Basics of Fluid Mechanics, 2014a

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LIST OF FIGURES xv 4.32 Polynomial shape dam description .................... 115 4.33 The difference between the slop and the direction angle . ........ 115 4.34 Schematic of Immersed Cylinder . .................... 117 4.35 The floating forces on Immersed Cylinder . ............... 118 4.36 Schematic of a thin wall floating body . ................. 118 4.37 Schematic of floating bodies ....................... 126 4.38 Schematic of floating cubic . ....................... 127 4.39 Stability analysis of floating body . .................... 127 4.40 Cubic body dimensions for stability analysis . .............. 130 4.41 Stability of cubic body infinity long .................... 131 4.42 The maximum height reverse as a function of density ratio . ...... 131 4.43 Stability of two triangles put tougher ................... 132 4.44 The effects of liquid movement on the GM ............... 134 4.45 Measurement of GM of floating body ................... 135 4.46 Calculations of GM for abrupt shape body . ............... 136 4.47 A heavy needle is floating on a liquid. . ................. 138 4.48 Description of depression to explain the Rayleigh–Taylor instability . . . 139 4.49 Description of depression to explain the instability . ........... 141 4.50 The cross section of the interface for max liquid. . ........... 142 4.51 Three liquids layers under rotation .................... 143 5.1 Control volume and system in motion . ................. 147 5.2 Piston control volume . .......................... 148 5.3 Schematics of velocities at the interface ................. 149 5.4 Schematics of flow in a pipe with varying density . ........... 150 5.5 Filling of the bucket and choices of the control volumes . ........ 153 5.6 Height of the liquid for example 5.4 ................... 156 5.7 Boundary Layer control mass ....................... 161 5.8 Control volume usage to calculate local averaged velocity ........ 166 5.9 Control volume and system in the motion . ............... 167 5.10 Circular cross section for finding U x ................... 168 5.11 Velocity for a circular shape . ....................... 169 5.12 Boat for example 5.14 .......................... 169 6.1 The explanation for the direction relative to surface ........... 174 6.2 Schematics of area impinged by a jet ................... 177 6.3 Nozzle schematic for forces calculations ................. 179 6.4 Propeller schematic to explain the change of momentum ........ 181 6.5 Toy Sled pushed by the liquid jet . .................... 182 6.6 A rocket with a moving control volume . ................. 183 6.7 Schematic of a tank seating on wheels . ................. 185 6.8 A new control volume to find the velocity in discharge tank . ...... 186 6.9 The impeller of the centrifugal pump and the velocities diagram . . . . 191 6.10 Nozzle schematics water rocket ...................... 192 6.11 Flow out of un symmetrical tank . .................... 195
xvi LIST OF FIGURES 6.12 The explanation for the direction relative to surface ........... 196 7.1 The work on the control volume . .................... 198 7.2 Discharge from a Large Container . ................... 200 7.3 Kinetic Energy and Averaged Velocity . ................. 202 7.4 Typical resistance for selected outlet configuration . ........... 210 (a) Projecting pipe K= 1 ........................ 210 (b) Sharp edge pipe connection K=0.5 . ................ 210 (c) Rounded inlet pipe K=0.04 . .................... 210 7.5 Flow in an oscillating manometer . .................... 210 7.6 A long pipe exposed to a sudden pressure difference ........... 218 7.7 Liquid exiting a large tank trough a long tube . ............. 220 7.8 Tank control volume for Example 7.2 .................. 221 8.1 The mass balance on the infinitesimal control volume .......... 228 8.2 The mass conservation in cylindrical coordinates ............. 230 8.3 Mass flow due to temperature difference . ................ 232 8.4 Mass flow in coating process . ...................... 234 8.5 Stress diagram on a tetrahedron shape . ................. 241 8.6 Diagram to analysis the shear stress tensor ................ 243 8.7 The shear stress creating torque . .................... 243 8.8 The shear stress at different surfaces ................... 245 8.9 Control volume at t and t + dt under continuous angle deformation . . 247 8.10 Shear stress at two coordinates in 45 ◦ orientations . ........... 248 8.11 Different rectangles deformations . .................... 249 (a) Deformations of the isosceles triangular . ............. 249 (b) Deformations of the straight angle triangle . ........... 249 8.12 Linear strain of the element ........................ 251 8.13 1–Dimensional free surface ........................ 256 8.14 Flow driven by surface tension ...................... 259 8.15 Flow in kendle with a surfece tension gradient . ............. 259 8.16 Flow between two plates when the top moving . ............. 260 8.17 One dimensional flow with shear between plates ............. 261 8.18 The control volume of liquid element in “short cut” ........... 262 8.19 Flow of Liquid between concentric cylinders . .............. 264 8.20 Mass flow due to temperature difference . ................ 267 8.21 Liquid flow due to gravity ......................... 269 9.1 Fitting rod into a hole ........................... 278 9.2 Pendulum for dimensional analysis . ................... 279 9.3 Resistance of infinite cylinder . ...................... 285 9.4 Oscillating Von Karman Vortex Street . ................. 312 10.1 Streamlines to explain stream function . ................. 334 10.2 Streamlines with different different element direction to explain stream function335
Page 2 and 3: Basics of Fluid Mechanics Genick Ba
Page 4 and 5: iii ‘We are like dwarfs sitting o
Page 6 and 7: CONTENTS Nomenclature xxiii GNU Fre
Page 8 and 9: CONTENTS vii 4 Fluids Statics 69 4.
