Vectors, tensors, and the basic equations of fluid mechanics:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Dover Publ.
1989
|
| Edition: | Unabridged and corr. republ. of the work first publ. by Prentice-Hall, Englewood Cliffs, NJ, in 1962 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 286 S. Ill., graph. Darst. |
| ISBN: | 0486661105 9780486661100 |
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MARC
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| 245 | 1 | 0 | |a Vectors, tensors, and the basic equations of fluid mechanics |c Rutherford Aris |
| 250 | |a Unabridged and corr. republ. of the work first publ. by Prentice-Hall, Englewood Cliffs, NJ, in 1962 | ||
| 264 | 1 | |a New York |b Dover Publ. |c 1989 | |
| 300 | |a XIV, 286 S. |b Ill., graph. Darst. | ||
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| 650 | 4 | |a Vektör analizi | |
| 650 | 4 | |a Calculus of tensors | |
| 650 | 4 | |a Fluid dynamics | |
| 650 | 4 | |a Vector analysis | |
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Record in the Search Index
| _version_ | 1821131183060156416 |
|---|---|
| adam_text |
Contents
1.
Introduction
1.1.
Mathematical theories and engineering science,
1. 1.2.
Scalars, vectors,
and tensors,
3. 1.3.
Preview,
6.
2.
Cartesian Vectors and Tensors: Their Algebra
S.U.
Definition of a vector,
8.
Z.1H. Examples of vectors,
10. 2.13.
Scalar multiplication,
11. 2.21.
Addition of vectors
—
Coplanar vectors,
11. 2.22.
Unit vectors,
13. 2.23.
A basis of non-coplanar vectors,
13. 2.31.
Scalar product
—
Orthogonality,
15. 2.82.
Vector product,
16.
2.S3.
Ve-
locity due to rigid body rotation,
17. 2.34.
Triple scalar product,
18. 2.35.
Triple vector product,
19. 2.86.
Reciprocal base systems,
20. 241·
Second
order tensors,
21. 242.
Examples of second order tensors,
22, 2.43.
Scalar
multiplication
and addition,
23. 244·
Contraction and multiplication,
23.
2.Ą5.
The vector of an antisymmetric tensor,
24. 2.6.
Canonical form of a
symmetric tensor,
25. 2.61.
Higher order tensors,
28. 2.62.
The quotient
rule,
29. 2.7.
Isotropie
tensors,
30. 2.81.
Dyadics and other notations,
34.
2.82.
Axial vectors,
36.
3.
Cartesian Vectors and Tensors: Their Calculus
38
3.11.
Tensor functions of atime-like variable,
38. 3.12.
Curves in space,
39.
8.18.
Une
integrals,
42.
Ѕ.Ц.
Surface integrals,
44.
S.1S. Volume inte¬
grals,
48. 8.16.
Change of variable with multiple integrals,
50. 8.21.
Vector fields,
51. 8.22.
The vector operator V
—
Gradient of a scalar,
51.
8.28.
The divergence of a vector field,
53.
8.2Ą.
The curl of a vector field,
55.
3.81.
Green'
s
theorem and some of its variants,
58. 8.82.
Stokes'theorem,
61.
xl
XÜ Contents
S.
41.
The classification and representation of
vector
fields,
63.
3Ą2.
Irrota·
tional vector fields,
65. 3.43.
Solenoidal vector fields,
67.
Ѕ.Ц.
Helmholtz'
representation,
70. 3.45.
Other representations,
72.
4.
The Kinematics of Fluid Motion
76
4.1t.
Particle paths,
76. 4.12.
Streamlines,
79. 4.13.
Streaklines,
81.
4.21.
Dilatation,
83. 4.22.
Reynold's transport theorem,
84.
Ą.S.
Conserva¬
tion of mass and the equation of continuity,
87.
4.4I. Deformation and rate
of strain,
88.
4.4S. Physical interpretation of the deformation tensor,
89. *
4.4З.
Principal axes of deformation,
92. 4-6.
Vorticity, vortex lines and
tubes,
95.
5.
Stress in Fluids
99
б.
lì. Cauchy's
stress principle and the conservation of momentum,
99. 5.
lê.
The stress tensor,
101. 5.13.
The symmetry of the stress tensor,
102.
S.I4.
Hydrostatic pressure,
105. 5.15.
Principal axes of stress and the notion of
isotropy,
105. 5.21.
The Stokesian fluid,
106. 5.22.
Constitutive equa¬
tions of the Stokesian fluid,
107. 5.23.
The Newtonian fluid,
110. 5.24.
Interpretation of the constants
λ
and
μ,
111.
6.
Equations of Motion and Energy in Cartesian Coordinates
113
6.11.
Equations of
motům
of a Newtonian fluid,
113. 6.12.
