Fluid dynamics of jets:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Toronto [u.a.]
Van Nostrand
1954
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 227 S. graph. Darst. |
Internformat
MARC
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| 100 | 1 | |a Pai, Shih-I |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Fluid dynamics of jets |c Shih-I Pai |
| 264 | 1 | |a Toronto [u.a.] |b Van Nostrand |c 1954 | |
| 300 | |a XV, 227 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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Datensatz im Suchindex
| _version_ | 1804116604540157952 |
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| adam_text | table of contents
CHAPTER page
Preface v
Introduction xiii
I FLOW OF A JET OF INVISCID AND INCOMPRESS-
* IBLE FLUID 1
1 Bernoulli’s theorem 1
2 Flow of a jet, deduced from Bernoulli’s theorem 2
(a) The efflux of fluid from a vessel as a result of grav-
ity 2
(b) The efflux of fluid from a tank as a result of ex-
cess pressure inside 3
3 Momentum theorem and reaction due to the flow of a jet 4
(a) Reaction due to the efflux of a jet 4
(b) Sudden enlargement of a pipe 5
(c) von Karman’s theory of thrust augmentation 5
4 Surface of discontinuity 6
5 Irrotational motion 7
6 Two-dimensional flow Impinging jets 9
7 Helmholtz problems and their extensions 13
8 Recent developments in free boundary theory 17
9 Rayleigh’s theory of three-dimensional flow of a jet of
ideal fluid 18
10 Experimental results The behavior of jets of incom-
pressible fluid 20
References 21
II SUBSONIC FLOW OF A JET OF INVISCID FLUID 23
1 Introductory remarks 23
2 One-dimensional steady flow of inviscid and compress-
ible fluid 24
(a) Fundamental equations 24
• (b) Velocity of sound and Mach number 25
(c) One-dimensional steady flow in a nozzle 27
3 Fundamental equations of two-dimensional flow of a
jet of compressible fluid 30
4 Chaplygin’s exact solution of gas jet 31
vii
viii TABLE OF CONTENTS
CHAPTER PACE
5 Subsonic gas jet from an infinitely wide vessel 33
6 Approximate solution of subsonic gas jet 35
7 Tricomi’s equation and transonic flow 37
8 Three-dimensional subsonic flow of a jet 38
References 39
III SUPERSONIC FLOW OF A JET OF INVISCID FLUID 41
1 Historic sketch of supersonic jet of gas 41
2 Phenomena in supersonic flow of a jet 42
3 Analysis of supersonic jet in medium at rest 46
4 Two-dimensional supersonic jet in a uniform stream 49
5 Axially symmetric supersonic jet in uniform stream 55
6 Supersonic jet from a vessel with plane wall 56
7 Method of characteristics 57
8 Shock wave 61
9 Reflections of shock waves from solid or free boundary 64
10 Two-dimensional supersonic flow of a jet—Method of
characteristics 66
11 Axially symmetric supersonic jet flow—Method of char-
acteristics 68
References 68
IV LAMINAR FLOW OF A JET OF VISCOUS FLUID 71
1 Introduction 71
2 Reynolds’ law of similarity and dimensional analysis 73
3 Plane jet mixing of an incompressible fluid 76
4 Axially symmetric jet mixing of an incompressible fluid 78
5 Laminar mixing of two uniform streams of incom-
pressible fluid 79
6 Two-dimensional laminar jet mixing of a compressible
fluid 81
7 Axially symmetric laminar jet mixing of a compress-
ible fluid 89
8 Jet mixing of a compressible fluid with over or under
pressure 92
References 94
V TURBULENT FLOW OF A JET OF INCOMPRESSI-
BLE FLUID 96
1 Introduction 96
2 Prandtl-Tollmien’s problems 98
(a) The free jet boundary 99
(b) The plane jet 102
TABLE OF CONTENTS
5 Subsonic gas jet from an infinitely wide vessel 33
6 Approximate solution of subsonic gas jet 35
7 Tricomi’s equation and transonic flow 37
8 Three-dimensional subsonic flow of a jet 38
References 39
UPERSONIC FLOW OF A JET OF INVISCID FLUID 41
1 Historic sketch of supersonic jet of gas 41
2 Phenomena in supersonic flow of a jet 42
3 Analysis of supersonic jet in medium at rest 46
4 Two-dimensional supersonic jet in a uniform stream 49
5 Axially symmetric supersonic jet in uniform stream 55
6 Supersonic jet from a vessel with plane wall 56
7 Method of characteristics 57
8 Shock wave 61
9 Reflections of shock waves from solid or free boundary 64
10 Two-dimensional supersonic flow of a jet—Method of
characteristics 66
11 Axially symmetric supersonic jet flow—Method of char-
acteristics 68
References 68
AMINAR FLOW OF A JET OF VISCOUS FLUID 71
1 Introduction 71
2 Reynolds’ law of similarity and dimensional analysis 73
3 Plane jet mixing of an incompressible fluid 76
4 Axially symmetric jet mixing of an incompressible fluid 78
5 Laminar mixing of two uniform streams of incom-
pressible fluid 79
6 Two-dimensional laminar jet mixing of a compressible
fluid 81
7 Axially symmetric laminar jet mixing of a compress-
ible fluid 89
8 Jet mixing of a compressible fluid with over or under
pressure 92
References 94
;
1
i
5
i
*
i
,1
:
?
