An introduction to the mechanics of fluids:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston u. a.
Birkhäuser
2000
|
| Series: | Modeling and simulation in science, engineering and technology
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 277 S. |
| ISBN: | 0817640142 3764340142 |
Staff View
MARC
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| 245 | 1 | 0 | |a An introduction to the mechanics of fluids |c C. Truesdell ; K. R. Rajagopal |
| 264 | 1 | |a Boston u. a. |b Birkhäuser |c 2000 | |
| 300 | |a XII, 277 S. | ||
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| 490 | 0 | |a Modeling and simulation in science, engineering and technology | |
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Record in the Search Index
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Contents
Preface xi
General References xiii
1 Bodies, Configurations, and Motions 1
1.1 Introduction 1
1.2 Reference Configuration 2
1.3 Descriptions of Motion 3
1.4 Deformation Gradient 5
1.5 Material Time Rates and Gradients in the Spatial Description . . 7
1.6 Change of Reference Configuration 8
1.7 Current Configuration as Reference 8
1.8 Boundaries and Boundary Conditions 10
2 Kinematics and Basic Laws 13
2.1 Stretch and Rotation 13
2.2 Stretching and Spin 15
2.3 Changes of Frame 22
2.4 Forces and Moments 25
2.5 Euler s Laws of Mechanics 26
2.6 Euler Cauchy Stress Principle 27
2.7 Cauchy s Laws of Continuum Mechanics 28
2.8 Equivalent Processes 30
3 Constitutive Equations, Reduced Constitutive Equations, and
Internal Constraints 31
3.1 Constitutive Equations 31
3.2 Axioms for Constitutive Equations 32
3.2.1 Principle of determinism 32
viii Contents
3.2.2 Principle of local action 32
3.2.3 Principle of material frame indifference 32
3.3 Simple Materials 33
3.4 Restriction for Material Frame Indifference 35
3.5 Internal Constraints 37
3.6 Principle of Determinism for Constrained Simple Materials ... 38
3.7 Examples of Internal Constraints 39
3.7.1 Incompressibility 39
3.7.2 Inextensibility 40
3.7.3 Rigidity 40
3.8 Importance of Constrained Materials 41
4 Simple Fluids 43
4.1 Definition of a Simple Fluid 43
4.2 Monotonous Motions 45
4.3 Reduction of the Constitutive Relation for a Simple Material in a
Monotonous Motion 51
5 Flows of Incompressible Fluids in General 55
5.1 Stress of an Incompressible Fluid in Viscometric Flows 55
5.2 Viscometric Functions: Normal Stress Effects in Steady
Viscometric Flows 60
5.3 Position of the Classical Theory of Viscometry 61
5.4 Dynamics of the Main Viscometric Flows 62
5.5 Some Unsteady Flows 73
5.6 Steady Flow between Rotating Parallel Plates 75
5.7 Impossibility of Steady Rectilinear Flow in Pipes 77
6 Some Flows of Particular Nonlinear Fluids 83
6.1 Rivlin Ericksen Fluids 83
6.2 Boundary Conditions and Perturbation Procedures 91
6.3 Secondary Steady Flow of a Simple Fluid
down a Straight Pipe: Preliminaries 92
6.4 Calculation of the Series Determining Secondary
Flow down a Straight Pipe 94
6.5 Secondary Flow down a Straight Pipe: Discussion 101
6.6 Universal Flows of Fluids of Grades 1,2, and 3 104
6.6.1 Navier Stokes fluid 104
6.6.2 Fluids of Grade 2 108
6.6.3 Fluids of Grade 3 109
6.6.4 Formal summary 112
6.6.5 An approach to determining all universal flows 112
Contents ix
7 Some Flows of Fluids of Grade 2 115
7.1 Fluids of Grade 2 115
7.2 Unsteady Lineal Flows 116
7.3 Unsteady Plane Flows 124
7.4 Steady Plane Flows 127
7.5 Steady Flow between Rotating Parallel Plates 133
7.6 Stability and Instability of Flows in a Closed Vessel 136
8 Navier Stokes Fluids 143
8.1 Purpose and Plan of Chapters 8 and 9 143
8.2 Condition of Compatibility 145
8.3 Some Bernoullian Theorems 146
8.4 Dynamical Similarity 148
8.5 Viscometry 150
