Fluid mechanics / created by Pijush K. Kundu, Ira M. Cohen and David R. Dowling

Includes bibliographical references and index.

1. Introduction
Fluid mechanics
Units of measurement
Solids, liquids, and gases
Continuum hypothesis
Molecular transport phenomena
Surface tension
Fluid statics
Classical thermodynamics
Perfect gas
Stability of stratified fluid media
Dimensional analysis
2. Cartesian tensors
Scalars, vectors, tensors, notation
Rotation of axes : formal definition of a vector
Multiplication of matrices
Second-order tensors
Contraction and multiplication
Force on a surface
Kronecker Delta and alternating tensor
Vector dot and cross products
Gradient, divergence, and curl
Symmetric and antisymmetric tensors
Eigenvalues and Eigenvectors of a symmetric tensor
Gauss' Theorem
Stokes' Theorem
3. Kinematics
Introduction and coordinate systems
Particle and field descriptions of fluid motion
Flow lines, fluid acceleration, and Galilean transformation
Strain and rotation rates
Kinematics of simple plane flows
Reynolds Transport Theorem
4. Conservation laws
Introduction
Conservation of mass
Stream functions
Conservation of momentum
constitutive equation for a Newtonian fluid
Navier-Stokes momentum equation
Noninertial frame of reference
Conservation of energy
Special forms of the equation
Boundary conditions
Dimensionless forms of the equations and dynamic similarity
5. Vorticity dynamics
Kelvin's and Helmholtz's Theorems
Vorticity equation in an inertial frame of reference
Velocity induced by a vortex filament : Law of Biot and Savart
Vorticity equation in a rotating frame of reference
Interaction of vortices
Vortex sheet
6. Computational fluid dynamics
The Advection-Diffusion equation
Incompressible flows in rectangular domains
Flow in complex domains
Velocity-pressure method for compressible flow
7. Ideal flow
Relevance of Irrotational Constant-Density Flow Theory
Two-dimensional stream function and velocity potential
Construction of elementary flows in two dimensions
Complex potential
Forces on a two-dimensional body
Conformal mapping
Axissymmetric ideal flow
Three-dimensional potential flow and apparent mass
8. Gravity waves
Linear liquid-surface gravity waves
Influence of surface tension
Standing waves
Group velocity, energy flux, and dispersion
Nonlinear waves in shallow and deep water
Waves on a density interface
Internal waves in a continuously stratified fluid
9. Laminar flow
Exact solutions for steady incompressible viscous flow
Elementary Lubrication Theory
Similarity solutions for unsteady incompressible viscous flow
Flows with oscillations
Low Reynolds Number viscous flow past a sphere
10. Boundary layers and related topics
Boundary-layer thickness definitions
Boundary layer on a flat plate : Blasius Solution
Falkner-Skan similarity solutions of the laminar boundary-layer equations
Von Karman Momentum Integral Equation
Thwaites' Method
Transition, pressure gradients, and boundary-layer separation
Flow past a circular cylinder
Flow past a sphere and the dynamics of sports balls
Two-dimensional jets
Secondary flows
11. Method of normal modes
Kelvin-Helmholtz instability
Thermal instability : the Bénard problem
Double-diffusive instability
Centrifugal instability : Taylor problem
Instability of continuously stratified parallel flows
Squire's theorem and the Orr-Sommerfeld equation
Inviscid stability of parallel flows
Experimental verification of boundary-layer instability
Comments on nonlinear effects
Transition
Deterministic chaos
12. Turbulence- - Nomenclature and statistics for turbulent flow
Correlations and spectra
Averaged equations of motion
Homogeneous isotropic turbulence
Turbulent energy cascade and spectrum
Free turbulent shear flows - Wall-bounded turbulent shear flows
Turbulence modeling
Taylor's Theory of Turbulent Dispersion
13. Geophysical fluid dynamics
Vertical variation of density in the atmosphere and ocean
Equations of motion for geophysical flows
Geostrophic flow
Ekman layers
Shallow-water equations
Normal modes in a continuously stratified layer
High- and low-frequency regimes in shallow-water equations
Gravity waves with rotation
Kelvin wave
Potential vorticity conservation in Shallow-Water Theory
INternal waves
Rossby wave
Barotropic instability
Baroclinic instability
Geostrophic turbulence
14. Aerodynamics
Aircraft terminology
Characteristics of airfoil sections
Conformal transformation for generating airfoil shapes
Life of Zhukhovsky Airfoil
Elementary lifting line theory for wings of finite span
Life and drag characteristics of airfoils
Propulsive mechanisms of fish and birds
Sailing against the wind
15. Compressible flow
Acoustics
One-dimensional steady isentropic compressible flow in variable-area ducts
Normal shock waves
Operation of nozzles at different back pressures
Effects of friction and heating in constant-area ducts
ONe-dimensional unsteady compressible flow in constant-area ducts
Two-dimensional steady compressible flow
Thin-airfoil theory in supersonic flow
16. Introduction to biofluid mechanics (online chapter) / Portonovo S. Ayyaswamy
The circulatory system in the human body
Modeling of flow in blood vessels
Introduction to the fluid mechanics of plants

Fluid mechanics, understanding and applying the principles of how motions and forces act upon fluids such as gases and liquids, is introduced and comprehensively covered in this text