URBULENT FLOW OF A JET OF INCOMPRESSI-
BLE FLUID 96
1 Introduction 96
2 Prandtl-Tollmien’s problems 98
(a) The free jet boundary 99
(b) The plane jet 102
TABLE of contents
CHAPTER
ef-
(c) Axially symmetric jet
(d) Calculation of pressure differences
3 Some extensions of Tollmien’s problems
(a) Plane jet issuing into a medium not at rest
(b) Velocity distribution of axially symmetric jet near
the nozzle
(c) Axially symmetric jet in uniform stream
(d) Mixing of two parallel streams including the
fects of initial boundary layers
4 Some improvements on Tollmien’s analysis
(a) Vorticity transfer theory
(b) Constant exchange coefficient hypothesis
(c) Prandtl’s new theory
(d) Theory including the effect of intermittency
5 Dimensional analysis on the theory of free turbulence
6 Integral relations of jet flow
7 Reichardt’s Inductive Theory of Free Turbulence
8 Experimental results on mean velocity distribution—
Intermittency for turbulence
(a) Half jet or free mixing region
(b) Plane jet
(c) Axially symmetric jet
(d) Intermittency
9 Properties of turbulent fluctuations
(a) Reynolds stresses
(b) Averaging processes in turbulent flow
(c) Standard deviations and turbulent intensities
(d) Correlations
(e) Spectrum of turbulence
(f) Probability distribution in turbulence
(g) Energy balance for turbulent flow
(h) Local isotropy
10 Experimental results on turbulent fluctuations
References
VI TURBULENT FLOW OF A JET OF COMPRESSIBLE
FLUID
1 Introduction
2 The temperature distribution in heated jets of low sub-
sonic speed
3 The turbulent jet mixing of a compressible fluid—Sub-
sonic speed and moderate temperature difference
IX
PAGE
104
107
108
108
109
110
110
111
111
112
112
113
113
114
116
118
118
119
119
120
121
121
122
123
124
125
127
129
130
132
136
139
139
140
141
I
TABLE OF CONTENTS
CHAPTER PAGE
4 The turbulent jet mixing of a compressible fluid at
supersonic speed and large temperature difference 143
5 Reichardt’s Inductive Theory 145
6 Experimental results of a subsonic heated turbulent jet 146
7 Experimental results of supersonic turbulent jet mixing 148
8 Noise emanating from a jet 149
References 151
VII JET MIXING OF GASES OF DIFFERENT KINDS 153
1 Introduction 153
2 Equation of diffusion 154
3 Theory of turbulent diffusion 155
4 Mixture of gases 158
5 Fundamental equations of two-dimensional laminar jet
mixing of two gases 160
6 Two-dimensional laminar jet mixing of two gases 162
7 Turbulent jet mixing of two gases at constant tempera-
ture 164
8 Some experimental results on mass transfer and of jet
mixing of two gases 172
References 173
VIII THE STABILITY OF A JET OF INCOMPRESSIBLE
FLUID 175
1 Introduction and historical sketch 175
2 Stability of ideal jet of incompressible fluid 176
3 Orr-Sommerfeld equation and its solution 179
4 Asymptotic behavior of the solution at infinity 182
5 Boundary value problems 183
6 Stability of a jet of an inviscid and an incompressible
fluid 184
7 Stability of a two-dimensional jet of viscous and in-
compressible fluid 186
8 Stability of a half jet of a viscous, incompressible fluid 189
9 Stability of a three-dimensional jet of an inviscid fluid 190
References 190
IX STABILITY OF A JET OF COMPRESSIBLE FLUID 193
1 Introduction 193
2 Stability of an ideal jet of a compressible fluid 194
3 Fundamental equations of stability of jet flow of com-
pressible fluid 196
OF CONT
4 Solution
behavi
5 Subsonic
6 Bounda
7 Stability
8 Stability
References
APPENDIX: FU
NAMICS
1 Introduc
2 Equatio
