195 195 198

II. MOST ECONOMICAL DIAMETER 200

A. Newtonian Fluids 203

B. Non-Newtonian Fluids 205

III. FRICTION LOSS IN VALVES AND FITTINGS 206

A. Loss Coefficient 207

B. Equivalent L/D Method 207

C. Crane Method 208

IV. NON-NEWTONIAN FLUIDS 214

V. PIPE FLOW PROBLEMS WITH FITTINGS 215

A. Unknown Driving Force 216

B. Unknown Flow Rate 217

C. Unknown Diameter 218

VI. SLACK FLOW 221

VII. PIPE NETWORKS 225 PROBLEMS 228 NOTATION 237 REFERENCES 238

8. PUMPS AND COMPRESSORS 239

I. PUMPS 239

A. Positive Displacement Pumps 239

B. Centrifugal Pumps 240

II. PUMP CHARACTERISTICS 241

III. PUMPING REQUIREMENTS AND PUMP SELECTION 243

A. Required Head 244

B. Composite Curves 245

IV. CAVITATION AND NET POSITIVE SUCTION

HEAD (NPSH) 247

A. Vapor Lock and Cavitation 247

B. NPSH 248

C. Specific Speed 249

D. Suction Specific Speed 250

V. COMPRESSORS 252

A. Isothermal Compression 254

B. Isentropic Compression 254

C. Staged Operation 255

D. Efficiency 256

PROBLEMS 256

NOTATION 265

REFERENCES 266

9. COMPRESSIBLE FLOWS 267

I. GAS PROPERTIES 267

A. Ideal Gas 267

B. The Speed of Sound 268

II. PIPE FLOW 270

A. Isothermal Flow 271

B. Adiabatic Flow 273

C. Choked Flow 273

D. The Expansion Factor 275

E. Ideal Adiabatic Flow 277

III. GENERALIZED EXPRESSIONS 279

A. Governing Equations 279

B. Applications 281

C. Solution of High-Speed Gas Problems 283 PROBLEMS 286 NOTATION 290 REFERENCES 291

10. FLOW MEASUREMENT AND CONTROL 293

I. SCOPE 293

II. THE PITOT TUBE 293

III. THE VENTURI AND NOZZLE 295

IV. THE ORIFICE METER 304

A. Incompressible Flow 305

B. Compressible Flow 306

V. LOSS COEFFICIENT 308

VI. ORIFICE PROBLEMS 310

A. Unknown Pressure Drop 311

B. Unknown Flow Rate 311

C. Unknown Diameter 312

VII. CONTROL VALVES 312

A. Valve Characteristics 313

B. Valve Sizing Relations 314

C. Compressible Fluids 327

D. Viscosity Correction 330 PROBLEMS 333

NOTATION 338

REFERENCES 339

11. EXTERNAL FLOWS 341

I. DRAG COEFFICIENT 341

A. Stokes Flow 342

B. Form Drag 343

C. All Reynolds Numbers 343

D. Cylinder Drag 344

E. Boundary Layer Effects 345

II. FALLING PARTICLES 347

A. Unknown Velocity 348

B. Unknown Diameter 349

C. Unknown Viscosity 349

III. CORRECTION FACTORS 350

A. Wall Effects 350

B. Drops and Bubbles 351

IV. NON-NEWTONIAN FLUIDS 352

A. Power Law Fluids 352

B. Wall Effects 357

C. Carreau Fluids 358

D. Bingham Plastics 358 PROBLEMS 361 NOTATION 363 REFERENCES 364

12. FLUID-SOLID SEPARATIONS BY FREE SETTLING 365

I. FLUID-SOLID SEPARATIONS 365

II. GRAVITY SETTLING 366

III. CENTRIFUGAL SEPARATION 367

A. Fluid-Solid Separation 367

B. Separation of Immiscible Liquids 371

IV. CYCLONE SEPARATIONS 375

A. General Characteristics 375

B. Aerocyclones 376

C. Hydrocyclones 382 PROBLEMS 385 NOTATION 389 REFERENCES 390

13. FLOW IN POROUS MEDIA 391

I. DESCRIPTION OF POROUS MEDIA 391

A. Hydraulic Diameter 392

B. Porous Medium Friction Factor 393

C. Porous Medium Reynolds Number 394

II. FRICTION LOSS IN POROUS MEDIA 394

A. Laminar Flow 394

B. Turbulent Flow 395

C. All Reynolds Numbers 395

III. PERMEABILITY 395

IV. MULTIDIMENSIONAL FLOW 396

V. PACKED COLUMNS 398

VI. FILTRATION 401

A. Governing Equations 401

B. Constant Pressure Operation 405

C. Constant Flow Operation 406

D. Cycle Time 406

E. Plate-and-Frame Filters 407

F. Rotary Drum Filter 408

G. Compressible Cake 408 PROBLEMS 409 NOTATION 417 REFERENCES 418

14. FLUIDIZATION AND SEDIMENTATION 419

I. FLUIDIZATION 419

A. Governing Equations 420

B. Minimum Bed Voidage 421

C. Nonspherical Particles 421

II. SEDIMENTATION 423

A. Hindered Settling 423

B. Fine Particles 425

C. Coarse Particles 428

D. All Flow Regimes 428

III. GENERALIZED SEDIMENTATION/ FLUIDIZATION 430

IV. THICKENING 430 PROBLEMS 436 NOTATION 441 REFERENCES 442

15. TWO-PHASE FLOW 443

I. SCOPE 443

II. DEFINITIONS 444

III. FLUID-SOLID TWO-PHASE PIPE FLOWS 447

A. Pseudohomogeneous Flows 447

B. Heterogeneous Liquid-Solid Flows 449

C. Pneumatic Solids Transport 454

IV. GAS-LIQUID TWO-PHASE PIPE FLOW 459 A. Flow Regimes 459

PROBLEMS 474

NOTATION 475

REFERENCES 477

Appendixes

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