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UNIT OPERATIONS OF CHEMICAL ENGINEERING McGraw-Hill Chemical Engineering Series Editorial Advisory Board James J Carberry, Professor of Chemical Engineering, University of Notre Dame James R Fair, Professor of Chemical Engineering, University of Texas, Austin William P Schowalter, Dean, School of Engineering, University of Illinois Matthew Tirrell, Professor of Chemical Engineering, University of Minnesota James Wei, Dean, School of Engineering, Princeton University Max S Peters, Emeritus, Professor of Chemical Engineering, University of Colorado Building the Literature of a Profession Fifteen prominent chemical engineers first met in New York more than 60 years ago to plan a continuing literature for their rapidly growing profession From Industry came such pioneer practitioners as Leo H Baekeland, Arthur D Little, Charles L Reese, John V N Dorr, M C Whitaker, and R S McBride From the universities came such eminent educators as William H Walker, Alfred H White, D D Jackson, J H James, Warren K Lewis, and Harry A Curtis H C Parmelee, then editor of Chemical and Metallurgical Engineering, served as chairman and was joined subsequently by S D Kirkpatrick as consulting editor After several meetings, this committee submitted its report to the McGrawHill Book Company in September 1925 In the report were detailed specifications for a correlated series of more than a dozen texts and reference books which have since become the McGraw-Hill Series in Chemical Engineering and which became the cornerstone of the chemical engineering curriculum From this beginning there has evolved a series of texts surpassing by far the scope and longevity envisioned by the founding Editorial Board The McGrawHill Series in Chemical Engineering stands as a unique historical record of the development of chemical engineering education and practice In the series one finds the milestones of the subject's evolution: industrial chemistry, stoichiometry, unit operations and processes, thermodynamics, kinetics, and transfer operations Chemical engineering is a dynamic profession, and its literature continues to evolve McGraw-Hill, with its editor, B J Clark and its consulting editors, remains committed to a publishing policy that will serve, and indeed lead, the needs of the chemical engineering profession during the years to come The Series Bailey and Ollis: Biochemical Engineering Fundamentals Bennett and Myers: Momentum, Heat, and Mass Transfer Brodkey and Hershey: Transport Phenomena: A Unified Approach Carberry: Chemical and Catalytic Reaction Engineering Constantinides: Applied Numerical Methods with Personal Computers Coughanowr: Process Systems Analysis and Control de Nevers: Fluid Mechanics for Chemical Engineers Douglas: Conceptual Design of Chemical Processes Edgar and Himmelblau: Optimization of Chemical Processes Gates, Katzer, and Schuit: Chemistry of Catalytic Processes Holland: Fundamentals of Multicomponent Distillation Holland and Liapis: Computer Methods for Solving Dynamic Separation Problems Katz and Lee: Natural Gas Engineering: Production and Storage King: Separation Processes Lee: Fundamentals of Microelectronics Processing Luyben: Process Modeling, Simulation, and Control for Chemical Engineers McCabe, Smith, and Harriott: Unit Operations of Chemical Engineering Mickley, Sherwood, and Reed: Applied Mathematics in Chemical Engineering Middleman and Hochberg: Process Engineering Analysis in Semiconductor Device Fabrication Nelson: Petroleum Refinery Engineering Perry and Chilton (Editors): Perry -s Chemical Engineers' Handbook Peters: Elementary Chemical Engineering Peters and Timmerhaus: Plant Design and Economics for Chemical Engineers Reid, Prausnitz, and Rolling: Properties of Gases and Liquids Smith: Chemical Engineering Kinetics Smith and Van Ness: Introduction to Chemical Engineering Thermodynamics Treybal: Mass Transfer Operations Valle-Riestra: Project Evaluation in the Chemical Process Industries Wei, Russell, and Swartzlander: The Structure of the Chemical Processing Industries Wentz: Hazardous Waste Management UNIT OPERATIONS OF CHEMICAL ENGINEERING Fifth Edition Warren L McCabe Late R J Reynolds Professor in Chemical Engineering North Carolina State University Julian C Smith Emeritus Professor of Chemical Engineering Cornell University Peter Harriott Fred H Rhodes Professor of Chemical Engineering Cornell University McGraw-Hill, Inc New York St Louis San Francisco Auckland Bogota Caracas Lisbon London Madrid Mexico Milan Montreal New Delhi Paris San Juan Singapore Sydney Tokyo Toronto UNIT OPERATIONS OF CHEMICAL ENGINEERING International