Boundary con¬
ditions,
115. 6.13.
The Reynolds number,
115. 6.14·
Dissipation
0}
energy
by viscous
f
orces,
117. 6.2.
Equations
f
or a Stokesian fluid,
119. 6.3.
The
energy equation,
120.
6.4I·
Résumé
of the development of the equations,
123.
6.4S. Special cases of the equations,
124. 6.51.
Bernoulli theorems,
131.
6.52.
Some further properties of barotropic flow,
132.
7.
Tensors
134
7.11.
Coordinate systems and conventions,
134. 7.12.
Proper transforma¬
tions,
136. 7.13.
General plan of presentation,
139. 7.21.
Contravariant
vectors,
140. 7.22.
Covarianl vectors,
141. 7.23.
The metric tensor,
142.
7.24.
Absolute and relative tensor fields,
144. 7.25.
Isotropie
tensors,
146.
7.31.
Tensor algebra,
146. 7.32.
The quotient rule,
148. 7.33
Lengthof
a
vector and angle between vectors,
149.
7.34- Principal directions of a sym¬
metric second order tensor,,
151. 7.35.
Covariant and
contravariant
base
vectors,
151. 7.41.
Physical components of vectors in orthogonal coordinate
systems,
153. 7.42.
Physical components of vectors in
nonorthogonal
coordi¬
nate systems,
155. 7.43.
Physical components of tensors,
156. 7
44-Лп
Contenti
ХІН
example,
157. 7.45.
AnhoUmomic components of
а
tensor,
159. 7.51.
Differentials of tensors,
160. 7.52.
Parallel vector fields,
161.
7.6S.
Christoffel
symbols,
162.
7.5Ą.
Christoffel
symbols in orthogonal coordinates,
164. 7.56.
Covariant differentiation,
166. 7.56.
The Laplacian, divergence,
and curl,
169. 7.57.
Green's and Stokes' theorems,
171. 7.6.
Euclidean
and other spaces,
172. .
8.
Equations of Fluid Flow in Euclidean space
.176
8.11.
Intrinsic derivatives,
176. 8.ÍS.
The transport theorem and equation
of continuity,
177.
8.1S. The equations of motion,
178. 8.21.
The New*
ionian
fluid,
180. 8.88.
The Navier-Stokes equations,
181.
8.S1. Con-
vected coordinates,
183. 8.88.
Convedive differentiation,
185.
8.SS. Strain
and rate of strain in convected coordinates,
187. 8.34·
Constitutive equations,
188.
8.Ą.
The general theory of constitutive equations,
190.
9.
The Geometry of Surfaces in Space
193
9.11.
Surface coordinates,
193. 9.18.
Transformations of surface coordi¬
nates
—
surface tensors,
194. 9.13.
The metric tensor,
196. 9.14.
Length
and direction of surface vectors,
198. 9.81. Christoffel
symbols,
199. 9.88.
Geodesies,
201. 9.83.
Geodesic coordinates,
204. 9.84.
Parallel vectors in a
surface,
206. 9.85.
Covariant surface' differentiation,
209. 9.86.
The
Gaussian or total curvature of a surface,
210. 9.31.
The surface in space,
212. 9.38.
The first fundamental form of the surface,
213. 9.33.
The
normal to the surface,
214. 9.34.
Covariant differentiation of hybrid tensors,
215. 9.35.
The second fundamental
J
'orm
of the surf'ace,
216. 9.36.
The third
fundamental form,
217.
9.S7. The relation between the three fundamental
forms
—
Gauss-Codazzi
equations,
218. 9.38.
Curves in the surface,
219.
9.41 ■
Differential operators in a surface,
222. 9.48.
Green's and Stokes'
theorems in a surface,
223.
1 0.
The Equations of Surface Flow
226
10.11.
Velocity in a surface,
227. 10.18.
Operations with a time dependent
metric,
228. 10.81.
Strain in the surface,
230. 10.88.
Stress in the surface,
231. 10.83.
Constitutive relations for the surface,
232. 10.31.
Intrinsic
equations of surf ace motion,
233. 10.32.
Intrinsic equations for a Newtonian
surface fluid,
234.
lOĄl.
The continuity of the surface and its surroundings,
235.
IO.48. Connection between surface strain and the surroundings,
237.
ІО.4З.
Dynamical connection between the surface and its surroundings,
238.
10.51
Surface equations as boundary conditions at an interface,
241. 10.68.
The plane interface,
242. 10.53.
The cylindrical interface,
243. 10.54.
The spherical interface,
243.
xiv
Contents
1 1.
Equations for Reacting Fluids
245
11.11.
The conservation of matter,
245. 11.12.
Mass fluxes,
247. 11.13.
StoichUrmetric and kinetic relations,
248. 11.2.
