Fundamental Mechanics of Fluids 3rd Edition by Kihong Shin, Prof Joseph Hammond ISBN 0470511885 9780470511886

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ISBN 10: 0470511885 
ISBN 13: 9780470511886
Author: Kihong Shin, Prof Joseph Hammond

Fundamental Mechanics of Fluids 3rd Table of contents:

Part I Governing Equations
Governing Equations
1 Basic Conservation Laws
1.1 Statistical and Continuum Methods
FIGURE 1.1 Individual molecule in small volume ΔV having mass Δm and velocity v.
1.2 Eulerian and Lagrangian Coordinates
1.3 Material Derivative
1.4 Control Volumes
1.5 Reynolds’ Transport Theorem
FIGURE 1.2 (a) Arbitrarily shaped control volume at times t and t + δt and (b) superposition of the control volumes at these times showing element δV of the volume change.
1.6 Conservation of Mass
FIGURE 1.3 Flow of density-stratified fluid in which Dρ/Dt = 0 but for which ∂ρ/∂x ≠ 0 and ∂ρ/∂y ≠ 0.
1.7 Conservation of Momentum
FIGURE 1.4 Representation of nine components of stress that may act at a point in a fluid.
1.8 Conservation of Energy
1.9 Discussion of Conservation Equations
1.10 Rotation and Rate of Shear
FIGURE 1.5 Infinitesimal element of fluid at time t = 0 (indicated by ABCD) and at time t = δt (indicated by A′B′C′D′).
1.11 Constitutive Equations
1.12 Viscosity Coefficients
1.13 Navier–Stokes Equations
1.14 Energy Equation
1.15 Governing Equations for Newtonian Fluids
1.16 Boundary Conditions
PROBLEMS
2 Flow Kinematics
2.1 Flow Lines
2.1.1 Streamlines
FIGURE 2.1 Comparison of the streamline through the point (1, 1) at t = 0 with the pathline of a particle that passed through the point (1, 1) at t = 0 and the streakline through the point (1, 1) at t = 0 for the flow field u = x(1 + 2t), v = y, w = 0.
2.1.2 Pathlines
2.1.3 Streaklines
2.2 Circulation and Vorticity
2.3 Stream Tubes and Vortex Tubes
FIGURE 2.2 (a) Stream tube and (b) vortex tube subtended by a contour of area A1 in a flow field.
2.4 Kinematics of Vortex Lines
PROBLEMS
3 Special Forms of the Governing Equations
3.1 Kelvin’s Theorem
3.2 Bernoulli Equation
3.3 Crocco’s Equation
3.4 Vorticity Equation
FIGURE 3.1 Results from the large eddy numerical simulation of a liquid jet in a gaseous cross flow showing the deformation and breakup of the liquid jet. The jet velocity is 40 m/s, its viscosity is 10−4 Pa-s, and its density is 14.4 kg/m3. The cross flow bulk velocity is 40 m/s, the gas viscosity is 10−5 Pa-s, and its density is 1.2 kg/m3.
FIGURE 3.2 Results from numerical calculations showing droplet dynamics and spray formation from an annular nozzle with outer and inner co-flowing gas. The droplets break up into smaller ones due to the high velocity gaseous flow, generating a spray of smaller droplets. The outer gas velocity is 140 m/s; the inner gas velocity, as well as the velocity of the droplets, is 40 m/s.
PROBLEMS
Further Reading—Part I
Part II Ideal-Fluid Flow
Ideal-Fluid Flow
II.1 Governing Equations and Boundary Conditions
II.2 Potential Flows
4 Two-Dimensional Potential Flows
4.1 Stream Function
FIGURE 4.1 Two streamlines showing the components of the volumetric flow rate across an element of control surface joining the streamlines.
4.2 Complex Potential and Complex Velocity
FIGURE 4.2 Decomposition of velocity vector OP into its Cartesian components (u, v) and its cylindrical components (uR, uθ).
4.3 Uniform Flows
FIGURE 4.3 Uniform flow in (a) x direction, (b) y direction, and (c) angle α to x direction.
4.4 Source, Sink, and Vortex Flows
FIGURE 4.4 Streamlines (shown solid) and equipotential lines (shown dashed) for (a) source flow and (b) vortex flow in the positive sense.
4.5 Flow in Sector
FIGURE 4.5 Streamlines (shown solid) and equipotential lines (shown dashed) for flow in a sector.
