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Hydrodynamics and Sound

ISBN-10: 0521868629

ISBN-13: 9780521868624

Edition: 2006

Authors: M. S. Howe

List price: $144.99
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Description:

This book is designed for a first graduate course in fluid dynamics. It focuses on knowledge and methods that find applications in most branches of fluid mechanics, and aims to supply a theoretical understanding that will permit sensible simplifications to be made in the formulation of problems and enable the reader to develop analytical models of practical significance. The study of simplified model problems can be used to guide experimental and numerical investigations. The first part (Chapter 1-4) is concerned entirely with the incompressible flow of homogeneous fluid. Chapters 5 and 6 deal with dispersive waves and acoustics.
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Book details

List price: $144.99
Copyright year: 2006
Publisher: Cambridge University Press
Publication date: 10/23/2006
Binding: Hardcover
Pages: 480
Size: 7.50" wide x 10.25" long x 0.75" tall
Weight: 0.396
Language: English

Preface
Equations of Motion
The fluid state
The material derivative
Conservation of mass: Equation of continuity
Momentum equation
Relative motion of neighbouring fluid elements
Viscous stress tensor
Navier-Stokes equation
The Reynolds equation and Reynolds stress
The energy equation
Alternative treatment of the energy equation
Energy equation for incompressible flow
Summary of governing equations
Boundary conditions
Potential Flow of an Incompressible Fluid
Ideal fluid
Kelvin's circulation theorem
The velocity potential
Bernoulli's equation
Impulsive pressure
Streamlines and intrinsic equations of motion
Bernoulli's equation in steady flow
Motion produced by a pulsating sphere
The point source
Free-space Green's function
Monopoles, dipoles, and quadrupoles
The vibrating sphere
Streamlines
Far field of a monopole distribution of zero strength
Green's formula
Volume and surface integrals
Green's formula
Sources adjacent to a plane wall
Determinancy of the motion
Fluid motion expressed in terms of monopole or dipole distributions
Determinancy of cyclic irrotational flow
Kinetic energy of cyclic irrotational flow
The kinetic energy
Converse of Kelvin's minimum-energy theorem
Energy of motion produced by a translating sphere
Problems with spherical boundaries
Legendre polynomials
Velocity potential of a point source in terms of Legendre polynomials
Interpretation in terms of images
The Stokes stream function
Stream function examples
Rankine solids
Rankine ovoid
Drag in ideal flow
Axisymmetric flow from a nozzle
Irrotational flow from a circular cylinder
Borda's mouthpiece
The incompressible far field
Deductions from Green's formula
Far field produced by motion of a rigid body
Inertia coefficients
Pressure in the far field
Force on a rigid body
Moment exerted on a rigid body
Sources near solid boundaries
The reciprocal theorem
Far-field Green's function
The Kirchhoff vector
Far-field Green's function for a sphere
Far-field Green's function for cylindrical bodies
The circular cylinder
The rigid strip
Symmetric far-field Green's function
Far field of an arbitrarily moving body
Far-field Green's function summary and special cases
General form
Airfoil of variable chord
Projection or cavity on a plane wall
Rankine ovoid
Circular aperture
Circular disc
Ideal Flow in Two Dimensions
Complex representation of fluid motion
The stream function
The complex potential
Uniform flow
Flow past a cylindrical surface
The circular cylinder
Circle theorem
Uniform flow past a circular cylinder
The line vortex
Circular cylinder with circulation
Equation of motion of a cylinder with circulation
The Blasius force and moment formulae
Blasius's force formula for a stationary rigid body
Blasius's moment formula for a stationary rigid body
Kutta-Joukowski lift force
Leading-edge suction
Sources and line vortices
Line vorrtices
Motion of a line vortex
Karman vortex street
Kinetic energy of a system of rectilinear vortices
Conformal transformations
Transformation of Laplace's equation
Equation of motion of a line vortex
Numerical integration of the vortex path equation
The Schwarz-Christoffel transformation
Irrotational flow from an infinite duct
Irrotational flow through a wall aperture
Free-streamline theory
Coanda edge flow
Mapping from the w plane to the t plane
Separated flow through an aperture
The wake of a flat plate
Flow past a curved boundary
The hodograph transformation formula
Chaplygin's singular point method
Jet produced by a point source
Deflection of trailing-edge flow by a source
The Joukowski transformation
The flat-plate airfoil
Calculation of the lift
Lift calculated from the Kirchhoff vector force formula
Lift developed by a starting airfoil
The Joukowski airfoil
Streamline flow past an airfoil
Separation and stall
Linear theory of separation
Sedov's method
Boundary conditions
Sedov's formula
Tandem airfoils
High-lift devices
Plain flap or aileron
Point sources and vortices
