Contents
1 Continuum Mechanics
1.1 The Continuum Assumption
1.2 Fundamental Concepts, Definitions, and Laws
1.3 Space and Time
1.4 Density, Velocity, and Internal Energy
1.5 The Interface Between Phases
1.6 Conclusions
Problems
2 Thermodynamics
2.1 Systems, Properties, and Processes
2.2 The Independent Variables
2.3 Temperature and Entropy
2.4 Fundamental Equations of Thermodynamics
2.5 Euler's Equation for Homogeneous Functions
2.6 The Gibbs-Duhem Equation
2.7 Intensive Forms of Basic Equations
2.8 Dimensions of Temperature and Entropy
2.9 Working Equations
2.10 The Ideal Gas
2.11 The Incompressible Substance
2.12 Conclusion
Problems
3 Vector Calculus and Index Notation
3.1 Index Notation Rules
3.2 Definition of Vectors and Tensors
3.3 Special Symbols and Isotropic Tensors
3.4 Direction Cosines and the Law of Cosines
3.5 Algebra with Vectors
3.6 Symmetric and Anti symmetric Tensors
3.7 Algebra with Tensors
3.8 Alternative Definitions of Vectors and Tensors
3.10 Principal Axes and Principal Values
3.11 Derivative Operations on Vector Fields
3.12 Integral Formulas of Gauss and Stokes
3.13 Leibnitz's Theorem
3.14 Conclusion
Problems
4 Kinematics of Local Fluid Motion
4.1 Lagrangian Viewpoint
4.2 Eulerian Viewpoint
4.3 Substantial Derivative
4.4 Decomposition of Motion
4.5 Elementary Motions in a Linear Shear Flow
*4.6 Proof of Vorticity Characteristics
*4.7 Rate-of-Strain Characteristics
4.8 Rate of Expansion
*4.9 Streamline Coordinates
4.10 Conclusion
Problems
5 Basic Laws
5.1 Continuity Equation
5.2 Momentum Equation
5.3 Surface Forces
*5.4 Stress-Tensor Derivation
5.5 Interpretation of the Stress-Tensor Components
5.6 Pressure and Viscous Stress Tensor
5.7 Differential Momentum Equation
*5.8 Angular-Momentum Equation and Symmetry of Tij
5.9 Energy Equation
5.10 Mechanical- and Thermal-Energy Equations
5.11 Energy Equation with Temperature as Dependent Variable
*5.12 Second Law of Thermodynamics
5.13 Integral Form of the Continuity Equation
5.14 Integral Form of the Momentum Equation
*5.15 Momentum Equation for a Deformable Particle of Variable Mass
*5.16 Other Laws in Integral Form; Energy Equation
5.17 Jump Equations at Interfaces and Discontinuities
5.18 Conclusion
Problems
6 Newtonian Fluids and the Navier-Stokes Equations
6.1 Newton's Viscosity Law
6.2 Molecular Model of Viscous Effects
6.3 Non-Newtonian Liquids
*6.4 The No-Slip Condition
6.5 Fourier's Heat-Conduction Law
6.6 Navier-Stokes Equations
6.7 Conclusion
Problems
7 Some Incompressible Flow Patterns
7.1 Pressure-Drive Flow in a Slot
7.2 Mechanical Energy and Bernoulli Equations
7.3 Plane Couette Flow
7.4 Pressure-Driven Flow in a Slot with a Moving Wall
7.5 Double Falling Film on a Wall
7.6 Rotary Viscous Coupling; Outer Solution
7.7 The Rayleigh Problem
7.8 Conclusion
Problems
8 Dimensional Analysis
8.1 Measurement and Dimensions
8.2 Variables and Functions
8.3 The Pi Theorem
8.4 Pump or Blower Analysis
8.5 Number of Primary Dimensions
*8.6 Proof of Bridgman's Equation
*8.7 Proof of the Pi Theorem
8.8 Dynamic Similarity
8.9 Similarity with Geometric Distortion
8.10 Nondimensional Formulation of Physical Problems
8.11 Conclusion
Problems
9 Compressible Flow
9.1 Compressible Couette Flow; Adiabatic Wall
9.2 Flow with Power-Law Transport Properties
9.3 Compressible Waves
9.4 Conclusion
Problems
10 Incompressible Flow
10.1 Characterization
10.2 Incompressible Flow as a Low-Mach-Number Flow with Adiabatic Walls
10.3 Nondimensional Problem Statement
10.4 Characteristics of Incompressible Flow
10.5 Splitting the Pressure into Kinetic and Hydrostatic Parts
*10.6 Mathematical Aspects of the Limit Process M2 -> 0
*10.7 Invariance of Incompressible-Flow Equations under Unsteady Motion
