Introduction, Importance and Development of Fluid Mechanics | p. 1 |
Fluid Flows and their Significance | p. 1 |
Sub-Domains of Fluid Mechanics | p. 4 |
Historical Developments | p. 9 |
References | p. 14 |
Mathematical Basics | p. 15 |
Introduction and Definitions | p. 15 |
Tensors of Zero Order (Scalars) | p. 16 |
Tensors of First Order (Vectors) | p. 17 |
Tensors of Second Order | p. 21 |
Field Variables and Mathematical Operations | p. 23 |
Substantial Quantities and Substantial Derivative | p. 26 |
Gradient, Divergence, Rotation and Laplace Operators | p. 27 |
Line, Surface and Volume Integrals | p. 29 |
Integral Laws of Stokes and Gauss | p. 31 |
Differential Operators in Curvilinear Orthogonal Coordinates | p. 32 |
Complex Numbers | p. 36 |
Axiomatic Introduction to Complex Numbers | p. 37 |
Graphical Representation of Complex Numbers | p. 38 |
The Gauss Complex Number Plane | p. 39 |
Trigonometric Representation | p. 39 |
Stereographic Projection | p. 41 |
Elementary Function | p. 42 |
References | p. 47 |
Physical Basics | p. 49 |
Solids and Fluids | p. 49 |
Molecular Properties and Quantities of Continuum Mechanics | p. 51 |
Transport Processes in Newtonian Fluids | p. 55 |
General Considerations | p. 55 |
Pressure in Gases | p. 58 |
Molecular-Dependent Momentum Transport | p. 62 |
Molecular Transport of Heat and Mass in Gases | p. 65 |
Viscosity of Fluids | p. 69 |
Balance Considerations and Conservation Laws | p. 73 |
Thermodynamic Considerations | p. 76 |
References | p. 81 |
Basics of Fluid Kinematics | p. 83 |
General Considerations | p. 83 |
Substantial Derivatives | p. 84 |
Motion of Fluid Elements | p. 85 |
Path Lines of Fluid Elements | p. 86 |
Streak Lines of Locally Injected Tracers | p. 90 |
Kinematic Quantities of Flow Fields | p. 94 |
Stream Lines of a Velocity Field | p. 94 |
Stream Function and Stream Lines of Two-Dimensional Flow Fields | p. 98 |
Divergence of a Flow Field | p. 101 |
Translation, Deformation and Rotation of Fluid Elements | p. 104 |
Relative Motions | p. 108 |
References | p. 112 |
Basic Equations of Fluid Mechanics | p. 113 |
General Considerations | p. 113 |
Mass Conservation (Continuity Equation) | p. 115 |
Newton's Second Law (Momentum Equation) | p. 119 |
The Navier-Stokes Equations | p. 123 |
Mechanical Energy Equation | p. 128 |
Thermal Energy Equation | p. 130 |
Basic Equations in Different Coordinate Systems | p. 135 |
Continuity Equation | p. 135 |
Navier-Stokes Equations | p. 136 |
Special Forms of the Basic Equations | p. 142 |
Transport Equation for Vorticity | p. 143 |
The Bernoulli Equation | p. 144 |
Crocco Equation | p. 146 |
Further Forms of the Energy Equation | p. 147 |
Transport Equation for Chemical Species | p. 150 |
References | p. 151 |
Hydrostatics and Aerostatics | p. 153 |
Hydrostatics | p. 153 |
Connected Containers and Pressure-Measuring Instruments | p. 163 |
Communicating Containers | p. 163 |
Pressure-Measuring Instruments | p. 166 |
Free Fluid Surfaces | p. 168 |
Surface Tension | p. 168 |
Water Columns in Tubes and Between Plates | p. 172 |
Bubble Formation on Nozzles | p. 175 |
Aerostatics | p. 183 |
Pressure in the Atmosphere | p. 183 |
Rotating Containers | p. 187 |
Aerostatic Buoyancy | p. 188 |
Conditions for Aerostatics: Stability of Layers | p. 191 |
References | p. 192 |
Similarity Theory | p. 193 |
Introduction | p. 193 |
Dimensionless Form of the Differential Equations | p. 197 |
General Remarks | p. 197 |
Dimensionless Form of the Differential Equations | p. 199 |
Considerations in the Presence of Geometric and Kinematic Similarities | p. 204 |
Importance of Viscous Velocity, Time and Length Scales | p. 207 |
Dimensional Analysis and ¿-Theorem | p. 212 |
References | p. 219 |
Integral Forms of the Basic Equations | p. 221 |
Integral Form ofthe Continuity Equation | p. 221 |
Integral Form ofthe Momentum Equation | p. 224 |
Integral Form of the Mechanical Energy Equation | p. 225 |
Integral Form of the Thermal Energy Equation | p. 228 |
Applications of the Integral Form of the Basic Equations | p. 230 |
Outflow from Containers | p. 230 |
