Basics of Fluid Mechanics, 2014a

More documents

Recommendations

Info

1.7. SURFACE TENSION 41 Example 1.19: Calculate the diameter of a water droplet to attain pressure difference of 1000[N/m 2 ]. You can assume that temperature is 20 ◦ C. Solution The pressure inside the droplet is given by equation (1.47). D =2R = 22σ ΔP = 4 × 0.0728 ∼ 2.912 10 −4 [m] 1000 End Solution Example 1.20: Calculate the pressure difference between a droplet of water at 20 ◦ C when the droplet has a diameter of 0.02 cm. Solution using equation ΔP = 2 σ r ∼ 2 × 0.0728 ∼ 728.0[N/m 2 ] 0.0002 End Solution Example 1.21: Calculate the maximum force necessary to lift a thin wire ring of 0.04[m] diameter from a water surface at 20 ◦ C. Neglect the weight of the ring. Solution F = 2(2 πrσ) cos β The actual force is unknown since the contact angle is unknown. However, the maximum Force is obtained when β =0and thus cos β =1. Therefore, F =4πrσ=4× π × 0.04 × 0.0728 ∼ .0366[N] In this value the gravity is not accounted for. End Solution Example 1.22: A small liquid drop is surrounded with the air and has a diameter of 0.001 [m]. The pressure difference between the inside and outside droplet is 1[kPa]. Estimate the surface tension? Solution
42 CHAPTER 1. INTRODUCTION TO FLUID MECHANICS To be continue End Solution Table -1.7. The surface tension for selected materials at temperature 20 ◦ C when not mentioned. Chemical component Surface Tension mN m T correction mN mK Acetic Acid 27.6 20 ◦ C n/a Acetone 25.20 - -0.1120 Aniline 43.4 22 ◦ C -0.1085 Benzene 28.88 - -0.1291 Benzylalcohol 39.00 - -0.0920 Benzylbenzoate 45.95 - -0.1066 Bromobenzene 36.50 - -0.1160 Bromobenzene 36.50 - -0.1160 Bromoform 41.50 - -0.1308 Butyronitrile 28.10 - -0.1037 Carbon disulfid 32.30 - -0.1484 Quinoline 43.12 - -0.1063 Chloro benzene 33.60 - -0.1191 Chloroform 27.50 - -0.1295 Cyclohexane 24.95 - -0.1211 Cyclohexanol 34.40 25 ◦ C -0.0966 Cyclopentanol 32.70 - -0.1011 Carbon Tetrachloride 26.8 - n/a Carbon disulfid 32.30 - -0.1484 Chlorobutane 23.10 - -0.1117 Ethyl Alcohol 22.3 - n/a Ethanol 22.10 - -0.0832 Ethylbenzene 29.20 - -0.1094 Ethylbromide 24.20 - -0.1159 Ethylene glycol 47.70 - -0.0890 Formamide 58.20 - -0.0842 Gasoline ∼ 21 - n/a Glycerol 64.0 - -0.0598 Helium 0.12 −269 ◦ C n/a Mercury 425-465.0 - -0.2049 Methanol 22.70 - -0.0773 Methyl naphthalene 38.60 - -0.1118 Methyl Alcohol 22.6 - n/a Neon 5.15 −247 ◦ C n/a Continued on next page
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 16 and 17:
LIST OF FIGURES xv 4.32 Polynomial
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
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 76 and 77: 2.5 2.0 1.5 1.0 0.5 0 100 200 300 4
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 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