*10.8 Low-Mach-Number Flows with Constant-Temperature Walls
*10.9 The Energy-Equation Paradox
10.10 Conclusion
Problems
11 Some Solutions of the Navier-Stokes Equations
11.1 Pressure-Drive Flow in Tubes of Various Cross Sections;
an Elliptical Tube
11.2 Flow in a Rectangular Tube
11.3 A Channel with Longitudinal Ribs
11.4 Stokes Oscillating Plate
11.5 Flow in a Slot with an Oscillating Pressure Gradient
11.6 Transient for Stokes Oscillating Plate
11.7 Flow in a Slot with an Oscillating Pressure Gradient
11.8 Decay of Line Vortices (Oseen Vortex)
11.9 Plane Stagnation-Point Flow (Hiemenz Flow)
11.10 Burgers Vortex
11.11 Rotary Viscous Coupling; Complete Solution
11.12 von Karman Viscous "Pump"
11.13 Conclusion
Problems
12 Stream Functions and the Velocity Potential
12.1 Streamlines
12.2 Stream Function for Plane Flows
12.3 Flow in a Slot with Porous Walls
*12.4 Streamlines and Streamsurfaces for a Three-Dimensional Flow
12.5 Velocity Potential and Unsteady Bernoulli Equation
12.6 Flow Caused by a Sphere with Variable Radius
12.7 Conclusion
Problems
13 Vorticity Dynamics
13.1 Vorticity
13.2 Kinematic Results Concerning Vorticity
13.3 Vorticity Equation
13.4 Vorticity Diffusion
13.5 Vorticity Intensification by Straining Vortex Lines
13.6 Hill's Spherical Vortex
13.7 Production of Vorticity at a Stationary Wall
13.8 Production of Vorticity at a Translating Wall
13.9 Helmholtz's Laws for Inviscid Flow
13.10 Kelvin's Theorem
13.11 Inviscid Motion of Point Vortices
13.12 Reconnection of Vortex Lines
13.13 Development of Typical Vorticity Distributions
13.14 Vortex Breakdown
13.15 Conclusion
Problems
14 Flows at Moderate Reynolds Numbers
14.1 Some Unusual Flow Patterns
14.2 Entrance Flows
14.3 Entrance Flow into a Cascade of Plates: Computer Solution
by the Stream-Function-Vorticity Method
14.4 Entrance Flow into a Cascade of Plates: Pressure Solution
14.5 Entrance Flow into a Cascade of Plates: Results
14.6 Flow around a Circular Cylinder
14.7 Conclusion
Problems
15 Asymptotic Analysis Methods
15.1 Oscillation of a Gas Bubble in a Liquid
15.2 Order Symbols, Gauge Functions, and Asymptotic Expansions
15.3 Inviscid Flow over a Wavy Wall
15.4 Non uniform Expansions; Friedrich's Problems
15.5 The Matching Process
15.6 Composite Expansions; Accuracy
*15.7 Characteristics of Overlap Regions
*15.8 Lagerstrom's Problems
*15.9 Conclusion
Problems
16 Characteristics of High-Reynolds-Number Flow
16.1 Physical Motivation
16.2 Inviscid Main Flows: Euler Equations
16.3 Pressure Changes in Flows; Bernoulli Equations
16.4 Boundary Layers
16.5 Conclusion
Problems
17 Kinematic Decomposition of Flow Fields
17.1 General Approach
17.2 Helmholtz's Decomposition
17.3 Line Vortex and Vortex Sheet
*17.4 Complex-Lamellar Decomposition
17.5 Conclusion
Problems
18 Ideal Flows in a Plane
18.1 Problem Formulation for Plane Ideal Flows
18.2 Simple Plane Flows
18.3 Line Source and Line Vortex
18.4 Flow over a Nose or a Cliff
18.5 Doublets
18.6 Cylinder in a Stream
18.7 Cylinder with Circulation in a Uniform Stream
18.8 Lift and Drag on Two-Dimensional Shapes
18.9 Magnus Effect
18.10 Conformal Transformations
18.11 Joukowski Transformation; Airfoil Geometry
18.12 Kutta Condition
18.13 Flow Over a Joukowski Airfoil; Airfoil Lift
18.14 A Numerical Method for Airfoils
18.15 Actual Airfoils
*18.16 Schwarz-Christoffel Transformation
*18.17 Diffuser or Contraction Flow
*18.18 Gravity Waves in Liquids
18.19 Conclusion
Problems
19 Axisymmetric and Three-Dimensional Ideal Flows
19.1 General Equations and Characteristics of
Three-Dimensional Ideal Flow
19.2 Swirling Flow Turned into an Annulus
19.3 Flow over a Weir
19.4 Point Source
19.5 Rankine Nose Shape