Editions 1993 Exclusive rights by McGraw-Hill Book Co - Singapore for manufacture and export Tllis book cannot be re-exported from the cowttry to which it is consigned by McGraw-Hill Copyright © 1993, 1985, 1976, 1967, 1956 by McGraw-Hill, Inc All rights reserved Except as pernlitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any fonn or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher I CWP PMP This book was set in Times Roman The editors were B.J Clark and Eleanor Castellano; the production supervisor was Louise Karam The cover was designed by Joseph Gi!lians Library of Congress Cataloging-in-Publication Data McCabe, Warren L (Warren Lee), (date) Unit operations of chemical engineering I Warren L McCabe, Julian C Smitl1, Peter Harriott -5th ed p em - (McGraw-Hill chemical engineering series) Includes index ISBN 0-07-044844-2 I Chenlical processes I Snlith, Julian C (Julian Cleveland), (date) II Harriott, Peter III Title IV Series 1P155 M393 1993 660' 2842-dc20 92-36218 When ordering this title, use ISBN 0-07-112738-0 Printed in Singapore ABOUT THE AUTHORS Julian C Smith (B.Chem., Chem.E., Cornell University) is Professor Emeritus of Chemical Engineering at Cornell University, where he joined the faculty in 1946 He was Director of Continuing Engineering Education at Cornell from 1965 to 1971, and Director of the School of Chemical Engineering from 1975 to 1983 He retired from active teaching in 1986 Before joining the faculty at Cornel~ he was employed as a chemical engineer by E.I duPont de Nemours and Co He has served as a consultant on process development to Du Pont, American Cyanamid, and many other companies, as well as government agencies He is a member of the American Chemical Society and a Fellow of the American Institute of Chemical Engineers Peter Harriott (B Chem.E., Cornell University, SeD., Massachusetts Institute of Technology) is the Fred H Rhodes Professor of Chemical Engineering at Cornell University Before joining the Cornell faculty in 1953, he worked as a chemical engineer for the E.L duPont de Nemours and Co and the General Electric Co In 1966 he was awarded an NSF Senior Postdoctoral Fellowship for study at the Institute for Catalysis in Lyon, France, and in 1988 he received a DOE fellowship for work at the Pittsburgh Energy Technology Center Professor Harriott is the author of Process Control and a member of the American Chemical Society and the American Institute of Chemical Engineers He has been a consultant to the U.S Department of Energy and several industrial firms on problems of mass transfer, reactor design, and air pollution control CONTENTS Preface xix Section Introduction Definitions and Principles Unit Operations Unit Systems Physical Quantities SI Units Cgs Units Gas Constant Fps Engineering Units Conversion of Units Units and Equations Dimensional Analysis Basic Concepts Equations of State of Gases Symbols Problems References 5 10 II 12 14 16 18 18 20 22 23 Section Fluid Mechanics 25 Fluid Statics and Its Applications 27 39 Symbols Problems References 40 41 ix INDEX Evaporators (Cont.) versus single-effect, 485-488 temperature drops in, 483 once-through, 465 single-effect calculations, 480 temperature drop in, effect of liquid head, 473 vapor recompression, 490-491 mechanical, 490 thermal, 491 Exchangers (see Heat exchangers) Extraction: application of McCabe-Thiele method to, 635 equipment for, 624-632 agitated tower extractors, 630 auxiliary equipment, 632 baffle towers, 629 centrifugal extractors, 631 mixer-settlers, 625 packed towers, 626-628 perforated plate towers, 629 performance of, 625 pulse columns, 631 rotating disk contactors, 630 spray towers, 626 York-Scheibel extractors, 630 flooding velocities, 627 HTU in, 625 mass transfer in, 730 mass-transfer coefficients in, 730 McCabe-Thiele method, use in, 635 objective of, 496, 623 phase equilibria in, 632-635 reflux in, 638-640 comparison with distillation, 640 limiting reflux ratios, 638 practical examples of, 639 solid (see Leaching) stage efficiency in, 625 Extraction battery, 615 Extractive distillation, 609 Extractors (see Extraction, equipment for) Extruders (see Mixer-extruders) Fans, 204-206 (See also Blowers) Feed line (see Fractionating columns) Fenske equation, 547 application to multicomponent systems, 595 Fick's law, 650 Filter aids, 1015 Filter media, 1015 resistance of, 1019 1119 Filters, 1002-1047 automatic belt, 1006 bag, 1031 cake, 1003 centrifugal, 1011-1014 automatic batch, 1013 continuous, 1014 principles of, 1027 reciprocating-conveyor, 1014 suspended batch, 1011 clarifying, I030 cartridge, 1030 gas cleaning, 1031 principles of, 1032 continuous pressure, 1009 