Page 126 and 127: 3.3. MOMENT OF INERTIA 63 or x (1 a
Page 128 and 129: 3.5. ANGULAR MOMENTUM AND TORQUE 65
Page 130 and 131: 3.5. ANGULAR MOMENTUM AND TORQUE 67
Page 132 and 133: CHAPTER 4 Fluids Statics 4.1 Introd
Page 134 and 135: 4.3. PRESSURE AND DENSITY IN A GRAV
Page 154 and 155:
4.3. PRESSURE AND DENSITY IN A GRAV
Page 156 and 157:
4.4. FLUID IN A ACCELERATED SYSTEM
Page 158 and 159:
Page 160 and 161:
Page 162 and 163:
Page 164 and 165:
4.5. FLUID FORCES ON SURFACES 101 T
Page 166 and 167:
4.5. FLUID FORCES ON SURFACES 103 x
Page 168 and 169:
Page 170 and 171:
4.5. FLUID FORCES ON SURFACES 107 I
Page 172 and 173:
Page 174 and 175:
4.5. FLUID FORCES ON SURFACES 111 C
Page 176 and 177:
4.5. FLUID FORCES ON SURFACES 113 A
Page 178 and 179:
4.5. FLUID FORCES ON SURFACES 115 F
Page 180 and 181:
4.6. BUOYANCY AND STABILITY 117 In
Page 182 and 183:
4.6. BUOYANCY AND STABILITY 119 ρ
Page 184 and 185:
4.6. BUOYANCY AND STABILITY 121 ( )
Page 186 and 187:
4.6. BUOYANCY AND STABILITY 123 The
Page 188 and 189:
4.6. BUOYANCY AND STABILITY 125 on
Page 190 and 191:
4.6. BUOYANCY AND STABILITY 127 A w
Page 192 and 193:
4.6. BUOYANCY AND STABILITY 129 It
Page 194 and 195:
4.6. BUOYANCY AND STABILITY 131 Thu
Page 196 and 197:
4.6. BUOYANCY AND STABILITY 133 The
Page 198 and 199:
4.6. BUOYANCY AND STABILITY 135 A n
Page 200 and 201:
4.6. BUOYANCY AND STABILITY 137 of
Page 202 and 203:
4.7. RAYLEIGH-TAYLOR INSTABILITY 13
Page 204 and 205:
4.7. RAYLEIGH-TAYLOR INSTABILITY 14
Page 206 and 207:
4.8. QUALITATIVE QUESTIONS 143 can
Page 208:
Part I Integral Analysis 145
Page 211 and 212:
148 CHAPTER 5. MASS CONSERVATION di
Page 213 and 214:
150 CHAPTER 5. MASS CONSERVATION It
Page 215 and 216:
152 CHAPTER 5. MASS CONSERVATION 5.
Page 217 and 218:
154 CHAPTER 5. MASS CONSERVATION Th
Page 219 and 220:
156 CHAPTER 5. MASS CONSERVATION Wh
Page 221 and 222:
158 CHAPTER 5. MASS CONSERVATION Th
Page 223 and 224:
Page 225 and 226:
162 CHAPTER 5. MASS CONSERVATION ri
Page 227 and 228:
Page 229 and 230:
166 CHAPTER 5. MASS CONSERVATION En
Page 231 and 232:
168 CHAPTER 5. MASS CONSERVATION Ex
Page 233 and 234:
170 CHAPTER 5. MASS CONSERVATION So
Page 235 and 236:
172 CHAPTER 5. MASS CONSERVATION In
Page 237 and 238:
174 CHAPTER 6. MOMENTUM CONSERVATIO
Page 239 and 240:
Page 241 and 242:
Page 243 and 244:
Page 245 and 246:
Page 247 and 248:
Page 249 and 250:
Page 251 and 252:
Page 253 and 254:
Page 255 and 256:
Page 257 and 258:
Page 259 and 260:
Page 261 and 262:
198 CHAPTER 7. ENERGY CONSERVATION
Page 263 and 264:
Page 265 and 266:
Page 267 and 268:
Page 269 and 270:
Page 271 and 272:
Page 273 and 274:
Page 275 and 276:
Page 277 and 278:
Page 279 and 280:
Page 281 and 282:
Page 283 and 284:
Page 285 and 286:
Page 287 and 288:
Page 290 and 291:
CHAPTER 8 Differential Analysis 8.1
Page 292 and 293:
