Introductory fluid mechanics : for physicists and mathematicians / Geoffrey Pert.

Format:

Book

Author/Creator:

Pert, Geoffrey.

Language:

English

Subjects (All):

Fluid mechanics.

Heat--Transmission.

Heat.

Hydrodynamics.

Physical Description:

1 online resource (xx, 468 p.) : ill.

Edition:

1st ed.

Place of Publication:

Chichester, England : John Wiley & Sons, c2013.

Summary:

This textbook presents essential methodology for physicists of the theory and applications of fluid mechanics within a single volume. Building steadily through a syllabus, it will be relevant to almost all undergraduate physics degrees which include an option on hydrodynamics, or a course in which hydrodynamics figures prominently.

Contents:

Cover

Title Page

Copyright

Contents

Preface

Chapter 1 Introduction

1.1 Fluids as a State of Matter

1.2 The Fundamental Equations for Flow of a Dissipationless Fluid

1.3 Lagrangian Frame

1.3.1 Conservation of Mass

1.3.2 Conservation of Momentum-Euler's Equation

1.3.3 Conservation of Angular Momentum

1.3.4 Conservation of Energy

1.3.5 Conservation of Entropy

1.4 Eulerian Frame

1.4.1 Conservation of Mass-Equation of Continuity

1.4.2 Conservation of Momentum

1.4.3 Conservation of Angular Momentum

1.4.4 Conservation of Energy

1.4.5 Conservation of Entropy

1.5 Hydrostatics

1.5.1 Isothermal Fluid-Thermal and Mechanical Equilibrium

1.5.2 Adiabatic Fluid-Lapse Rate

1.5.3 Stability of an Equilibrium Configuration

1.6 Streamlines

1.7 Bernoulli's Equation: Weak Form

1.8 Polytropic Gases

1.8.1 Applications of Bernoulli's Theorem

1.8.1.1 Vena Contracta

1.8.1.2 Flow of gas along a pipe of varying cross-section

Case study 1.I Munroe Effect-Shaped Charge Explosive

Chapter 2 Flow of Ideal Fluids

2.1 Introduction

2.2 Kelvin's Theorem

2.2.1 Vorticity and Helmholtz's Theorems

2.2.1.1 Simple or rectilinear vortex

2.2.1.2 Vortex sheet

2.3 Irrotational Flow

2.3.1 Crocco's Equation

2.4 Irrotational Flow-Velocity Potential and the Strong Form of Bernoulli's Equation

2.5 Incompressible Flow-Streamfunction

2.5.1 Planar Systems

2.5.2 Axisymmetric Flow-Stokes Streamfunction

2.6 Irrotational Incompressible Flow

2.6.1 Simply and Multiply Connected Spaces

2.7 Induced Velocity

2.7.1 Streamlined Flow around a Body Treated as a Vortex Sheet

2.8 Sources and Sinks

2.8.1 Doublet Sources

2.8.1.1 Doublet sheets

2.8.2 Flow Around a Body Treated as a Source Sheet

2.8.3 Irrotational Incompressible Flow Around a Sphere.

Case study 2.I Rankine Ovals

2.9 Two-Dimensional Flow

2.9.1 Irrotational Incompressible Flow

2.10 Applications of Analytic Functions in Fluid Mechanics

2.10.1 Flow from a Simple Source and a Simple Vortex

2.10.1.1 Free vortex

2.10.1.2 Two-dimensional doublets and vortex loops

2.10.2 Flow Around a Body Treated as a Sheet of Complex Sources and Doublets

Case study 2.II Application of Complex Function Analysis to the Flow around a Thin Wing

