v
This page has been reformatted by Knovel to provide easier navigation.
Contents
Preface ..................................................................................
1. Fluid Motion: Introduction to Kinematics ...................
1.1 Fluids and Solids ...............................................................
1.2 Fluid Parcels and Flow Kinematics .................................... 2
1.3 Coordinates, Velocity, and Acceleration ............................ 4
1.4 Fluid Velocity and Streamlines ..........................................
1.5 Point Particles and Their Trajectories ................................
1.6 Material Surfaces and Elementary Motions ....................... 27
1.7 Interpolation ....................................................................... 38
2. Fluid Motion: More on Kinematics .............................. 49
2.1 Fundamental Modes of Fluid Parcel Motion ...................... 49
2.2 Fluid Parcel Expansion ...................................................... 61
2.3 Fluid Parcel Rotation and Vorticity .....................................
2.4 Fluid Parcel Deformation ...................................................
2.5 Numerical Differentiation ................................................... 72
2.6 Areal and Volumetric Flow Rate ........................................
2.7 Mass Flow Rate, Mass Conservation, and the
Continuity Equation ............................................................
2.8 Properties of Point Particles .............................................. 93
2.9 Incompressible Fluids and Stream Functions .................... 101
2.10 Kinematic Conditions at Boundaries .................................. 106
3. Flow Computation Based on Kinematics .................... 111
3.1 Flow Classification Based on Kinematics .......................... 111
vi Contents
This page has been reformatted by Knovel to provide easier navigation.
3.2 Irrotational Flows and the Velocity Potential ...................... 114
3.3 Finite-Difference Methods .................................................. 122
3.4 Linear Solvers .................................................................... 131
3.5 Two-Dimensional Point Sources and Point-Source
Dipoles ............................................................................... 135
3.6 Three-Dimensional Point Sources and Point-Source
Dipoles ............................................................................... 149
3.7 Point Vortices and Line Vortices ........................................ 154
4. Forces
and
Stresses ..................................................... 164
4.1 Body Forces and Surface Forces ...................................... 164
4.2 Traction and the Stress Tensor ......................................... 166
4.3 Traction Jump across a Fluid Interface .............................. 173
4.4 Stresses in a Fluid at Rest ................................................. 181
4.5 Viscous and Newtonian Fluids ........................................... 185
4.6 Simple Non-Newtonian Fluids ........................................... 194
4.7 Stresses in Polar Coordinates ........................................... 19
4.8 Boundary Condition on the Tangential Velocity ................. 203
4.9 Wall Stresses in Newtonian Fluids .................................... 205
5. Hydrostatics .................................................................. 208
5.1 Equilibrium of Pressure and Body Forces ......................... 208
5.2 Force Exerted on Immersed Surfaces ............................... 217
5.3 Archimedes' Principle ........................................................ 224
5.4 Shapes of Two-Dimensional Interfaces ............................. 227
5.5 A Semi-Infinite Interface Attached to an Inclined
Plate ................................................................................... 231
5.6 Meniscus between Two Parallel Plates ............................. 235
5.7 A Two-Dimensional Drop on a Horizontal Plane ............... 241
5.8 Axisymmetric Shapes ........................................................ 246
Contents vii
This page has been reformatted by Knovel to provide easier navigation.
6. Equation of Motion and Vorticity Transport ............... 252
6.1 Newton's Second Law for the Motion of a Parcel .............. 252
6.2 Integral Momentum Balance .............................................. 258
6.3 Cauchy's Equation of Motion ............................................. 263
6.4 Euler's and Bernoulli's Equations ...................................... 270
6.5 The Navier-Stokes Equation .............................................. 281
6.6 Vorticity Transport .............................................................. 288
6.7 Dynamic Similitude, the Reynolds Number, and
Dimensionless Numbers in Fluid Dynamics ...................... 296
7. Channel, Tube, and Film Flows ................................... 306
7.1 Steady Flow in a Two-Dimensional Channel ..................... 306
7.2 Steady Film Flow Down an Inclined Plane ........................ 315
7.3 Steady Flow through a Circular or Annular Tube ............... 319
7.4 Steady Flow through Channels and Tubes with
Various Cross-Sections ..................................................... 327
7.5 Steady Swirling Flow ......................................................... 336
7.6 Transient Flow in a Channel .............................................. 339
7.7 Oscillatory Flow in a Channel ............................................ 347
7.8 Transient and Oscillatory Flow in a Circular Tube ............. 354
8. Finite-Difference
Methods ............................................ 364
8.1 Choice of Governing Equations ......................................... 364
8.2 Unidirectional Flow; Velocity/Pressure Formulation ........... 366
8.3 Unidirectional Flow; Velocity/Vorticity Formulation ............ 377
8.4 Unidirectional Flow; Stream Function/Vorticity
Formulation ........................................................................ 382
8.5 Two-Dimensional Flow; Stream Function/Vorticity
Formulation ........................................................................ 386
8.6 Velocity/Pressure Formulation ........................................... 395
8.7 Operator Splitting and Solenoidal Projection ..................... 399
viii Contents
This page has been reformatted by Knovel to provide easier navigation.
