Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings

Table of Contents......Page 0
Hydraulics of Pipeline Systems......Page 1
The Authors......Page 3
ACKNOWLEDGMENTS......Page 4
TABLE OF CONTENTS......Page 5
INTRODUCTION......Page 10
2.1.1. THE BASIC EQUATIONS......Page 15
2.1.2. ENERGY AND HYDRAULIC GRADE LINES......Page 16
2.2.1. PIPE FRICTION......Page 17
2.2.2. DARCY-WEISBACH EQUATION......Page 18
2.2.3. EMPIRICAL EQUATIONS......Page 20
2.2.4. EXPONENTIAL FORMULA......Page 22
Example Problem 2.1......Page 23
2.2.5. LOCAL AND MINOR LOSSES......Page 24
2.3 PUMP THEORY AND CHARACTERISTICS......Page 26
Example Problem 2.2......Page 28
Example Problem 2.3......Page 29
2.4.2. SERIES PIPE FLOW WITH PUMP(S)......Page 30
Example Problem 2.4......Page 31
Example Problem 2.5......Page 32
2.4.3. PARALLEL PIPE FLOW, EQUIVALENT PIPES......Page 33
Example Problem 2.7......Page 34
2.5 PROBLEMS......Page 36
3.2.1. NO FRICTION......Page 40
3.2.2. BARREL FRICTION ONLY......Page 41
3.2.3. BARREL FRICTION WITH JUNCTION LOSSES......Page 42
Example Problem 3.1......Page 48
3.3 A HYDRAULIC DESIGN PROCEDURE......Page 52
3.4 PROBLEMS......Page 57
4.1 INTRODUCTION......Page 60
4.1.1. DEFINING AN APPROPRIATE PIPE SYSTEM......Page 61
4.1.2. BASIC RELATIONS BETWEEN NETWORK ELEMENTS......Page 62
4.2 EQUATION SYSTEMS FOR STEADY FLOW IN NETWORKS......Page 63
4.2.1. SYSTEM OF Q-EQUATIONS......Page 64
Example Problem 4.1......Page 66
4.2.2. SYSTEM OF H-EQUATIONS......Page 67
4.2.3. SYSTEM OF Q-EQUATIONS......Page 69
4.3 PRESSURE REDUCTION AND BACK PRESSURE VALVES......Page 72
4.3.1. Q-EQUATIONS FOR NETWORKS WITH PRV\'S/BPV\'S......Page 73
4.3.2. H-EQUATIONS FOR NETWORKS WITH PRV\'S/BPV\'S......Page 79
4.3.3. Q-EQUATIONS FOR NETWORKS WITH PRV\'S/BPV\'S......Page 81
4.4.1. NEWTON METHOD FOR LARGE SYSTEMS OF EQUATIONS......Page 85
Example Problem 4.5......Page 95
4.4.2. SOLVING THE THREE EQUATION SYSTEMS VIA NEWTON......Page 101
4.4.3. COMPUTER SOLUTIONS TO NETWORKS......Page 105
Example Problem 4.6......Page 107
Example Problem 4.8......Page 109
4.4.4. INCLUDING PRESSURE REDUCING VALVES......Page 110
Example Problem 4.9......Page 113
4.4.5. SYSTEMATIC SOLUTION OF THE Q-EQUATIONS......Page 114
Example Problem 4.10......Page 117
Example Problem 4.11......Page 118
Example Problem 4.12......Page 119
4.4.6. SYSTEMATIC SOLUTION OF THE H-EQUATIONS......Page 120
Example Problem 4.14......Page 122
4.4.7. SYSTEMATIC SOLUTION OF THE Q-EQUATIONS......Page 124
Example Problem 4.15......Page 129
4.5 CONCLUDING REMARKS......Page 131
4.6 PROBLEMS......Page 133
5.1.2. SOLUTION BASED ON THE DARCY-WEISBACH EQUATION......Page 148
5.1.4. BRANCHED PIPE NETWORKS......Page 152
Example Problem 5.1......Page 153
5.2 LARGE BRANCHED SYSTEMS OF PIPES......Page 157
5.2.1. NETWORK LAYOUT......Page 158
5.2.2. COEFFICIENT MATRIX......Page 161
Example Problem 5.3......Page 162
5.3 LOOPED NETWORK DESIGN SOLUTION CRITERIA......Page 165
Example Problem 5.4......Page 178