2.10.3 Flow Around a Cylinder with Zero Circulation

2.10.4 Flow Around a Cylinder with Circulation

2.10.5 The Flow Around a Corner

2.11 Force on a Body in Steady Two-Dimensional Incompressible Ideal Flow

2.12 Conformal Transforms

Appendix 2.A Drag in Ideal Flow

2.A.1 Helmholtz's Flow and Separation

2.A.2 Lines of Vortices

2.A.2.1 Single infinite row of vortices

2.A.2.2 Two parallel symmetric rows of vortices

2.A.2.3 Two parallel alternating rows of vortices

Chapter 3 Viscous Fluids

3.1 Basic Concept of Viscosity

3.2 Differential Motion of a Fluid Element

3.3 Strain Rate

3.4 Stress

3.5 Viscous Stress

3.5.1 Momentum Equation

3.5.2 Energy Equation

3.5.3 Entropy Creation Rate

3.6 Incompressible Flow-Navier-Stokes Equation

3.6.1 Vorticity Diffusion

3.6.2 Couette or Plane Poiseuille Flow

3.7 Stokes' or Creeping Flow

3.7.1 Stokes' Flow around a Sphere

3.7.1.1 Oseen's correction

3.7.1.2 Proudman and Pearson's solution

3.7.1.3 Lamb's solution for a cylinder

3.8 Dimensionless Analysis and Similarity

3.8.1 Similarity and Modelling

3.8.2 Self-similarity

Appendix 3.A Buckingham's II Theorem and the Complete Set of Dimensionless Products

Chapter 4 Waves and Instabilities in Fluids

4.1 Introduction

4.2 Small-Amplitude Surface Waves

4.2.1 Surface Waves at a Free Boundary of a Finite Medium.

4.2.1.1 Capillary waves

4.2.1.2 Gravity waves

4.2.1.3 Transmission of energy

Case study 4.I The Wake of a Ship-Wave Drag

4.I.i Two-dimensional wake, Kelvin wedge

4.3 Surface Waves in Infinite fluids

4.3.1 Surface Wave at a Contact Discontinuity

4.3.2 Rayleigh-Taylor Instability

4.4 Surface Waves with Velocity Shear Across a Contact Discontinuity

4.5 Shallow Water Waves

4.6 Waves in a Stratified Fluid

4.7 Stability of Laminar Shear Flow

4.8 Nonlinear Instability

Chapter 5 Turbulent Flow

5.1 Introduction

5.1.1 The Generation of Turbulence

5.2 Fully Developed Turbulence

5.3 Turbulent Stress-Reynolds Stresses

5.4 Similarity Model of Shear in a Turbulent Flow-von Karman's Hypothesis

5.5 Velocity Profile near a Wall in Fully Developed Turbulence-Law of the Wall

5.6 Turbulent Flow Through a Duct

5.6.1 Prandtl's Distribution Law

5.6.2 Von Karman's Distribution Law

Case study 5.I Turbulent Flow Through a Horizontal Uniform Pipe

5.I.i Blasius wall stress correlation

Appendix 5.A Prandtl's Mixing Length Model

Chapter 6 Boundary Layer Flow

6.1 Introduction

6.2 The Laminar Boundary Layer in Steady Incompressible Two-Dimensional Flow-Prandtl's Approximation

6.3 Laminar Boundary Layer over an Infinite Flat Plate-Blasius's Solution

6.4 Laminar Boundary Layer-von Karman's Momentum Integral Method

6.4.1 Application to Boundary Layers with an Applied Pressure Gradient

6.5 Boundary Layer Instability and the Onset of Turbulence-Tollmein-Schlichting Instability

6.6 Turbulent Boundary Layer on a Flat Smooth Plate

6.6.1 Turbulent Boundary Layer-Power Law Distribution

6.7 Boundary Layer Separation

6.7.1 Viscous Flow Over a Cylinder

6.8 Drag

Case study 6.I Control of Separation in Aerodynamic Structures

6.9 Laminar Wake.

6.10 Separation in the Turbulent Boundary Layer

6.10.1 Turbulent Wake

Appendix 6.A Singular Perturbation Problems and the Method of Matched Asymptotic Expansion