Exit Velocity of a Nozzle | p. 231 |
Momentum on a Plane Vertical Plate | p. 232 |
Momentum on an Inclined Plane Plate | p. 234 |
Jet Deflection by an Edge | p. 236 |
Mixing Process in a Pipe of Constant Cross-Section | p. 237 |
Force on a Turbine Blade in a Viscosity-Free Fluid | p. 239 |
Force on a Periodical Blade Grid | p. 240 |
Euler's Turbine Equation | p. 242 |
Power of Flow Machines | p. 245 |
References | p. 247 |
Stream Tube Theory | p. 249 |
General Considerations | p. 249 |
Derivations of the Basic Equations | p. 251 |
Continuity Equation | p. 251 |
Momentum Equation | p. 253 |
Bernoulli Equation | p. 254 |
The Total Energy Equation | p. 256 |
Incompressible Flows | p. 257 |
Hydro-Mechanical Nozzle Flows | p. 257 |
Sudden Cross-Sectional Area Extension | p. 258 |
Compressible Flows | p. 260 |
Influences of Area Changes on Flows | p. 260 |
Pressure-Driven Flows Through Converging Nozzles | p. 263 |
References | p. 273 |
Potential Flows | p. 275 |
Potential and Stream Functions | p. 275 |
Potential and Complex Functions | p. 280 |
Uniform Flow | p. 283 |
Corner and Sector Flows | p. 284 |
Source or Sink Flows and Potential Vortex Flow | p. 288 |
Dipole-Generated Flow | p. 291 |
Potential Flow Around a Cylinder | p. 293 |
Flow Around a Cylinder with Circulation | p. 296 |
SummaryofImportant Potential Flows | p. 299 |
Flow Forces on Bodies | p. 302 |
References | p. 307 |
Wave Motions in Non-Viscous Fluids | p. 309 |
General Considerations | p. 309 |
Longitudinal Waves: Sound Waves in Gases | p. 313 |
Transversal Waves: Surface Waves | p. 318 |
General Solution Approach | p. 318 |
Plane Standing Waves | p. 323 |
Plane Progressing Waves | p. 325 |
References to Further Wave Motions | p. 329 |
References | p. 330 |
Introduction to Gas Dynamics | p. 331 |
Introductory Considerations | p. 331 |
Mach Lines and Mach Cone | p. 335 |
Non-Linear Wave Propagation, Formation of Shock Waves | p. 338 |
Alternative Forms of the Bernoulli Equation | p. 341 |
Flow with Heat Transfer (Pipe Flow) | p. 344 |
Subsonic Flow | p. 347 |
Supersonic Flow | p. 347 |
Rayleigh and Fanno Relations | p. 351 |
Normal Compression Shock (Rankine-Hugoniot Equation) | p. 355 |
References | p. 360 |
Stationary, One-Dimensional Fluid Flows of Incompressible, Viscous Fluids | p. 361 |
General Considerations | p. 361 |
Plane Fluid Flows | p. 362 |
Cylindrical Fluid Flows | p. 363 |
Derivations of the Basic Equations for Fully Developed Fluid Flows | p. 364 |
Plane Fluid Flows | p. 364 |
Cylindrical Fluid Flows | p. 366 |
Plane Couette Flow | p. 366 |
Plane Fluid Flow Between Plates | p. 369 |
Plane Film Flow on an Inclined Plate | p. 372 |
Axi-Symmetric Film Flow | p. 376 |
Pipe Flow (Hagen-Poiseuille Flow) | p. 379 |
Axial Flow Between Two Cylinders | p. 383 |
Film Flows with Two Layers | p. 386 |
Two-Phase Plane Channel Flow | p. 388 |
References | p. 391 |
Time-Dependent, One-Dimensional Flows of Viscous Fluids | p. 393 |
General Considerations | p. 393 |
Accelerated and Decelerated Fluid Flows | p. 397 |
Stokes First Problem | p. 397 |
Diffusion of a Vortex Layer | p. 399 |
Channel Flow Induced by Movements of Plates | p. 402 |
Pipe Flow Induced by the Pipe Wall Motion | p. 407 |
Oscillating Fluid Flows | p. 414 |
Stokes Second Problem | p. 414 |
Pressure Gradient-Driven Fluid Flows | p. 417 |
Starting Flow in a Channel | p. 417 |
Starting Pipe Flow | p. 422 |
References | p. 427 |
Fluid Flows of Small Reynolds Numbers | p. 429 |
General Considerations | p. 429 |
Creeping Fluid Flows Between Two Plates | p. 431 |
Plane Lubrication Films | p. 433 |
Theory of Lubrication in Roller Bearings | p. 438 |
The Slow Rotation of a Sphere | p. 443 |
The Slow Translatory Motion of a Sphere | p. 445 |
The Slow Rotational Motion of a Cylinder | p. 451 |
The Slow Translatory Motion of a Cylinder | p. 453 |
Diffusion and Convection Influences on Flow Fields | p. 459 |
References | p. 461 |
Flows of Large Reynolds Numbers Boundary-Layer Flows | p. 463 |
General Considerations and Derivations | p. 463 |
Solutions of the Boundary-Layer Equations | p. 468 |
Flat Plate Boundary Layer (Blasius Solution) | p. 470 |