Flow through a cascade
Unsteady thin-airfoil theory
The vortex sheet wake
Translational oscillations
The unsteady lift
Leading-edge suction force
Energy dissipated by vorticity production
Hankel function formulae
Rotational Incompressible Flow
The vorticity equation
Vortex lines
Vortex tubes
Movement of vortex lines: Helmholtz's vortex theorem
Crocco's equation
Convection and diffusion of vorticity
Vortex sheets
The Biot-Savart law
The far field
Kinetic energy
The Biot-Savart formula in the presence of an internal boundary
The Biot-Savart formula for irrotational flow
Examples of axisymmetric vortical flow
Circular vortex filament
Rate of production of vorticity at a nozzle
Blowing out a candle
Axisymmetric steady flow of an ideal fluid
Hill's spherical vortex
Some viscous flows
Diffusion of vorticity from an impulsively started plane wall
Diffusion of vorticity from a line vortex
Creeping flow
Motion of a sphere at very small Reynolds number
The Oseen approximation
Laminar flow in a tube (Hagen-Poiseuille flow)
Boundary layer on a flat plate; Karman momentum integral method
Force on a rigid body
Surface force in terms of the impulse
The Kirchhoff vector force formula
The Kirchhoff vector force formula for irrotational flow
Arbitrary motion in a viscous fluid
Body moving without rotation
Surface force in two dimensions
Bluff body drag at high Reynolds number
Modelling vortex shedding from a sphere
Force and impulse in fluid of non-uniform density
Integral identities
Surface moment
Moment for a non-rotating body
Airfoil lift, drag, and moments
Vortex-surface interactions
Pressure expressed in terms of the total enthalpy
Equation for B
Solution of the B equation
The far field
Surface Gravity Waves
Introduction
Conditions at the free surface
Wave motion within the fluid
Linearised approximation
Time harmonic, plane waves on deep water
Water of finite depth
Surface wave energy
Wave-energy density
Wave-energy flux
Group velocity
Viscous damping of surface waves
The interior damping
Boundary-layer damping
Comparison of boundary-layer and internal damping for long waves
Shallow-water waves
Waves on water of variable depth
Shallow-water Green's function
Waves generated by a localised pressure rise
Waves approaching a sloping beach
Method of stationary phase
Formulation of initial-value dispersive-wave problems
Evaluation of Fourier integrals by the method of stationary phase
Numerical results for the surface displacement
Conservation of energy
Rayleigh's proof that energy propagates at the group velocity
Surface wave-energy equation
Waves generated by a submarine explosion
Initial-value problems in two surface dimensions
Waves generated by a surface elevation symmetric about the origin
The energy equation in two dimensions
Surface motion near a wavefront
One-dimensional waves
Waves generated by motion of the seabed
Tsunami produced by an undersea earthquake
Periodic wave sources
One-dimensional waves
Periodic sources in two surface dimensions
The surface wave power
Surface wave amplitude
Ship waves
Moving line pressure source
Wave-making resistance
Moving point-like pressure source
Plotting the wave crests
Behaviour at the caustic
Wave-making power
Wave amplitude calculated from the power
Ray theory
Kinematic theory of wave crests
Ray tracing in an inhomogeneous medium
Refraction of waves at a sloping beach
Wave action
Variational description of a fully dispersed wave group
Fully dispersed waves in a non-uniformly moving medium
General wave-bearing media
Diffraction of surface waves by a breakwater
Diffraction by a long, straight breakwater
Solution of the diffraction problem
The surface wave pattern
Uniform asymptotic approximation: Method of steepest descents
Introduction to Acoustics
The wave equation
The linear wave equation
Plane waves
Speed of sound
Acoustic Green's function
The impulsive point source
Green's function
Retarded potential
Sound from a vibrating sphere
Acoustic energy flux
Green's function in one space dimension: Method of descent
Waves generated by a one-dimensional volume source
Kirchhoff's formula
Compact Green's function
Generalized Kirchhoff formula
The time harmonic wave equation
The compact approximation
Rayleigh scattering: Scattering by a compact body
One-dimensional propagation through junctions
Continuity of volume velocity
Continuity of pressure
Reflection and transmission at a junction
Branching systems
Fundamental formula
Energy transmission
Acoustically compact cavity
The Helmholtz resonator
Acoustic filter
Admittance of a narrow constriction
Radiation from an open end
Rayleigh's method for low-frequency sound
The reflection coefficient
Admittance of the open end
Open-end input admittance
Flanged opening
Physical significance of the end correction
Admittance of a circular aperture
Webster's equation
Radiation into a semi-infinite duct
The compact Green's function
Wave generation by a train entering a tunnel
Damping of sound in a smooth-walled duct
Time harmonic propagation in a duct
The viscous contribution
The thermal contribution
The thermo-viscous damping coefficient
Bibliography
Index