8.2. MASS CONSERVATION 229 The firs
Page 294 and 295:
8.2. MASS CONSERVATION 231 Combinin
Page 296 and 297:
8.2. MASS CONSERVATION 233 Equation
Page 298 and 299:
8.2. MASS CONSERVATION 235 The dens
Page 300 and 301:
8.2. MASS CONSERVATION 237 Example
Page 302 and 303:
8.3. CONSERVATION OF GENERAL QUANTI
Page 304 and 305:
8.4. MOMENTUM CONSERVATION 241 8.4
Page 306 and 307:
8.4. MOMENTUM CONSERVATION 243 The
Page 308 and 309:
8.5. DERIVATIONS OF THE MOMENTUM EQ
Page 310 and 311:
Page 312 and 313:
Page 314 and 315:
Page 316 and 317:
Page 318 and 319:
8.6. BOUNDARY CONDITIONS AND DRIVIN
Page 320 and 321:
8.6. BOUNDARY CONDITIONS AND DRIVIN
Page 322 and 323:
8.7. EXAMPLES FOR DIFFERENTIAL EQUA
Page 324 and 325:
Page 326 and 327:
Page 328 and 329:
Page 330 and 331:
Page 332 and 333:
Page 334 and 335:
Page 336 and 337:
CHAPTER 9 Dimensional Analysis This
Page 338 and 339:
9.1. INTRODUCTORY REMARKS 275 the r
Page 340 and 341:
9.1. INTRODUCTORY REMARKS 277 End S
Page 342 and 343:
9.1. INTRODUCTORY REMARKS 279 Deriv
Page 344 and 345:
9.2. BUCKINGHAM-π-THEOREM 281 para
Page 346 and 347:
9.2. BUCKINGHAM-π-THEOREM 283 magn
Page 348 and 349:
9.2. BUCKINGHAM-π-THEOREM 285 Tabl
Page 350 and 351:
9.2. BUCKINGHAM-π-THEOREM 287 End
Page 352 and 353:
9.2. BUCKINGHAM-π-THEOREM 289 Equa
Page 354 and 355:
9.2. BUCKINGHAM-π-THEOREM 291 the
Page 356 and 357:
9.2. BUCKINGHAM-π-THEOREM 293 than
Page 358 and 359:
9.2. BUCKINGHAM-π-THEOREM 295 Unde
Page 360 and 361:
9.2. BUCKINGHAM-π-THEOREM 297 Solu
Page 362 and 363:
9.3. NUSSELT’S TECHNIQUE 299 The
Page 364 and 365:
9.3. NUSSELT’S TECHNIQUE 301 boun
Page 366 and 367:
9.3. NUSSELT’S TECHNIQUE 303 Noti
Page 368 and 369:
9.3. NUSSELT’S TECHNIQUE 305 In t
Page 370 and 371:
9.3. NUSSELT’S TECHNIQUE 307 Wher
Page 372 and 373:
9.4. SUMMARY OF DIMENSIONLESS NUMBE
Page 374 and 375:
Page 376 and 377:
Page 378 and 379:
Page 380 and 381:
Page 382 and 383:
9.5. SUMMARY 319 It can be noticed
Page 384 and 385:
9.6. APPENDIX SUMMARY OF DIMENSIONL
Page 386 and 387:
BIBLIOGRAPHY [1] Buckingham, E. On
Page 388 and 389:
CHAPTER 10 Inviscid Flow or Potenti
Page 390 and 391:
10.1. INTRODUCTION 327 where in thi
Page 392 and 393:
10.1. INTRODUCTION 329 With the ide
Page 394 and 395:
10.1. INTRODUCTION 331 The partial
Page 396 and 397:
10.2. POTENTIAL FLOW FUNCTION 333 T
Page 398 and 399:
10.2. POTENTIAL FLOW FUNCTION 335 t
Page 400 and 401:
Page 402 and 403:
Page 404 and 405:
10.2. POTENTIAL FLOW FUNCTION 341 9
Page 406 and 407:
10.3. POTENTIAL FLOW FUNCTIONS INVE
Page 408 and 409:
Page 410 and 411:
Page 412 and 413:
Page 414 and 415:
Page 416 and 417:
Page 418 and 419:
Page 420 and 421:
Page 422 and 423:
Page 424 and 425:
Page 426 and 427:
Page 428 and 429:
Page 430 and 431:
Page 432 and 433:
10.4. CONFORMING MAPPING 369 flow d
Page 434 and 435:
10.4. CONFORMING MAPPING 371 The un