9. Flows at Low Reynolds Numbers ................................ 410
9.1 Flows in Narrow Channels ................................................. 411
9.2 Film Flow on a Horizontal or Down Plane Wall .................. 424
9.3 Two-Layer Channel Flow ................................................... 436
9.4 Flow Due to the Motion of a Sphere .................................. 443
9.5 Point Forces and Point Sources in Stokes Flow ................ 450
9.6 Two-Dimensional Stokes Flow .......................................... 459
9.7 Flow near Corners ............................................................. 465
10. Flows at High Reynolds Numbers ............................... 475
10.1 Changes in the Structure of a Flow with Increasing
Reynolds Number .............................................................. 476
10.2 Prandtl Boundary-Layer Analysis ...................................... 479
10.3 Prandtl Boundary Layer on a Flat Surface ......................... 485
10.4 Von Kàrmàn's Integral Method .......................................... 501
10.5 Instability of Shear Flows ................................................... 512
10.6 Turbulent Motion ................................................................ 525
10.7 Analysis of Turbulent Motion ............................................. 539
11. Vortex Motion ................................................................ 548
11.1 Vorticity and Circulation in Two-Dimensional Flow ............ 549
11.2 Motion of Point Vortices ..................................................... 551
11.3 Two-Dimensional Flow with Distributed Vorticity ............... 566
11.4 Vorticity, Circulation, and Three-Dimensional Flow
Induced by Vorticity ........................................................... 581
11.5 Axisymmetric Flow Induced by Vorticity ............................ 586
11.6 Three-Dimensional Vortex Motion ..................................... 600
12. Aerodynamics ............................................................... 606
12.1 General Features of Flow Past an Aircraft ......................... 607
12.2 Airfoils and the Kutta-Joukowski Condition ........................ 609
Contents ix
This page has been reformatted by Knovel to provide easier navigation.
12.3 Vortex Panels .................................................................... 612
12.4 Vortex Panel Method ......................................................... 620
12.5 Vortex Sheet Representation ............................................. 629
12.6 Point-Source-Dipole Panels ............................................... 638
12.7 Point-Source Panels and Green's Third Identity ................ 645
FDLIB Software Library ....................................................... 651
FDLIB Directories ................................................................ 653
References ........................................................................... 666
Subject Index ....................................................................... 668
668
This page has been reformatted by Knovel to provide easier navigation.
Subject Index
Index terms
Links
A
acceleration 14
of a point particle
aerodynamics 606
airfoil 609
thin-airfoil theory
alternating tensor
Archimedis principle
atmospheric pressure
distribution 214
Avogadro number
axisymmetric
flow
extensional 193
flow rate in
stream function
vorticity of
interfaces 246
B
baroclinic production of vorticity
bearing 414
Beltrami flow
Bernoulli's equations
669
Index terms
Links
This page has been reformatted by Knovel to provide easier navigation.
Bessel
functions
Bickley jet
biharmonic operator
Bingham plastic
Biot-Savart integral
Blasius equation
body,
force 165
neutrally-buoyant 226
rigid 3
Bond number
Boundary
conditions,
Dirichlet 119
for Euler's equation
for the Navier-Stokes equation
Neumann 118
no-penetration 107
for the pressure
elements 458
layer,
traction 172
Bubble, expanding
Buoyancy force
Burgers equation
Boussinèsq eddy viscosity
670
Index terms
Links
This page has been reformatted by Knovel to provide easier navigation.
