# Fluid Mechanics

## 5th Edition

**Authors:**Pijush Kundu Ira Cohen David Dowling

**eBook ISBN:**9780123821010

**Hardcover ISBN:**9780123821003

**Imprint:**Academic Press

**Published Date:**8th September 2011

**Page Count:**920

## Description

Fluid mechanics, the study of how fluids behave and interact under various forces and in various applied situations—whether in the liquid or gaseous state or both—is introduced and comprehensively covered in this widely adopted text. Revised and updated by Dr. David Dowling, *Fluid Mechanics, 5e *is suitable for both a first or second course in fluid mechanics at the graduate or advanced undergraduate level.

## Key Features

- Along with more than 100 new figures, the text has been reorganized and consolidated to provide a better flow and more cohesion of topics.
- Changes made to the book's pedagogy in the first several chapters accommodate the needs of students who have completed minimal prior study of fluid mechanics.
- More than 200 new or revised end-of-chapter problems illustrate fluid mechanical principles and draw on phenomena that can be observed in everyday life

## Readership

Senior undergraduate/graduate students in mechanical, civil, aerospace, chemical and biomedical engineering; Senior undergraduate/graduate students in physics, chemistry, meteorology, geophysics, and applied mathematics

## Table of Contents

Founders of Modern Fluid Dynamics

Dedication

In Memory of Pijush Kundu

In Memory of Ira Cohen

About the Third Author

About the DVD

Preface

Companion Website

Acknowledgments

Nomenclature

Notation

Symbols

Chapter 1. Introduction

Chapter Objectives

1.1 Fluid Mechanics

1.2 Units of Measurement

1.3 Solids, Liquids, and Gases

1.4 Continuum Hypothesis

1.5 Molecular Transport Phenomena

1.6 Surface Tension

1.7 Fluid Statics

1.8 Classical Thermodynamics

1.9 Perfect Gas

1.10 Stability of Stratified Fluid Media

1.11 Dimensional Analysis

Exercises

Literature Cited

Supplemental Reading

Chapter 2. Cartesian Tensors

Chapter Objectives

2.1 Scalars, Vectors, Tensors, Notation

2.2 Rotation of Axes: Formal Definition of a Vector

2.3 Multiplication of Matrices

2.4 Second-Order Tensors

2.5 Contraction and Multiplication

2.6 Force on a Surface

2.7 Kronecker Delta and Alternating Tensor

2.8 Vector, Dot, and Cross Products

2.9 Gradient, Divergence, and Curl

2.10 Symmetric and Antisymmetric Tensors

2.11 Eigenvalues and Eigenvectors of a Symmetric Tensor

2.12 Gauss’ Theorem

2.13 Stokes’ Theorem

2.14 Comma Notation

Exercises

Literature Cited

Supplemental Reading

Chapter 3. Kinematics

Chapter Objectives

3.1 Introduction and Coordinate Systems

3.2 Particle and Field Descriptions of Fluid Motion

3.3 Flow Lines, Fluid Acceleration, and Galilean Transformation

3.4 Strain and Rotation Rates

3.5 Kinematics of Simple Plane Flows

3.6 Reynolds Transport Theorem

Exercises

Literature Cited

Supplemental Reading

Chapter 4. Conservation Laws

Chapter Objectives

4.1 Introduction

4.2 Conservation of Mass

4.3 Stream Functions

4.4 Conservation of Momentum

4.5 Constitutive Equation for a Newtonian Fluid

4.6 Navier-Stokes Momentum Equation

4.7 Noninertial Frame of Reference

4.8 Conservation of Energy

4.9 Special Forms of the Equations

4.10 Boundary Conditions

4.11 Dimensionless Forms of the Equations and Dynamic Similarity

Exercises

Literature Cited

Supplemental Reading

Chapter 5. Vorticity Dynamics

Chapter Objectives

5.1 Introduction

5.2 Kelvin’s Circulation Theorem

5.3 Helmholtz’s Vortex Theorems

5.4 Vorticity Equation in a Nonrotating Frame

5.5 Velocity Induced by a Vortex Filament: Law of Biot and Savart

5.6 Vorticity Equation in a Rotating Frame

5.7 Interaction of Vortices

5.8 Vortex Sheet

Exercises

Literature Cited

Supplemental Reading

Chapter 6. Ideal Flow