The conservation of momen¬
tum,
249. 11.31.
The conservation of energy,
250. 11.32.
The diffusion of
heat and matter,
251. 11.33.
Transport in binary mixtures,
252.
Appendix
A. Résumé
of Three-dimensional Coordinate Geometry and
Matrix Theory
254
A.I. Cartesian coordinate systems,
254.
A.2. The projection of one line on
another
—
Orthogonality,
256.
A.3. The line, plane, and surface,
257.
A.A.
Row and column vectors
—
change of origin and scale,
258.
A.5.
Matrices and quadrics,
259.
A.6. Matrices and rotations of axes,
262.
A.7. The laws of
mátrixalgebra,
263.
A.8. Determinants
—
the inverse of a
matrix,
265.
A.
9.
Partitioned matrices
—
Laplacian expansion
—
product
of determinants,
268.
A.10. Latent roots and vectors of a symmetric matrix,
270.
A.ll. Canonical form of symmetric matrices and quadrics,
271.
A.12. Stationary properties,
274.
Appendix B. Implicit Functions and Jacobians
276
Index
281 |
| any_adam_object | 1 |
| author | Aris, Rutherford 1929-2005 |
| author_GND | (DE-588)12346420X |
| author_facet | Aris, Rutherford 1929-2005 |
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| ctrlnum | (OCoLC)20318500 (DE-599)BVBBV004279476 |
| dewey-full | 532 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532 |
| dewey-search | 532 |
| dewey-sort | 3532 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| edition | Unabridged and corr. republ. of the work first publ. by Prentice-Hall, Englewood Cliffs, NJ, in 1962 |
| format | Book |
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| id | DE-604.BV004279476 |
| illustrated | Illustrated |
| indexdate | 2025-01-13T11:00:35Z |
| institution | BVB |
| isbn | 0486661105 9780486661100 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002661325 |
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| physical | XIV, 286 S. Ill., graph. Darst. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
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| publisher | Dover Publ. |
| record_format | marc |
| spelling | Aris, Rutherford 1929-2005 Verfasser (DE-588)12346420X aut Vectors, tensors, and the basic equations of fluid mechanics Rutherford Aris Unabridged and corr. republ. of the work first publ. by Prentice-Hall, Englewood Cliffs, NJ, in 1962 New York Dover Publ. 1989 XIV, 286 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mecanica E Dinamica Dos Fluidos larpcal Sıvı dinamiği Tensörler hesabı Vektör analizi Calculus of tensors Fluid dynamics Vector analysis Vektorrechnung (DE-588)4062471-7 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Tensorrechnung (DE-588)4192487-3 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 s Mathematische Physik (DE-588)4037952-8 s Vektorrechnung (DE-588)4062471-7 s DE-604 Tensorrechnung (DE-588)4192487-3 s Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002661325&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aris, Rutherford 1929-2005 Vectors, tensors, and the basic equations of fluid mechanics Mecanica E Dinamica Dos Fluidos larpcal Sıvı dinamiği Tensörler hesabı Vektör analizi Calculus of tensors Fluid dynamics Vector analysis Vektorrechnung (DE-588)4062471-7 gnd Mathematische Physik (DE-588)4037952-8 gnd Tensorrechnung (DE-588)4192487-3 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| subject_GND | (DE-588)4062471-7 (DE-588)4037952-8 (DE-588)4192487-3 (DE-588)4077970-1 |
| title | Vectors, tensors, and the basic equations of fluid mechanics |
| title_auth | Vectors, tensors, and the basic equations of fluid mechanics |
| title_exact_search | Vectors, tensors, and the basic equations of fluid mechanics |
| title_full | Vectors, tensors, and the basic equations of fluid mechanics Rutherford Aris |
| title_fullStr | Vectors, tensors, and the basic equations of fluid mechanics Rutherford Aris |
| title_full_unstemmed | Vectors, tensors, and the basic equations of fluid mechanics Rutherford Aris |
| title_short | Vectors, tensors, and the basic equations of fluid mechanics |
| title_sort | vectors tensors and the basic equations of fluid mechanics |
| topic | Mecanica E Dinamica Dos Fluidos larpcal Sıvı dinamiği Tensörler hesabı Vektör analizi Calculus of tensors Fluid dynamics Vector analysis Vektorrechnung (DE-588)4062471-7 gnd Mathematische Physik (DE-588)4037952-8 gnd Tensorrechnung (DE-588)4192487-3 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| topic_facet | Mecanica E Dinamica Dos Fluidos Sıvı dinamiği Tensörler hesabı Vektör analizi Calculus of tensors Fluid dynamics Vector analysis Vektorrechnung Mathematische Physik Tensorrechnung Strömungsmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002661325&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT arisrutherford vectorstensorsandthebasicequationsoffluidmechanics |