# Fundamental Mechanics of Fluids

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## Book Description

**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:

deals with the derivation of the basic conservation laws, flow kinematics, and some basic theorems of fluid mechanics.*Governing Equations*covers two- and three-dimensional potential flows and surface waves.**Ideal-Fluid Flow**discusses exact solutions, low-Reynolds-number approximations, boundary-layer theory, and buoyancy-driven flows.**Viscous Flows of Incompressible Fluids**addresses shockwaves as well as one- and multidimensional flows.**Compressible Flow of Inviscid Fluids**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.**Methods of Mathematical Analysis**

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.

## Table of Contents

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__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

Doublet

Rotlet

Stokeslet

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

Enthalpy

Specific Heats

Adiabatic, Reversible Processes

Entropy

Second Law

Canonical Equations of State

Reciprocity Relations

## Author(s)

### Biography

**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.

## Reviews

"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