19.6 Experiments on the Nose Drag of Slender Shapes
19.7 Flow from a Doublet
19.8 Flow over a Sphere
19.9 Kinetic Energy
19.10 Wake Drag of Bodies in Ideal Flows
19.11 Induced Drag; Drag Due to Lift
19.12 Lifting-Line Theory
19.13 Added Mass of Accelerating Bodies
19.14 Conclusion
Problems
20 Boundary Layers
20.1 Blasius Flow over a Flat Plate
20.2 Displacement Thickness
20.3 Karman Momentum Integral
20.4 Karman-Pohlhausen Approximate Method
20.5 Falkner-Skan Similarity Solutions
20.6 Arbitrary Two-Dimensional Layers: Crank-Nicolson Difference Method
*20.7 Vertical Velocity
20.8 Joukowski-Airfoil Boundary Layer
20.9 Boundary Layer on a Bridge Piling
20.10 Plane Boundary-Layer Separation
20.11 Axisymmetric Boundary Layers
20.12 Jets
20.13 Far Wake of Non lifting Bodies
20.14 Free Shear Layers
20.15 Unsteady and Erupting Boundary Layers
*20.16 Entrance Flow into a Cascade
*20.17 Three-Dimensional Boundary Layers
*20.18 Boundary Layer with a Constant Transverse Pressure Gradient
*20.19 Howarth's Stagnation Point
*20.20 Three-Dimensional Separation
20.21 Conclusion
Problems
21 Low-Reynolds-Number Flows
21.1 General Relations for Re-> 0; Stokes Equations
21.2 Global Equations for Stokes Flow
21.3 Flow in Tubes and Channels with Varying Cross Sections
21.4 Reynolds Equations for Lubrication Theory
21.5 Slipper-Pad Bearing
*21.6 Squeeze Film Lubrication; Viscous Adhesion
21.7 Plane Corner Flows: Moffatt Vortices
21.8 Axisymmetric Flow: Cones, Orifices, and Tubes
21.9 Flow Over a Sphere
21.3 Stokes Flow over a Sphere
*21.10 Nonuniformity of Stokes Flow on Infinite Domains
*21.11 Asymptotic Analysis of Flow Over a Sphere
21.12 Stokes Flow Near a Circular Cylinder
*21.13 Oseen's Equations
*21.14 Bubble or Droplet in an Infinite Fluid
*21.15 Stokes Flow over Particles of Arbitrary Shape
*21.16 Interference Effects
21.17 Conclusion
Problems
22 Introduction to Stability and Transition
22.1 Linear Stability and Normal Modes as Perturbations
22.2 Kelvin-Helmholtz Inviscid Shear-Layer Instability
22.3 Stability Problem for Nearly Parallel Viscous Flows
22.4 Orr-Sommerfeld Equation
22.5 Inviscid Stability of Nearly Parallel Flows
22.6 Viscous Stability of Nearly Parallel Flows
22.7 Experiments on Blasius Boundary Layers
22.8 Transition; Secondary Instability; Bypass
22.9 Spatially Developing Open Flow
22.10 Transition in Free Shear Flows
22.11 Poiseuille and Plane Couette Flow
22.12 Inviscid Instability of Flows with Curved Streamlines
22.13 Taylor Instability of Couette Flow
22.14 Stability of Regions of Concentrated Vorticity
22.15 Some Other Instabilities: Taylor; Capillary Jets; Curved Pipe;
Goetler; Viscous Fingering
22.16 Conclusion
23 Introduction to Turbulent Flow
23.1 Types of Turbulent Flow
23.2 Characteristics of Turbulent Flows
23.3 Reynolds Decomposition
23.4 Reynolds Stress
23.5 Free Turbulence; Plane Shear Layers
23.6 Free Turbulence; The Turbulent Jet
23.7 Bifurcating and Blooming Jets
23.8 Correlations of Fluctuations
23.9 Mean and Turbulent Kinetic Energy
23.10 Energy Cascade; Kolmogorov Scales, Taylor Microscale
23.11 Wall Turbulence; Channel Flow
23.12 Wall Layers; Experiments and Empirical Correlation
23.13 Turbulent Structures
23.14 Conclusion
APPENDIX A Properties of Fluids
APPENDIX B Differential Operations in Cylindrical and
Spherical Coordinates
APPENDIX C Basic Equations in Rectangular, Cylindrical,
and Spherical Coordinates
APPENDIX D Streamfunction Relations in Rectangular,
Cylindrical, and Spherical Coordinates
APPENDIX E Computer Code for Runge-Kutta Integration
APPENDIX F Computer Code for Entrance Flow into a Cascade
APPENDIX G Computer Code for Boundary-Layer Analysis
Supplemental Reading List
References
Index