3 Equatio
(a) Equ
(b) Equ
fl
(c) Equ
(d) Rey
(e) Rey
4 Equatio
(a) Eq
(b) Eq
(c) Equ
c
(d) Eq
5 Equatio
I AUTHOR INDEX
f SUBJECT INDEX
TABLE OF CONTENTS
4 The turbulent jet mixing of a compressible fluid at
supersonic speed and large temperature difference 143
5 Reichardt’s Inductive Theory 145
6 Experimental results of a subsonic heated turbulent jet 146
7 Experimental results of supersonic turbulent jet mixing 148
8 Noise emanating from a jet 149
References 151
JET MIXING OF GASES OF DIFFERENT KINDS 153
1 Introduction 153
2 Equation of diffusion 154
3 Theory of turbulent diffusion 155
4 Mixture of gases 158
5 Fundamental equations of two-dimensional laminar jet
mixing of two gases 160
6 Two-dimensional laminar jet mixing of two gases 162
7 Turbulent jet mixing of two gases at constant tempera-
ture 164
8 Some experimental results on mass transfer and of jet
mixing of two gases 172
References 173
HE STABILITY OF A JET OF INCOMPRESSIBLE
FLUID 175
1 Introduction and historical sketch 175
2 Stability of ideal jet of incompressible fluid 176
3 Orr-Sommerfeld equation and its solution 179
4 Asymptotic behavior of the solution at infinity 182
5 Boundary value problems 183
6 Stability of a jet of an inviscid and an incompressible
fluid 184
7 Stability of a two-dimensional jet of viscous and in-
compressible fluid 186
8 Stability of a half jet of a viscous, incompressible fluid 189
9 Stability of a three-dimensional jet of an inviscid fluid 190
References 190
TABILITY OF A JET OF COMPRESSIBLE FLUID 193
1 Introduction 193
2 Stability of an ideal jet of a compressible fluid 194
3 Fundamental equations of stability of jet flow of com-
pressible fluid 196
TABLE OF CONTENTS
: CHAPTER PACE
4 Solution of stability equations and their asymptotic
I behaviors 198
5 Subsonic, sonic, and supersonic disturbances 202
| 6 Boundary value problems 204
| 7 Stability of a two-dimensional jet of an inviscid fluid 205
8 Stability of the two-dimensional jet of a viscous fluid 207
References 208
5 APPENDIX: FUNDAMENTAL EQUATIONS OF FLUID DY-
I NAMICS 209
| 1 Introduction 209
| 2 Equation of continuity 209
| 3 Equations of motion 211
| (a) Equations of motion of a viscous compressible fluid 211
(b) Equations of motion of a laminar boundary layer
flow 212
U (c) Equations of motion of an inviscid fluid 212
| (d) Reynolds equations of motion of turbulent flow 216
(e) Reynolds equations of jet mixing flow 216
§ 4 Equation of energy 218
| (a) Equation of energy of a viscous compressible fluid 218
I (b) Equation of a laminar boundary layer flow 219
(c) Equation of energy of an inviscid and nonheat-
^ conducting fluid 219
f; (d) Equation of energy of turbulent jet mixing flow 220
* 5 Equation of state 220
f References 221
AUTHOR INDEX 223
V SUBJECT INDEX 225
|
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| author_sort | Pai, Shih-I |
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| bvnumber | BV002149841 |
| ctrlnum | (OCoLC)230067592 (DE-599)BVBBV002149841 |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:41:09Z |
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| language | English |
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| spelling | Pai, Shih-I Verfasser aut Fluid dynamics of jets Shih-I Pai Toronto [u.a.] Van Nostrand 1954 XV, 227 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001410340&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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