.10 Principal Axes and Values 41 --
3.11 Derivative Operations on Vector Fields 42 --
3.12 Integral Formulas of Gauss and Stokes 45 --
3.13 Leibnitz's Theorem 47 --
4 Kinematics of Local Fluid Motion 51 --
4.1 Lagrangian Viewpoint 51 --
4.2 Eulerian Viewpoint 54 --
4.3 Substantial Derivative 56 --
4.4 Decomposition of Motion 57 --
4.5 Elementary Motions in a Linear Shear Flow 61 --
4.6 Proof of Vorticity Characteristics 64 --
4.7 Rate-of-Strain Characteristics 65 --
4.8 Rate of Expansion 66 --
4.9 Streamline Coordinates 67 --
5 Basic Laws 71 --
5.1 Continuity Equation 71 --
5.2 Momentum Equation 75 --
5.3 Surface Forces 76 --
5.4 Stress Tensor Derivation 76 --
5.5 Interpretation of the Stress Tensor Components 78 --
5.6 Pressure and Viscous Stress Tensor 80 --
5.7 Differential Momentum Equation 81 --
5.8 Moment of Momentum, Angular Momentum, and Symmetry of T[subscript ij] 85 --
5.9 Energy Equation 86 --
5.10 Mechanical and Thermal Energy Equations 89 --
5.11 Energy Equation with Temperature as the Dependent Variable 91 --
5.12 Second Law of Thermodynamics 91 --
5.13 Integral Form of the Continuity Equation 92 --
5.14 Integral Form of the Momentum Equation 94 --
5.15 Momentum Equation for a Deformable Particle of Variable Mass 97 --
5.16 Energy Equation in Integral Form 100 --
5.17 Jump Equations at Interfaces 101 --
6 Newtonian Fluids and the Navier-Stokes Equations 105 --
6.1 Newton's Viscosity Law 105 --
6.2 Molecular Model of Viscous Effects 108 --
6.3 Non-Newtonian Liquids 112 --
6.4 No-Slip Condition 115 --
6.5 Fourier's Heat Conduction Law 117 --
6.6 Navier-Stokes Equations 119 --
7 Some Incompressible Flow Patterns 121 --
7.1 Pressure-Driven Flow in a Slot 121 --
7.2 Mechanical Energy, Head Loss, and Bernoulli Equations 126 --
7.3 Plane Couette Flow 132 --
7.4 Pressure-Driven Flow in a Slot with a Moving Wall 133 --
7.5 Double Falling Film on a Wall 134 --
7.6 Outer Solution for Rotary Viscous Coupling 137 --
7.7 Rayleigh Problem 138 --
8 Dimensional Analysis 145 --
8.1 Measurement and Dimensions 145 --
8.2 Variables and Functions 147 --
8.3 Pi Theorem and Its Application 150 --
8.4 Pump or Blower Analysis: Use of Extra Assumptions 153 --
8.5 Number of Primary Dimensions 157 --
8.6 Proof of Bridgman's Equation 159 --
8.7 Proof of the Pi Theorem 161 --
8.8 Dynamic Similarity 164 --
8.9 Similarity with Geometric Distortion 165 --
8.10 Nondimensional Formulation of Physical Problems 168 --
9 Compressible Flow 175 --
9.1 Compressible Couette Flow: Adiabatic Wall 175 --
9.2 Flow with Power Law Transport Properties 178 --
9.3 Inviscid Compressible Waves: Speed of Sound 180 --
10 Incompressible Flow 188 --
10.1 Characterization 188 --
10.2 Incompressible Flow as Low-Mach-Number Flow with Adiabatic Walls 189 --
10.3 Nondimensional Problem Statement 191 --
10.4 Characteristics of Incompressible Flow 195 --
10.5 Splitting the Pressure into Kinetic and Hydrostatic Parts 197 --
10.6 Mathematical Aspects of the Limit Process M[superscript 2] to 0 200 --
10.7 Invariance of Incompressible Flow Equations under Unsteady Motion 201 --
