Fluid mechanics : an introduction to the theory of fluid flows / / Franz Durst

• Autore: Durst F.
• Pubblicazione: Berlin, Germany : , : Springer, , [2022]; ©2022
• Edizione: Second and extended edition.
• Descrizione fisica: 1 online resource (828 pages) : illustrations (black and white, and color)
• Disciplina: 620.106
• Soggetto topico: Fluid mechanics; Hydraulic engineering; Physics
• Note generali: Includes index.
• Nota di contenuto: Intro -- Preface to the German Edition -- Preface to the English Edition -- Preface to the Second Edition -- Contents -- 1 Introduction, Importance and Development of Fluid Mechanics -- Abstract -- 1.1 Fluid Flows and Their Significance -- 1.2 Sub-Domains of Fluid Mechanics -- 1.3 Historical Developments -- Further Readings -- 2 Mathematical Basics -- Abstract -- 2.1 Introduction and Definitions -- 2.2 Tensors of Zero Order (Scalars) -- 2.3 Tensors of First Order (Vectors) -- 2.4 Tensors of Second Order -- 2.5 Field Variables and Mathematical Operations -- 2.6 Substantial Quantities and Substantial Derivative -- 2.7 Gradient, Divergence, Rotation and Laplace Operators -- 2.8 Complex Numbers -- 2.8.1 Axiomatic Introduction to Complex Numbers -- 2.8.2 Graphical Representation of Complex Numbers -- 2.8.3 The Gauss Complex Number Plane -- 2.8.4 Trigonometric Representation -- 2.8.5 Stereographic Projection -- 2.8.6 Elementary Function -- Further Readings -- 3 Physical Basics -- Abstract -- 3.1 Solids and Fluids -- 3.2 Molecular Properties and Quantities of Continuum Mechanics -- 3.3 Transport Processes in Newtonian Fluids -- 3.3.1 General Considerations -- 3.3.2 Pressure in Gases -- 3.3.3 Molecular-Dependent Momentum Transport -- 3.3.4 Molecular Transport of Heat and Mass in Gases -- 3.4 Viscosity of Fluids -- 3.5 Balance Considerations and Conservation Laws -- 3.6 Thermodynamic Considerations -- Further Readings -- 4 Basics of Fluid Kinematics -- Abstract -- 4.1 General Considerations -- 4.2 Substantial Derivatives -- 4.3 Motion of Fluid Elements -- 4.3.1 Path Lines of Fluid Elements -- 4.3.2 Streak Lines of Locally Injected Tracers -- 4.4 Kinematic Quantities of Flow Fields -- 4.4.1 Stream Lines of a Velocity Field -- 4.4.2 Stream Function and Stream Lines of Two-Dimensional Flow Fields -- 4.4.3 Divergence of a Flow Field. ; 4.5 Translation, Deformation and Rotation of Fluid Elements -- 4.6 Relative Motions -- Further Readings -- 5 Basic Equations of Fluid Mechanics -- Abstract -- 5.1 General Considerations -- 5.2 Mass Conservation (Continuity Equation) -- 5.3 Newton's Second Law (Momentum Equation) -- 5.4 The Navier-Stokes Equations -- 5.5 Mechanical Energy Equation -- 5.6 Thermal Energy Equation -- 5.7 Basic Equations in Different Coordinate Systems -- 5.7.1 Continuity Equation -- 5.7.2 Navier-Stokes Equations -- 5.8 Special Forms of the Basic Equations -- 5.8.1 Transport Equation for Vorticity -- 5.8.2 The Bernoulli Equation -- 5.8.3 Crocco Equation -- 5.8.4 Further Forms of the Energy Equation -- 5.9 Transport Equation for Chemical Species -- Further Readings -- 6 Extended Basic Equations of Fluid Mechanics -- Abstract -- 6.1 General Introduction -- 6.2 Extended Diffusive Transport Equations -- 6.2.1 Mass Transport Equations -- 6.2.2 Heat Transport Equations -- 6.2.3 Momentum Transport Equations -- 6.3 Analytical and Numerical Treatments of Micro-Channel and Micro-Capillary Flows -- 6.3.1 Summary of Numerical Investigations -- 6.3.1.1 Self-Diffusion in Ideal Gas Flows -- 6.3.1.2 Numerical Predictions and Results -- 6.3.2 Analytical Treatments -- 6.3.2.1 Micro-Channel Flows -- 6.3.2.2 Micro-Capillary Flows -- 6.4 Pressure Gradient Versus Wall Reflection Effects -- Further Readings -- 7 Hydrostatics and Aerostatics -- Abstract -- 7.1 Hydrostatics -- 7.2 Connected Containers and Pressure-Measuring Instruments -- 7.2.1 Interconnected Containers -- 7.2.2 Pressure-Measuring Instruments -- 7.3 Free Fluid Surfaces -- 7.3.1 Surface Tension -- 7.3.2 Water Columns in Tubes and Between Plates -- 7.3.3 Bubble Formation on Nozzles -- 7.4 Aerostatics -- 7.4.1 Pressure in the Atmosphere -- 7.4.2 Rotating Containers -- 7.4.3 Aerostatic Buoyancy. ; 7.4.4 Conditions for Aerostatics: Stability of Layers -- Further Readings -- 8 Similarity Theory -- Abstract -- 8.1 Introduction -- 8.2 Dimensionless Form of the Differential Equations -- 8.2.1 General Remarks -- 8.3 Dimensionless Form of the Differential Equations -- 8.3.1 Considerations in the Presence of Geometric and Kinematic Similarities -- 8.3.2 Importance of Viscous Velocity, Time and Length Scales -- 8.4 Dimensional Analysis and π-Theorem -- Further Readings -- 9 Integral Forms of the Basic Equations -- Abstract -- 9.1 Integral Form of the Continuity Equation -- 9.2 Integral Form of the Momentum Equation -- 9.3 Integral Form of the Mechanical Energy Equation -- 9.4 Integral Form of the Thermal Energy Equation -- 9.5 Applications of the Integral Form of the Basic Equations -- 9.5.1 Outflow from Containers -- 9.5.2 Exit Velocity of a Nozzle -- 9.5.3 Momentum on a Plane Vertical Plate -- 9.5.4 Momentum on an Inclined Plane Plate -- 9.5.5 Jet Deflection by an Edge -- 9.5.6 Mixing Process in a Channel of Constant Cross-Section in the Flow Direction -- 9.5.7 Force on a Turbine Blade in a Viscosity-Free Fluid -- 9.5.8 Force on a Grid with Periodical Blades -- 9.5.9 Euler's Turbine Equation -- 9.5.10 Power of Flow Machines -- Further Readings -- 10 Stream Tube Theory -- Abstract -- 10.1 General Considerations -- 10.2 Derivations of the Basic Equations -- 10.2.1 Continuity Equation -- 10.2.2 Momentum Equation -- 10.2.3 Bernoulli Equation -- 10.2.4 Total Energy Equation -- 10.3 Incompressible Flows -- 10.3.1 Hydromechanical Nozzle Flows -- 10.3.2 Sudden Cross-Sectional Area Extension -- 10.4 Compressible Flows -- 10.4.1 Influences of Area Changes on Flows -- 10.4.2 Pressure-Driven Flows Through Converging Nozzles -- Further Readings -- 11 Potential Flows -- Abstract -- 11.1 Potential and Stream Functions -- 11.2 Potential and Complex Functions. ; 11.3 Uniform Flow -- 11.4 Corner and Sector Flows -- 11.5 Source or Sink Flows and Potential Vortex Flow -- 11.6 Dipole-Generated Flow -- 11.7 Potential Flow Around a Cylinder -- 11.8 Flow Around a Cylinder With Circulation -- 11.9 Summary of Important Potential Flows -- 11.10 Flow Forces on Bodies -- Further Readings -- 12 Wave Motions in Non-Viscous Fluids -- Abstract -- 12.1 General Considerations -- 12.2 Longitudinal Waves: Sound Waves in Gases -- 12.3 Transverse Waves: Surface Waves -- 12.3.1 General Solution Approach -- 12.4 Plane Standing Waves -- 12.5 Plane Progressing Waves -- 12.6 References to Further Wave Motions -- Further Readings -- 13 Introduction to Gas Dynamics -- Abstract -- 13.1 Introductory Considerations -- 13.2 Mach Lines and Mach Cone -- 13.3 Non-Linear Wave Propagation, Formation of Shock Waves -- 13.4 Alternative Forms of the Bernoulli Equation -- 13.5 Flow with Heat Transfer (Pipe Flow) -- 13.5.1 Subsonic Flow -- 13.5.2 Supersonic Flow -- 13.6 Rayleigh and Fanno Relations -- Further Readings -- 14 Stationary One-Dimensional Fluid Flows of Incompressible Viscous Fluids -- Abstract -- 14.1 General Considerations -- 14.1.1 Equations for Plane Fluid Flows -- 14.1.2 Cylindrical Fluid Flows -- 14.2 Derivations of the Basic Equations for Fully Developed Fluid Flows -- 14.2.1 Equations for Plane Fluid