4.6 Flow around Sharp Edge
FIGURE 4.6 Streamlines (shown solid) and equipotential lines (shown dashed) for flow around a sharp edge.
4.7 Flow due to Doublet
FIGURE 4.7 (a) Superposition of a source and a sink leading to (b) streamline pattern for the limit ε → 0 with mε = constant.
4.8 Circular Cylinder without Circulation
FIGURE 4.8 (a) Flow field represented by the complex potential F(z) = U(z + a2/z) and (b) flow around a circular cylinder of radius a.
4.9 Circular Cylinder with Circulation
FIGURE 4.9 Flow of approach velocity U around a circular cylinder of radius a having a negative bound circulation of magnitude Γ for (a) 0 < Γ/(4πUa) 1.
4.10 Blasius Integral Laws
FIGURE 4.10 Arbitrarily shaped body enclosed by an arbitrary control surface. X, Y, and M are the drag, lift, and moment acting on the body, respectively.
4.11 Force and Moment on Circular Cylinder
4.12 Conformal Transformations
FIGURE 4.11 Original and mapped planes for the mapping ζ = f(z) where f is an analytic function.
FIGURE 4.12 Arbitrary closed contour C with an element dl resolved into its coordinate components.
4.13 Joukowski Transformation
FIGURE 4.13 (a) Coordinate system used to investigate the critical points of the Joukowski transformation and (b) coordinate changes corresponding to a smooth curve passing through ζ = c.
4.14 Flow around Ellipses
FIGURE 4.14 (a) Uniform flow approaching a horizontal ellipse at an angle of attack and (b) uniform parallel flow approaching a vertical ellipse.
4.15 Kutta Condition and Flat-Plate Airfoil
FIGURE 4.15 Flow around a flat plate at shallow angle of attack (a) without circulation and (b) satisfying the Kutta condition.
4.16 Symmetrical Joukowski Airfoil
FIGURE 4.16 Symmetrical Joukowski airfoil: (a) mapping planes and (b) uniform flow past the airfoil.
4.17 Circular-Arc Airfoil
FIGURE 4.17 Circular-arc airfoil: (a) mapping planes and (b) uniform flow past the airfoil.
4.18 Joukowski Airfoil
FIGURE 4.18 Joukowski airfoil: (a) mapping planes and (b) uniform flow past the airfoil.
4.19 Schwarz–Christoffel Transformation
FIGURE 4.19 Flow around a vertical flat plate assuming that the flow does not separate: (a) Schwarz–Christoffel mapping planes and (b) flow field.
4.20 Source in Channel
FIGURE 4.20 (a) Mapping planes for a source in a channel, (b) flow field for a full or semi-infinite channel, (c) flow field for the source at the wall, and (d) infinite array of sources.
4.21 Flow through Aperture
FIGURE 4.21 (a) Mapping planes for flow through a slit and (b) geometry of one of the free bounding streamlines.
4.22 Flow Past Vertical Flat Plate
FIGURE 4.22 Mapping planes for flow over a flat plate that is oriented perpendicular to a uniform flow.
PROBLEMS
5 Three-Dimensional Potential Flows
FIGURE 5.1 Definition sketch of spherical coordinates.
5.1 Velocity Potential
5.2 Stokes’ Stream Function
FIGURE 5.2 Velocity components and flow areas defined by a reference point P and neighboring point P′.
5.3 Solution of Potential Equation
5.4 Uniform Flow
FIGURE 5.3 Geometry for evaluating the stream function for a uniform flow.
5.5 Source and Sink
FIGURE 5.4 Geometry for evaluating the stream function for flow due to a source.
5.6 Flow due to Doublet
FIGURE 5.5 Superposition of a source and a sink that become a doublet as δx → 0.
5.7 Flow near Blunt Nose
FIGURE 5.6 Flow around an axisymmetric body created by a source in a uniform flow.
5.8 Flow around Sphere
5.9 Line-Distributed Source
FIGURE 5.7 Geometry connecting a field point P to a line source of length L distributed uniformly along the reference axis.
5.10 Sphere in Flow Field of Source
FIGURE 5.8 Superposition of a line sink of strength q per unit length, a source of strength Q*, and a source of strength Q near a sphere of a radius a.
5.11 Rankine Solids
FIGURE 5.9 (a) Superposition of uniform flow, source and sink, and (b) uniform flow approaching a Rankine solid.