10.8 Low-Mach-Number Flows with Constant-Temperature Walls 203 --
10.9 Energy Equation Paradox 206 --
11 Some Solutions of the Navier-Stokes Equations 210 --
11.1 Pressure-Driven Flow in Tubes of Various Cross Sections: Elliptical Tube 211 --
11.2 Flow in a Rectangular Tube 213 --
11.3 Channel with Longitudinal Ribs 216 --
11.4 Stokes's Oscillating Plate 218 --
11.5 Wall under an Oscillating Free Stream 221 --
11.6 Transient for a Stokes Oscillating Plate 224 --
11.7 Flow in a Slot with a Steady and Oscillating Pressure Gradient 226 --
11.8 Decay of an Ideal Line Vortex (Oseen Vortex) 230 --
11.9 Plane Stagnation-Point Flow (Hiemenz Flow) 235 --
11.10 Burgers Vortex 241 --
11.11 Complete Solution for Rotary Coupling 242 --
11.12 Von Karman Viscous Pump 244 --
12 Streamfunctions and the Velocity Potential 251 --
12.1 Streamlines 251 --
12.2 Streamfunction for Plane Flows 254 --
12.3 Flow in a Slot with Porous Walls 256 --
12.4 Streamlines and Streamsurfaces for a Three-Dimensional Flow 259 --
12.5 Vector Potential and the E[superscript 2] Operator 262 --
12.6 Velocity Potential and the Unsteady Bernoulli Equation 266 --
12.7 Flow Caused by a Sphere with Variable Radius 267 --
13 Vorticity Dynamics 271 --
13.1 Vorticity 271 --
13.2 Kinematic Results Concerning Vorticity 272 --
13.3 Vorticity Equation 274 --
13.4 Vorticity Diffusion 275 --
13.5 Vorticity Intensification by Straining Vortex Lines 277 --
13.6 Hill's Spherical Vortex 278 --
13.7 Production of Vorticity at a Stationary Wall 280 --
13.8 Production of Vorticity at a Translating Wall 282 --
13.9 Helmholtz's Laws for Inviscid Flow 284 --
13.10 Kelvin's Theorem 285 --
13.11 Inviscid Motion of Point Vortices 286 --
13.12 Reconnection of Vortex Lines 288 --
13.13 Development of Typical Vorticity Distributions 288 --
13.14 Vortex Breakdown 294 --
14 Flows at Moderate Reynolds Numbers 300 --
14.1 Some Unusual Flow Patterns 301 --
14.2 Entrance Flows 303 --
14.3 Entrance Flow into a Cascade of Plates: Computer Solution by the Streamfunction-Vorticity Method 305 --
14.4 Entrance Flow into a Cascade of Plates: Pressure Solution 313 --
14.5 Entrance Flow into a Cascade of Plates: Results 316 --
14.6 Flow around a Circular Cylinder 320 --
14.7 Jeffrey-Hamel Flow in a Wedge 336 --
14.8 Limiting Cases for Re to 0 and Re to -[infinity] 340 --
15 Asymptotic Analysis Methods 347 --
15.1 Oscillation of a Gas Bubble in a Liquid 347 --
15.2 Order Symbols, Gauge Functions, and Asymptotic Expansions 350 --
15.3 Inviscid Flow over a Wavy Wall 353 --
15.4 Nonuniform Expansions: Friedrich's Problem 356 --
15.5 Matching Process: Van Dyke's Rule 358 --
15.6 Composite Expansions 363 --
15.7 Characteristics of Overlap Regions 365 --
15.8 Lagerstrom's Problems 370 --
16 Characteristics of High-Reynolds-Number Flows 376 --
16.1 Physical Motivation 376 --
16.2 Inviscid Main Flows: Euler Equations 378 --
16.3 Pressure Changes in Steady Flows: Bernoulli Equations 381 --
16.4 Boundary Layers 385 --
17 Kinematic Decomposition of Flow Fields 396 --
17.1 General Approach 396 --