continuous vacuum, 1007-1011 automatic belt, 1006 rotary-drum, 1007 crossflow, 1033 discontinuous pressure, 1004 discontinuous vacuum, 1007 filter press, 1004 granular bed, 1031 horizontal belt, 1010 precoat, 1010 shell-and-leaf, 1004 types of, 1002 ultrafilters, 1034-1046 (See also Filtration; Microfiltration) Filtration: cake resistance, 1018 equations for, 1020 compressibility coefficient, 1021 of compressible cakes, 1018-1019 constant-pressure, 1020 constant-rate, 1026 continuous, 1024 crossflow, 1033 of incompressible cakes, 1018 pressure drop, 1016 principles, 1016 purposes of, 1002 washing of cake, 1029 (See also Filters) Fin efficiency, 446 Fittings, 183 resistance of, I07 Flash evaporation, 478 Flocculation, 1052 Flooding velocities: in packed absorption towers, 692 in packed extraction towers, 627 Flow meters (see Full-bore flow meters; Insertion meters) 1120 INDEX Flow number, 245 Flow patterns in membrane separators, 844 Fluid flow: compressible fluids: adiabatic flow with friction, 126, 133-137 in beds of solids, 155 change in gas properties, 134 mass velocity, 135 maximum conduit length, 155 asterisk condition, 124 friction parameter, 133 isentropic flow, 126-133 change in gas properties, 129 critical pressure ratio, 128, 130 effect of cross~sectional area, 130 mass velocity, 130 velocity in nozzle, 129 isothermal flow with friction, 126, 137-139 heat transfer in, 139 stagnation point, 150 enthalpy, 124 pressure, 150 temperature, 124 fields of: shear-stress, 44 velocity, 43 velocity gradient, 43 kinetic energy of stream, 74 correlation factor for, 74, 88, 96 laminar, 41 in hollow fibers, 874 newtonian fluids, 86 89 average velocity, 87 kinetic-energy correction factor, 88 momentum correction factor, 88 transition to turbulent flow, 58, 101, 115 non-newtonian fluids, 89-91 transition to turbulent flow, 101 in layers, 112-115 within pipes, 115 transition to turbulent flow, 115 mass balance in, 64 66 momentum balance, 68-72 momentum correction factor, 69, 87-88, 96 one-dimensional, 43 time-dependent, 45 transfer of momentum, 47 turbulent: deviating velocities in, 51 diffusion in, 658 intensity of, 54 isotropic turbulence, 54 nature of, 50 in pipes, 92-98 Fluid flow (Cont.) average velocity, 95 kinetic-energy correction factor, 96 maximum velocity, 97 momentum correction factor, 96 Reynolds number-friction factor Jaw, 96 universal velocity equations, 93 velocity distribution, 92 Reynolds stresses in, 55 scale of, 54 statistical nature of, 53 temperature fluctuations in, 349 Fluid friction: in beds of solids, 151-155 for compressible fluids, 155 effect of particle shape, 152 in mixtures of particles, 155 from changes in velocity or direction, 105-110 minimizing of, 111 from sudden contraction, 106 from sudden expansion, 105 contraction-loss coefficient, 106 expansion-loss coefficient, 105 in fittings and valves, 107 relations among parameters, 86 skin friction and wall shear, 85 stress distribution in pipes, 84 Fluidization, 165-177 aggregative, 169 applications of, 173 bubble velocity in, 173 bubbling, !69, 172 conditions for, 165 drying in, 798 expansion of beds, 170 minimum bed porosity, 166 minimum velocity for, 166 particulate, 170-172 pressure drop in beds, 166 slugging in, 169 types of, I 69 velocity range in, 170-173 Fluids: compressible, 27 (See also Fluid flow) incompressible, 27 (See also Fluid flow) nature of, 27 newtonian, 45 non-newtonian, 45 rate of shear versus shear stress, 48 Force, 6, 11 Form drag, 144, 149 Fouling factors, 324 INDEX Fourier number, 301, 336 Fourier's law, 289 Fractionating columns: analysis by McCabe-Thiele method, 531-553 condenser, 533 constant molal overflow, 532 construction of operating lines, 539 feed line and feed plate location, 538-541 feed plate, 536-541 heating and cooling requirements, 541 invariant zone, 548 minimum number of plates, 545 minimum reflux ratio, 547 nearly pure products, 557 optimum reflux ratio, 549 partial condenser, 534 reboiler, 535 reflux ratio, 532 enthalpy balances in, 553 material balances in, 529 net flow rates, 529 operating lines, 531, 539 (See also Distillation) Francis equation for weir flow, 563 Free settling, 159 Free turbulence, 50 Freundlich equation, 815 Freundlich isotherm, 816 Friction, fluid (see Fluid friction; Friction factor) Friction factor: Blasius, 85 charts for, 99, 101 newtonian fluids, 99 non-newtonian fluids, 101 Darcy, 85 with drag reduction, 102 effect of heat transfer on, 102 effect of roughness, 97 Fanning, 85 for noncircular channels, 103 in supersonic flow, 133 Friction parameter, compressible fluids, 133 FrOssling equation, 670 Froude number, 249, 251, 258 significance of, 250 