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By William Graebel, Professor Emeritus,Department of Mechanical Engineering,University of Michigan
Description Fluid mechanics is the study of how fluids behave and interact under various forces and in various applied situations, whether in liquid
or gas state or both. The author compiles pertinent information that are introduced in the more advanced classes at the senior level
and at the graduate level. ?Advanced Fluid Mechanics? courses typically cover a variety of topics involving fluids in various multiple
states (phases), with both elastic and non-elastic qualities, and flowing in complex ways. This new text will integrate both the simple
stages of fluid mechanics (?Fundamentals?) with those involving more complex parameters, including Inviscid Flow in multi-dimensions,
Viscous Flow and Turbulence, and a succinct introduction to Computational Fluid Dynamics. It will offer exceptional pedagogy, for both
classroom use and self-instruction, including many worked-out examples, end-of-chapter problems, and actual computer programs that can
be used to reinforce theory with real-world applications.
Professional engineers as well as Physicists and Chemists working in the analysis
of fluid behavior in complex systems will find the contents of this book useful.All manufacturing companies involved in any sort of systems
that encompass fluids and fluid flow analysis (e.g., heat exchangers, air conditioning and refrigeration, chemical processes, etc.) or
energy generation (steam boilers, turbines and internal combustion engines, jet propulsion systems, etc.), or fluid systems and fluid
power (e.g., hydraulics, piping systems, and so on)will reap the benefits of this text.
Audience
Graduate-level students in Mechanical, Aerospace & Aeronautical, Chemical, Environmental and Biomechanical Engineering; Graduate-level
students in Chemistry and Physics ; Professional engineers in mechanical, chemical, materials, environmental, and biomedical engineering;
Physicists and Chemists working in the analysis of fluid behavior in complex systems
Contents Chapter 1 - Fundamentals
1.1 Introduction
1.2 Velocity, acceleration and the material derivative
1.3 The local continuity equation
1.4 Path lines, stream lines and the stream function
a. Lagrange?s stream function for two-dimensional flows
b. Stream functions
for three-dimensional flows,including Stokes stream function
1.5 Newton?s momentum equation
1.6 Stress
1.7 Rates of deformation
1.8 Constitutive relations for Newtonian fluids
1.9 Equations for Newtonian fluids
1.10 Boundary conditions
1.11 Vorticity and
circulation
1.12 The vorticity equation
1.13 The work-energy equation
1.14 The first law of thermodynamics
1.15 Dimensionless
parameters
1.16.Non-Newtonian fluids
1.17 Moving coordinate systems
Problems
Chapter 2 - Inviscid irrotational flows
2.1 Inviscid
flows
2.2 Irrotational flows and the velocity potential
a. Intersection of velocity potential lines
and streamlines
in two dimensions
b. Basic two-dimensional irrotational flows
c. Hele-Shaw flows
d. Basic three-dimensional irrotational flows
e. Superposition and the method of images
f. Vortices near walls
g. Rankine half body
h. Rankine oval
i. Circular cylinder
or sphere in a uniform stream
2.3 Singularity distribution methods
a. Two and three-dimensional slender body theory
b. Panel methods
2.4 Forces acting on a translating sphere
2.5 Added mass and the Lagally theorem
2.6 Theorems for irrotational flow
a. Mean
value and maximum modulus theorem
b. Maximum-minimum potential theorem
c. Maximum-minimum speed theorem
d. Kelvin?s minimum kinetic
energy theorem
e. Maximum kinetic energy theorem
f. Uniqueness theorem
g. Kelvin?s persistence of circulation theorem
h. Weiss and
Butler sphere theorems
Problems
Chapter 3 - Irrotational Two-Dimensional Flows
3.1 Complex variable theory applied to
two-dimensional
irrotational flows
3.2 Flow past a circular cylinder with circulation
3.3 Flow past an elliptical cylinder with circulation
3.4
The Joukowski airfoil
3.5 Karman-Trefftz and Jones-McWilliams airfoils 3.6 NACA airfoils
3.7 Lifting line theory
3.8 Karman
vortex street
3.9 Conformal mapping and the Schwarz-Christoffel transformation
3.10 Cavity flows
3.11 Added mass and forces and
moments for two-dimensional bodies
Problems
Chapter 4 - Surface and interfacial waves
4.1 Linearized free surface wave theory
a. Infinitely long channel
b. Waves in a container of finite size
4.2 Group velocity
4.3 Waves at the interface of two dissimilar
fluids
4.4 Waves in an accelerating container
4.5 Stability of a round jet
4.6 Local surface disturbance on a large body of fluid
- Kelvin?s ship wave
4.7 Shallow depth free surface waves - cnoidal and solitary waves
4.8 Ray theory of gravity waves for non-uniform
depths
Problems
Chapter 5 - Exact solutions of the Navier-Stokes equations
5.1 Solutions to the steady-state Navier-Stokes
equations when convective acceleration is absent
a. Two-dimensional flow between parallel planes
b. Poiseuille flow in a rectangular
conduit
c. Poiseuille flow in a round tube
d. Poiseuille flow in tubes of arbitrarily shaped cross-section
e. Couette flow between
circular cylinders 5.2 Unsteady flows when convective acceleration is absent
a. Stokes? first problem-impulsive motion of a plate
b. Stokes? second problem-oscillation of a plate 5.3 Other unsteady flows when convective acceleration is absent