5.4 DESIGNING SPECIAL COMPONENTS......Page 182
5.5.1. LOGIC AND USE OF NETWEQS1......Page 190
5.5.2. DATA TO DESCRIBE THE PIPE SYSTEM......Page 192
5.5.3. COMBINATIONS THAT CAN NOT BE UNKNOWNS......Page 194
Example Problem 5.5......Page 197
Example Problem 5.6......Page 198
Example Problem 5.7......Page 202
5.6.1. WITHIN RANGE POLYNOMIAL INTERPOLATION......Page 203
Example Problem 5.8......Page 204
5.6.2. SPLINE FUNCTION INTERPOLATION......Page 205
Example Problem 5.9......Page 208
Example Problem 5.10......Page 209
5.7 SENSITIVITY ANALYSES......Page 210
Example Problem 5.11......Page 215
Example Problem 5.12......Page 219
5.8 PROBLEMS......Page 223
6.1 INTRODUCTION......Page 234
6.2 EXTENDED TIME SIMULATIONS......Page 235
Example Problem 6.1......Page 236
6.3 ELEMENTS OF ENGINEERING ECONOMICS......Page 245
6.3.1. ECONOMICS APPLIED TO WATER SYSTEMS......Page 248
6.3.2. LEAST COST......Page 249
Example Problem 6.4......Page 253
Example Problem 6.2......Page 247
6.4.1. ONE PRINCIPAL SUPPLY SOURCE......Page 254
Example Problem 6.5......Page 255
6.4.2. DESIGN GUIDELINES FOR COMPLEX NETWORKS......Page 275
6.5 PROBLEMS......Page 278
7.2 QUASI-STEADY FLOW......Page 283
Example Problem 7.1......Page 287
7.3.1. THE EULER EQUATION......Page 290
7.3.2. RIGID-COLUMN FLOW IN CONSTANT-DIAMETER PIPES......Page 291
Example Problem 7.2......Page 294
Example Problem 7.3......Page 296
7.3.3. WATER HAMMER......Page 301
7.4 PROBLEMS......Page 306
C.1 GLOBE AND ANGLE VALVES......Page 311
C.3 BALL VALVES......Page 313
8.1 THE EQUATION FOR PRESSURE HEAD CHANGE H......Page 314
8.2.1. NET MASS INFLOW......Page 316
8.2.3. CHANGE IN PIPE VOLUME DUE TO ELASTICITY......Page 317
Wave Speed Solution for Case (b) Restraint......Page 319
Example Problem 8.1......Page 321
Example Problem 8.2......Page 324
8.3.3. REINFORCED CONCRETE PIPE......Page 325
Example Problem 8.3......Page 326
8.4 EFFECT OF AIR ENTRAINMENT ON WAVE SPEED......Page 327
8.5 DIFFERENTIAL EQUATIONS OF UNSTEADY FLOW......Page 328
8.5.1. CONSERVATION OF MASS......Page 329
8.5.2. INTERPRETATION OF THE DIFFERENTIAL EQUATIONS......Page 331
8.6 PROBLEMS......Page 333
9.1.1. DEVELOPMENT OF THE CHARACTERISTIC EQUATIONS......Page 337
9.1.2. THE FINITE DIFFERENCE REPRESENTATION......Page 340
9.1.3. SETTING UP THE NUMERICAL PROCEDURE......Page 342
Constant speed pump boundary condition (upstream end of pipe)......Page 343
9.1.4. COMPUTERIZING THE NUMERICAL PROCEDURE......Page 344
Constant-speed pump revisited......Page 345
9.1.5. ELEMENTARY COMPUTER PROGRAMS......Page 347
Example Problem 9.1......Page 350
Example Problem 9.2......Page 353
9.2.1. THE COMPLETE EQUATIONS......Page 355
9.2.2. THE NUMERICAL SOLUTION......Page 356
9.2.3. THE Ds-Dt GRID......Page 359
9.3.1. THE EFFECT OF FRICTION......Page 360
9.3.2. THE EFFECT OF THE SIZE OF N......Page 361
9.3.4. NUMERICAL INSTABILITY AND ACCURACY......Page 362
9.4 PROBLEMS......Page 364
10.1.1. INTERNAL BOUNDARY CONDITIONS......Page 373
10.1.2. SELECTION OF  t......Page 374