Integral Properties of Wall Boundary Layers | p. 474 |
The Laminar, Plane, Two-Dimensional Free Shear Layer | p. 480 |
The Plane, Two-Dimensional, Laminar Free Jet | p. 481 |
Plane, Two-Dimensional Wake Flow | p. 486 |
ConvergingChannel Flow | p. 489 |
References | p. 492 |
Unstable Flows and Laminar-Turbulent Transition | p. 495 |
General Considerations | p. 495 |
Causes of Flow Instabilities | p. 501 |
Stability of Atmospheric Temperature Layers | p. 502 |
Gravitationally Caused Instabilities | p. 505 |
Instabilities in Annular Clearances Caused by Rotation | p. 507 |
Generalized Instability Considerations (Orr-Sommerfeld Equation) | p. 512 |
Classifications of Instabilities | p. 517 |
Transitional Boundary-Layer Flows | p. 519 |
References | p. 522 |
Turbulent Flows | p. 523 |
General Considerations | p. 523 |
Statistical Description of Turbulent Flows | p. 527 |
Basics of Statistical Considerations of Turbulent Flows | p. 528 |
Fundamental Rules of Time Averaging | p. 528 |
Fundamental Rules for Probability Density | p. 530 |
Characteristic Function | p. 537 |
Correlations, Spectra and Time-Scales of Turbulence | p. 538 |
Time-Averaged Basic Equations of Turbulent Flows | p. 542 |
The Continuity Equation | p. 543 |
The Reynolds Equation | p. 544 |
Mechanical Energy Equation for the Mean Flow Field | p. 546 |
Equation for the Kinetic Energy of Turbulence | p. 550 |
Characteristic Scales of Length, Velocity and Time of Turbulent Flows | p. 553 |
Turbulence Models | p. 557 |
General Considerations | p. 557 |
General Considerations Concerning Eddy Viscosity Models | p. 560 |
Zero-Equation Eddy Viscosity Models | p. 565 |
One-Equation Eddy Viscosity Models | p. 573 |
Two-Equation Eddy Viscosity Models | p. 576 |
Turbulent Wall Boundary Layers | p. 578 |
References | p. 585 |
Numerical Solutions of the Basic Equations | p. 587 |
General Considerations | p. 587 |
General Transport Equation and Discretization of the Solution Region | p. 591 |
Discretization by Finite Differences | p. 595 |
Finite-Volume Discretization | p. 598 |
General Considerations | p. 598 |
Discretization in Space | p. 600 |
Discretization with Respect to Time | p. 611 |
Treatments of the Source Terms | p. 613 |
Computation of Laminar Flows | p. 614 |
Wall Boundary Conditions | p. 615 |
Symmetry Planes | p. 615 |
Inflow Planes | p. 615 |
Outflow Planes | p. 615 |
Computations of Turbulent Flows | p. 616 |
Flow Equations to be Solved | p. 616 |
Boundary Conditions for Turbulent Flows | p. 620 |
References | p. 626 |
Fluid Flows with Heat Transfer | p. 627 |
General Considerations | p. 627 |
Stationary, Fully Developed Flow in Channels | p. 630 |
Natural Convection Flow Between Vertical Plane Plates | p. 633 |
Non-Stationary Free Convection Flow Near a Plane Vertical Plate | p. 637 |
Plane-Plate Boundary Layer with Plate Heating at Small Prandtl Numbers | p. 641 |
Similarity Solution for a Plate Boundary Layer with Wall Heating and Dissipative Warming | p. 644 |
Vertical Plate Boundary-Layer Flows Caused by Natural Convection | p. 647 |
Similarity Considerations for Flows with Heat Transfer | p. 649 |
References | p. 651 |
Introduction to Fluid-Flow Measurement | p. 653 |
Introductory Considerations | p. 653 |
Measurements of Static Pressures | p. 656 |
Measurements of Dynamic Pressures | p. 660 |
Applications of Stagnation-Pressure Probes | p. 662 |
Basics of Hot-Wire Anemometry | p. 664 |
Measuring Principle and Physical Principles | p. 664 |
Properties of Hot-Wires and Problems of Application | p. 667 |
Hot-Wire Probes and Supports | p. 672 |
Cooling Laws for Hot-Wire Probes | p. 676 |
Static Calibration of Hot-Wire Probes | p. 680 |
Turbulence Measurements with Hot-Wire Anemometers | p. 685 |
Laser Doppler Anemometry | p. 694 |
Theory of Laser Doppler Anemometry | p. 694 |
Optical Systems for Laser Doppler Measurements | p. 701 |
Electronic Systems for Laser Doppler Measurements | p. 705 |
Execution of LDA-Measurements: One-Dimensional LDA Systems | p. 715 |
References | p. 717 |
Index | p. 719 |
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