5.12 D’Alembert’s Paradox
FIGURE 5.10 Spherical control surface S0 enclosing an arbitrarily shaped body of surface area S. The force acting on the body is F, and the unit normal to the body surface is n.
5.13 Forces Induced by Singularities
FIGURE 5.11 (a) Control surfaces for a body located at the origin and a point singularity at x = xi and (b) a source and a sink close together near the body.
5.14 Kinetic Energy of Moving Fluid
FIGURE 5.12 Control surface for an arbitrary body moving through a quiescent fluid.
5.15 Apparent Mass
PROBLEMS
6 Surface Waves
6.1 General Surface-Wave Problem
FIGURE 6.1 Coordinate system for surface-wave problems.
6.2 Small-Amplitude Plane Waves
6.3 Propagation of Surface Waves
FIGURE 6.2 Parameters for a pure sinusoidal wave.
FIGURE 6.3 Propagation speed c for small-amplitude surface waves of sinusoidal form.
6.4 Effect of Surface Tension
FIGURE 6.4 Element of liquid surface showing forces due to surface tension.
FIGURE 6.5 Propagation speed for sinusoidal waves including the effects of surface tension.
6.5 Shallow-Liquid Waves of Arbitrary Form
FIGURE 6.6 (a) Arbitrary waveform on a shallow-liquid layer, (b) mass-flow-rate balance for an element, and (c) momentum and force balance in the x direction.
6.6 Complex Potential for Traveling Waves
6.7 Particle Paths for Traveling Waves
FIGURE 6.7 (a) Coordinate system for establishing particle paths, (b) particle trajectories due to a sinusoidal wave, and (c) trajectories in deep liquids.
6.8 Standing Waves
6.9 Particle Paths for Standing Waves
FIGURE 6.8 Particle trajectories induced by a sinusoidal standing wave of amplitude ε and wavelength λ.
6.10 Waves in Rectangular Vessels
FIGURE 6.9 (a) Geometry for liquid in a rectangular container and (b) first four fundamental modes of surface oscillation.
6.11 Waves in Cylindrical Vessels
FIGURE 6.10 (a) Geometry for liquid in a cylindrical container and (b) Bessel functions of the first and second kind.
6.12 Propagation of Waves at Interface
FIGURE 6.11 Wave-shaped interface separating two different fluids traveling at different average speeds.
PROBLEMS
Further Reading—Part II
Part III Viscous Flows of Incompressible Fluids
Viscous Flows of Incompressible Fluids
7 Exact Solutions
7.1 Couette Flow
FIGURE 7.1 (a) Flow between parallel surfaces, (b) plane Couette flow, and (c) general Couette flow.
7.2 Poiseuille Flow
FIGURE 7.2 Viscous flow along conduits of various cross sections: (a) arbitrary, (b) circular, and (c) elliptic.
7.3 Flow between Rotating Cylinders
FIGURE 7.3 Geometry for flow between concentric rotating circular cylinders.
7.4 Stokes’ First Problem
FIGURE 7.4 (a) Definition sketch for Stokes’ first problem and (b) solution curves in terms of the similarity variable and in terms of dimensional variables.
7.5 Stokes’ Second Problem
FIGURE 7.5 (a) Definition sketch for Stokes’ second problem and (b) typical velocity profiles.
7.6 Pulsating Flow between Parallel Surfaces
7.7 Stagnation-Point Flow
FIGURE 7.6 (a) Flow configuration for a plane stagnation point and (b) functional form of the solution.
7.8 Flow in Convergent and Divergent Channels
FIGURE 7.7 (a) Flow configuration and (b) velocity profiles for flow in convergent and divergent channels.
7.9 Flow over Porous Wall
FIGURE 7.8 Uniform flow over a plane boundary with suction.
PROBLEMS
8 Low Reynolds Number Solutions
8.1 Stokes Approximation
8.2 Uniform Flow
8.3 Doublet
8.4 Rotlet
FIGURE 8.1 (a) Typical streamline due to a rotlet and (b) spherical control surface surrounding a rotlet.
8.5 Stokeslet
8.6 Rotating Sphere in Fluid
8.7 Uniform Flow Past Sphere
FIGURE 8.2 Drag coefficient as a function of Reynolds number for flow around a sphere.
8.8 Uniform Flow Past Circular Cylinder
8.9 Oseen Approximation
PROBLEMS
FIGURE 8.3 Heptane droplet striking a stainless steel surface at a temperature of 160°C.