Chapter 7 Convective Heat Transfer

7.1 Introduction

7.2 Forced Convection

7.2.1 Empirical Heat Transfer Rates from a Flowing Fluid

7.2.1.1 Heat transfer from a fluid flowing along a pipe

7.2.1.2 Heat transfer from a fluid flowing across a pipe

7.2.1.3 Heat exchanger design

7.2.1.4 Logarithmic mean temperature

7.2.2 Friction and Heat Transfer Analogies in Turbulent Flow

7.2.2.1 Reynolds analogy

7.2.2.2 Prandtl-Taylor correction

7.2.2.3 Von Karman's correction

7.2.2.4 Martinelli's correction

7.2.2.5 Colburn's modification

7.3 Heat Transfer in a Laminar Boundary Layer

7.3.1 Boundary Integral Method

7.4 Heat Transfer in a Turbulent Boundary Layer on a Smooth Flat Plate

7.5 Free or Natural Convection

7.5.1 Boussinesq Approximation

7.5.2 Free Convection from a Vertical Plate

7.5.2.1 Similarity analysis

7.5.2.2 Boundary layer integral approximation

7.5.3 Free Convection from a Heated Horizontal Plate

7.5.4 Free Convection between Parallel Horizontal Plates

7.5.4.1 Rayleigh-Be´nard instability

7.5.5 Free Convection around a Heated Horizontal Cylinder

Case study 7.I Positive Column of an Arc

Chapter 8 Compressible Flow and Sound Waves

8.1 Introduction

8.2 Propagation of Small Disturbances

8.2.1 Plane Waves

8.2.2 Energy of Sound Waves

8.3 Reflection and Transmission of a Sound Wave at an Interface

8.4 Spherical Sound Waves

8.5 Cylindrical Sound Waves

Chapter 9 Characteristics and Rarefactions

9.1 Mach Lines and Characteristics

9.2 Characteristics

9.2.1 Uniqueness Theorem

9.2.2 Weak Discontinuities

9.2.3 The Hodograph Plane

9.2.4 Simple Waves.

9.3 One-Dimensional Time-Dependent Expansion

9.3.1 The Centred Rarefaction

9.3.2 Reflected Rarefaction

9.3.3 Isothermal Rarefaction

9.4 Steady Two-Dimensional Irrotational Expansion

9.4.1 Characteristic Invariants

9.4.2 Expanding Supersonic Flow around a Corner

9.4.3 Flow around a Sharp Corner-Centred Rarefaction

9.4.3.1 The complete Prandtl-Meyer flow

9.4.3.2 Weak rarefaction

Chapter 10 Shock Waves

10.1 Introduction

10.2 The Shock Transition and the Rankine-Hugoniot Equations

10.2.1 Rankine-Hugoniot Equations for a Polytropic Gas

10.2.1.1 Strong shocks

10.3 The Shock Adiabat

10.3.1 Weak Shocks and the Entropy Jump

10.4 Shocks in Real Gases

10.5 The Hydrodynamic Structure of the Shock Front

10.5.1 Polytropic Gas Shocks

10.5.1.1 Shocks supported by heat transfer

10.5.2 Weak Shocks

10.6 The Shock Front in Real Gases

10.7 Shock Tubes

10.7.1 Shock Tube Theory

10.8 Shock Interaction

10.8.1 Planar Shock Reflection at a Rigid Wall

10.8.1.1 Collision between two planar shocks

10.8.2 Overtaking Interactions

10.8.2.1 Shock overtaking a shock

10.8.2.2 Shock-rarefaction overtaking

10.8.2.3 Shock interaction with a contact surface

10.9 Oblique Shocks

10.9.1 Large Mach Number

10.9.2 The Shock Polar

10.9.3 Supersonic Flow Incident on a Body

10.10 Adiabatic Compression

Appendix 10.A An Alternative Approach to the General Conservation Law Form of the Fluid Equations

10.A.1 Hyperbolic Equations

10.A.2 Formal Solution

10.A.3 Discontinuities

10.A.4 Weak Solutions

Chapter 11 Aerofoils in Low-Speed Incompressible Flow

11.1 Introduction

11.1.1 Aerofoils

11.2 Two-Dimensional Aerofoils

11.2.1 Kutta Condition

11.3 Generation of Lift on an Aerofoil

11.4 Pitching Moment about the Wing

11.5 Lift from a Thin Wing.

11.6 Application of Conformal Transforms to the Properties of Aerofoils.

Notes:

Includes bibliographical references and index.

Description based on online resource; title from title page (ebrary, viewed April 12, 2013).

Description based on publisher supplied metadata and other sources.

ISBN:

1118574052

9781118574058

1-118-57405-2

1-119-94485-6

1-118-57406-0

1-299-31592-5

1-118-57403-6

OCLC:

831118414