Full-bore flow meters, 214-229 Gas absorption, 496, 686, 697 with chemical reaction, 728 cocurrent flow, 730 HTU in, 704-709 limiting gas-liquid ratio, 699 logarithmic mean driving force, 705 1121 Gas absorption (Cont.) material balances, 697 multicomponent, 709 number of transfer units, 704 relation to theoretical plates, 704 phase equilibria in, 508 in plate columns, 721 plate efficiency in, 721 rate of, 701 HTU method, 704-709 application to rich gases, 723 definitions, 705 experimental values, 715-716 overall HTUs, 705 individual and overall coefficients, 701-702 interface composition, 702 two-film theory, 674 use of overall coefficients, 703 from rich gases, 722 stage efficiency in, 676-679 temperature variations in, effect of, 700, 706 Gas constant, 10, 1080 Gas law, ideal, 19, 123 (See also Ideal gas) Gas-liquid contact, 690 Gas-solid equilibria, 774, 814 adsdrption isotherms, 814-818 bound water versus unbound water, 775 equilibrium moisture content, 774 free moisture, 774 Gases: compressibility factor, 19 equations of state, 18 virial coefficients, 18 (See also Ideal gas) Gel concentration, 1039 Gel layer, 1044 Graetz number, 336 Grashof number, 364 Greenhouse effect, 419 Grinders (see Crushing and grinding) Grinding (see Comminution) Hagen-Poiseuille equation, 88, 875, 1037 Heat: conduction of, 289 one-dimensional, 290 in solids: through cylinder, 296 series resistances, 293 steady-state, 292 unsteady-state, 299 (See also Slab; Sphere) 1122 INDEX Heat exchange equipment, 309, 427 design of, 427 extendedMsurface, 445-451 calculations for, 447 fin efficiency, 446 types of, 446 temperature approach in, 311 temperature range in, 311 (See also Condensers; Heat exchangers) Heat exchangers: airMcooled, 450 crossflow, 436 correction of LMTD in, 436 double~pipe, 311 enthalpy balances in, 313 heat-transfer coefficients in, 432 multipass, 319, 430 correction of LMTD in, 436 parallel-countercurrent 1-2 type, 430 2-4 type, 431 plate type, 439 RODbaffie, 430 scraped-surface, 453 single-pass 1-1 type, 428 standards for, 428 tubes and tubing, data, 1088 Heat flux, 315 Heat of vaporization, 532 Heat transfer: dimensional analysis in, 341, 360 in dryers, 771-773 effect on friction factor, 102 estimation of wall temperature, 343 in fluids, regimes of, 330 interpretation of dimensionless groups in, 356-359 in laminar flow, 333-340 effect of natural convection, 366 to flat plate, 334 in tubes, 336, 340 to liquid metals, 355 critical Peclet number, 356 in natural convection, 362 368 to non-newtonian fluids, 340 outside tubes, 359, 432-435 to single tube, 360 in packed beds, 362, 455-457 penetration theory in, 453 in plug flow, 337 by radiation (see Radiation) in recuperative exchangers, 831 to single sphere, 362 in transition region of flow, 353 in tubes, 336-359 Heat transfer (Cont.) at high velocities, 347-348 in turbulent flow: analogy with momentum transfer, 348-352 Colburn analogy, 352 Friend and Metzner analogy, 352 Reynolds analogy, 351 (See also Analogy theory) dimensional analysis of, 341 Heat-transfer coefficients: in agitated vessels, 451 in dryers, 772 effective, in unsteady-state heat transfer, 327 in evaporators, 474 in film boiling, 392 in film-type condensation, 376-383 on horizontal tubes, 379 on vertical tubes, 377 in heat exchangers, 432 individual, 319-323 classification of, 326 magnitude of, 326 in laminar flow, 334-340 correction for heating or cooling, 339 in non-newtonian fluids, 340 in liquid metals, 355 in nucleate boiling, 388 overall, 315 calculation from individual coefficients, 323-325 resistance form, 324 special cases, 326 variation along heating surface, 319 in packed beds, 455 in shell-and-tube exchangers, 432 in turbulent flow: average value of, 342 effect of roughness, 347 effect of temperature, 343 effect of tube length, 342 empirical equations for, 341 in noncircular cross sections, 344 (See also Boiling liquids; Condensing vapor; Natural convection to air) Heat-transfer units, in dryers, 773 Heavy-fluid separation, 1049 Helium separation with membranes, 857 Henry's Jaw, 552, 840 HETP (height equivalent to a theoretical plate), 731 High-energy pumps, 203 Hildebrandt extractor, 616 Hindered settling, 159 HTU (height of a transfer unit): in adiabatic humidification, 761 INDEX HTU (Cont.) in extraction, 625 in gas absorption, 704-709 overall, 705 for packed columns, 625, 704-709 Humid heat, 739 Humid volume, 739 Humidifiers, 753 action in, 753 adiabatic, 760 use of HTU, 761 Humidity, 738 measurement of, 747 percentage, 739 relative, 739 Humidity chart, 743 air-water system, 744 construction of, 746 use of, 745 Hydraulic radius, 103 Hydraulic transport, 175 Hydrogen