Basics of Fluid Mechanics, 2014a

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2.5 2.0 1.5 1.0 0.5 0 100 200 300 400 500 600 700 800 900 1.5. VISCOSITYVISCOSITY 13 Table -1.3. Viscosity of selected liquids (continue) Chemical component Chemical formula Temperature T [ ◦ C] Viscosity [ N sec m 2 ] (C 2 H 5 )O 20 0.000245 C 6 H 6 20 0.000647 Br 2 26 0.000946 C 2 H 5 OH 20 0.001194 Hg 25 0.001547 H 2 SO 4 25 0.01915 Olive Oil 25 0.084 Castor Oil 25 0.986 Clucuse 25 5-20 Corn Oil 20 0.072 SAE 30 - 0.15-0.200 SAE 50 ∼ 25 ◦ C 0.54 SAE 70 ∼ 25 ◦ C 1.6 Ketchup ∼ 20 ◦ C 0,05 Ketchup ∼ 25 ◦ C 0,098 Benzene ∼ 20 ◦ C 0.000652 Firm glass - ∼ 1 × 10 7 Glycerol 20 1.069 Liquid Metals Liquid metal can be considered as a Newtonian fluid for many applications. Furthermore, many aluminum alloys are behaving as a Newtonian liquid until the first solidification appears (assuming steady state thermodynamics properties). Even when there is a solidification (mushy zone), the metal behavior can be estimated as a Newtonian material (further μ[ Nsec m ] 2 May 1, 2008 Liquid Metal viscosity Temperature [ ◦ C] Fig. -1.10. Liquid metals viscosity as a function of the temperature. reading can be done in this author’s book “Fundamentals of Die Casting Design”). Figure 1.10 exhibits several liquid metals (from The Reactor Handbook, Vol. Atomic Energy Commission AECD-3646 U.S. Government Printing Office, Washington D.C. May 1995 p. 258.) The General Viscosity Graphs Li Na K Hg Pb
14 CHAPTER 1. INTRODUCTION TO FLUID MECHANICS coefficients ❵❵❵❵❵❵❵❵❵❵❵❵ Material Chemical formula Sutherland T iO [K] μ 0 (N sec/m 2 ) ammonia NH 3 370 527.67 0.00000982 standard air 120 524.07 0.00001827 carbon dioxide CO 2 240 527.67 0.00001480 carbon monoxide CO 118 518.67 0.00001720 hydrogen H 2 72 528.93 0.0000876 nitrogen N 2 111 540.99 0.0001781 oxygen O 2 127 526.05 0.0002018 sulfur dioxide SO 2 416 528.57 0.0001254 Table -1.1. The list for Sutherland’s equation coefficients for selected materials. Substance Chemical formula Temperature T [ ◦ C] Viscosity [ N sec m 2 ] i − C 4 H 10 23 0.0000076 CH 4 20 0.0000109 CO 2 20 0.0000146 oxygen O 2 20 0.0000203 mercury vapor Hg 380 0.0000654 Table -1.2. Viscosity of selected gases.
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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
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
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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
Page 66 and 67: 1.2. BRIEF HISTORY 3 lay is one of
Page 68 and 69: 1.3. KINDS OF FLUIDS 5 results. The
Page 70 and 71: 1.4. SHEAR STRESS 7 For cases where
Page 72 and 73: 1.5. VISCOSITYVISCOSITY 9 The veloc
Page 74 and 75: 1.5. VISCOSITYVISCOSITY 11 always p
Page 78 and 79: 1.5. VISCOSITYVISCOSITY 15 Chemical
Page 80 and 81: 1.5. VISCOSITYVISCOSITY 17 2 Reduce
Page 82 and 83: 1.5. VISCOSITYVISCOSITY 19 In very
Page 84 and 85: 1.6. FLUID PROPERTIES 21 The total
Page 86 and 87: 1.6. FLUID PROPERTIES 23 straight.
Page 88 and 89: 1.6. FLUID PROPERTIES 25 Table -1.5
Page 90 and 91: 1.6. FLUID PROPERTIES 27 Two layers
Page 92 and 93: 1.6. FLUID PROPERTIES 29 1.6.2.1 Bu
Page 94 and 95: 1.7. SURFACE TENSION 31 terials. Th
Page 96 and 97: 1.7. SURFACE TENSION 33 or Or after
Page 98 and 99: 1.7. SURFACE TENSION 35 The maximum
Page 100 and 101: 1.7. SURFACE TENSION 37 kipenii,”
Page 102 and 103: 1.7. SURFACE TENSION 39 Equation (1
Page 104 and 105: 1.7. SURFACE TENSION 41 Example 1.1
Page 106 and 107: 1.7. SURFACE TENSION 43 Table -1.7.
Page 108 and 109: CHAPTER 2 Review of Thermodynamics
Page 110 and 111: 2.1. BASIC DEFINITIONS 47 Since the
Page 112 and 113: 2.1. BASIC DEFINITIONS 49 when the
Page 114 and 115: 2.1. BASIC DEFINITIONS 51 Utilizing
Page 116 and 117: CHAPTER 3 Review of Mechanics This
Page 118 and 119: 3.2. CENTER OF MASS 55 3.2 Center o
Page 120 and 121: 3.3. MOMENT OF INERTIA 57 The momen
Page 122 and 123: 3.3. MOMENT OF INERTIA 59 Equation
Page 124 and 125: 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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