9 Boundary Layers
FIGURE 9.1 Nature of flow around an arbitrarily shaped bluff body.
9.1 Boundary-Layer Thicknesses
FIGURE 9.2 Definition sketch for (a) boundary-layer thickness and (b) displacement thickness.
9.2 Boundary-Layer Equations
FIGURE 9.3 Development of a boundary layer on a plane surface.
9.3 Blasius Solution
9.4 Falkner–Skan Solutions
9.5 Flow over a Wedge
FIGURE 9.4 Boundary-layer flow over a wedge.
9.6 Stagnation-Point Flow
9.7 Flow in Convergent Channel
FIGURE 9.5 Boundary-layer flow on the wall of a convergent channel.
9.8 Approximate Solution for Flat Surface
9.9 General Momentum Integral
9.10 Kármán–Pohlhausen Approximation
FIGURE 9.6 (a) Form of functions F(η) and G(η), and (b) velocity profiles for various values of the parameter Λ(x).
FIGURE 9.7 Exact form of the function H(K) (solid line) and straight-line approximation (dashed line).
9.11 Boundary-Layer Separation
FIGURE 9.8 Velocity profiles in a boundary layer in the vicinity of separation.
9.12 Stability of Boundary Layers
FIGURE 9.9 (a) Undisturbed boundary-layer velocity profile, (b) stability calculation results for fixed V, and (c) stability diagram.
PROBLEMS
FIGURE 9.10 Liquid flowing down a vertical surface.
FIGURE 9.11 Wake behind a NACA 0025 airfoil at 5° angle of attack and Reynolds number of 105.
10 Buoyancy-Driven Flows
10.1 Boussinesq Approximation
10.2 Thermal Convection
10.3 Boundary-Layer Approximations
FIGURE 10.1 Development of thermal and momentum boundary layers on a vertical heated surface.
10.4 Vertical Isothermal Surface
10.5 Line Source of Heat
FIGURE 10.2 Thermal convection from a line or point source of heat.
10.6 Point Source of Heat
10.7 Stability of Horizontal Layers
FIGURE 10.3 Horizontal layer of fluid heated from below.
PROBLEMS
Further Reading—Part III
Part IV Compressible Flow of Inviscid Fluids
Compressible Flow of Inviscid Fluids
IV.1 Governing Equations and Boundary Conditions
11 Shock Waves
11.1 Propagation of Infinitesimal Disturbances
FIGURE 11.1 Fluid velocity induced by (a) compression wave front and (b) expansion wave front.
11.2 Propagation of Finite Disturbances
FIGURE 11.2 Progression of finite-amplitude disturbance.
11.3 Rankine–Hugoniot Equations
FIGURE 11.3 (a) Shock-wave configuration and (b) results from the Rankine–Hugoniot and isentropic relations.
11.4 Conditions for Normal Shock Waves
11.5 Normal-Shock-Wave Equations
FIGURE 11.4 Conditions downstream of a normal shock wave: (a) Mach number, (b) density, and (c) pressure.
11.6 Oblique Shock Waves
FIGURE 11.5 Configuration of an oblique shock wave.
FIGURE 11.6 Oblique-shock-wave relations: (a) shock-wave inclination β, (b) downstream Mach number M2, and (c) pressure ratio across the shock wave.
FIGURE 11.7 Supersonic flow approaching a blunt-nosed body and a sharp-nosed body.
PROBLEMS
12 One-Dimensional Flows
12.1 Weak Waves
FIGURE 12.1 (a) Characteristics and Riemann invariants in the xt plane and (b) basis of evaluating the field variables at an arbitrary point P.
12.2 Weak Shock Tubes
FIGURE 12.2 (a) Shock tube, (b) initial pressure distribution, (c) xt diagram, and (d) typical pressure distribution for t > 0.
12.3 Wall Reflection of Waves
FIGURE 12.3 (a) Shock tube, (b) xt diagram; (c) pressure distribution at some time and (d) at a later time.
12.4 Reflection and Refraction at Interface
FIGURE 12.4 Shock tube with gas interface and xt diagram subsequent to bursting the diaphragm.
12.5 Piston Problem
FIGURE 12.5 (a) Piston and cylinder, (b) actual xt diagram, and (c) linearized xt diagram.
