Hydromechanics Theory and Fundamentals

, by Sinaiski, Emmanuil G.; Braun, Moritz

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ISBN: 9783527410262 | 3527410260
Cover: Hardcover
Copyright: 4/11/2011

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Written by an experienced author with a strong background in applications of this field, this monograph provides a comprehensive and detailed account of the theory behind hydromechanics. He includes numerous appendices with mathematical tools, backed by extensive illustrations. The result is a must-have for all those needing to apply the methods in their research, be it in industry or academia.

Dedication	p. v
Preface	p. xiii
List of Symbols	p. xvii
Introduction	p. 1
Goals and Methods of Continuum Mechanics	p. 1
The Main Hypotheses of Continuum Mechanics	p. 3
Kinematics of the Deformed Continuum	p. 5
Dynamics of the Continuum in the Lagrangian Perspective	p. 5
Dynamics of the Continuum in the Eulerian Perspective	p. 8
Scalar and Vector Fields and Their Characteristics	p. 8
Theory of Strains	p. 13
The Tensor of Strain Velocities	p. 24
The Distribution of Velocities in an Infinitesimal Continuum Particle	p. 25
Properties of Vector Fields. Theorems of Stokes and Gauss	p. 30
Dynamic Equations of Continuum Mechanics	p. 39
Equation of Continuity	p. 39
Equations of Motion	p. 43
Equation of Motion for the Angular Momentum	p. 51
Closed Systems of Mechanical Equations for the Simplest Continuum Models	p. 55
Ideal Fluid and Gas	p. 55
Linear Elastic Body and Linear Viscous Fluid	p. 58
Equations in Curvilinear Coordinates	p. 63
Equation of Continuity	p. 64
Equation of Motion	p. 65
Gradient of a Scalar Function	p. 66
Laplace Operator	p. 66
Complete System of Equations of Motion for a Viscous, Incompressible Medium in the Absence of Heating	p. 67
Foundations and Main Equations of Thermodynamics	p. 69
Theorem of the Living Forces	p. 69
Law of Conservation of Energy and First Law of Thermodynamics	p. 72
Thermodynamic Equilibrium, Reversible and Irreversible Processes	p. 76
Two Parameter Media and Ideal Gas	p. 77
The Second Law of Thermodynamics and the Concept of Entropy	p. 80
Thermodynamic Potentials of Two-Parameter Media	p. 83
Examples of Ideal and Viscous Media, and Their Thermodynamic Properties, Heat Conduction	p. 86
The Model of the Ideal, Incompressible Fluid	p. 87
The Model of the Ideal, Compressible Gas	p. 88
The Model of Viscous Fluid	p. 90
First and Second Law of Thermodynamics for a Finite Continuum Volume	p. 93
Generalized Thermodynamic Forces and Currents, Onsager's Reciprocity Relations	p. 94
Problems Posed in Continuum Mechanics	p. 97
Initial Conditions and Boundary Conditions	p. 97
Typical Simplifications for Some Problems	p. 101
Conditions on the Discontinuity Surfaces	p. 105
Discontinuity Surfaces in Ideal Compressible Media	p. 111
Dimensions of Physical Quantities	p. 118
Parameters that Determine the Class of the Phenomenon	p. 120
Similarity and Modeling of Phenomena	p. 127
Hydrostatics	p. 131
Equilibrium Equations	p. 131
Equilibrium in the Gravitational Field	p. 132
Force and Moment that Act on a Body from the Surrounding Fluid	p. 133
Equilibrium of a Fluid Relative to a Moving System of Coordinates	p. 135
Stationary Continuum Movement of an Ideal Fluid	p. 137
Bernoulli's Integral	p. 137
Examples of the Application of Bernoulli's Integral	p. 139
Dynamic and Hydrostatic Pressure	p. 141
Flow of an Incompressible Fluid in a Tube of Varying Cross Section	p. 142
The Phenomenon of Cavitation	p. 143
Bernoulli's Integral for Adiabatic Flows of an Ideal Gas	p. 144
Bernoulli's Integral for the Flow of a Compressible Gas	p. 147
Application of the Integral Relations on Finite Volumes	p. 151
Integral Relations	p. 151
Interaction of Fluids and Gases with Bodies Immersed in the Flow	p. 153
Potential Flows for Incompressible Fluids	p. 159
The Cauchy-Lagrange Integral	p. 160
Some Applications for the General Theory of Potential Flows	p. 161
Potential Movements for an Incompressible Fluid	p. 163
Movement of a Sphere in the Unlimited Volume of an Ideal, Incompressible Fluid	p. 171
Kinematic Problem of the Movement of a Solid Body in the Unlimited Volume of an Incompressible Fluid	p. 176
Energy, Movement Parameters and Moments of Movement Parameters for a Fluid during the Movement of a Solid Body in the Fluid	p. 177
Stationary Potential Flows of an Incompressible Fluid in the Plane	p. 181
Method of Complex Variables	p. 182
Examples of Potential Flows in the Plane	p. 183
Application of the Method of Conformal Mapping to the Solution of Potential Flows around a Body	p. 192
Examples of the Application of the Method of Conformal Mapping	p. 195
Main Moment and Main Vector of the Pressure Force Exerted on a Hydrofoil Profile	p. 199
Movement of an Ideal Compressible Gas	p. 203
