Elsevier S & T

Advanced Fluid Mechanics

Graebel, William

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Table of contents
  • Cover
  • Table of Contentsvii
  • Prefacexiv
  • Chapter 1 Fundamentals1
  • 1.1 Introduction1
  • 1.2 Velocity, Acceleration, and the Material Derivative4
  • 1.3 The Local Continuity Equation5
  • 1.4 Path Lines, Streamlines, and Stream Functions7
  • 1.4.1 Lagrange’s Stream Function for Two-Dimensional Flows7
  • 1.4.2 Stream Functions for Three-Dimensional Flows, Including Stokes Stream Function11
  • 1.5 Newton's Momentum Equation13
  • 1.6 Stress14
  • 1.7 Rates of Deformation21
  • 1.8 Constitutive Relations24
  • 1.9 Equations for Newtonian Fluids27
  • 1.10 Boundary Conditions28
  • 1.11 Vorticity and Circulation29
  • 1.12 The Vorticity Equation34
  • 1.13 The Work-Energy Equation36
  • 1.14 The First Law of Thermodynamics37
  • 1.15 Dimensionless Parameters39
  • 1.16 Non-Newtonian Fluids40
  • 1.17 Moving Coordinate Systems41
  • Problems43
  • Chapter 2 Inviscid Irrotational Flows46
  • 2.1 Inviscid Flows46
  • 2.2 Irrotational Flows and the Velocity Potential47
  • 2.2.1 Intersection of Velocity Potential Lines and Streamlines in Two Dimensions49
  • 2.2.2 Basic Two-Dimensional Irrotational Flows51
  • 2.2.3 Hele-Shaw Flows57
  • 2.2.4 Basic Three-Dimensional Irrotational Flows58
  • 2.2.5 Superposition and the Method of Images59
  • 2.2.6 Vortices Near Walls61
  • 2.2.7 Rankine Half-Body65
  • 2.2.8 Rankine Oval67
  • 2.2.9 Circular Cylinder or Sphere in a Uniform Stream68
  • 2.3 Singularity Distribution Methods69
  • 2.3.1 Two- and Three-Dimensional Slender Body Theory69
  • 2.3.2 Panel Methods71
  • 2.4 Forces Acting on a Translating Sphere77
  • 2.5 Added Mass and the Lagally Theorem79
  • 2.6 Theorems for Irrotational Flow81
  • 2.6.1 Mean Value and Maximum Modulus Theorems81
  • 2.6.2 Maximum-Minimum Potential Theorem81
  • 2.6.3 Maximum-Minimum Speed Theorem82
  • 2.6.4 Kelvin’s Minimum Kinetic Energy Theorem82
  • 2.6.5 Maximum Kinetic Energy Theorem83
  • 2.6.6 Uniqueness Theorem84
  • 2.6.7 Kelvin’s Persistence of Circulation Theorem84
  • 2.6.8 Weiss and Butler Sphere Theorems84
  • Problems85
  • Chapter 3 Irrotational Two-Dimensional Flows87
  • 3.1 Complex Variable Theory Applied to Two-Dimensional Irrotational Flow87
  • 3.2 Flow Past a Circular Cylinder with Circulation91
  • 3.3 Flow Past an Elliptical Cylinder with Circulation93
  • 3.4 The Joukowski Airfoil95
  • 3.5 Kármán-Trefftz and Jones-McWilliams Airfoils98
  • 3.6 NACA Airfoils99
  • 3.7 Lifting Line Theory101
  • 3.8 Kármán Vortex Street103
  • 3.9 Conformal Mapping and the Schwarz-Christoffel Transformation108
  • 3.10 Cavity Flows110
  • 3.11 Added Mass and Forces and Moments for Two-Dimensional Bodies112
  • Problems114
  • Chapter 4 Surface and Interfacial Waves118
  • 4.1 Linearized Free Surface Wave Theory118
  • 4.1.1 Infinitely Long Channel118
  • 4.1.2 Waves in a Container of Finite Size122
  • 4.2 Group Velocity123
  • 4.3 Waves at the Interface of Two Dissimilar Fluids125
  • 4.4 Waves in an Accelerating Container127
  • 4.5 Stability of a Round Jet128
  • 4.6 Local Surface Disturbance on a Large Body of Fluid„Kelvin's Ship Wave130
  • 4.7 Shallow-Depth Free Surface Waves—Cnoidal and Solitary Waves132
  • 4.8 Ray Theory of Gravity Waves for Nonuniform Depths136
  • Problems139
  • Chapter 5 Exact Solutions of the Navier-Stokes Equations140
  • 5.1 Solutions to the Steady-State Navier-Stokes Equations When Convective Acceleration Is Absent140
  • 5.1.1 Two-Dimensional Flow Between Parallel Plates141
  • 5.1.2 Poiseuille Flow in a Rectangular Conduit142
  • 5.1.3 Poiseuille Flow in a Round Conduit or Annulus144
  • 5.1.4 Poiseuille Flow in Conduits of Arbitrarily Shaped Cross-Section145
  • 5.1.5 Couette Flow Between Concentric Circular Cylinders147
  • 5.2 Unsteady Flows When Convective Acceleration Is Absent147
  • 5.2.1 Impulsive Motion of a Plate„Stokess First Problem147
  • 5.2.2 Oscillation of a Plate„Stokess Second Problem149
  • 5.3 Other Unsteady Flows When Convective Acceleration Is Absent152
  • 5.3.1 Impulsive Plane Poiseuille and Couette Flows152
  • 5.3.2 Impulsive Circular Couette Flow153
  • 5.4 Steady Flows When Convective Acceleration Is Present154
  • 5.4.1 Plane Stagnation Line Flow155
  • 5.4.2 Three-Dimensional Axisymmetric Stagnation Point Flow158
  • 5.4.3 Flow into Convergent or Divergent Channels158
  • 5.4.4 Flow in a Spiral Channel162
  • 5.4.5 Flow Due to a Round Laminar Jet163
  • 5.4.6 Flow Due to a Rotating Disk165
  • Problems168
  • Chapter 6 The Boundary Layer Approximation170
  • 6.1 Introduction to Boundary Layers170
  • 6.2 The Boundary Layer Equations171
  • 6.3 Boundary Layer Thickness174
  • 6.4 Falkner-Skan Solutions for Flow Past a Wedge175
  • 6.4.1 Boundary Layer on a Flat Plate176