recovery with membranes, 855-857, 880 Hypersorber, 814 Ideal contact stages, 501, 509, 525 determination of number of, 509-511 absorption factor method, 512-517 McCabe-Thiele method, 510, 531-553 rectification on, 525 Ideal gas, 19, 31, 123 Mach number of, 123 velocity of sound in, 124 Ideal plate (see Ideal contact stages) Impingement, separation by, 1032 Initial breeding, in crystallization, 892 Insertion meters, 229-231 Ion exchange, 810, 832 backwashing of beds, 172 Isentropic compression, 209 Isolation train, for solids from solution, 806 Isothermal compression, 209 Jet ejector, 212 Jet mixers, 261 ju-factor, 352 ju-factor, 667 K values, 588, 1110 1111 (See also Distribution coefficients; Vapor-liquid equilibria) 1123 Kelvin equation, 895 Kick's crushing law, 963 Kinetic-energy correction factor, 74, 88, 96 Kinetics of nucleation, 895 Kirchhoff's law of radiation, 403 Kneaders, 943-946 continuous, 945 Knudsen dilfusivity, 839 Kozeny-Carman equation, 153 Kremser equation, 513 Laminar flow (see Fluid flow, laminar) Laminar sublayer (see Viscous sublayer) Langmuir isotherm, 815 Lantern gland, 185 Layer flow: free surface, 112 in pipes, 115 Reynolds number in, 114 transition to turbulent flow, 115 Leaching, 614-623 application of absorption factor to, 618 continuous countercurrent, 617-623 application of McCabe-Thiele method to, 618 equipment for, 615 for dispersed solids, 616 moving bed, 615 Shanks process, 615 stationary solid beds, 615 ideal stages with variable underflow, 620 liquid-solid equilibria in, 618 in saturated solutions, 622 stage efficiency in, 622, 679 Leakage: prevention of, 184 by mechanical seals, 185 by stuffing boxes, 184 Leakproof pumps, 203 Leidenfrost point, 387 Lewis relation, 750 Liquid extraction (see Extraction) Liquid-liquid equilibria, 632 plait point, 633 tie lines, 633 triangular coordinates for, 632 types of systems, 632 Liquid-solid equilibria in leaching, 618 LMTD (see Logarithmic mean, temperature difference) Logarithmic mean: concentration difference, 705 1124 INDEX Logarithmic mean (Com.) radius, 297 relation to arithmetic mean, 297-298 temperature difference, 316 correction for crossflow in heat exchangers, 436 where not used, 317 LUB (length of unused bed), 821-824 Mach number, 120, 123 Magnesium sulfate-water system: enthalpy-concentration diagram, 888 phase diagram, 886 Magnetic flow meters, 227 Manometers, 33-35 inclined, 34 Mass, conservation of, 20 Mass balance in fluid flow, 64-67 Mass flow from bins, 940 Mass transfer: in boundary layers, 661, 860, 863 dimensional analysis in, 665 to drops and bubbles, 673 in dryers, 773, 779 in extraction, 730 film theory, 658 one-way diffusion, effect of, 660 in packed beds, 671, 713-718 Peclet number for, 671 penetration theory of, 662 role of diffusion in, 648 on sieve plates, 676 to suspended particles, 672 to tube bundles, 669 two-film theory, 674 Mass-transfer coefficients, 658 in adsorption, 826 alternate forms of, 706 boundary-layer theory, 661 for cylinders, 669 definitions, 659 for drops and bubbles, 673 in extraction, 730 for known areas, 665 measurement of, 663-665 normal to cylinders, 669 overall, 675 in packed beds, 671, 713-718 inside pipes, 666 for spheres, 670 for suspended particles, 672 in wetted-wall tower, 668 Mass-transfer operations: definitions, 495 terminology and symbols for, 497 Mass velocity, 66 Material balances, 64-67, 505, 529, 697 McCabe /).L law of crystal growth, 902 McCabe-Thiele method, 510, 531-553 application to batch distillation, 579 based on enthalpy balances, 554 use in extraction, 635 use in leaching, 618 Mechanical energy (see Energy brilance, mechanical) Membrane separators: How patterns in, 844 for gas separation, 838-859 for liquid separation, 859-877 multicomponent separations in, 849 radial-flow, 845 for solid-liquid separation, 1034-1047 stage cut in, 850 Membranes, 838-877, 1034-1047 alumina, 1036 asymmetric, 842, 844, 854, 859, 871, 1034 hollow fiber, 874 hydrophilic, 863 hydrophobic, 863 nonporous, 840 polymer, 840, 1036 porous, 838 selectivity, 841 sintered metal, 1035 solute rejection by, 1035, 1043 spiral-wound, 876, 1036 structure of, 842 Metals, liquid, heat transfer in, 355 Methanol-water system, 583 Microfiltration, 1033 Mikro-atomizer, 983 Mixer-extruders, 947 Mixers: for free-flowing solids, 952-956 impact wheel, 954 internal screw, 953 ribbon,952 tumbling (see Tumbling mixers) motionless, 262 for pastes and plastic masses, 943-952 axial mixing in, 951 change-can, 943 continuous kneaders, 945 dispersers, 943 double-motion, 943 internal, 945 kneaders, 943 INDEX Mixers (Cont.) masticators, 943 mixing rolls, 947 mullers, 947 power requirements, 948 pugmill, 