Fluid Mechanics for Mechanical Engineers

Preface
Contents
Part I Fundamental Concepts and Scaling Laws
1 Introduction and Fundamentals
	1.1 Physical Properties of Fluids
		1.1.1 Density
		1.1.2 Viscosity
		1.1.3 Viscosity Measurement
		1.1.4 Surface Tension
	1.2 Vector Notation
		1.2.1 Vector and Tensor Algebra
		1.2.2 Differential Operators
		1.2.3 Examples
	1.3 Fluid Statics
		1.3.1 Forces Acting on a Quiescent Fluid (Pascal\'s Law)
		1.3.2 Pressure Distribution in a Quiescent Fluid
		1.3.3 Pressure Distribution in a Compressible Fluid
		1.3.4 Pressure Forces on Solid Surfaces
		1.3.5 Archimedes\' Principle
		1.3.6 Hydraulic Transmission of Forces
		1.3.7 Pressure Measurement
		1.3.8 Examples
		1.3.9 Problems
2 Physical Models for Friction Forces
	2.1 Dimensional Analysis
		2.1.1 Introduction
		2.1.2 Buckingham\'s Theorem
	2.2 Friction Forces for Flows in Pipelines
		2.2.1 Flow in Smooth Pipes
		2.2.2 Physical Meaning of the Reynolds Number
		2.2.3 Power and Dissipation
		2.2.4 Flows in Commercial Pipes
		2.2.5 Flow in Pipes of Non-Circular Cross-Section
		2.2.6 Examples
	2.3 Friction Forces for Flow Past a Sphere
		2.3.1 Steady Flow Past a Sphere
		2.3.2 Unsteady Flow Past a Sphere
		2.3.3 Examples
	2.4 Flow in Porous Beds
Part II Conservation Equations
3 Differential Form of Conservation Equations
	3.1 Conservation Law
	3.2 Mass Conservation and Continuity Equation
	3.3 Material Derivative (or Lagrangian)
		3.3.1 Examples
	3.4 Momentum Conservation and Navier–Stokes Equations
		3.4.1 Eulerian Derivation
		3.4.2 Lagrangian Derivation
		3.4.3 Stress Tensor
		3.4.4 Navier–Stokes Equations for Newtonian Fluids
		3.4.5 Navier–Stokes Equations for Incompressible Fluids
	3.5 Energy Conservation
		3.5.1 Mechanical Energy Equation
		3.5.2 Bernoulli Equation
		3.5.3 Examples
4 Exact Solutions for Unidirectional Steady Flows
	4.1 Unidirectional Flows
		4.1.1 Plane Couette Flow
		4.1.2 Plane Poiseuille Flow
		4.1.3 Poiseuille Flow in a Pipe
		4.1.4 Torsional Flow
		4.1.5 Unidirectional Free-Surface Flow
		4.1.6 Examples
5 Approximate Solutions for Low Reynolds Number Flows
	5.1 Dimensionless Form of the Conservation Equations
	5.2 Creeping Flow
		5.2.1 Flow Between Coaxial Disks in Relative Rotation
		5.2.2 Flow Past a Sphere (Stokes Problem)
		5.2.3 Examples
	5.3 Lubrication Theory
		5.3.1 Analysis of the Navier-Stokes Equations
		5.3.2 Velocity Distribution
		5.3.3 Pressure Distribution
		5.3.4 Calculation of Pressure Forces and Shear Forces
		5.3.5 Examples
6 Approximate Solutions for High Reynolds Number Flows
	6.1 Potential Flow
	6.2 Vorticity
		6.2.1 Examples
	6.3 Vorticity Transport Equation
		6.3.1 Three-Dimensional Steady Flow
		6.3.2 Self-amplification and Distribution of Vorticity
		6.3.3 Baroclinicity (Density Variation Effects)
		6.3.4 Two-Dimensional Steady Flow
	6.4 Stream Function
		6.4.1 Streamlines
		6.4.2 Examples
	6.5 Velocity Potential
		6.5.1 Iso-Potential Lines
		6.5.2 Complex Velocity Potential
		6.5.3 Examples
	6.6 D\'Alembert\'s Paradox
		6.6.1 Examples
	6.7 Examples of Plane Potential Flows
		6.7.1 Uniform Flow
		6.7.2 Source and Sink
		6.7.3 Free (or Irrotational) Vortex
		6.7.4 Dipole and Doublet
		6.7.5 Flow Around a Rankine Oval
		6.7.6 Flow Around a Rotating Cylinder
7 Boundary Layers and Self-Similar Solutions
	7.1 Flows with Self-Similar Solution
	7.2 Boundary Layer Equations
	7.3 Boundary Layer on a Flat Plate
		7.3.1 Examples
	7.4 Boundary Layer on a Wall Suddenly Set into Motion
		7.4.1 Examples
	7.5 Separation of the Boundary Layer
	7.6 Plane Free Jet
8 Introduction to Turbulent Flows
	8.1 Laminar and Turbulent Flows
	8.2 Reynolds Procedure
		8.2.1 Time Averages
		8.2.2 Time-Averaged Continuity Equation
		8.2.3 Time-Avaraged Navier-Stokes Equations
		8.2.4 Reynolds Stresses
		8.2.5 Turbulent (or Eddy) Viscosity
		8.2.6 Prandtl\'s Mixing Length Model
	8.3 Turbulent Pipe Flow
		8.3.1 Examples
	8.4 Turbulent Boundary Layer
Part III  Design of One-Dimensional Flow Systems
9 Macroscopic Balance Equations
	9.1 Mass Conservation
	9.2 Energy Conservation
		9.2.1 Bernoulli Equation
	9.3 Conservation of Momentum
10 Analysis and Design of One-Dimensional Flow Systems
	10.1 Velocity Measurement
		10.1.1 Pitot Tube
		10.1.2 Examples
	10.2 Flowrate Measurement
		10.2.1 Calibrated Orifice
		10.2.2 Venturi Tube (Venturimeter)
		10.2.3 Rotameter
		10.2.4 Examples
	10.3 Examples of One-Dimensional Flow Systems
		10.3.1 Pressure Loss Due to a Sudden Section Enlargement
		10.3.2 Force on a Pipe Bend
		10.3.3 Jet Pump
		10.3.4 Flow Distribution in Manifolds
		10.3.5 Examples
11 Fluid Transport in Piping Systems
	11.1 Distributed and Localised Losses
		11.1.1 Examples
	11.2 Minimum Cost Pipe System Design
		11.2.1 Examples
Appendix A Suggested Readings
Appendix B Equations in Cartesian, Cylindrical and Spherical Coordinates
B.1 Continuity Equation
B.2 Cauchy Equations
B.2.1 Cauchy Equations in Cartesian Coordinates
B.2.2 Cauchy Equations in Cylindrical Coordinates
B.2.3 Cauchy Equations in Spherical Coordinates
B.3 Components of the Stress Tensor
B.3.1 Cartesian Coordinates
B.3.2 Cylindrical Coordinates
B.3.3 Spherical Coordinates
B.4 Navier-Stokes Equations
B.4.1 Navier-Stokes Equations in Cartesian Coordinates
B.4.2 Navier-Stokes Equations in Cylindrical Coordinates
B.4.3 Navier Stokes Equations in Spherical Coordinates
B.5 Components of the Vorticity Vector
B.5.1 Cartesian Coordinates
B.5.2 Cylindrical Coordinates
B.5.3 Spherical Coordinates