8.6 Flow against and along a Plate 150
8.7 Flow about a Rotating Circular Cylinder with Suction 152
8.8 Flow between Intersecting Planes 154
8.9 Flow in a Round Jet 156
8.10 Swirling Flow between Rotating Plates 158
8.10.1 Axially symmetric solutions 158
8.10.2 Solutions that are not axially symmetric 159
8.11 Flow Driven by Coriolis Force 163
8.12 Serrin s Swirling Vortex 164
8.13 Stability and Uniqueness 172
8.14 Instability 184
8.15 Some Unsteady Flows 186
8.16 Some Oscillatory Flows 187
8.17 Flow Due to a Plane Boundary Moved Suddenly from Rest ... 188
8.18 Flow Due to the Sudden Application of a Pressure Gradient ... 190
8.19 Unsteady Flow Impinging on a Flat Plate 191
8.20 Linearly Polarized Waves 192
8.21 Further Unsteady Plane Flows 193
9 Incompressible Euler Fluids 197
9.1 Preliminaries 197
9.2 Compatibility: General Solution of Euler s
Dynamical Equation 198
9.3 Accelerationless Flows: Hydrostatics 201
9.4 Irrotational Flows: General Aspects 202
9.5 Irrotational Flows: Reactions on Submerged Obstacles
andCavitites 203
9.6 Rotational Flows: Vorticity, Bernoullian Theorems 208
9.7 Rotational Flows: Gerstner Waves 211
9.8 Stokes Conjecture for the Height of Irrotational Waves 215
x Contents
9.9 Ring Vortices 223
9.10 Baroclinic Flow: Theorem of V. Bjerknes 229
10 Compressible Euler Fluids 233
10.1 Barotropic Fluids 233
10.2 Irrotational Motion 234
10.3 Munk Prim Substitution 236
10.4 Uniqueness 237
10.5 Linear Waves 241
10.6 Steady Flow in an Axially Symmetric Tube 243
10.7 One Dimensional Flows 244
10.8 Equilibrium of a Gaseous Mass under Self gravitation 246
10.9 Equilibrium of a Gaseous Mass under a
Constant Body Force Field 247
11 Singular Surfaces and Waves 249
11.1 Introductory Remarks 249
11.2 Motion of Singular Surfaces 251
11.3 Classification of Singular Surfaces 253
11.4 Singular Surfaces of Order 2: Acceleration Waves 254
A Some Elementary Results from Real Analysis 257
Index 273
|
| any_adam_object | 1 |
| author | Truesdell, Clifford 1919-2000 Rajagopal, K. R. |
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| discipline | Physik |
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| spelling | Truesdell, Clifford 1919-2000 Verfasser (DE-588)121263983 aut An introduction to the mechanics of fluids C. Truesdell ; K. R. Rajagopal Boston u. a. Birkhäuser 2000 XII, 277 S. txt rdacontent n rdamedia nc rdacarrier Modeling and simulation in science, engineering and technology Strömungsmechanik Fluid mechanics Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Strömungsmechanik (DE-588)4077970-1 s DE-604 Rajagopal, K. R. Verfasser (DE-588)114750807 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008614944&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Truesdell, Clifford 1919-2000 Rajagopal, K. R. An introduction to the mechanics of fluids Strömungsmechanik Fluid mechanics Strömungsmechanik (DE-588)4077970-1 gnd |
| subject_GND | (DE-588)4077970-1 (DE-588)4123623-3 |
| title | An introduction to the mechanics of fluids |
| title_auth | An introduction to the mechanics of fluids |
| title_exact_search | An introduction to the mechanics of fluids |
| title_full | An introduction to the mechanics of fluids C. Truesdell ; K. R. Rajagopal |
| title_fullStr | An introduction to the mechanics of fluids C. Truesdell ; K. R. Rajagopal |
| title_full_unstemmed | An introduction to the mechanics of fluids C. Truesdell ; K. R. Rajagopal |
| title_short | An introduction to the mechanics of fluids |
| title_sort | an introduction to the mechanics of fluids |
| topic | Strömungsmechanik Fluid mechanics Strömungsmechanik (DE-588)4077970-1 gnd |
| topic_facet | Strömungsmechanik Fluid mechanics Lehrbuch |
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