  • 6.4.2 Stagnation Point Boundary Layer Flow178
  • 6.4.3 General Case178
  • 6.5 The Integral Form of the Boundary Layer Equations179
  • 6.6 Axisymmetric Laminar Jet182
  • 6.7 Flow Separation183
  • 6.8 Transformations for Nonsimilar Boundary Layer Solutions184
  • 6.8.1 Falkner Transformation185
  • 6.8.2 von Mises Transformation186
  • 6.8.3 Combined Mises-Falkner Transformation187
  • 6.8.4 Crocco’s Transformation187
  • 6.8.5 Mangler’s Transformation for Bodies of Revolution188
  • 6.9 Boundary Layers in Rotating Flows188
  • Problems191
  • Chapter 7 Thermal Effects193
  • 7.1 Thermal Boundary Layers193
  • 7.2 Forced Convection on a Horizontal Flat Plate195
  • 7.2.1 Falkner-Skan Wedge Thermal Boundary Layer195
  • 7.2.2 Isothermal Flat Plate195
  • 7.2.3 Flat Plate with Constant Heat Flux196
  • 7.3 The Integral Method for Thermal Convection197
  • 7.3.1 Flat Plate with a Constant Temperature Region198
  • 7.3.2 Flat Plate with a Constant Heat Flux199
  • 7.4 Heat Transfer Near the Stagnation Point of an Isothermal Cylinder200
  • 7.5 Natural Convection on an Isothermal Vertical Plate201
  • 7.6 Natural Convection on a Vertical Plate with Uniform Heat Flux202
  • 7.7 Thermal Boundary Layer on Inclined Flat Plates203
  • 7.8 Integral Method for Natural Convection on an Isothermal Vertical Plate203
  • 7.9 Temperature Distribution in an Axisymmetric Jet204
  • Problems205
  • Chapter 8 Low Reynolds Number Flows207
  • 8.1 Stokes Approximation207
  • 8.2 Slow Steady Flow Past a Solid Sphere209
  • 8.3 Slow Steady Flow Past a Liquid Sphere210
  • 8.4 Flow Due to a Sphere Undergoing Simple Harmonic Translation212
  • 8.5 General Translational Motion of a Sphere214
  • 8.6 Oseen's Approximation for Slow Viscous Flow214
  • 8.7 Resolution of the Stokes/Whitehead Paradoxes216
  • Problems217
  • Chapter 9 Flow Stability218
  • 9.1 Linear Stability Theory of Fluid Flows218
  • 9.2 Thermal Instability in a Viscous Fluid„Rayleigh-Bénard Convection219
  • 9.3 Stability of Flow Between Rotating Circular Cylinders—Couette-Taylor Instability226
  • 9.4 Stability of Plane Flows228
  • Problems231
  • Chapter 10 Turbulent Flows233
  • 10.1 The Why and How of Turbulence233
  • 10.2 Statistical Approach—One-Point Averaging234
  • 10.3 Zero-Equation Turbulent Models240
  • 10.4 One-Equation Turbulent Models242
  • 10.5 Two-Equation Turbulent Models242
  • 10.6 Stress-Equation Models243
  • 10.7 Equations of Motion in Fourier Space244
  • 10.8 Quantum Theory Models246
  • 10.9 Large Eddy Models248
  • 10.10 Phenomenological Observations249
  • 10.11 Conclusions250
  • Chapter 11 Computational Methods„Ordinary Differential Equations251
  • 11.1 Introduction251
  • 11.2 Numerical Calculus262
  • 11.3 Numerical Integration of Ordinary Differential Equations267
  • 11.4 The Finite Element Method272
  • 11.5 Linear Stability Problems—Invariant Imbedding and Riccati Methods274
  • 11.6 Errors, Accuracy, and Stiff Systems279
  • Problems281
  • Chapter 12 Multidimensional Computational Methods283
  • 12.1 Introduction283
  • 12.2 Relaxation Methods284
  • 12.3 Surface Singularities288
  • 12.4 One-Step Methods297
  • 12.4.1 Forward Time, Centered Space„Explicit297
  • 12.4.2 Dufort-Frankel Method„Explicit298
  • 12.4.3 Crank-Nicholson Method„Implicit298
  • 12.4.4 Boundary Layer Equations„Crank-Nicholson299
  • 12.4.5 Boundary Layer Equation„Hybrid Method303
  • 12.4.6 Richardson Extrapolation303
  • 12.4.7 Further Choices for Dealing with Nonlinearities304
  • 12.4.8 Upwind Differencing for Convective Acceleration Terms304
  • 12.5 Multistep, or Alternating Direction, Methods305
  • 12.5.1 Alternating Direction Explicit (ADE) Method305
  • 12.5.2 Alternating Direction Implicit (ADI) Method305
  • 12.6 Method of Characteristics306
  • 12.7 Leapfrog Method—Explicit309
  • 12.8 Lax-Wendroff Method—Explicit310
  • 12.9 MacCormack's Methods311
  • 12.9.1 MacCormack’s Explicit Method312
  • 12.9.2 MacCormack’s Implicit Method312
  • 12.10 Discrete Vortex Methods (DVM)313
  • 12.11 Cloud in Cell Method (CIC)314
  • Problems315
  • Appendix318
  • A.1 Vector Differential Calculus318
  • A.2 Vector Integral Calculus320
  • A.3 Fourier Series and Integrals323
  • A.4 Solution of Ordinary Differential Equations325
  • A.4.1 Method of Frobenius325
  • A.4.2 Mathieu Equations326
  • A.4.3 Finding Eigenvalues„The Riccati Method327
  • A.5 Index Notation329
  • A.6 Tensors in Cartesian Coordinates333
  • A.7 Tensors in Orthogonal Curvilinear Coordinates337
  • A.7.1 Cylindrical Polar Coordinates339
  • A.7.2 Spherical Polar Coordinates340
  • A.8 Tensors in General Coordinates341
  • References346
  • Index356
Book details
  • Vendor Elsevier S & T
  • SKU 9780123708854R30
  • ISBN-13 9780080549088
  • Author Graebel, William
  • Category Technology & Engineering
  • Subject Mechanical