Page 10 and 11: CONTENTS ix 9.2.1 Construction of t
Page 12 and 13: CONTENTS xi 12.5 The Working Equati
Page 14 and 15: LIST OF FIGURES 1.1 Diagram to expl
Page 18 and 19: LIST OF FIGURES xvii (a) Streamline
Page 20 and 21: LIST OF FIGURES xix 12.22The angles
Page 22 and 23: LIST OF TABLES 1 Books Under Potto
Page 24 and 25: NOMENCLATURE ¯R Universal gas cons
Page 26 and 27: LIST OF TABLES xxv w Work per unit
Page 28 and 29: The Book Change Log Version 0.3.4.0
Page 30 and 31: LIST OF TABLES xxix ˆ Add discussi
Page 32 and 33: LIST OF TABLES xxxi ˆ Add the open
Page 34 and 35: Notice of Copyright For This Docume
Page 36 and 37: GNU FREE DOCUMENTATION LICENSE xxxv
Page 38 and 39: GNU FREE DOCUMENTATION LICENSE xxxv
Page 40 and 41: GNU FREE DOCUMENTATION LICENSE 7. A
Page 42 and 43: CONTRIBUTOR LIST How to contribute
Page 44 and 45: CREDITS Typo corrections and other
Page 46 and 47: About This Author Genick Bar-Meir i
Page 48 and 49: Prologue For The POTTO Project This
Page 50 and 51: CREDITS xlix process. Someone has t
Page 52 and 53: CREDITS li have a new version every
Page 54 and 55: Prologue For This Book Version 0.3.
Page 56 and 57: VERSION 0.1 APRIL 22, 2008 lv and t
Page 58 and 59: How This Book Was Written This book
Page 60 and 61: Preface "In the beginning, the POTT
Page 62 and 63: To Do List and Road Map This book i
Page 64 and 65: CHAPTER 1 Introduction to Fluid Mec
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1.2. BRIEF HISTORY 3 lay is one of
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1.3. KINDS OF FLUIDS 5 results. The
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1.4. SHEAR STRESS 7 For cases where
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1.5. VISCOSITYVISCOSITY 9 The veloc
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1.5. VISCOSITYVISCOSITY 11 always p
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2.5 2.0 1.5 1.0 0.5 0 100 200 300 4
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1.5. VISCOSITYVISCOSITY 15 Chemical
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1.5. VISCOSITYVISCOSITY 17 2 Reduce
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1.5. VISCOSITYVISCOSITY 19 In very
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1.6. FLUID PROPERTIES 21 The total
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1.6. FLUID PROPERTIES 23 straight.
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1.6. FLUID PROPERTIES 25 Table -1.5
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1.6. FLUID PROPERTIES 27 Two layers
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1.6. FLUID PROPERTIES 29 1.6.2.1 Bu
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1.7. SURFACE TENSION 31 terials. Th
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1.7. SURFACE TENSION 33 or Or after
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1.7. SURFACE TENSION 35 The maximum
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1.7. SURFACE TENSION 37 kipenii,”
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1.7. SURFACE TENSION 39 Equation (1
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1.7. SURFACE TENSION 41 Example 1.1
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1.7. SURFACE TENSION 43 Table -1.7.
