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Overview
Fluid Mechanics
Richard Fitzpatrick
Professor of Physics
The University of Texas at Austin
Overview
Intended Audience
Major Sources
To Do List
Mathematical Models of Fluid Motion
Introduction
What is a Fluid?
Volume and Surface Forces
General Properties of Stress Tensor
Stress Tensor in a Static Fluid
Stress Tensor in a Moving Fluid
Viscosity
Conservation Laws
Mass Conservation
Convective Time Derivative
Momentum Conservation
Navier-Stokes Equation
Energy Conservation
Equations of Incompressible Fluid Flow
Equations of Compressible Fluid Flow
Dimensionless Numbers in Incompressible Flow
Dimensionless Numbers in Compressible Flow
Fluid Equations in Cartesian Coordinates
Fluid Equations in Cylindrical Coordinates
Fluid Equations in Spherical Coordinates
Exercises
Hydrostatics
Introduction
Hydrostatic Pressure
Buoyancy
Equilibrium of Floating Bodies
Vertical Stability of Floating Bodies
Angular Stability of Floating Bodies
Determination of Metacentric Height
Energy of a Floating Body
Curve of Buoyancy
Rotational Hydrostatics
Equilibrium of a Rotating Liquid Body
Maclaurin Spheroids
Jacobi Ellipsoids
Roche Ellipsoids
Exercises
Surface Tension
Introduction
Young-Laplace Equation
Spherical Interfaces
Capillary Length
Angle of Contact
Jurin's Law
Capillary Curves
Axisymmetric Soap-Bubbles
Exercises
Incompressible Inviscid Fluid Dynamics
Introduction
Streamlines, Stream Tubes, and Stream Filaments
Bernoulli's Theorem
Vortex Lines, Vortex Tubes, and Vortex Filaments
Circulation and Vorticity
Kelvin Circulation Theorem
Irrotational Flow
Two-Dimensional Flow
Two-Dimensional Uniform Flow
Two-Dimensional Sources and Sinks
Two-Dimensional Vortex Filaments
Two-Dimensional Irrotational Flow in Cylindrical Coordinates
Inviscid Flow Past a Cylindrical Obstacle
Inviscid Flow Past a Semi-Infinite Wedge
Inviscid Flow Over a Semi-Infinite Wedge
Velocity Potentials and Stream Functions
Exercises
2D Potential Flow
Introduction
Complex Functions
Cauchy-Riemann Relations
Complex Velocity Potential
Complex Velocity
Method of Images
Conformal Maps
Complex Line Integrals
Theorem of Blasius
Exercises
Incompressible Boundary Layers
Introduction
No Slip Condition
Boundary Layer Equations
Self-Similar Boundary Layers
Boundary Layer on a Flat Plate
Wake Downstream of a Flat Plate
Von Kármán Momentum Integral
Boundary Layer Separation
Criterion for Boundary Layer Separation
Approximate Solutions of Boundary Layer Equations
Exercises
Incompressible Aerodynamics
Introduction
Theorem of Kutta and Zhukovskii
Cylindrical Airfoils
Zhukovskii's Hypothesis
Vortex Sheets
Induced Flow
Three-Dimensional Airfoils
Aerodynamic Forces
Ellipsoidal Airfoils
Simple Flight Problems
Exercises
Incompressible Viscous Flow
Introduction
Flow Between Parallel Plates
Flow Down an Inclined Plane
Poiseuille Flow
Taylor-Couette Flow
Flow in Slowly-Varying Channels
Lubrication Theory
Stokes Flow
Axisymmetric Stokes Flow
Axisymmetric Stokes Flow Around a Solid Sphere
Axisymmetric Stokes Flow In and Around a Fluid Sphere
Exercises
Waves in Incompressible Fluids
Introduction
Gravity Waves
Gravity Waves in Deep Water
Gravity Waves in Shallow Water
Energy of Gravity Waves
Wave Drag on Ships
Ship Wakes
Gravity Waves in a Flowing Fluid
Gravity Waves at an Interface
Steady Flow over a Corrugated Bottom
Surface Tension
Capillary Waves
Capillary Waves at an Interface
Wind Driven Waves in Deep Water
Exercises
Equilibrium of Compressible Fluids
Introduction
Isothermal Atmosphere
Adiabatic Atmosphere
Atmospheric Stability
Eddington Solar Model
Exercises
Vectors and Vector Fields
Introduction
Scalars and Vectors
Vector Algebra
Cartesian Components of a Vector
Coordinate Transformations
Scalar Product
Vector Area
Vector Product
Rotation
Scalar Triple Product
Vector Triple Product
Vector Calculus
Line Integrals
Vector Line Integrals
Surface Integrals
Vector Surface Integrals
Volume Integrals
Gradient
Grad Operator
Divergence
Laplacian Operator
Curl
Useful Vector Identities
Exercises
Cartesian Tensors
Introduction
Tensors and Tensor Notation
Tensor Transformation
Tensor Fields
Isotropic Tensors
Exercises
Non-Cartesian Coordinates
Introduction
Orthogonal Curvilinear Coordinates
Cylindrical Coordinates
Spherical Coordinates
Exercises
Calculus of Variations
Euler-Lagrange Equation
Conditional Variation
Multi-Function Variation
Exercises
Ellipsoidal Potential Theory
About this document ...
Richard Fitzpatrick 2012-04-27