Chapter Objectives

6.1 Relevance of Irrotational Constant-Density Flow Theory

6.2 Two-Dimensional Stream Function and Velocity Potential

6.3 Construction of Elementary Flows in Two Dimensions

6.4 Complex Potential

6.5 Forces on a Two-Dimensional Body

6.6 Conformal Mapping

6.7 Numerical Solution Techniques in Two Dimensions

6.8 Axisymmetric Ideal Flow

6.9 Three-Dimensional Potential Flow and Apparent Mass

6.10 Concluding Remarks

Exercises

Literature Cited

Supplemental Reading

Chapter 7. Gravity Waves

Chapter Objectives

7.1 Introduction

7.2 Linear Liquid-Surface Gravity Waves

7.3 Influence of Surface Tension

7.4 Standing Waves

7.5 Group Velocity, Energy Flux, and Dispersion

7.6 Nonlinear Waves in Shallow and Deep Water

7.7 Waves on a Density Interface

7.8 Internal Waves in a Continuously Stratified Fluid

Exercises

Literature Cited

Chapter 8. Laminar Flow

Chapter Objectives

8.1 Introduction

8.2 Exact Solutions for Steady Incompressible Viscous Flow

8.3 Elementary Lubrication Theory

8.4 Similarity Solutions for Unsteady Incompressible Viscous Flow

8.5 Flow Due to an Oscillating Plate

8.6 Low Reynolds Number Viscous Flow Past a Sphere

8.7 Final Remarks

Exercises

Literature Cited

Supplemental Reading

Chapter 9. Boundary Layers and Related Topics

Chapter Objectives

9.1 Introduction

9.2 Boundary-Layer Thickness Definitions

9.3 Boundary Layer on a Flat Plate: Blasius Solution

9.4 Falkner-Skan Similarity Solutions of the Laminar Boundary-Layer Equations

9.5 Von Karman Momentum Integral Equation

9.6 Thwaites’ Method

9.7 Transition, Pressure Gradients, and Boundary-Layer Separation

9.8 Flow Past a Circular Cylinder

9.9 Flow Past a Sphere and the Dynamics of Sports Balls

9.10 Two-Dimensional Jets

9.11 Secondary Flows

Exercises

Literature Cited

Supplemental Reading

Chapter 10. Computational Fluid Dynamics

Chapter Objectives

10.1 Introduction

10.2 Finite-Difference Method

10.3 Finite-Element Method

10.4 Incompressible Viscous Fluid Flow

10.5 Three Examples

10.6 Concluding Remarks

Exercises

Literature Cited

Supplemental Reading

Chapter 11. Instability

Chapter Objectives

11.1 Introduction

11.2 Method of Normal Modes

11.3 Kelvin-Helmholtz Instability

11.4 Thermal Instability: The Bénard Problem

11.5 Double-Diffusive Instability

11.6 Centrifugal Instability: Taylor Problem

11.7 Instability of Continuously Stratified Parallel Flows

11.8 Squire’s Theorem and the Orr-Sommerfeld Equation

11.9 Inviscid Stability of Parallel Flows

11.10 Results for Parallel and Nearly Parallel Viscous Flows

11.11 Experimental Verification of Boundary-Layer Instability

11.12 Comments on Nonlinear Effects

11.13 Transition

11.14 Deterministic Chaos

Exercises

Literature Cited

Chapter 12. Turbulence

Chapter Objectives

12.1 Introduction

12.2 Historical Notes

12.3 Nomenclature and Statistics for Turbulent Flow

12.4 Correlations and Spectra

12.5 Averaged Equations of Motion

12.6 Homogeneous Isotropic Turbulence

12.7 Turbulent Energy Cascade and Spectrum

12.8 Free Turbulent Shear Flows

12.9 Wall-Bounded Turbulent Shear Flows

12.10 Turbulence Modeling

12.11 Turbulence in a Stratified Medium

12.12 Taylor’s Theory of Turbulent Dispersion

12.13 Concluding Remarks

Exercises

Literature Cited

Supplemental Reading

Chapter 13. Geophysical Fluid Dynamics

Chapter Objectives

13.1 Introduction

13.2 Vertical Variation of Density in the Atmosphere and Ocean

13.3 Equations of Motion

13.4 Approximate Equations for a Thin Layer on a Rotating Sphere

13.5 Geostrophic Flow

13.6 Ekman Layer at a Free Surface

13.7 Ekman Layer on a Rigid Surface

13.8 Shallow-Water Equations

13.9 Normal Modes in a Continuously Stratified Layer

13.10 High- and Low-Frequency Regimes in Shallow-Water Equations

13.11 Gravity Waves with Rotation