C
capillary
length 230
rise
Cauchy equation of motion
cavity flow
centrifugal force
CFDLAB 652
channel flow,
finite-difference methods for
two-layer flow
steady 306
multi-layer 311
semi-infinite 333
two-layer 309
wavy 418
unsteady 339
circulation
circulatory flow
conjugate gradients
contact
angle 228
line
continuum mechanics
contour dynamics,
for axisymmetric flow
for two-dimensional flow
coordinates,
Cartesian 4
cylindrical polar
plane polar
spherical polar
671
Index terms
Links
This page has been reformatted by Knovel to provide easier navigation.
Coriolis force
corners, flow inside
correlations 545
Couette flow,
circular 336
plane or rectilinear
Crank-Nicolson method
creeping flow
curl of a vector field
curvature
of an ellipse
of an interface
of a line
of a surface
cylinder, circular,
boundary layer around
flow past
potential flow past
Stokes flow due to the motion of
D
deformation 3
of a fluid parcel
Deissler correlation
delta function
density 93
difference,
backward 72
centered 73
forward 72
differentiation, numerical
of a function of two variables
672
Index terms
Links
This page has been reformatted by Knovel to provide easier navigation.
dilatant fluid
dipole
of a point source
of a point vortex
Dirac delta function
displacement thickness
divergence
theorem 83
of a vector field
drop, resting on a plane
E
eigenvalues and eigenvectors
Einstein summation convention
ellipse, curvature of
elliptic integrals
error function
Euler
modified 24
for a system of equations
equation of motion
for a parcel
for a point particle
evolution equation,
for the density
for the velocity
for the velocity potential
for the vorticity
expansion of a parcel
673
Index terms
Links
This page has been reformatted by Knovel to provide easier navigation.
extensional flow
extensive property
F
Falkner-Skan boundary layers
Fast Fourier transform
FDLIB 651
FFT
film flow,
down an inclined plane
multi-layered 316
finite differences, see differences
finite difference methods,
for the continuity equation
for Laplace's equation
for the Navier-Stokes equation
finite-volume method
flow rate,
areal and volumetric
mass 87
flux,
areal and volumetric
mass 87
force,
body force
hydrodynamic volume force
in polar coordinates
surface force
on an immersed surface
Fourier decomposition
frequency parameter of a flow
friction velocity
674
Index terms
Links
This page has been reformatted by Knovel to provide easier navigation.
Froude number
fundamental
modes of parcel motion
solutions of Laplace's equation
G
Gauss
divergence theorem
elimination 132
quadrature 575
-Siedel method
gradient of a function
Green's third identity
growth rate of a perturbation
H
Hagen flow,
steady 308
transient 346
oscillatory 352
harmonic functions
Helmholtz
velocity of a vortex ring
high-Reynolds-number flow
Hill's vortex
Holstein-Bohlen parameter
homogeneous boundary conditions
hump, flow over
hydrostatics 208
stress tensor in
675
Index terms
Links
This page has been reformatted by Knovel to provide easier navigation.
I
ideal
fluid 192
gas law
incompressible fluid
inner vector product
instability of shear flows
integration, numerical
intensive property
interface,
shape in hydrostatics
traction exerted on
traction jump across
interpolation
of a function
of one variable
of two variables
of three variables
of the velocity
irreducible loop
irrotational flow
J
Jacobi method
Joukowski transformation
K
Kàrmàn, von
constant 544
integral method
-Pohlhausen solution
676
Index terms
Links
This page has been reformatted by Knovel to provide easier navigation.
Kàrmàn, von (Continued)
vortex street
Kelvin
circulation theorem
functions 360
-Helmholtz instability
kinematics 1
Kronecker delta
Kutta-Joukowski
L
laminar flow
Laplace
equation and operator
in polar coordinates
-Young equation
LIA
line vortex
linear
equations 132
momentum 100
stability analysis
linearization of a function
local induction approximation
logarithmic law of the wall in turbulent flow
logistic mapping
lubrication flow
677
Index terms
Links
This page has been reformatted by Knovel to provide easier navigation.