Flows -- 14.2.2 Equations for Cylindrical Fluid Flows -- 14.3 Plane Couette Flow -- 14.4 Plane Fluid Flow Between Plates -- 14.5 Plane Film Flow on an Inclined Plate -- 14.6 Axisymmetric Film Flow -- 14.7 Pipe Flow (Hagen-Poiseuille Flow) -- 14.8 Axial Flow Between Two Cylinders -- 14.9 Film Flows with Two Layers -- 14.10 Two-Phase Plane Channel Flow -- Further Readings -- 15 Time-Dependent, One-Dimensional Flows of Viscous Fluids -- Abstract -- 15.1 General Considerations -- 15.2 Accelerated and Decelerated Fluid Flows. ; 15.2.1 Stokes First Problem -- 15.2.2 Diffusion of a Vortex Layer -- 15.2.3 Channel Flow Induced by Movements of Plates -- 15.2.4 Pipe Flow Induced by the Pipe Wall Motion -- 15.3 Oscillating Fluid Flows -- 15.3.1 Stokes Second Problem -- 15.4 Pressure Gradient-Driven Fluid Flows -- 15.4.1 Starting Flow in a Channel -- 15.4.2 Starting Pipe Flow -- Further Readings -- 16 Fluid Flows of Small Reynolds Numbers -- Abstract -- 16.1 General Considerations -- 16.2 Creeping Fluid Flows Between Two Plates -- 16.3 Plane Lubrication Films -- 16.4 Theory of Lubrication in Roller Bearings -- 16.5 The Slow Rotation of a Sphere -- 16.6 The Slow Translatory Motion of a Sphere -- 16.7 The Slow Rotational Motion of a Cylinder -- 16.8 The Slow Translatory Motion of a Cylinder -- 16.9 Diffusion and Convection Influences on Flow Fields -- Further Readings -- 17 Flows of Large Reynolds Number Boundary-Layer Flows -- Abstract -- 17.1 General Considerations and Derivations -- 17.2 Solutions of the Boundary-Layer Equations -- 17.3 Flat Plate Boundary Layer (Blasius Solution) -- 17.4 Integral Properties of Wall Boundary Layers -- 17.5 The Laminar, Plane, Two-Dimensional Free Shear Layer -- 17.6 The Plane, Two-Dimensional, Laminar Free Jet -- 17.7 Plane, Two-Dimensional Wake Flow -- 17.8 Converging Channel Flow -- Further Readings -- 18 Unstable Flows and Laminar-Turbulent Transition -- Abstract -- 18.1 General Considerations -- 18.2 Causes of Flow Instabilities -- 18.2.1 Stability of Atmospheric Temperature Distributions -- 18.2.2 Gravitationally Caused Instabilities -- 18.2.3 Instabilities in Annular Clearances Caused by Rotation -- 18.3 Generalized Instability Considerations (Orr-Sommerfeld Equation) -- 18.4 Classifications of Instabilities -- 18.5 Transitional Boundary-Layer Flows -- Further Readings -- 19 Turbulent Flows -- Abstract -- 19.1 General Considerations. ; 19.2 Statistical Description of Turbulent Flows.
• Sommario/riassunto: This book provides the fundamental knowledge allowing students in engineering and natural sciences to enter fluid mechanics and its applications in various fields where fluid flows need to be dealt with. Analytical treatments of flows are provided based on the Conventional Navier-Stokes-Equations (CNSE). The physics and mathematics of fundamental flow problems are explained in such detail that the reader receives a good introduction into the subject. Numerical methods and experimental techniques, applied in fluid mechanics, are also introduced. This second edition of the book stresses that the CNSE are incomplete. They are missing molecular transport terms. These terms are derived in the book to yield the Extended Navier-Stokes-Equations. These equations allow flows with strong fluid property gradients to be treated correctly, while the CNSE do not allow this. The main benefit the reader will derive from the book is a sound introduction into various aspects of fluid mechanics.
• Titolo autorizzato: Fluid Mechanics
• ISBN: 9783662639153; 9783662639139
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910584482803321
• Lo trovi qui: Univ. Federico II
• Serie: Graduate texts in physics.