Incompressible Flow – Ronald L. Panton – 4th Edition

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 Continuum Assumption
1.2 Fundamental Concepts, Definitions, and Laws
1.3 Space and Time
1.4 Density, Velocity, and Internal Energy
1.5 Interface between Phases
1.6 Conclusions
Problems

2 Thermodynamics
2.1 Systems, Properties, and Processes
2.2 Independent Variables
2.3 Temperature and Entropy
2.4 Fundamental Equations of Thermodynamics
2.5 Euler’s Equation for Homogenous Functions
2.6 Gibbs–Duhem Equation
2.7 Intensive Forms of Basic Equations
2.8 Dimensions of Temperature and Entropy
2.9 Working Equations
2.10 Ideal Gas
2.11 Incompressible Substance
2.12 Compressible Liquids
2.13 Conclusions
Problems

3 Vector Calculus and Index Notation
3.1 Index Notation Rules and Coordinate Rotation
3.2 Definition of Vectors and Tensors
3.3 Special Symbols and Isotropic Tensors
3.4 Direction Cosines and the Laws of Cosines
3.5 Algebra with Vectors
3.6 Symmetric and Antisymmetric Tensors
3.7 Algebra with Tensors
3.8 Vector Cross-Product
*3.9 Alternative Definitions of Vectors
*3.10 Principal Axes and Values
3.11 Derivative Operations on Vector Fields
3.12 Integral Formulas of Gauss and Stokes
3.13 Leibnitz’s Theorem
3.14 Conclusions
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 Conclusions
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 Moment of Momentum, Angular Momentum, and Symmetry of Tij
5.9 Energy Equation
5.10 Mechanical and Thermal Energy Equations
5.11 Energy Equation with Temperature as the 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 Integral Form of the Energy Equation
5.17 Integral Mechanical Energy Equation
5.18 Jump Equations at Interfaces
5.19 Conclusions
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 Wall Boundary Conditions; The No-Slip Condition
6.5 Fourier’s Heat Conduction Law
6.6 Navier–Stokes Equations
6.7 Conclusions
Problems

7 Some Incompressible Flow Patterns
7.1 Pressure-Driven Flow in a Slot
7.2 Mechanical Energy, Head Loss, and Bernoulli Equation
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 Outer Solution for Rotary Viscous Coupling
7.7 The Rayleigh Problem
7.8 Conclusions
Problems

8 Dimensional Analysis
8.1 Measurement, Dimensions, and Scale Change Ratios
8.2 Physical Variables and Functions
8.3 Pi Theorem and Its Applications
8.4 Pump or Blower Analysis: Use of Extra Assumptions
8.5 Number of Primary Dimensions
*8.6 Proof of Bridgman’s Equation
*8.7 Proof of the Pi Theorem
8.8 Dynamic Similarity and Scaling Laws
8.9 Similarity with Geometric Distortion
8.10 Nondimensional Formulation of Physical Problems
8.11 Conclusions
Problems

9 Compressible Flow
9.1 Compressible Couette Flow: Adiabatic Wall
9.2 Flow with Power Law Transport Properties
9.3 Inviscid Compressible Waves: Speed of Sound
9.4 Steady Compressible Flow
9.5 Conclusions
Problems

10 Incompressible Flow
10.1 Characterization
10.2 Incompressible Flow as 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 Energy Equation Paradox
10.10 Conclusions
Problems

11 Some Solutions of the Navier–Stokes Equations
11.1 Pressure-Driven Flow in Tubes of Various Cross Sections: Elliptical Tube
11.2 Flow in a Rectangular Tube
11.3 Asymptotic Suction Flow
11.4 Stokes’s Oscillating Plate
11.5 Wall under an Oscillating Free Stream
*11.6 Transient for a Stokes Oscillating Plate
11.7 Flow in a Slot with a Steady and Oscillating Pressure Gradient
11.8 Decay of an Ideal Line Vortex (Oseen Vortex)
11.9 Plane Stagnation Point Flow (Hiemenz Flow)
11.10 Burgers Vortex
11.11 Composite Solution for the Rotary Viscous Coupling
11.12 Von K´arm´an Viscous Pump
11.13 Conclusions
Problems