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CHAPTER 2 Review of Thermodynamics
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2.1. BASIC DEFINITIONS 47 Since the
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2.1. BASIC DEFINITIONS 49 when the
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2.1. BASIC DEFINITIONS 51 Utilizing
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CHAPTER 3 Review of Mechanics This
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3.2. CENTER OF MASS 55 3.2 Center o
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3.3. MOMENT OF INERTIA 57 The momen
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3.3. MOMENT OF INERTIA 59 Equation
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3.3. MOMENT OF INERTIA 61 Example 3
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3.3. MOMENT OF INERTIA 63 or x (1 a
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3.5. ANGULAR MOMENTUM AND TORQUE 65
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3.5. ANGULAR MOMENTUM AND TORQUE 67
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CHAPTER 4 Fluids Statics 4.1 Introd
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4.3. PRESSURE AND DENSITY IN A GRAV
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4.4. FLUID IN A ACCELERATED SYSTEM
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4.5. FLUID FORCES ON SURFACES 101 T
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4.5. FLUID FORCES ON SURFACES 103 x
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4.5. FLUID FORCES ON SURFACES 107 I
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4.5. FLUID FORCES ON SURFACES 111 C
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4.5. FLUID FORCES ON SURFACES 113 A
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4.5. FLUID FORCES ON SURFACES 115 F
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4.6. BUOYANCY AND STABILITY 117 In
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4.6. BUOYANCY AND STABILITY 119 ρ
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4.6. BUOYANCY AND STABILITY 121 ( )
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4.6. BUOYANCY AND STABILITY 123 The
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4.6. BUOYANCY AND STABILITY 125 on
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4.6. BUOYANCY AND STABILITY 127 A w
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4.6. BUOYANCY AND STABILITY 129 It
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4.6. BUOYANCY AND STABILITY 131 Thu
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4.6. BUOYANCY AND STABILITY 133 The
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4.6. BUOYANCY AND STABILITY 135 A n
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4.6. BUOYANCY AND STABILITY 137 of
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4.7. RAYLEIGH-TAYLOR INSTABILITY 13
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4.7. RAYLEIGH-TAYLOR INSTABILITY 14
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4.8. QUALITATIVE QUESTIONS 143 can
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Part I Integral Analysis 145
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148 CHAPTER 5. MASS CONSERVATION di
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150 CHAPTER 5. MASS CONSERVATION It
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152 CHAPTER 5. MASS CONSERVATION 5.
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154 CHAPTER 5. MASS CONSERVATION Th
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156 CHAPTER 5. MASS CONSERVATION Wh
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158 CHAPTER 5. MASS CONSERVATION Th
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162 CHAPTER 5. MASS CONSERVATION ri
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166 CHAPTER 5. MASS CONSERVATION En
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168 CHAPTER 5. MASS CONSERVATION Ex
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170 CHAPTER 5. MASS CONSERVATION So
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172 CHAPTER 5. MASS CONSERVATION In
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174 CHAPTER 6. MOMENTUM CONSERVATIO
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198 CHAPTER 7. ENERGY CONSERVATION
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CHAPTER 8 Differential Analysis 8.1
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8.2. MASS CONSERVATION 229 The firs
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8.2. MASS CONSERVATION 231 Combinin
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8.2. MASS CONSERVATION 233 Equation
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8.2. MASS CONSERVATION 235 The dens
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8.2. MASS CONSERVATION 237 Example
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8.3. CONSERVATION OF GENERAL QUANTI
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8.4. MOMENTUM CONSERVATION 241 8.4
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8.4. MOMENTUM CONSERVATION 243 The
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8.5. DERIVATIONS OF THE MOMENTUM EQ
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8.6. BOUNDARY CONDITIONS AND DRIVIN
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8.6. BOUNDARY CONDITIONS AND DRIVIN
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8.7. EXAMPLES FOR DIFFERENTIAL EQUA
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CHAPTER 9 Dimensional Analysis This
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9.1. INTRODUCTORY REMARKS 275 the r
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9.1. INTRODUCTORY REMARKS 277 End S
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9.1. INTRODUCTORY REMARKS 279 Deriv
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9.2. BUCKINGHAM-π-THEOREM 281 para
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9.2. BUCKINGHAM-π-THEOREM 283 magn
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9.2. BUCKINGHAM-π-THEOREM 285 Tabl