Movement of an Ideal Gas Under Small Perturbations	p. 203
Propagation of Waves with Finite Amplitude	p. 207
Plane Vortex-Free Flow of an Ideal Compressible Gas	p. 211
Subsonic Flow around a Thin Profile	p. 215
Supersonic Flow around a Thin Profile	p. 216
Dynamics of the Viscous Incompressible Fluid	p. 219
Rheological Laws of the Viscous Incompressible Fluid	p. 219
Equations of the Newtonian Viscous Fluid and Similarity Numbers	p. 221
Integral Formulation for the Effect of Viscous Fluids on a Moving Body	p. 223
Stationary Flow of a Viscous Incompressible Fluid in a Tube	p. 226
Oscillating Laminar Flow of a Viscous Fluid through a Tube	p. 231
Simplification of the Navier-Stokes Equations	p. 233
Flow of a Viscous Incompressible Fluid for Small Reynolds Numbers	p. 237
General Properties of Stokes Flows	p. 237
Flow of a Viscous Fluid around a Sphere	p. 240
Creeping Spatial Flow of a Viscous Incompressible Fluid	p. 247
The Laminar Boundary Layer	p. 251
Equation of Motion for the Fluid in the Boundary Layer	p. 251
Asymptotic Boundary Layer on a Plate	p. 255
Problem of the Injected Beam	p. 257
Turbulent Flow of Fluid	p. 263
General Information on Laminar and Turbulent Flows	p. 263
Momentum Equation of a Viscous Incompressible Fluid	p. 264
Equations of Heat Inflow, Heat Conduction and Diffusion	p. 267
The Condition for the Beginning of Turbulence	p. 269
Hydrodynamic Instability	p. 270
The Reynolds Equations	p. 272
The Equation of Turbulent Energy Balance	p. 277
Isotropic Turbulence	p. 281
The Local Structure of Fully Developed Turbulence	p. 291
Models of Turbulent Flow	p. 301
Semi-empirical Theories of Turbulence	p. 302
The Use of Transport Equations	p. 308
References	p. 312
Foundations of Vectorial and Tensorial Analysis	p. 315
Vectors	p. 316
Tensors	p. 325
Curvilinear Systems of Coordinates and Physical Components	p. 338
Calculation of Lengths, Surface Areas and Volumes	p. 341
Differential Operators and Integral Theorems	p. 344
Some Differential Geometry	p. 349
Curves on a Plane	p. 349
Vectorial Definition of Curves	p. 350
Curvature of a Curve in the Plane	p. 353
Curves in Space	p. 355
Curvature of Spatial Curves	p. 358
Surfaces in Space	p. 360
Fundamental Forms of the Surface	p. 363
Curvature of a Curve on the Surface	p. 367
Internal Geometry of a Surface	p. 371
Surface Vectors	p. 376
Geodetic Lines on a Surface	p. 379
Vector Fields on the Surface	p. 384
Hybrid Tensors	p. 386
Foundations of Probability Theory	p. 389
Events and Set of Events	p. 389
Probability	p. 390
Common and Conditional Probability, Independent Events	p. 391
Random Variables	p. 392
Distribution of Probability Density and Mean Values	p. 393
Generalized Functions	p. 394
Methods of Averaging	p. 396
Characteristic Function	p. 398
Moments and Cumulants of Random Quantities	p. 400
Correlation Functions	p. 402
Poisson, Bernoulli and Gaussian Distributions	p. 404
Stationary Random Functions and Homogeneous Random Fields	p. 408
Isotropic Random Fields	p. 410
Stochastic Processes, Markovian Processes and Chapman-Kolmogorov Integral Equation	p. 412
Differential Equations of Chapman-Kolmogorov et al.	p. 415
Stochastic Differential Equations and the Langevin Equation	p. 427
Basics of Complex Analysis	p. 433
Complex Numbers	p. 433
Operations with Complex Numbers	p. 433
Geometrical Interpretation of Complex Numbers	p. 434
Complex Variables	p. 436
Geometrical Notions	p. 436
Functions of a Complex Variable	p. 437
Differentiation and Analyticity of Complex Functions	p. 438
Elementary Functions	p. 439
Functions	p. 439
Joukowski Function	p. 442
Integration of Complex Variable Functions	p. 443
Integral of Complex Variable Functions	p. 443
Some Theorems of Integral Calculus in Simply Connected Regions	p. 444
Extension of Integral Calculus to Multiply Connected Regions	p. 446
Cauchy Formula	p. 448
Representation of a Function as a Series	p. 450
Taylor Series	p. 450
Laurent Series	p. 450
Singular Points	p. 452
Theorem about Residues	p. 453
Infinitely Remote Point	p. 456
Conformal Transformations	p. 458
Notion of Conformal Transformation	p. 458
Main Problem	p. 461
Correspondence of Boundaries	p. 462
Linear Fractional Function	p. 462
Particular Cases	p. 464
Application of the Theory of Complex Variables to Boundary-Value Problems	p. 467
Harmonic Functions	p. 467
Dirichlet Problem	p. 468
Physical Representations and Formulation of Problems	p. 470
Plane Field and Complex Potential	p. 470
Examples of Plane Fields	p. 474
References to Appendix	p. 481
Index	p. 483
Table of Contents provided by Ingram. All Rights Reserved.

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Hydromechanics Theory and Fundamentals

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Table of Contents

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