12 Streamfunctions and the Velocity Potential
12.1 Streamlines
12.2 Streamfunction for Plane Flows
12.3 Flow in a Slot with Porous Walls
*12.4 Streamlines and Streamsurfaces for a Three-Dimensional Flow
*12.5 Vector Potential and the E2 Operator
12.6 Stokes’s Streamfunction for Axisymmetric Flow
12.7 Velocity Potential and the Unsteady Bernoulli Equation
12.8 Flow Caused by a Sphere with Variable Radius
12.9 Conclusions
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 Production of Vorticity at Walls
13.7 Typical Vorticity Distributions
13.8 Development of Vorticity Distributions
13.9 Helmholtz’s Laws for Inviscid Flow
13.10 Kelvin’s Theorem
13.11 Vortex Definitions
13.12 Inviscid Motion of Point Vortices
13.13 Circular Line Vortex
13.14 Fraenkel–Norbury Vortex Rings
13.15 Hill’s Spherical Vortex
13.16 Breaking and Reconnection of Vortex Lines
13.17 Vortex Breakdown
13.18 Conclusions
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 Streamfunction–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 Jeffrey–Hamel Flow in a Wedge
14.8 Limiting Case for Re ? 0; Stokes Flow
14.9 Limiting Case for Re?-8
14.10 Conclusions
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 Nonuniform Expansions: Friedrich’s Problem
15.5 Matching Process: Van Dyke’s Rule
15.6 Composite Expansions
15.7 Characteristics of Overlap Regions and Common Parts
15.8 Composite Expansions and Data Analysis
15.9 Lagerstrom’s Problems
15.10 Conclusions
Problems

16 Characteristics of High-Reynolds-Number Flows
16.1 Physical Motivation
16.2 Inviscid Main Flows: Euler Equations
16.3 Pressure Changes in Steady Flows: Bernoulli Equations
16.4 Boundary Layers
16.5 Conclusions
Problems

17 Kinematic Decomposition of Flow Fields
*17.1 General Approach
*17.2 Helmholtz’s Decomposition; Biot–Savart Law
*17.3 Line Vortex and Vortex Sheet
*17.4 Complex Lamellar Decomposition
*17.5 Conclusions
*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 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 Conclusions
Problems

19 Three-Dimensional Ideal Flows
19.1 General Equations and Characteristics of Three-Dimensional Ideal Flows
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 Work to Move a Body in a Still Fluid
19.10 Wake Drag of Bodies
*19.11 Induced Drag: Drag due to Lift
*19.12 Lifting Line Theory
19.13 Winglets
*19.14 Added Mass of Accelerating Bodies
19.15 Conclusions
Problems

20 Boundary Layers
20.1 Blasius Flow over a Flat Plate
20.2 Displacement Thickness
20.3 Von K´arm´an Momentum Integral
20.4 Von K´arm´an–Pohlhausen Approximate Method
20.5 Falkner–Skan Similarity Solutions
20.6 Arbitrary Two-Dimensinoal 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 Boundary Layers Beginning at Infinity
20.11 Plane Boundary Layer Separation
20.12 Axisymmteric Boundary Layers
20.13 Jets
20.14 Far Wake of Nonlifting Bodies
20.15 Free Shear Layers
20.16 Unsteady and Erupting Boundary Layers
*20.17 Entrance Flow into a Cascade, Parabolized Navier–Stokes Equations
*20.18 Three-Dimensional Boundary Layers
*20.19 Boundary Layer with a Constant Transverse Pressure Gradient
*20.20 Howarth’s Stagnation Point
*20.21 Three-Dimensional Separation Patterns
20.22 Conclusions
Problems