948 (See also Agitated vessels; Agitation; Mixing) Mixing, 257-263, 941-956 axial: on distillation trays, 570 of pastes, 951 characteristics of materials, 942 comparison with blending, 941 criteria for, 257, 948 effectiveness, 948-951 in fluidized beds, 958 by jets, 261 of miscible liquids, 257-263 of pseudoplastics, 260 rate of: for free-flowing solids, 956 for pastes and plastic masses, 951 selection of equipment for, 262 stratified, in storage tanks, 261 times: of dispersions, 260 of liquids, 258-260 of solids, 956 (See also Agitated vessels; Agitation; Mixing) Mixing index: for granular solids, 954 for pastes and plastic masses, 949 Mohr rupture envelope, 938 Mohr stress circle, 938 Moisture: bound versus unbound, 775 capillary flow of, 784 equilibrium: air-solid systems, 774, 815 free moisture, 774 Molecular sieves, 815-816 (See also Adsorbents) Momentum, angular, 79 Momentum balance, 68-72 momentum correction factor, 69, 87-88, 96 Momentum flux, 47 Motionless mixers, 262 Multicomponent systems, 518, 588-610, 849 Natural convection to air, 366 heat transfer in, 362-368 Needle breeding, in crystallization, 892 Net positive suction head (NPSH), 191 Newtonian fluids, 45, 86-89 Newton's law: of drag, 160 1125 Newton's Jaw (Cont.) of motion, conversion factors for, 12 Non-newtonian fluids, 45, 50, 89-91, 100-101, 255-256, 340 transition to turbulent flow, 101 Nozzles, flow of compressible fluids in, 126-133 NPSH (Net positive suction head), 191 Nucleation, 892-899 contact, 898,917 factors influencing, 892 heterogeneous, 896 homogeneous, 894 primary, 893 rate of, 895 secondary, 898 fluid-shear, 898 (See also Crystallization; Crystallizers) Nusselt equations, 376-380 Nusselt number, 322, 341 interpretations of, 322, 335, 359 limiting values of, 338 Nutsch, 1007 Operating lines, 507-509 constru-ction of, for fractionating columns, 531, 539 Orifice coefficient, 219 Orifice meters, 217 equations for, 219, 222 expansion factor for, 222 pressure recovery in, 220 vena contracta in, 219 Orifice taps, 218-219 Osmotic pressure, 871 Ostwald ripening, 895 Ostwald-de Waele equation, 48 Overall coefficients (see Heat-transfer coefficients; Mass-transfer coefficients) Oxygen-nitrogen system, 584 Packed beds: effective thermal conductivity in, 457 heat transfer in, 362, 455-457 heat-transfer coefficients in, 455 mass transfer in, 671, 713-718 mass-transfer coefficients in, 671, 713-718 radiation in, 457 Reynolds number for, 146, 151 temperature and velocity profiles in, 455 void fraction in, 155 wall coefficients in, 456-457 (See also Packed columns) 1126 INDEX Packed columns: channeling in, 690 design of, 686-697 distillation, use for, 731 gas-liquid contact in, 690 HTUs for, 625, 704-709 limiting flow rates in, 691 loading and flooding in, 692 pressure drop in, 691 temperature variation in, 700 (See also Packed beds) Parallel-current flow, 312 Particles: average size of, 930 characterization of, 927 masses of, 936-939 pressures in, 936 properties of, 936 mean diameters, 930 measurement of fine particles, 934 mixed sizes, 929 motion through fluids, 155-163 from centrifugal force, 157 from gravitational force, 157 terminal velocity of, 157 in hindered settling, 162 number in mixture, 931 shape, 928 size, 928 distributions of, 929 slurry transport of, 175 specific surface, 930 sphericity, 928 Particulate fluidization, 170 172 Peclet number, 336, 356, 570, 671 for liquid-metal heat transfer, 356 for mass transfer, 671 on sieve plate, 570 Penetration theory: in heat transfer, 453 in mass transfer, 662 Permeability, 841 coefficient, 841 Permeate composition, 839, 847 Penneate flux, 1036 Pervaporation, 864-870 Phase rule, 498-500 Piezometer ring, 214 Pipe, 181-184 allowance for expansion, 184 economic size of, 182 materials of construction for, 182 recommended practice, 187 schedule number of, 182 Pipe (Cont.) selection of, 182 sizes of, 182 standard steel, data on, 1086 Pipe fittings, 183 Pipe joints, 183 Pitot tube, 229 Planck's law, 401 Plate columns: design of, 529-575 in gas absorption, 721 (See also Fractionating columns; Sieve-plate columns) Plate efficiency, 568-575 effect of mixing, 570 factors influencing, 574 in gas absorption, 721 local, 569 Murphree, 568 overall, 568 prediction of, 676 use of, 571 (See also Stage efficiency) Plug cocks, 187 Plug flow, heat transfer in, 337 Pneumatic transport, 174 Podbelniak centrifugal extractor, 631 Polarization factor, 873 Polytropic compression, 210 Porosity of beds of solids, 152 Potential flow, 42, 70-74 Pound force, 11 Power number, 249-252 effect of system geometry on, 252 significance of, 250 Power-law fluids, 48 Prandtl number, 332, 341 of gases, 1105 