4th Edition

Fundamental Mechanics of Fluids

By I.G. Currie Copyright 2013
    604 Pages 135 B/W Illustrations
    by CRC Press

    Fundamental Mechanics of Fluids, Fourth Edition addresses the need for an introductory text that focuses on the basics of fluid mechanics—before concentrating on specialized areas such as ideal-fluid flow and boundary-layer theory. Filling that void for both students and professionals working in different branches of engineering, this versatile instructional resource comprises five flexible, self-contained sections:

    • Governing Equations deals with the derivation of the basic conservation laws, flow kinematics, and some basic theorems of fluid mechanics.
    • Ideal-Fluid Flow covers two- and three-dimensional potential flows and surface waves.
    • Viscous Flows of Incompressible Fluids discusses exact solutions, low-Reynolds-number approximations, boundary-layer theory, and buoyancy-driven flows.
    • Compressible Flow of Inviscid Fluids addresses shockwaves as well as one- and multidimensional flows.
    • Methods of Mathematical Analysis summarizes some commonly used analysis techniques. Additional appendices offer a synopsis of vectors, tensors, Fourier series, thermodynamics, and the governing equations in the common coordinate systems.

    The book identifies the phenomena associated with the various properties of compressible, viscous fluids in unsteady, three-dimensional flow situations. It provides techniques for solving specific types of fluid-flow problems, and it covers the derivation of the basic equations governing the laminar flow of Newtonian fluids, first assessing general situations and then shifting focus to more specific scenarios.

    The author illustrates the process of finding solutions to the governing equations. In the process, he reveals both the mathematical methodology and physical phenomena involved in each category of flow situation, which include ideal, viscous, and compressible fluids. This categorization enables a clear explanation of the different solution methods and the basis for the various physical consequences of fluid properties and flow characteristics. Armed with this new understanding, readers can then apply the appropriate equation results to deal with the particular circumstances of their own work.