21 Flow at Low Reynolds Numbers
21.1 General Relations for Re ? 0: Stokes’s Equations
21.2 Global Equations for Stokes Flow
21.3 Streamfunction for Plane and Axisymmetric Flows
21.4 Local Flows, Moffatt Vortices
21.5 Plane Internal Flows
21.6 Flows between Rotating Cylinders
21.7 Flows in Tubes, Nozzles, Orifices, and Cones
21.8 Sphere in a Uniform Stream
21.9 Composite Expansion for Flow over a Sphere
21.10 Stokes Flow near a Circular Cylinder
*21.11 Axisymmetric Particles
*21.12 Oseen’s Equations
*21.13 Interference Effects
21.14 Conclusions
Problems

22 Lubrication Approximation
22.1 Basic Characteristics: Channel Flow
22.2 Flow in a Channel with a Porous Wall
22.3 Reynolds Equation for Bearing Theory
22.4 Slipper Pad Bearing
22.5 Squeeze-Film Lubrication: Viscous Adhesion
22.6 Journal Bearing
22.7 Hele-Shaw Flow
22.8 Conclusions
Problems

23 Surface Tension Effects
23.1 Interface Concepts and Laws
23.2 Statics: Plane Interfaces
23.3 Statics: Cylindrical Interfaces
23.4 Statics: Attached Bubbles and Drops
23.5 Constant-Tension Flows: Bubble in an Infinite Stream
23.6 Constant-Tension Flows: Capillary Waves
23.7 Moving Contact Lines
23.8 Constant-Tension Flows: Coating Flows
23.9 Marangoni Flows
23.10 Conclusions
Problems

24 Introduction to Microflows
24.1 Molecules
24.2 Continuum Description
24.3 Compressible Flow in Long Channels
24.4 Simple Solutions with Slip
24.5 Gases
24.6 Couette Flow in Gases
24.7 Poiseuille Flow in Gases
24.8 Gas Flow over a Sphere
24.9 Liquid Flows in Tubes and Channels
24.10 Liquid Flows near Walls; Slip Boundaries
24.11 Conclusions

25 Stability and Transition
25.1 Linear Stability and Normal Modes as Perturbations
25.2 Kelvin–Helmholtz Inviscid Shear Layer Instability
25.3 Stability Problems for Nearly Parallel Viscous Flows
25.4 Orr–Sommerfeld Equation
25.5 Invsicid Stability of Nearly Parallel Flows
25.6 Viscous Stability of Nearly Parallel Flows
25.7 Experiments on Blasius Boundary Layers
25.8 Transition, Secondary, Instability, and Bypass
25.9 Spatially Developing Open Flows
25.10 Transition in Free Shear Flows
25.11 Poiseuille and Plane Couette Flows
25.12 Inviscid Instability of Flows with Curved Streamlines
25.13 Taylor Instability of Couette Flow
25.14 Stability of Regions of Concentrated Vorticity
25.15 Other Instabilities: Taylor, Curved, Pipe, Capillary Jets, and G¨ortler
25.16 Conclusions

26 Turbulent Flows
26.1 Types of Turbulent Flows
26.2 Characteristics of Turbulent Flows
26.3 Reynolds Decomposition
26.4 Reynolds Stress
*26.5 Correlation of Fluctuations
*26.6 Mean and Turbulent Kinetic Energy
*26.7 Energy Cascade: Kolmogorov Scales and Taylor Microscale
26.8 Wall Turbulence: Channel Flow Analysis
26.9 Channel and Pipe Flow Experiments
26.10 Boundary Layers
26.11 Wall Turbulence: Fluctuations
26.12 Turbulent Structures
26.13 Free Turbulence: Plane Shear Layers
26.14 Free Turbulence: Turbulent Jet
26.15 Bifurcating and Blooming Jets
26.16 Conclusions

A Properties of Fluids
B Differential Operations in Cylindrical and Spherical Coordinates
C Basic Equations in Rectangular, Cylindrical, and Spherical Coordinates
D Streamfunction Relations in Rectangular, Cylindrical, and Spherical Coordinates
E Matlab R Stagnation Point Solver
F Matlab R Program for Cascade Entrance
G Matlab R Boundary Layer Program
References
Index