Incompressible Flow (4th Revised edition)

Incompressible Flow (4th Revised edition)

By: Ronald L. Panton (author)Hardback

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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 Navier-Stokes equations * Classic-style Fortran programs for the Hiemenz flow, the Psi-Omega 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 Fraenkel-Norbury 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.

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About Author

RONALD L. PANTON is the J. H. Herring Centennial Professor Emeritus in the Department of Mechanical Engineering at The University of Texas at Austin.

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 Cross-Product 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 Rate-of-Strain 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 Non-Newtonian Liquids 118 *6.4 Wall Boundary Conditions; The No-Slip 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 Pressure-Driven Flow in a Slot 127 7.2 Mechanical Energy, Head Loss, and Bernoulli Equation 132 7.3 Plane Couette Flow 136 7.4 Pressure-Driven 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 Low-Mach-Number 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 Low-Mach-Number Flows with Constant-Temperature 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 Pressure-Driven 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 Three-Dimensional 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 High-Reynolds-Number 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 Two-Dimensional 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 Three-Dimensional Ideal Flows 502 19.1 General Equations and Characteristics of Three-Dimensional 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 Two-Dimensinoal 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 Three-Dimensional Boundary Layers 589 *20.19 Boundary Layer with a Constant Transverse Pressure Gradient 593 *20.20 Howarth s Stagnation Point 598 *20.21 Three-Dimensional 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 Squeeze-Film Lubrication: Viscous Adhesion 659 22.6 Journal Bearing 660 22.7 Hele-Shaw 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 Constant-Tension Flows: Bubble in an Infinite Stream 683 23.6 Constant-Tension Flows: Capillary Waves 686 23.7 Moving Contact Lines 688 23.8 Constant-Tension 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

Product Details

  • publication date: 27/09/2013
  • ISBN13: 9781118013434
  • Format: Hardback
  • Number Of Pages: 912
  • ID: 9781118013434
  • weight: 1416
  • ISBN10: 1118013433
  • edition: 4th Revised edition

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