a. Impulsive
plane Poiseuille and Couette flows
b. Impulsive circular Couette flow
5.4 Steady flows when convective acceleration is present.
a. Plane stagnation point flow
b. Three-dimensional stagnation point flow c. Flow into convergent or divergent channels
d. Flow
in a spiral channel
e. Flow due to a round laminar jet
f. Flow due to a rotating disk
Problems
Chapter 6 - The Boundary Layer
Approximation
6.1 Introduction to boundary layers
6.2 The boundary layer equations
6.3 Boundary layer thickness
6.4 Falkner-Skan
solutions for flow past a wedge
a. Boundary layer on a flat plate
b. Stagnation point boundary layer flow
c. General case
6.5
The integral form of the boundary layer equation
6.6 Axisymmetric laminar jet
6.7 Flow separation
6.8 Transformations for
non-similar boundary layer solutions
a. Falkner transformation
b. von Mises transformation
c. Combined Mises-Falkner transformation
d. Crocco?s transformation
e. Mangler?s transformation for bodies of revolution
6.8 Boundary layers in rotating flows
Problems
Chapter 7 - Thermal Effects
7.1 Thermal boundary layers
7.2 Forced convection on a horizontal flat plate
a. Falkner-Skan wedge thermal
boundary layer
b. Isothermal flat plate
c. Flat plate with constant heat flux
7.3 The integral method for thermal convection
a. Flat plate with a constant temperature region
b. Flat plate with constant heat flux
7.4 Heat transfer near the stagnation point
of an isothermal cylinder
7.5 Natural convection on an isothermal vertical plate
7.6 Natural convection on a vertical plate with
uniform heat flux
7.7 Thermal boundary layer on inclined flat plates 7.8 Integral method for natural convection on an isothermal
vertical plate
7.9 Temperature distribution in an axisymmetric jet
Problems
Chapter 8 - Low Reynolds number Flows
8.1 Stokes approximation
1. Doublet
2a. Stokeslet for steady flows
2b. Stokeslet for unsteady flows
3a. Rotlet for steady flows
3b. Rotlet for unsteady
flows
8.2 Slow steady flow past a solid sphere
8.3 Slow steady flow past a liquid sphere
8.4 Flow due to a sphere undergoing simple
harmonic motion
8.5 General translation of a sphere
8.6 Oseen?s approximation for slow viscous flow
8.7 Resolution of the Stokes/Whitehead
paradoxes
Problems
Chapter 9 - Flow stability
9.1 Linear stability theory of fluid flows
9.2 Thermal instability in a viscous fluid
- Rayleigh-Benard convection
9.3 Stability if flow between rotating circular cylinders - Couette-Taylor
instability
9.4 Stability
of plane flows
Problems
Chapter 10 - Turbulence and transition to turbulence
10.1 The why and the how of turbulence
10.2 Statistical
approach - one point averaging
10.3 Zero-equation turbulent models
10.4 One-equation turbulent models
10.5 Two-equation turbulent
models
10.6 Stress-equation models
10.7 Equations of motion in Fourier space
10.8 Quantum theory models
10.9 Large eddy models
10.10 Phenomenologic observations
10.11 Conclusions
Chapter 11 - An Introduction To Computational Fluid Dynamics
11.1 Introduction
11.2 Numerical calculus
11.3 Numerical integration of ordinary differential equations
11.4 The finite element method
11.5 Linear stability problems - invariant imbedding and Riccati methods
11.6 Errors, accuracy, and stiff equations
Problems
Chapter 12 - Numerical solution of partial differential equations
12.1 Introduction
12.2 Relaxation methods
12.3 Surface singularities
12.4 One step methods
a. Forward time, centered space - explicit
b. Dufort-Frankel method - explicit
c. Crank-Nicholson method
- implicit
d. Boundary layer equations - Crank-Nicholson
e. Boundary layer equations - hybrid method
f. Richardson extrapolation
g. Further choices for dealing with nonlinearities
h. Upwind differencing for convective acceleration terms
12.5 Multi-step, or alternating
direction, methods
a. Alternating direction explicit (ADE) method
b.Alternating direction implicit (ADI) method
12.6 Method of characteristics
12.7 Leapfrog method - explicit
12.8 Lax-Wendroff method - explicit
12,9 MacCormack?s methods
a. MacCormack?s explicit method
b. MacCormack?s implicit method
12.10 Discrete vortex methods (DVM)
12.11 Cloud in cell method (CIC)
Problems
Appendix - Mathematical
aids
A1. Vector differential calculus
A2. Vector integral calculus
A3. Fourier series and integrals
A4. Solution of ordinary
differential equations
a. Method of Frobenius
b. Mathieu equation
c. Finding eigenvalues - the Riccatti method
A5. Index notation
A6. Tensors in Cartesian coordinates
A7. Tensors in orthogonal curvilinear coordinates
a. Cylindrical polar coordinates
b. Spherical
polar coordinates
A8. Tensors in general coordinates
References
Index
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