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Fluid mechanics is the study of how fluids behave and interact under various forces and in various applied situations, whether in liquid or gas state or both. The author compiles pertinent information that are introduced in the more advanced classes at the senior level and at the graduate level. “Advanced Fluid Mechanics” courses typically cover a variety of topics involving fluids in various multiple states (phases), with both elastic and non-elastic qualities, and flowing in complex ways. This new text will integrate both the simple stages of fluid mechanics (“Fundamentals”) with those involving more complex parameters, including Inviscid Flow in multi-dimensions, Viscous Flow and Turbulence, and a succinct introduction to Computational Fluid Dynamics. It will offer exceptional pedagogy, for both classroom use and self-instruction, including many worked-out examples, end-of-chapter problems, and actual computer programs that can be used to reinforce theory with real-world applications.

Professional engineers as well as Physicists and Chemists working in the analysis of fluid behavior in complex systems will find the contents of this book useful.All manufacturing companies involved in any sort of systems that encompass fluids and fluid flow analysis (e.g., heat exchangers, air conditioning and refrigeration, chemical processes, etc.) or energy generation (steam boilers, turbines and internal combustion engines, jet propulsion systems, etc.), or fluid systems and fluid power (e.g., hydraulics, piping systems, and so on)will reap the benefits of this text.

• Offers detailed derivation of fundamental equations for better comprehension of more advanced mathematical analysis
• Provides groundwork for more advanced topics on boundary layer analysis, unsteady flow, turbulent modeling, and computational fluid dynamics
• Includes worked-out examples and end-of-chapter problems as well as a companion web site with sample computational programs and Solutions Manual