M
manometer 215
Marangoni traction
mass
conservation of
flow rate and flux
material
derivative 88
parcel 27
surface 27
mean free path
meniscus 235
mid-point rule
momentum
integral balance
of a parcel
rate of change of
N
Navier-Stokes equation
neutrally-buoyant body
Newton's
method
for a nonlinear equation
for two nonlinear equations
for eigenvalues
second law of motion for a parcel
Newtonian fluid
non-Newtonian fluid
Nusslet film
678
Index terms
Links
This page has been reformatted by Knovel to provide easier navigation.
O
operator splitting
Orr-Sommerfeld equation
oscillatory flow
in a channel
in a tube
Oseen
Flow
tensor 451
Ostwald - de Waele model
outer vector product
P
panel method
parcel
of a fluid
deformation 29
expansion 29
Newton's law for the motion of
rotation
phase velocity
pipe flow,
see tube and channel flow
through an enlargement
pivoting of a linear system
plane polar coordinates
path line
plastic fluid
flow due to the motion of
point
force 450
particle 18
679
Index terms
Links
This page has been reformatted by Knovel to provide easier navigation.
point (Continued)
properties of
source 136
in bounded flow
panel 639
in Stokes flow
in uniform flow
source dipole
panel 640
vortex 154
dipole 163
periodic array of
Pohlhausen polynomials
Poiseuille
flow
law
potential of the velocity
power
-law
fluid
spectrum 536
Prandtl
boundary layers
mixing length
pressure
boundary conditions
in hydrostatics
force due to
Poisson equation
for the pressure
integral formula
680
Index terms
Links
This page has been reformatted by Knovel to provide easier navigation.
pump, ejector
pycnometer 223
R
Rayleigh
equation of hydrodynamic stability
equation for an expanding bubble
-Taylor instability
reducible loop
rescaling 298
Reynolds
stresses 539
rigid body
motion 3
rotation 2
translation 2
rotation
matrix 33
of a parcel
rotational flow
rotlet
S
Sakiadis boundary layer
scraper, flow due to the motion of
secant method
separation of a flow
simple
fluid 187
shear
flow
681
Index terms
Links
This page has been reformatted by Knovel to provide easier navigation.
shape factor
shear
function 507
-thinning and -thickening
shooting
method
similitude 296
sloshing of a fluid
smoothing, numerical
solenoidal
vector field
projection 399
solid
source, see point source
sparse matrix
sphere
floating 218
potential flow past
Stokes flow due to the motion of
spherical polar coordinates
stability, hydrodynamic
stagnation point
Stokes flow
Stokes
circulation theorem
boundary layer
flow
law
streaklines 25
stream function,
for axisymmetric flow
no-penetration condition
682
Index terms
Links
This page has been reformatted by Knovel to provide easier navigation.
stream function (Continued)
for two-dimensional flow
-vorticity formulation
streamlines 18
stress
in polar coordinates
symmetry of
tensor 168
Strouhal number
surface
force 165
material 27
tension 174
suspension 2
swirling
flow
T
tangent vector
Taylor
hypothesis 538
microscale 539
tensor 54
thin-airfoil theory
Thomas algorithm
thread of a fluid, extending
Toricelli's law
traction 166
on a boundary
jump across an interface
on an interface
trapezoidal rule
683
Index terms
Links
This page has been reformatted by Knovel to provide easier navigation.
tridiagonal matrix
determinant of
troposphere 216
tube flow,
steady,
annular 321
circular 319
elliptical 328
rectangular 330
triangular 334
transient and oscillatory in a tube
turbulent
flow
two-dimensional flow
vorticity of
U
unidirectional flow,
see channel and tube flow
unit vectors
V
vector
inner product
outer product
velocity
fluid 16
gradient tensor
of a molecule
potential 114
-pressure formulation
Venturi flume
684
Index terms
Links
This page has been reformatted by Knovel to provide easier navigation.
viscosity 188
extensional 186
of a gas
shear 187
viscous force
vortex
flow
axisymmetric 596
two-dimensional 567
point- 154
ring,
with finite-size core
line 590
sheet 614
stretching 292
vorticity 62
flow induced by
in terms of the stream function
transport equation
vorton 601
Y
yield stress
685
Index terms
Links
This page has been reformatted by Knovel to provide easier navigation.
W
wall stress
Weber number
wind tunnel
Womersley number