12.6 Finite-Strength Shock Tubes
FIGURE 12.6 (a) Shock tube configuration, (b) initial pressure distribution, (c) xt diagram, and (d) typical pressure distribution for t > 0.
12.7 Nonadiabatic Flows
FIGURE 12.7 (a) Element of one-dimensional flow field and (b) flow through a typical nozzle.
12.8 Isentropic-Flow Relations
12.9 Flow through Nozzles
PROBLEMS
13 Multidimensional Flows
13.1 Irrotational Motion
13.2 Janzen–Rayleigh Expansion
13.3 Small-Perturbation Theory
13.4 Pressure Coefficient
13.5 Flow over Wave-Shaped Wall
FIGURE 13.1 (a) Wave-shaped wall, (b) flow for M∞ 1.
FIGURE 13.2 (a) Wave-shaped wall, (b) surface pressure coefficient for subsonic flow and (c) supersonic flow, and (d) drag coefficient versus Mach number.
13.6 Prandtl–Glauert Rule for Subsonic Flow
13.7 Ackeret’s Theory for Supersonic Flows
FIGURE 13.3 (a) Parameters for supersonic airfoil and (b) definitions of the half-thickness function τ(x) and the camber function γ(x).
13.8 Prandtl–Meyer Flow
FIGURE 13.4 (a) Prandtl–Meyer fan and (b) velocity change through a typical Mach wave.
PROBLEMS
Further Reading—Part IV
Part V Methods of Mathematical Analysis
Methods of Mathematical Analysis
14 Some Useful Methods of Analysis
14.1 Fourier Series
FIGURE 14.1 Square wave of (a) general form, (b) even form, and (c) odd form.
14.2 Complex Variables
14.2.1 Analytic Functions
14.2.2 Integral Representations
FIGURE 14.2 Contour of integration for evaluating a function at the point z0 using the Cauchy integral formula.
14.2.3 Series Representations
FIGURE 14.3 Contour of integration for establishing the Laurent series about the point z0.
14.2.4 Residues and Residue Theorem
14.2.5 Conformal Transformations
FIGURE 14.4 Corresponding regions in the original plane (z plane) and the mapped plane (ζ plane) for the Schwarz–Christoffel transformation.
14.3 Separation of Variable Solutions
14.4 Similarity Solutions
FIGURE 14.5 (a) Definition sketch for an impulsively moving surface, (b) expected form of the solution curves, and (c) typical curve that represents u/U = constant.
14.5 Group Invariance Methods
FIGURE 14.6 Free vibrations of a spring mass system with no damping.
PROBLEMS
Further Reading—Part V
Back Matter
Appendix A: Vector Analysis
A.1 Vector Identities
A.2 Integral Theorems
A.3 Orthogonal Curvilinear Coordinates
FIGURE A.1 Relationship between Cartesian coordinates and (a) cylindrical coordinates and (b) spherical coordinates.
Appendix B: Tensors
B.1 Notation and Definition
B.1.1 Notation
B.1.2 Definition
B.2 Tensor Algebra
B.2.1 Addition
B.2.2 Multiplication
B.2.3 Contraction
B.2.4 Symmetry
B.3 Tensor Operations
B.3.1 Gradient
B.3.2 Divergence
B.3.3 Curl
B.4 Isotropic Tensors
B.4.1 Definition
B.4.2 Isotropic Tensors of Rank 0
B.4.3 Isotropic Tensors of Rank 1
B.4.4 Isotropic Tensors of Rank 2
B.4.5 Isotropic Tensors of Rank 3
B.4.6 Isotropic Tensors of Rank 4
B.5 Integral Theorems
B.5.1 Gauss’ Theorem (Divergence Theorem)
B.5.2 Stokes’ Theorem
Appendix C: Governing Equations
C.1 Cartesian Coordinates
C.2 Cylindrical Coordinates
C.3 Spherical Coordinates
Appendix D: Fourier Series
Appendix E: Thermodynamics
E.1 Zeroth Law
E.2 First Law
E.3 Equations of State
E.3.1 Thermally Perfect Gas
E.3.2 Van der Waals Equation
E.4 Enthalpy
E.5 Specific Heats
E.5.1 Constant Volume
E.5.2 Constant Pressure
E.5.3 Perfect Gas
E.6 Adiabatic, Reversible Processes
E.7 Entropy
E.8 Second Law
E.9 Canonical Equations of State
E.10 Reciprocity Relations

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