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9.2. BUCKINGHAM-π-THEOREM 287 End
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9.2. BUCKINGHAM-π-THEOREM 289 Equa
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9.2. BUCKINGHAM-π-THEOREM 291 the
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9.2. BUCKINGHAM-π-THEOREM 293 than
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9.2. BUCKINGHAM-π-THEOREM 295 Unde
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9.2. BUCKINGHAM-π-THEOREM 297 Solu
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9.3. NUSSELT’S TECHNIQUE 299 The
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9.3. NUSSELT’S TECHNIQUE 301 boun
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9.3. NUSSELT’S TECHNIQUE 303 Noti
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9.3. NUSSELT’S TECHNIQUE 305 In t
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9.3. NUSSELT’S TECHNIQUE 307 Wher
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9.4. SUMMARY OF DIMENSIONLESS NUMBE
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9.5. SUMMARY 319 It can be noticed
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9.6. APPENDIX SUMMARY OF DIMENSIONL
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BIBLIOGRAPHY [1] Buckingham, E. On
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CHAPTER 10 Inviscid Flow or Potenti
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10.1. INTRODUCTION 327 where in thi
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10.1. INTRODUCTION 329 With the ide
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10.1. INTRODUCTION 331 The partial
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10.2. POTENTIAL FLOW FUNCTION 333 T
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10.2. POTENTIAL FLOW FUNCTION 335 t
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10.2. POTENTIAL FLOW FUNCTION 341 9
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10.3. POTENTIAL FLOW FUNCTIONS INVE
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10.4. CONFORMING MAPPING 369 flow d
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10.4. CONFORMING MAPPING 371 The un
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10.5. UNSTEADY STATE BERNOULLI IN A
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10.6. QUESTIONS 375 Table -10.2. Di
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CHAPTER 11 Compressible Flow One Di
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11.3. SPEED OF SOUND 379 to be cont
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11.3. SPEED OF SOUND 381 Solution T
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11.3. SPEED OF SOUND 383 consider a
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11.4. ISENTROPIC FLOW 385 Now, subs
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11.4. ISENTROPIC FLOW 387 Static Pr
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11.4. ISENTROPIC FLOW 389 that the
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11.4. ISENTROPIC FLOW 391 Using the
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11.4. ISENTROPIC FLOW 393 Solution
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11.4. ISENTROPIC FLOW 395 Expressin
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11.4. ISENTROPIC FLOW 397 The tempe
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11.4. ISENTROPIC FLOW 399 Table -11
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11.4. ISENTROPIC FLOW 405 Example 1
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11.5. NORMAL SHOCK 407 In a shock w
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11.5. NORMAL SHOCK 409 Energy equat
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11.5. NORMAL SHOCK 411 The density
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11.5. NORMAL SHOCK 413 or in a dime
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11.5. NORMAL SHOCK 415 which differ
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11.5. NORMAL SHOCK 417 is different
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11.5. NORMAL SHOCK 419 Table -11.3.
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11.6. ISOTHERMAL FLOW 421 Table -11
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11.6. ISOTHERMAL FLOW 423 Rearrangi
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11.6. ISOTHERMAL FLOW 425 dT 0 T 0
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11.6. ISOTHERMAL FLOW 427 10 2 0 1
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11.6. ISOTHERMAL FLOW 429 The fact
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11.6. ISOTHERMAL FLOW 431 Calculati
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11.6. ISOTHERMAL FLOW 433 maximum M
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11.6. ISOTHERMAL FLOW 435 From the
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11.7. FANNO FLOW 437 The energy con
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11.7. FANNO FLOW 439 Differentiatin
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11.7. FANNO FLOW 441 11.7.3 The Mec
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11.7. FANNO FLOW 443 pressure on th
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11.7. FANNO FLOW 445 10 2 0 1 2 3 4
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11.7. FANNO FLOW 447 End Solution A
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11.7. FANNO FLOW 449 M x M y T y T
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11.7. FANNO FLOW 451 11.7.5.1 Maxim
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11.7. FANNO FLOW 453 At the startin
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11.7. FANNO FLOW 455 Fanno Flow 5 4
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11.7. FANNO FLOW 457 11.7.7.1 Choki
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11.7. FANNO FLOW 459 back pressure
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11.7. FANNO FLOW 461 The solution i
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11.7. FANNO FLOW 463 11.7.8 The Pra
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11.7. FANNO FLOW 465 0.9 0.8 0.7 0.