of liquids, 1106 significance of, 350 Pressure, 28 Pressure-swing adsorption, 813, 855 Pseudoplastic fluids, 45 Psychrometric line, 750 Pumps: cavitation in, 191 centrifugal (see Centrifugal pumps) comparison of types of, 213 developed head of, 189 efficiency of, 78, 193, 203 high-energy, 203 leakproof, 203 NPSH, 191 positive-displacement, 193-195 INDEX Pumps (Cont.) reciprocating, 193 rotary, 195 volumetric efficiency of, 194 power requirements of, 190, 203 suction lift, 191 vacuum, 212 (See also Blowers; Compressors) Quantity: dimensions of, 17 physical, Radial-flow membrane separator, 845 Radiation: absorption coefficient, 417 absorption length, 417 absorptivity, 397, 402 attenuation of, 417 black-body, 399 practical source of, 401 combined with conduction-convection, 422 cosine law of, 403, 408 emissive power, 399 emissivity: monochromatic, 399 of solids, 400 in film boiling, 423 intensity, 408 monochromatic, 399 nature of, 397 in packed beds, 457 Planck's law, 401 reflectivity of solids, 402 to semitransparent materials, 406 421 absorbing gases, 419-421 effect of geometry, 421 layers of liquid or solid, 418 spectrum of, 400-401 Stefan-Boltzmann law, 401 between surfaces, 405-416 angle of vision, 407 nonblack surfaces, 413 with refractory surfaces, 412 square-of-distance effect, 407 transmissivity of, 397 Wien's displacement law, 402 Raoult's Jaw, 546, 552, 589 Rayleigh equation, 577 Rectification, 503, 525 combined with stripping, 526 on ideal plate, 525 1127 Reflux, 502 Reflux ratio, 532 (See also Extraction; Fractionating columns) Relative volatility, 545 Resistance, thermal, 293 Reverse osmosis, 859, 871 Reynolds analogy, 351 Reynolds' experiments, 48 Reynolds number, 49, 58 in agitation, 249, 256 in layer flow, 114 for non-newtonian fluids, 50, 100 for particles or packed beds, 146, 151 transition of laminar to turbulent flow, 49, 58, 101, 115 Reynolds stresses, 55 Rheopectic fluid, 46 Rittinger's crushing law, 963 Rotameters, 223-225 theory and calibration of, 224 Roughness parameter in pipes, 98 Scaleup: of adsorbers, 821 of agitated vessels, 277 of centrifuges, 1070 in solids suspensions, 266 of tumbling mixers, 954 Schmidt number, 666 of gases, 1107 Screen analyses, 931-934 cumulative, 934 differential, 933 Tyler standard screens, 931, 1108 Screens, 931, 994 actual versus ideal, 997 blinding, 997 capacity of, 1000 centrifugal sifter, 997 effectiveness of, 999 grizzlies, 996 gyrating, 996 material balances over, 998 mesh size, effect of, 1001 particle-size limitations of, 995 standard, 931, 1108 vibrating, 997 Seals, mechanical, 185 Sedimentation, 1049-1072 centrifugal, 1060-1072 principles of, 1068 equipment, 1053 flocculation in, 1052 1128 INDEX Sedimentation (Com.) heavy-fluid methods, 1049 mechanism of, 1052 rate of, 1053 sink-and-float methods, 1049 (See also Thickeners) Selectivity of membranes, 841 Semi-infinite solid, heat conduction in, 314 Separation: by differential settling, 1050 factor, in cyclones, 1061 heavy-fluid methods, 1049 by impingement, 1032 of solids from gases, 1031, 1060 (See also Sedimentation) Settling criterion, 160 Settling tanks, 1048 Shanks process, 615 Shape faclors, 152, 249, 884, 928 Shear rate (see Velocity gradients) Shear-induced dispersions, 1047 Sherwood number, 666 SI units, Sieve-plate columns: design of, 560-576 counterflow trays, 575 downcomer level, 564 heads in downcomers 564 limiting vapor velocity, 565 pressure drop across plate, 562 valve trays, 576 weir height, 563 flow patterns in large columns, 571 holdup of liquid, 563 normal operation, 561 pressure drops in, 562 Sieve plates, 561 mass transfer on, 676 operating limits of, 565 Peclet number on, 570 stage efficiency of, 574-575, 676 Sigma value, 1070 Size reduction (see Comminution) Slab: heat conduction in, unsteady state, 300-303 penetration of heat into, 304 Slugging, 169 Slurry transport, 175 Sodium hydroxide-water system: boiling points, 471-472 enthalpy-concentration diagram, 478-479 Solids storage: in bins, 939 flow from, 940 bulk, 939 Solubility: coefficient, 841 curves, 885 effect of particle size on, 895 Solute rejection by membranes, 1035, 1043 Solution-.diffusion mechanism, 840, 859 Solvent extraction (see Extraction) Sorting classifiers, 1049 Space lattice, 883 Specific heats: of gases, 1103 of liquids, 1105 Specific surface of particles, 930 Sphere: drag coefficient for, 147, 158 heat conduction in, unsteady state, 301, 327 mass-transfer coefficient for, 670 Sphericity, 152, 928 Stage cut, in membrane separations, 850 Stage efficiency: in distillation and absorption, 676-679 in extraction, 625 in leaching, 622, 679 of sieve plates, 574-575, 676 (See also Plate