Example Problem 10.1......Page 377
10.2.1. THREE-PIPE JUNCTIONS......Page 380
10.2.2. FOUR-PIPE JUNCTIONS......Page 383
10.3 INTERIOR MAJOR LOSSES......Page 384
10.4.1. VALVE IN THE INTERIOR OF A PIPELINE......Page 386
10.4.2. VALVE AT DOWNSTREAM END OF PIPE AT RESERVOIR......Page 387
10.4.3. EXPRESSING K L AS A FUNCTION OF TIME......Page 388
10.4.4. LINEAR INTERPOLATION......Page 390
10.4.5. PARABOLIC INTERPOLATION......Page 391
Example Problem 10.2......Page 393
10.5.1. QUICK-RESPONSE PRESSURE-REDUCING VALVES......Page 394
10.6.1. SERIES PIPE JUNCTIONS......Page 396
10.6.2. TEE JUNCTIONS......Page 397
Example Problem 10.5......Page 398
10.7.1. COLUMN SEPARATION AND RELEASED AIR......Page 399
10.7.2. ANALYSIS WITH COLUMN SEPARATION AND RELEASED AIR......Page 400
10.8 PROBLEMS......Page 403
11.1 PUMP POWER FAILURE RUNDOWN......Page 407
11.1.1. SETTING UP THE EQUATIONS FOR BOOSTER PUMPS......Page 409
11.1.2. FINDING THE CHANGE IN SPEED......Page 411
11.1.3. SOLVING THE EQUATIONS......Page 412
Example Problem 11.1......Page 413
11.1.4. SETTING UP THE EQUATIONS FOR SOURCE PUMPS......Page 414
Example Problem 11.2......Page 415
Example Problem 11.3......Page 417
11.3 PROBLEMS......Page 420
12.2.1. THE GOVERNING EQUATIONS......Page 424
12.2.2. THREE-PIPE PROBLEM......Page 425
12.3.1. THE METHOD......Page 429
12.3.2. AN EXAMPLE......Page 430
12.4 SEVERAL PUMPS SUPPLYING A PIPE LINE......Page 434
Example Problem 12.1......Page 435
12.5 AIR CHAMBERS, SURGE TANKS AND STANDPIPES......Page 436
Example Problem 12.2......Page 437
Example Problem 12.3......Page 439
12.6.1. THE INITIAL STEADY STATE SOLUTION......Page 442
Example Problem 12.4......Page 444
Example Problem 12.5......Page 449
Example Problem 12.6......Page 455
Example Problem 12.7......Page 456
12.7 PROBLEMS......Page 458
13.1.1. VALVE MOVEMENT......Page 470
13.1.3. AIR IN LINES......Page 471
13.1.5. PUMP POWER FAILURE......Page 472
13.2.1. CONTROLLED VALVE MOVEMENT......Page 473
Example Problem 13.1......Page 474
13.2.5. SURGE TANKS......Page 476
One-way surge tanks......Page 477
Example Problem 13.2......Page 479
13.2.6. AIR CHAMBERS......Page 480
Air chamber appurtenances......Page 486
Example Problem 13.3......Page 487
Air-vacuum valves......Page 491
Pump inertia control......Page 492
13.3 PROBLEMS......Page 493
REFERENCES......Page 495
A.2.1. GAUSSIAN ELIMINATION......Page 498
A.2.2. USE OF THE LINEAR ALGEBRA SOLVER SOLVEQ......Page 499
A.3.1. TRAPEZOIDAL RULE......Page 501
A.3.2. SIMPSON\'S RULE......Page 503
Example Problem A.1......Page 504
Example Problem A.2......Page 505
A.4.2. RUNGE-KUTTA METHOD......Page 506
Example Problem A.3......Page 510
A.4.3. USE OF ODE SOLVER ODESOL......Page 512
Example Problem A.4......Page 514
PUMP CHARACTERISTIC CURVES......Page 518
CHAPTER 4......Page 526
CHAPTER 6......Page 527
CHAPTER 8......Page 528
CHAPTER 9......Page 529
CHAPTER 10......Page 530
CHAPTER 11......Page 531
CHAPTER 12......Page 532
CHAPTER 13......Page 533