    Part I: Governing Equations

    Basic Conservation Laws

    Statistical and Continuum Methods

    Eulerian and Lagrangian Coordinates

    Material Derivative

    Control Volumes

    Reynolds’ Transport Theorem

    Conservation of Mass

    Conservation of Momentum

    Conservation of Energy

    Discussion of Conservation Equations

    Rotation and Rate of Shear

    Constitutive Equations

    Viscosity Coefficients

    Navier–Stokes Equations

    Energy Equation

    Governing Equations for Newtonian Fluids

    Boundary Conditions

    Flow Kinematics

    Flow Lines

    Circulation and Vorticity

    Stream Tubes and Vortex Tubes

    Kinematics of Vortex Lines

    Special Forms of the Governing Equations

    Kelvin’s Theorem

    Bernoulli Equation

    Crocco’s Equation

    Vorticity Equation


    Part II: Ideal-Fluid Flow

    Two-Dimensional Potential Flows

    Stream Function

    Complex Potential and Complex Velocity

    Uniform Flows

    Source, Sink, and Vortex Flows

    Flow in Sector

    Flow around Sharp Edge

    Flow due to Doublet

    Circular Cylinder without Circulation

    Circular Cylinder with Circulation

    Blasius Integral Laws

    Force and Moment on Circular Cylinder

    Conformal Transformations

    Joukowski Transformation

    Flow around Ellipses

    Kutta Condition and Flat-Plate Airfoil

    Symmetrical Joukowski Airfoil

    Circular-Arc Airfoil

    Joukowski Airfoil

    Schwarz–Christoffel Transformation

    Source in Channel

    Flow through Aperture

    Flow Past Vertical Flat Plate

    Three-Dimensional Potential Flows

    Velocity Potential

    Stokes’ Stream Function

    Solution of Potential Equation

    Uniform Flow

    Source and Sink

    Flow due to Doublet

    Flow near Blunt Nose

    Flow around Sphere

    Line-Distributed Source

    Sphere in Flow Field of Source

    Rankine Solids

    D’Alembert’s Paradox

    Forces Induced by Singularities

    Kinetic Energy of Moving Fluid

    Apparent Mass

    Surface Waves

    General Surface-Wave Problem

    Small-Amplitude Plane Waves

    Propagation of Surface Waves

    Effect of Surface Tension

    Shallow-Liquid Waves of Arbitrary Form

    Complex Potential for Traveling Waves

    Particle Paths for Traveling Waves

    Standing Waves

    Particle Paths for Standing Waves

    Waves in Rectangular Vessels

    Waves in Cylindrical Vessels

    Propagation of Waves at Interface


    Part III: Viscous Flows of Incompressible Fluids

    Exact Solutions

    Couette Flow

    Poiseuille Flow

    Flow between Rotating Cylinders

    Stokes’ First Problem

    Stokes’ Second Problem

    Pulsating Flow between Parallel Surfaces

    Stagnation-Point Flow

    Flow in Convergent and Divergent Channels

    Flow over Porous Wall

    Low Reynolds Number Solutions

    Stokes Approximation

    Uniform Flow




    Rotating Sphere in Fluid

    Uniform Flow Past Sphere

    Uniform Flow Past Circular Cylinder

    Oseen Approximation

    Boundary Layers

    Boundary-Layer Thicknesses

    Boundary-Layer Equations

    Blasius Solution

    Falkner–Skan Solutions

    Flow over a Wedge

    Stagnation-Point Flow

    Flow in Convergent Channel

    Approximate Solution for Flat Surface

    General Momentum Integral

    Kármán–Pohlhausen Approximation

    Boundary-Layer Separation

    Stability of Boundary Layers

    Buoyancy-Driven Flows

    Boussinesq Approximation

    Thermal Convection

    Boundary-Layer Approximations

    Vertical Isothermal Surface

    Line Source of Heat

    Point Source of Heat

    Stability of Horizontal Layers


    Part IV: Compressible Flow of Inviscid Fluids

    Shock Waves

    Propagation of Infinitesimal Disturbances

    Propagation of Finite Disturbances

    Rankine-Hugoniot Equations

    Conditions for Normal Shock Waves

    Normal-Shock-Wave Equations

    Oblique Shock Waves

    One-Dimensional Flows

    Weak Waves

    Weak Shock Tubes

    Wall Reflection of Waves

    Reflection and Refraction at Interface

    Piston Problem

    Finite-Strength Shock Tubes

    Nonadiabatic Flows

    Isentropic-Flow Relations

    Flow through Nozzles

    Multidimensional Flows

    Irrotational Motion

    Janzen–Rayleigh Expansion

    Small-Perturbation Theory

    Pressure Coefficient

    Flow over Wave-Shaped Wall

    Prandtl–Glauert Rule for Subsonic Flow

    Ackeret’s Theory for Supersonic Flows

    Prandtl–Meyer Flow


    Part V: Methods of Mathematical Analysis

    Some Useful Methods of Analysis

    Fourier Series

    Complex Variables

    Separation of Variable Solutions

    Similarity Solutions

    Group Invariance Methods

    Appendix A: Vector Analysis

    Vector Identities

    Integral Theorems

    Orthogonal Curvilinear Coordinates

    Appendix B: Tensors

    Notation and Definition

    Tensor Algebra

    Tensor Operations

    Isotropic Tensors

    Integral Theorems

    Appendix C: Governing Equations

    Cartesian Coordinates

    Cylindrical Coordinates

    Spherical Coordinates

    Appendix D: Fourier Series

    Appendix E: Thermodynamics

    Zeroth Law

    First Law

    Equations of State


    Specific Heats

    Adiabatic, Reversible Processes


    Second Law

    Canonical Equations of State

    Reciprocity Relations


    Iain G. Currie is a Professor Emeritus in the Department of Mechanical and Industrial Engineering at University of Toronto, Canada. He holds a Bachelor’s degree in Mechanical Engineering from the University of Strathclyde, a Master’s degree from the University of British Columbia, and Ph.D. from the California Institute of Technology. He has taught fluid mechanics at the undergraduate and graduate levels for many years. His research involves fluid structure interactions, and he has become involved in studying low Reynolds number flows of both Newtonian and non-Newtonian fluids.

    "There are many graduate-level books in fluid mechanics. Currie’s book is unique in that it covers more topics than usual but the coverage is sufficiently concise to keep the book from becoming a giant one. In doing so, the students are not lost in the details and are kept engaged."
    —Mohamed Gad-el-Hak, Virginia Commonwealth University, Richmond, USA

    "This book is very systematically and clearly presented. ... It is a well-structured book and it provides the fundamental knowledge and materials to be of interest to engineers and researchers."
    —Yitung Chen, University of Nevada Las Vegas, USA

    "The selection and coverage of the topics are very appropriate for a first graduate course in fluid mechanics. The text maintains its tradition as a readable text by an interested reader demanding no elaborate supplements. It also contains an appropriate coverage of mathematical tools in its appendices, so making the text self-contained."
    —Jay M. Khodadadi, Department of Mechanical Engineering, Auburn University, Alabama, USA

    "This book has a unique place among the existing fluid mechanics textbooks. Simplicity and an easy-to-follow approach, combined with a broad coverage of topics, are among the unique features of the book."
    ––Heat Transfer Engineering, 2014