17.2 Helmholtz's Decomposition 397 --
17.3 Line Vortex and Vortex Sheet 398 --
17.4 Complex Lamellar Decomposition 401 --
18 Ideal Flows in a Plane 405 --
18.1 Problem Formulation for Plane Ideal Flows 406 --
18.2 Simple Plane Flows 409 --
18.3 Line Source and Line Vortex 412 --
18.4 Flow over a Nose or a Cliff 414 --
18.5 Doublets 420 --
18.6 Cylinder in a Stream 422 --
18.7 Cylinder with Circulation in a Uniform Stream 424 --
18.8 Lift and Drag on Two-Dimensional Shapes 426 --
18.9 Magnus Effect 429 --
18.10 Conformal Transformations 431 --
18.11 Joukowski Transformation: Airfoil Geometry 434 --
18.12 Kutta Condition 439 --
18.13 Flow over a Joukowski Airfoil: Airfoil Lift 442 --
18.14 Numerical Method for Airfoils 448 --
18.15 Actual Airfoils 451 --
18.16 Schwarz-Christoffel Transformation 453 --
18.17 Diffuser or Contraction Flow 455 --
18.18 Gravity Waves in Liquids 460 --
19 Axisymmetric and Three-Dimensional Ideal Flows 468 --
19.1 General Equations and Characteristics of Three-Dimensional Ideal Flows 468 --
19.2 Swirling Flow Turned into an Annulus 470 --
19.3 Flow over a Weir 471 --
19.4 Point Source 473 --
19.5 Rankine Nose Shape 474 --
19.6 Experiments on the Nose Drag of Slender Shapes 477 --
19.7 Flow from a Doublet 478 --
19.8 Flow over a Sphere 481 --
19.9 Kinetic Energy 483 --
19.10 Wake Drag of Bodies 484 --
19.11 Induced Drag: Drag due to Lift 486 --
19.12 Lifting Line Theory 490 --
19.13 Added Mass of Accelerating Bodies 491 --
20 Boundary Layers 498 --
20.1 Blasius Flow over a Flat Plate 498 --
20.2 Displacement Thickness 503 --
20.3 Von Karman Momentum Integral 505 --
20.4 Von Karman-Pohlhausen Approximate Method 506 --
20.5 Falkner-Skan Similarity Solutions 508 --
20.6 Arbitrary Two-Dimensional Layers: Crank-Nicolson Difference Method 513 --
20.7 Vertical Velocity 521 --
20.8 Joukowski Airfoil Boundary Layer 524 --
20.9 Boundary Layer on a Bridge Piling 527 --
20.10 Boundary Layers Beginning at Infinity 530 --
20.11 Plane Boundary Layer Separation 535 --
20.12 Axisymmetric Boundary Layers 537 --
20.13 Jets 540 --
20.14 Far Wake of Nonlifting Bodies 543 --
20.15 Free Shear Layers 546 --
20.16 Unsteady and Erupting Boundary Layers 548 --
20.17 Entrance Flow into a Cascade 551 --
20.18 Three-Dimensional Boundary Layers 553 --
20.19 Boundary Layer with a Constant Transverse Pressure Gradient 557 --
20.20 Howarth's Stagnation Point 561 --
20.21 Three-Dimensional Separation 564 --
21 Flows at Low Reynolds Numbers 571 --
21.1 General Relations for Re to 0: Stokes's Equations 571 --
21.2 Global Equations for Stokes Flow 574 --
21.3 Streamfunction for Plane and Axisymmetric Flows 577 --
21.4 Internal Flows: Plane 579 --
21.5 Internal Flows: Three-Dimensional and Axisymmetric 587 --
21.6 Local Flows: Plane (Moffatt Vortices) 591 --
21.7 Local Flows: Axisymmetric 596 --
21.8 External Flow: Sphere in a Uniform Stream 599 --
21.9 Composite Expansion for Flow over a Sphere 604 --
21.10 Stokes Flow near a Circular Cylinder 605 --
21.11 Axisymmetric Particles 606 --
21.12 Oseen's Equations 608 --
21.13 Interference Effects 609 --
22 Lubrication Approximation 613 --
22.1 Basic Characteristics: Channel Flow 613 --
22.2 Flow in a Channel with a Porous Wall 616 --
22.3 Reynolds Equation for Bearing Theory 618 --
22.4 Slipper Pad Bearing 620 --
22.5 Squeeze-Film Lubrication: Viscous Adhesion 622 --
22.6 Journal Bearing 623 --
23 Surface Tension Effects 629 --
23.1 Interface Concepts and Laws 629 --
23.2 Statics: Plane Interfaces 636 --
23.3 Statics: Cylindrical Interfaces 639 --
23.4 Statics: Attached Bubbles and Drops 641 --
23.5 Constant-Tension Flows: Bubble in Infinite Stream 643 --
23.6 Constant-Tension Flows: Capillary Waves 646 --
23.7 Moving Contact Lines 648 --
23.8 Constant-Tension Flows: Coating Flows 651 --
23.9 Marangoni Flow 656 --
24 Introduction to Microflows 667 --
24.1 Molecules 667 --
24.2 Continuum Description 669 --
24.3 Compressible Flows in Long Channels 670 --
24.4 Simple Solutions with Slip 673 --
24.5 Gases 676 --
24.6 Couette Flow in Gases 680 --
24.7 Poiseuille Flow in Gases 682 --
24.8 Gas Flow over a Sphere 687 --
24.9 Liquid Flows in Tubes and Channels 690 --
24.10 Liquid Flows near Walls 692 --
25 Introduction to Stability and Transition 698 --
25.1 Linear Stability and Normal Modes as Perturbations 699 --
25.2 Kelvin-Helmholtz Inviscid Shear Layer Instability 700 --
25.3 Stability Problem for Nearly Parallel Viscous Flows 704 --
25.4 Orr-Sommerfeld Equation 707 --
25.5 Inviscid Stability of Nearly Parallel Flows 708 --
25.6 Viscous Stability of Nearly Parallel Flows 709 --
25.7 Experiments on Blasius Boundary Layers 712 --
25.8 Transition, Secondary Instability, and Bypass 714 --
25.9 Spatially Developing Open Flows 719 --
25.10 Transition in Free Shear Flows 719 --
25.11 Poiseuille and Plane Couette Flows 721 --
25.12 Inviscid Instability of Flows with Curved Streamlines 723 --
25.13 Taylor Instability of Couette Flow 725 --
25.14 Stability of Regions of Concentrated Vorticity 727 --
25.15 Other Instabilities: Taylor, Curved Pipe, Capillary Jets, and Gortler 728 --
26 Introduction to Turbulent Flows 732 --
26.1 Types of Turbulent Flows 732 --
26.2 Characteristics of Turbulent Flows 733 --
26.3 Reynolds Decomposition 736 --
26.4 Reynolds Stress 737 --
26.5 Free Turbulence: Plane Shear Layers 740 --
26.6 Free Turbulence: Turbulent Jet 741 --
26.7 Bifurcating and Blooming Jets 747 --
26.8 Correlations of Fluctuations 747 --
26.9 Mean and Turbulent Kinetic Energy 750 --
26.10 Energy Cascade: Kolmogorov Scales and Taylor Microscale 752 --
26.11 Wall Turbulence: Channel Flow Analysis 756 --
26.12 Wall Layers: Experiments and Empirical Correlation 764 --
26.13 Turbulent Structures 768 --
A Properties of Fluids 775 --
B Differential Operations in Cylindrical and Spherical Coordinates 776 --
C Basic Equations in Rectangular, Cylindrical, and Spherical Coordinates 781 --
D Streamfunction Relations in Rectangular, Cylindrical, and Spherical Coordinates 786 --
E Computer Code for Entrance Flow into a Cascade 790 --
F Computer Code for Boundary Layer Analysis 793.
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