13.12 Kelvin Wave

13.13 Potential Vorticity Conservation in Shallow-Water Theory

13.14 Internal Waves

13.15 Rossby Wave

13.16 Barotropic Instability

13.17 Baroclinic Instability

13.18 Geostrophic Turbulence

Exercises

Literature Cited

Supplemental Reading

Chapter 14. Aerodynamics

Chapter Objectives

14.1 Introduction

14.2 Aircraft Terminology

14.3 Characteristics of Airfoil Sections

14.4 Conformal Transformation for Generating Airfoil Shapes

14.5 Lift of a Zhukhovsky Airfoil

14.6 Elementary Lifting Line Theory for Wings of Finite Span

14.7 Lift and Drag Characteristics of Airfoils

14.8 Propulsive Mechanisms of Fish and Birds

14.9 Sailing against the Wind

Exercises

Literature Cited

Supplemental Reading

Chapter 15. Compressible Flow

Chapter Objectives

15.1 Introduction

15.2 Acoustics

15.3 Basic Equations for One-Dimensional Flow

15.4 Reference Properties in Compressible Flow

15.5 Area-Velocity Relationship in One-Dimensional Isentropic Flow

15.6 Normal Shock Waves

15.7 Operation of Nozzles at Different Back Pressures

15.8 Effects of Friction and Heating in Constant-Area Ducts

15.9 Pressure Waves in Planar Compressible Flow

15.10 Thin Airfoil Theory in Supersonic Flow

Exercises

Literature Cited

Supplemental Reading

Chapter 16. Introduction to Biofluid Mechanics

Chapter Objectives

16.1 Introduction

16.2 The Circulatory System in the Human Body

16.3 Modeling of Flow in Blood Vessels

16.4 Introduction to the Fluid Mechanics of Plants

Exercises

Acknowledgment

Literature Cited

Supplemental Reading

Appendix A. Conversion Factors, Constants, and Fluid Properties

A.1 Conversion Factors

A.2 Physical Constants

A.3 Properties of Pure Water at Atmospheric Pressure

A.4 Properties of Dry Air at Atmospheric Pressure

A.5 The Standard Atmosphere

Appendix B. Mathematical Tools and Resources

B.1 Partial and Total Differentiation

B.2 Changing Independent Variables

B.3 Basic Vector Calculus

B.4 The Dirac Delta function

B.5 Common Three-Dimensional Coordinate Systems

B.6 Equations in Curvilinear Coordinate Systems

Appendix C. Founders of Modern Fluid Dynamics

Ludwig Prandtl (1875–1953)

Geoffrey Ingram Taylor (1886–1975)

Appendix D. Visual Resources

Index

## Details

- No. of pages:
- 920

- Language:
- English

- Copyright:
- © Academic Press 2012

- Published:
- 8th September 2011

- Imprint:
- Academic Press

- eBook ISBN:
- 9780123821010

- Hardcover ISBN:
- 9780123821003

## About the Authors

### Pijush Kundu

### Affiliations and Expertise

Nova University, U.S.A.(deceased)

### Ira Cohen

### Affiliations and Expertise

University of Pennsylvania, U.S.A. (deceased)

### David Dowling

While in college, David R. Dowling held summer positions at Hughes Aircraft Co. and the Los Angeles Air Force Station. He completed his doctorate in 1988 at Graduate Aeronautical Laboratories of the California Institute of Technology and moved north to Seattle to accomodate his wife's career in medicine. While there, he worked for a year in the laser technology group at Boeing Aerospace, and then for almost three years as a post-doc at the Applied Physics Laboratory of the University of Washington. In 1992, he accepted a faculty position at the University of Michigan. Prof. Dowling is currently conducting research in acoustics and fluid mechanics. He is a fellow of the Acoustical Society of America, a member of the American Society of Mechanical Engineers, and a member of the American Physical Society. He is a US citizen.

Positions at the University of Michigan :

Professor, Sept 2005 to Present

Associate Professor, Sept 1999 thru August 2005

Assistant Professor, Sept 1992 thru August 1999

Visiting Assistant Professor, July 1992 thru August 1992

### Affiliations and Expertise

Professor, Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI