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| Preface | |
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| Introduction | |
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| Fluid dynamics | |
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| Structure of the text | |
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| Method of working | |
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| Reference | |
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| Mathematical preliminaries | |
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| Background knowledge | |
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| Polar coordinate systems | |
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| The vector derivative, [down triangle, open] | |
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| Cartesian tensor methods | |
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| Integration formulae | |
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| Formulae in polar coordinates | |
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| Exercises | |
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| References | |
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| Physical preliminaries | |
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| Background knowledge | |
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| Mathematical modelling | |
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| Properties of fluids | |
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| Dimensional reasoning | |
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| Exercise | |
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| Observational preliminaries | |
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| The continuum model | |
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| Fluid velocity and particle paths | |
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| Definitions | |
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| Streamlines and streaklines | |
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| Exercises | |
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| References | |
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| Mass conservation and stream functions | |
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| The continuity equation | |
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| The convective derivative | |
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| The stream function for two-dimensional flows | |
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| Some basic stream functions | |
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| Some flow models and the method of images | |
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| The (Stokes) stream function for axisymmetric flows | |
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| Models using the Stokes stream function | |
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| Exercises | |
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| References | |
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| Vorticity | |
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| Analysis of the motion near a point | |
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| Simple model flows | |
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| Models for vortices | |
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| Definitions and theorems for vorticity | |
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| Examples of vortex lines and motions | |
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| Exercises | |
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| References | |
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| Hydrostatics | |
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| Body forces | |
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| The stress tensor | |
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| The form of the stress tensor | |
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| Hydrostatic pressure and forces | |
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| Exercises | |
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| References | |
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| Thermodynamics | |
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| Basic ideas and equations of state | |
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| Energy and entropy | |
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| The perfect gas model | |
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| The atmosphere | |
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| Exercises | |
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| References | |
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| The equation of motion | |
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| The fundamental form | |
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| Stress and rate of strain | |
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| The Navier-Stokes equation | |
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| Discussion of the Navier-Stokes equation | |
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| Exercises | |
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| References | |
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| Solutions of the Navier-Stokes equations | |
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| Flows with only one coordinate | |
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| Some flows with two variables | |
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| A boundary layer flow | |
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| Flow at high Reynolds number | |
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| Exercises | |
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| References | |
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| Inviscid flow | |
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| Euler's equation | |
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| The vorticity equation | |
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| Kelvin's theorem | |
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| Bernoulli's equation | |
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| Examples using Bernoulli's equation | |
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| A model for the force on a sphere in a stream | |
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| Exercises | |
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| References | |
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| Potential theory | |
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| The velocity potential and Laplace's equation | |
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| General properties of Laplace's equation | |
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| Simple irrotational flows | |
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| Solutions by separation of variables | |
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| Separation of variables for an axisymmetric flow: Legendre polynomials | |
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| Two unsteady flows | |
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| Bernoulli's equation for unsteady irrotational flow | |
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| The force on an accelerating cylinder | |
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| D'Alembert's paradox | |
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| Exercises | |
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| References | |
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| Sound waves in fluids | |
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| Background | |
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| The linear equations for sound in air | |
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| Plane sound waves | |
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| Plane waves in musical instruments | |
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| Plane waves interacting with boundaries | |
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| Energy and energy flow in sound waves | |
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| Sound waves in three dimensions | |
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| Exercises | |
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| References | |
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| Water waves | |
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| Background | |
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| The linear equations | |
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| Plane waves on deep water | |
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| Energy flow and group velocity | |
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| Waves at an interface | |
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| Waves on shallower water | |
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| Oscillations in a container | |
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| Bessel functions | |
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| Exercises | |
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| References | |
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| High speed flow of air | |
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| Subsonic and supersonic flows | |
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| The use of characteristics | |
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| The formation of discontinuities | |
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| Plane shock waves | |
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| Exercises | |
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| References | |
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| Steady surface waves in channels | |
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| One-dimensional approximation | |
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| Hydraulic jumps or bores | |
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| Changes across a hydraulic jump | |
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| Solitary waves | |
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| Exercises | |
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| References | |
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| The complex potential | |
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| Simple complex potentials | |
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| More complicated potentials | |
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| Potentials for systems of vortices | |
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| Image theorems | |
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| Calculation of forces | |
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| Exercises | |
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| References | |
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| Conformal mappings and aerofoils | |
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| An example | |
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| Mappings in general | |
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| Particular mappings | |
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| A sequence of mappings | |
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| The Joukowski transformation of an ellipse | |
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| The cambered aerofoil | |
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| Further details on aerofoils | |
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| Exercises | |
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| References | |
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| Hints for exercises | |
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| Answers for exercises | |
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| Books for reference | |
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| Index | |