Fluid mechanics is one of the most major areas of successful applications of mathematics. It can be considered as one of branches of applied mathematics. Although fluid motion is concerned in both gas or liquids, as both of them are fluids, this book mainly deals with the motion of liquids in general, and water in particular. The theory of fluid mechanics has grown so considerably in recent years that study of the mechanics of fluids is important in many aspects of our real life. This book on an important area of applied mathematics is a compendium of the work of many pioneering authors and of research works from throughout the author's career. It explains theory clearly and provides applications. It is intended to provide background for young scientists and graduate students as well as applied mathematicians and professional engineers. Some knowledge of vector calculus including the integral theorems such as Green's theorem, Stokes's theorem and divergence theorem is assumed on the part of the reader. Isotropic tensor calculus is used sparingly in some chapters. A familiarity with the Bessel functions, Legendre polynomials and hypergeometric functions is also expected.

Table of Contents:
Contents Chapter 1 Introduction; Preliminary background; Real and ideal fluids; Specification of the motion; Outline of the book Chapter 2 The equations of fluid motion; Introduction; The equations of motion; The mechanical energy equation; The Boussinesq approximation; The Bernoulli equation; The Reynolds stresses; Derivations of equations of motion, Conservation of mass; Euler's equation of motion; Bernoulli's equation revisited; The existence of irrotational motion; Two-dimensional flow; Physical interpretation of velocity potential; Physical interpretation of stream function; Complex potential; Flow along a stream tube; Vortex kinematics; Vortexlines and vortextubes; Circulation; Vortex dynamics; The persistence of circulation; Line vortices and vortex sheets; Navier-Stokes equations of motion; Cartesian Coordinates; Cylindrical polar coordinates; Spherical polar coordinates; Exercises Chapter 3 Mechanics of viscous fluids; Introduction; Motion of a liquid in two-dimensions; Pressure distribution; The drag force on the cylinder; Motion in an axially symmetric 3D-body; Pressure distribution; The drag force on the sphere; Distinction between ideal and real fluids; Drag forces in a real fluid; Secondary Flows; Some exact solutions of Navier-Stokes equations; Steady flow between two-dimensional channel; -c - z; Steady flow through a circular section of radius c; Steady flow through the annular region b - c; Steady flow through an elliptic cylinder; Steady flow in a rectangular section; Steady Couette flow between rotating cylinders; Steady flow between parallel planes; Reynolds theory of lubrication; Steady flow due to a rotating circular disc; Some solutions of Navier-Stokes equations for unsteady flows; Flow due to motion of an infinite plate; Flow due to constant pressure gradient and motion of the plate; Flow due to oscillation of the plate; Very slow motion; Stokes's flow using tensor calculus; Stokes flow using vector calculus; Oseen flow; Exercises Chapter 4 Laminar boundary layers; Introduction; The concept of the boundary layer; Mathematical expression of the boundary-layer thickness d(x); Boundary layer Separation; Derivation of the boundary layer equations for flow along a flat plate; Boundary conditions for steady flow; Boundary layer equations for flow along a curved surface; Boundary-layer thicknesses, skin friction, and energy dissipation; Momentum and energy equations; Momentum integral; Energy integral; The von Mises transformation for steady flow; Analytical solutions of boundary layer equations; Flow along a flat plate at zero incidence in a uniform stream; Method of solution; Steady flow in the boundary layer along a cylinder near the forward stagnation point; Steady flow along a wedge: the Falkner-Skan solutions; Pohlhausen's method; Flow in laminar wakes and jets; Exercises147 Chapter 5 Similarity analysis in fluid flow; Introduction; Concept and definition of heat and mass diffusion; General statement of the problem; Similarity analysis of the basic equations; Use of the similarity variable; Use of the similarity variable; Natural convection flow along a vertical plate; Mathematical formulation; Method of numerical solution; Numerical results; Exercises Chapter 6 Turbulence; Introduction; The mechanism of transition to turbulence; The essential characteristics of turbulence; Reynolds equations for turbulent motion; Turbulent flow between parallel planes; Mixing-length theories of turbulence; Turbulent boundary layers; Correlation theory of homogeneous turbulence; Theoretical development of correlation theory; Isotropic turbulence; Spectral theory of homogeneous turbulence; Probability distribution of u(x); Calculation of the pressure covariance in isotropic turbulence; Exercises