efficiency) Stage operations: enthalpy balances, 506 material balances, 505 multicomponent systems, 588-610 terminology for, 505 Stagnation point, 150 enthalpy, 124 pressure, 150 temperature, 124 Stanton number, 341 Steam properties, 1090 Steam-jet ejectors, 212 Stefan-Boltzmann Jaw of radiation, 401 Stokes' law, 146, 160 Stokes-Einstein equation, 1041 Storage of solids (see Solids storage) Stream tube, 64 Streamlines, 64 Streamlining, 149 Stripping (see Desorption) Stripping factor, 515 Structured packings, 689 Suction lift, 191 Sulfolane process, 640 Sulfur dioxide, absorption of, 724 Supercritical fluid extraction, 641 commercial process, 642 decaffeination of coffee, 642 phase equilibria, 641 Supersaturation, methods of generating, 890 Suspension of solid particles, 264 268 INDEX Suspension of solid particles (Cont.) critical stirrer speed for, 265 degrees of, 264 power requirements, 266-267 scaleup, 266 Target efficiency, 1032 Target meters, 226 Temperature of liquid stream, average, 315 Terminal velocity, 157, 162, 167 Thermal boundary layer, 331 Thermal conductivity, 291 effective, in packed beds, 457 of gases, 1100 of liquids, 1101-1102 of metals, 1097 of various solids and insulating materials, 1098 Thermal diffusivity, 300 Thermal expansion, coefficient of, 364-365 Thermal flow meters, 229 Thermal resistance, 293 Thickeners, 1051-1060 design of, 1056 limiting flux in, 1057 mechanically agitated, 1053 zones in, 1059 Thixotropic fluids, 46 Tie lines, 633 Time-dependent flow, 45 Torque, 80 Tortuosity, 153, 839, 861, 1037 Tower packings, 686 690 characteristics of, 689 requirements for, 688 Transfer units (see HTU) Transition: laminar to turbulent flow, 49, 58, 101, 115 length, 59 Trichloroethylene, stripping of, 712 Tubes and tubing, 181-182 condenser, data, 1088 heat-exchanger, data, 1088 (See also Pipe) Tubular pinch effect, 1047 Tumbling mills (see Crushers and grinders) Tumbling mixers, 953 scaleup of, 954 Tunnel flow from bins, 940 Turbine impellers: gas-handling capacity, 273 power input, dispersers, 271 standard design, 242 Turbine meters, 227 1129 Turbulence, 50-54 isotropic, 54 Tyler standard screens, 931, 1108 Ultrafiltration, 1034-1046 of cheese whey, 1041 of milk, 1039 of polymer solutions, 1040 Ultrasonic meters, 227 Underwood equation, 601-602 Unit operations, foundations of, Unit systems, cgs, fps, II SI, Units, consistent, 14 conversion of, 12 factors for, 1081 multiples and submultiples, 1079 Unsteady-state heat transfer, 299-306, 327 effective coefficients in, 327 Uranium isotope separation, 840 V-element meters, 222 Vacuum pumps, 212 Valves: ball, 187 check, 187 gate, 186 globe, 186 plug cocks, 187 Vapor-liquid equilibria: boiling-point diagrams, 524, 527 bubble-point curve, 527 dew-point curve, 527 distribution coefficients (K values), 1110 1111 in humidification, 744 y-x diagrams, 523, 549 Vapor recompression (see Evaporators) Velocity: in diffusion, 649 of fluids., average, 87, 95 terminal, 157, 162, 167 universal distribution of, in pipes, 93 Velocity gradients, 43, 87 in agitated vessels, 246, 255 in non-newtonian fluids, 89-91, 255-256 Velocity heads, use of, in design, 110 Vena contracta, 106 in orifice meters, 219 Venturi meters, 214-216 coefficients for, 216 expansion factor for, 222 1130 INDEX Venturi meters (Cont.) flow rates in, 216 pressure recovery in, 216 Virial equation, 18 Viscosity, 46 of gases, 47, 1092 kinematic, 48 of liquids, 47, 1094 of suspensions, 163 Viscous dissipation, 348 Viscous sublayer, 57, 92 Void fraction: for dumped packing, 155 for fluidized beds, 166, 170 von Karman equation, 96 Vortex street, 148 Vortex-shedding meters, 226 Wake formation (see Boundary layer, separation of) Wall turbulence, 50 Water, properties of, 1090, 1102 Weber ,r.umber, 276 Wet-~lb temperature, 747-750 thJory of, 748 W7tted-wall tower, 664 mass-transfer coefficients in, 668 Wien's displacement law of radiation, 402 Work index for crushing, 963 Zero velocity at wall: anomaly with non-newtonian fluids, 91 0-07-112738-0 780071 12 7387 .. .UNIT OPERATIONS OF CHEMICAL ENGINEERING McGraw-Hill Chemical Engineering Series Editorial Advisory Board James J Carberry, Professor of Chemical Engineering, University of Notre Dame... Fair, Professor of Chemical Engineering, University of Texas, Austin William P Schowalter, Dean, School of Engineering, University of Illinois Matthew Tirrell, Professor of Chemical Engineering, ... text covers that portion of chemical engineering known as the unit operations UNIT OPERATIONS An economical method of organizing much of the subject matter of chemical engineering is based on
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