Page 436 and 437:
10.5. UNSTEADY STATE BERNOULLI IN A
Page 438 and 439:
10.6. QUESTIONS 375 Table -10.2. Di
Page 440 and 441:
CHAPTER 11 Compressible Flow One Di
Page 442 and 443:
11.3. SPEED OF SOUND 379 to be cont
Page 444 and 445:
11.3. SPEED OF SOUND 381 Solution T
Page 446 and 447:
11.3. SPEED OF SOUND 383 consider a
Page 448 and 449:
11.4. ISENTROPIC FLOW 385 Now, subs
Page 450 and 451:
11.4. ISENTROPIC FLOW 387 Static Pr
Page 452 and 453:
11.4. ISENTROPIC FLOW 389 that the
Page 454 and 455:
11.4. ISENTROPIC FLOW 391 Using the
Page 456 and 457:
11.4. ISENTROPIC FLOW 393 Solution
Page 458 and 459:
11.4. ISENTROPIC FLOW 395 Expressin
Page 460 and 461:
11.4. ISENTROPIC FLOW 397 The tempe
Page 462 and 463:
11.4. ISENTROPIC FLOW 399 Table -11
Page 464 and 465:
Page 466 and 467:
Page 468 and 469:
11.4. ISENTROPIC FLOW 405 Example 1
Page 470 and 471:
11.5. NORMAL SHOCK 407 In a shock w
Page 472 and 473:
11.5. NORMAL SHOCK 409 Energy equat
Page 474 and 475:
11.5. NORMAL SHOCK 411 The density
Page 476 and 477:
11.5. NORMAL SHOCK 413 or in a dime
Page 478 and 479:
11.5. NORMAL SHOCK 415 which differ
Page 480 and 481:
11.5. NORMAL SHOCK 417 is different
Page 482 and 483:
11.5. NORMAL SHOCK 419 Table -11.3.
Page 484 and 485:
11.6. ISOTHERMAL FLOW 421 Table -11
Page 486 and 487:
11.6. ISOTHERMAL FLOW 423 Rearrangi
Page 488 and 489:
11.6. ISOTHERMAL FLOW 425 dT 0 T 0
Page 490 and 491:
11.6. ISOTHERMAL FLOW 427 10 2 0 1
Page 492 and 493:
11.6. ISOTHERMAL FLOW 429 The fact
Page 494 and 495:
11.6. ISOTHERMAL FLOW 431 Calculati
Page 496 and 497:
11.6. ISOTHERMAL FLOW 433 maximum M
Page 498 and 499:
11.6. ISOTHERMAL FLOW 435 From the
Page 500 and 501:
11.7. FANNO FLOW 437 The energy con
Page 502 and 503:
11.7. FANNO FLOW 439 Differentiatin
Page 504 and 505:
11.7. FANNO FLOW 441 11.7.3 The Mec
Page 506 and 507:
11.7. FANNO FLOW 443 pressure on th
Page 508 and 509:
11.7. FANNO FLOW 445 10 2 0 1 2 3 4
Page 510 and 511:
11.7. FANNO FLOW 447 End Solution A
Page 512 and 513:
11.7. FANNO FLOW 449 M x M y T y T
Page 514 and 515:
11.7. FANNO FLOW 451 11.7.5.1 Maxim
Page 516 and 517:
11.7. FANNO FLOW 453 At the startin
Page 518 and 519:
11.7. FANNO FLOW 455 Fanno Flow 5 4
Page 520 and 521:
11.7. FANNO FLOW 457 11.7.7.1 Choki
Page 522 and 523:
11.7. FANNO FLOW 459 back pressure
Page 524 and 525:
11.7. FANNO FLOW 461 The solution i
Page 526 and 527:
11.7. FANNO FLOW 463 11.7.8 The Pra
Page 528 and 529:
11.7. FANNO FLOW 465 0.9 0.8 0.7 0.
Page 530 and 531:
11.7. FANNO FLOW 467 3.0 2.5 2.0 Co
Page 532 and 533:
11.8. THE TABLE FOR FANNO FLOW 469
Page 534 and 535:
11.9. RAYLEIGH FLOW 471 Table -11.6
Page 536 and 537:
11.10. INTRODUCTION 473 or in simpl
Page 538 and 539:
11.10. INTRODUCTION 475 or explicit
Page 540 and 541:
11.10. INTRODUCTION 477 Table -11.7
Page 542 and 543:
11.10. INTRODUCTION 479 Example 11.
Page 544 and 545:
11.10. INTRODUCTION 481 Example 11.
Page 546 and 547:
11.10. INTRODUCTION 483 what the ma
Page 548 and 549:
CHAPTER 12 Compressible Flow 2-Dime
Page 550 and 551:
12.2. OBLIQUE SHOCK 487 12.2 Obliqu
Page 552 and 553:
12.2. OBLIQUE SHOCK 489 The relatio
Page 554 and 555:
12.2. OBLIQUE SHOCK 491 Where S = 3
Page 556 and 557:
12.2. OBLIQUE SHOCK 493 by evaluati
Page 558 and 559:
12.2. OBLIQUE SHOCK 495 Figure (12.
Page 560 and 561:
12.2. OBLIQUE SHOCK 497 be made. Th
Page 562 and 563:
12.2. OBLIQUE SHOCK 499 demonstrate
Page 564 and 565:
12.2. OBLIQUE SHOCK 501 or explicit
Page 566 and 567:
12.2. OBLIQUE SHOCK 503 Fig. -12.9.
Page 568 and 569:
12.2. OBLIQUE SHOCK 505 Table -12.1
Page 570 and 571:
12.2. OBLIQUE SHOCK 507 Example 12.
Page 572 and 573:
12.2. OBLIQUE SHOCK 509 In the obli
Page 574 and 575:
12.2. OBLIQUE SHOCK 511 M x M ys M
Page 576 and 577:
12.2. OBLIQUE SHOCK 513 M x M y T y
Page 578 and 579:
12.2. OBLIQUE SHOCK 515 M x M yw θ
Page 580 and 581:
12.2. OBLIQUE SHOCK 517 The pressur
Page 582 and 583:
12.2. OBLIQUE SHOCK 519 From these
Page 584 and 585:
12.3. PRANDTL-MEYER FUNCTION 521 as
Page 586 and 587:
12.3. PRANDTL-MEYER FUNCTION 523 Th
Page 588 and 589:
12.3. PRANDTL-MEYER FUNCTION 525 No
Page 590 and 591:
1 2 12.7. FLAT BODY WITH AN ANGLE O
Page 592 and 593:
12.8. EXAMPLES FOR PRANDTL-MEYER FU
Page 594 and 595:
12.9. COMBINATION OF THE OBLIQUE SH
Page 596 and 597:
12.9. COMBINATION OF THE OBLIQUE SH
Page 598 and 599:
CHAPTER 13 Multi-Phase Flow 13.1 In
Page 600 and 601:
13.4. KIND OF MULTI-PHASE FLOW 537
Page 602 and 603:
13.5. CLASSIFICATION OF LIQUID-LIQU
Page 604 and 605:
13.5. CLASSIFICATION OF LIQUID-LIQU
Page 606 and 607:
13.6. MULTI-PHASE FLOW VARIABLES DE
Page 608 and 609:
13.6. MULTI-PHASE FLOW VARIABLES DE
Page 610 and 611:
13.7. HOMOGENEOUS MODELS 547 13.7 H
Page 612 and 613:
13.7. HOMOGENEOUS MODELS 549 There
Page 614 and 615:
13.8. SOLID-LIQUID FLOW 551 where
Page 616 and 617:
13.8. SOLID-LIQUID FLOW 553 So far
Page 618 and 619:
13.9. COUNTER-CURRENT FLOW 555 The
Page 620 and 621:
Page 622 and 623:
Page 624 and 625:
13.9. COUNTER-CURRENT FLOW 561 For
Page 626 and 627:
Page 628 and 629:
13.10. MULTI-PHASE CONCLUSION 565 1
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 644 and 645:
Page 646 and 647:
Page 648 and 649:
Page 650 and 651:
Page 652 and 653:
Page 654 and 655:
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
Page 666 and 667:
AUTHORS INDEX 603 Authors Index B B
show all

Basics of Fluid Mechanics, 2014a

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?