Basics of Fluid Mechanics, 2014a

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AUTHORS INDEX 603 Authors Index B Bhuckingham, 4 Blasiu, 4 Blasius, 4 Bossut, 4 Brahms, 4 Buckingham, 273, 275 C Chezy, 4 Cichilli, 549 Coulomb, 4 D d’Aubisson, 4 Darcy, 4 de Saint Venant, Barré, 227 Dubuat, 4 Duckler, 536, 549 Dupuit, 4 E Euler, 4 Euler, Leonahard, 314 Evangelista Torricelli, 209 F Fabre, 4 Fanning, 4 Fourier Jean B. J., 274 Froude, William, 4, 274 G Ganguillet, 4 Gauss, Carl Friedrich, 572 H Hagen, 4 Helmhoitz, 4 Helmholtz, Hermann von, 4 Henderson, 508 K Kelvin, 4 Kirchh<strong>of</strong>f, 4 Kutta, Martin Wilhelm, 368 Kutta-Joukowski, 4 L La Grange, 4 Leibniz, 158 Lockhart, 536 M Manning, 4 Martinelli, 274, 536 Maxwell, 274 Menik<strong>of</strong>f, 508 Meye, 4 Mikhail Vasilievich Ostrogradsky, 572 N Navier, Claude–Louis, 227 Newton, 274 Nikuradse, 4 Nusselt, Ernst Kraft Wilhelm, 266, 273, 275 O Olivier Vallee, 589 P Pierre-Simon Laplace, 572 Poiseuille, Jean Louis, 262 Poisseuille, 4 Poisson, Simon-Denis, 227 Prandtl, 4 R Rankine, 4 Rayleigh, 4, 139, 274 Reiner, M., 311 Reynolds, Osborne, 158, 275 Riabouchunsky, 275 Rose, 4
604 APPENDIX A. MATHEMATICS FOR FLUID MECHANICS S Schmidt, 273 Smeaton, John, 274 Stanton, 4 Stokes, George Gabriel, 227 Strouhal, Vincenz, 320 T Taitle, 536 Taylor, G.I., 139 Thompson, 490 Torricelli, Evangelista, 209 V Vaschy, Aiméem, 274 Von Karman, 4, 312 W Weisbach, 4 Westinghouse, 538 Z Zhukovsky, Nikolay Yegorovich, 368
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Basics of Fluid Mechanics Genick Ba
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iii ‘We are like dwarfs sitting o
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CONTENTS Nomenclature xxiii GNU Fre
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CONTENTS vii 4 Fluids Statics 69 4.
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CONTENTS ix 9.2.1 Construction of t
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CONTENTS xi 12.5 The Working Equati
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LIST OF FIGURES 1.1 Diagram to expl
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LIST OF FIGURES xv 4.32 Polynomial
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LIST OF FIGURES xvii (a) Streamline
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LIST OF FIGURES xix 12.22The angles
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LIST OF TABLES 1 Books Under Potto
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NOMENCLATURE ¯R Universal gas cons
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LIST OF TABLES xxv w Work per unit
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The Book Change Log Version 0.3.4.0
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LIST OF TABLES xxix ˆ Add discussi
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LIST OF TABLES xxxi ˆ Add the open
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Notice of Copyright For This Docume
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GNU FREE DOCUMENTATION LICENSE xxxv
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GNU FREE DOCUMENTATION LICENSE xxxv
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GNU FREE DOCUMENTATION LICENSE 7. A
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CONTRIBUTOR LIST How to contribute
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CREDITS Typo corrections and other
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About This Author Genick Bar-Meir i
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Prologue For The POTTO Project This
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CREDITS xlix process. Someone has t
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CREDITS li have a new version every
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Prologue For This Book Version 0.3.
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VERSION 0.1 APRIL 22, 2008 lv and t
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How This Book Was Written This book
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Preface "In the beginning, the POTT
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To Do List and Road Map This book i
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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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Page 630 and 631: APPENDIX A The Mathematics Backgrou
Page 632 and 633: A.1. VECTORS 569 where θ is the an
Page 634 and 635: A.1. VECTORS 571 Divergence The sam
Page 636 and 637: A.1. VECTORS 573 R · S =(xî + y 2
Page 638 and 639: A.1. VECTORS 575 The curl is writte
Page 640 and 641: A.1. VECTORS 577 The divergence of
Page 642 and 643: A.2. ORDINARY DIFFERENTIAL EQUATION
Page 656 and 657: A.3. PARTIAL DIFFERENTIAL EQUATIONS
Page 658 and 659: A.4. TRIGONOMETRY 595 A.4 Trigonome
Page 660 and 661: SUBJECTS INDEX 597 Subjects Index S
Page 662 and 663: SUBJECTS INDEX 599 Ideal gas, 91 Re
Page 664 and 665: SUBJECTS INDEX 601 Slip condition r
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