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11.7. FANNO FLOW 467 3.0 2.5 2.0 Co
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11.8. THE TABLE FOR FANNO FLOW 469
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11.9. RAYLEIGH FLOW 471 Table -11.6
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11.10. INTRODUCTION 473 or in simpl
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11.10. INTRODUCTION 475 or explicit
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11.10. INTRODUCTION 477 Table -11.7
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11.10. INTRODUCTION 479 Example 11.
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11.10. INTRODUCTION 481 Example 11.
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11.10. INTRODUCTION 483 what the ma
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CHAPTER 12 Compressible Flow 2-Dime
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12.2. OBLIQUE SHOCK 487 12.2 Obliqu
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12.2. OBLIQUE SHOCK 489 The relatio
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12.2. OBLIQUE SHOCK 491 Where S = 3
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12.2. OBLIQUE SHOCK 493 by evaluati
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12.2. OBLIQUE SHOCK 495 Figure (12.
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12.2. OBLIQUE SHOCK 497 be made. Th
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12.2. OBLIQUE SHOCK 499 demonstrate
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12.2. OBLIQUE SHOCK 501 or explicit
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12.2. OBLIQUE SHOCK 503 Fig. -12.9.
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12.2. OBLIQUE SHOCK 505 Table -12.1
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12.2. OBLIQUE SHOCK 507 Example 12.
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12.2. OBLIQUE SHOCK 509 In the obli
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12.2. OBLIQUE SHOCK 511 M x M ys M
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12.2. OBLIQUE SHOCK 513 M x M y T y
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12.2. OBLIQUE SHOCK 515 M x M yw θ
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12.2. OBLIQUE SHOCK 517 The pressur
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12.2. OBLIQUE SHOCK 519 From these
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12.3. PRANDTL-MEYER FUNCTION 521 as
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12.3. PRANDTL-MEYER FUNCTION 523 Th
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12.3. PRANDTL-MEYER FUNCTION 525 No
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1 2 12.7. FLAT BODY WITH AN ANGLE O
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12.8. EXAMPLES FOR PRANDTL-MEYER FU
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12.9. COMBINATION OF THE OBLIQUE SH
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12.9. COMBINATION OF THE OBLIQUE SH
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CHAPTER 13 Multi-Phase Flow 13.1 In
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13.4. KIND OF MULTI-PHASE FLOW 537
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13.5. CLASSIFICATION OF LIQUID-LIQU
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13.5. CLASSIFICATION OF LIQUID-LIQU
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13.6. MULTI-PHASE FLOW VARIABLES DE
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13.6. MULTI-PHASE FLOW VARIABLES DE
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13.7. HOMOGENEOUS MODELS 547 13.7 H
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13.7. HOMOGENEOUS MODELS 549 There
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13.8. SOLID-LIQUID FLOW 551 where
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13.8. SOLID-LIQUID FLOW 553 So far
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13.9. COUNTER-CURRENT FLOW 555 The
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13.9. COUNTER-CURRENT FLOW 561 For
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13.10. MULTI-PHASE CONCLUSION 565 1
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APPENDIX A The Mathematics Backgrou
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A.1. VECTORS 569 where θ is the an
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A.1. VECTORS 571 Divergence The sam
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A.1. VECTORS 573 R · S =(xî + y 2
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A.1. VECTORS 575 The curl is writte
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A.1. VECTORS 577 The divergence of
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A.2. ORDINARY DIFFERENTIAL EQUATION
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A.3. PARTIAL DIFFERENTIAL EQUATIONS
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A.4. TRIGONOMETRY 595 A.4 Trigonome
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SUBJECTS INDEX 597 Subjects Index S
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SUBJECTS INDEX 599 Ideal gas, 91 Re
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SUBJECTS INDEX 601 Slip condition r
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AUTHORS INDEX 603 Authors Index B B
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