unit operations in food engineering

Unit Operations in Food Engineering © 2003 by CRC Press LLC FOOD PRESERVATION TECHNOLOGY SERIES Series Editor Gustavo V Barbosa-Cánovas Innovations in Food Processing Editors: Gustavo V Barbosa-Cánovas and Grahame W Gould Trends in Food Engineering Editors: Jorge E Lozano, Cristina ón, Efrén Parada-Arias, and Gustavo V Barbosa-Cánovas Pulsed Electric Fields in Food Processing: Fundamental Aspects and Applications Editors: Gustavo V Barbosa-Cánovas and Q Howard Zhang Osmotic Dehydration and Vacuum Impregnation: Applications in Food Industries Editors: Pedro Fito, Amparo Chiralt, Jose M Barat, Walter E L Spiess, and Diana Behsnilian Engineering and Food for the 21st Century Editors: Jorge Welti-Chanes, Gustavo V Barbosa-Cánovas, and José Miguel Aguilera Unit Operations in Food Engineering Albert Ibarz and Gustavo V Barbosa-Cánovas © 2003 by CRC Press LLC Unit Operations in Food Engineering Albert Ibarz, Ph.D University of Lleida Lleida, Spain Gustavo V Barbosa-Cánovas, Ph.D Washington State University Pullman, Washington CRC PR E S S Boca Raton London New York Washington, D.C © 2003 by CRC Press LLC TX69299 fm frame Page Friday, September 20, 2002 8:01 AM Library of Congress Cataloging-in-Publication Data Ibarz, Albert [Operaciones unitarias en la engenierâia de alimentos English] Unit operations in food engineering / by Albert Ibarz, Gustavo V Barbosa-Cánovas p cm (Food preservation technology series) Includes bibliographical references and index ISBN 1-56676-929-9 Food industry and trade I Barbosa-Cánovas, Gustavo V II Title III Series TP370 I2313 2002 664—dc21 2002017480 CIP This book contains information obtained from authentic and highly regarded sources Reprinted material is quoted with permission, and sources are indicated A wide variety of references are listed Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale Specific permission must be obtained in writing from CRC Press LLC for such copying Direct all inquiries to CRC Press LLC, 2000 N.W Corporate Blvd., Boca Raton, Florida 33431 Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe Visit the CRC Press Web site at www.crcpress.com © 2003 by CRC Press LLC No claim to original U.S Government works International Standard Book Number 1-56676-929-9 Library of Congress Card Number 2002017480 Printed in the United States of America Printed on acid-free paper © 2003 by CRC Press LLC TX69299 fm frame Page Tuesday, September 10, 2002 1:42 PM To our families © 2003 by CRC Press LLC TX69299 fm frame Page Tuesday, September 10, 2002 1:42 PM Preface One of the primary objectives of the food industry is to transform, by a series of operations, raw agricultural materials into foods suitable for consumption Many different types of equipment and several stages are used to perform these transformations The efficient calculation and design of each stage — called unit or basic operation — is one of the main purposes of food engineering The systematic study of unit operations began in the chemical engineering field, where calculation tools were developed to describe, based on engineering principles, the changes taking place in each processing step This knowledge has been applied to food engineering and, at the same time, has been adapted to the particular and distinctive nature of the raw materials used The goal of any series of operations is not just to obtain optimum production, but also a food product suitable for consumption and of the highest quality Thus, in the application of unit operations to a food process, exhaustive and careful calculation is essential to obtaining process stages that cause minimum damage to the food that is being processed The main objective of this book is to present, in progressive and systematic form, the basic information required to design food processes, including the necessary equipment The number of food engineering unit operations is quite extensive, but some are rarely applied because they are quite specific to a given commodity or process This book covers those unit operations that, in the opinion of the authors, are most relevant to the food industry in general The first chapters contain basic information on transport phenomena governing key unit operations, followed by chapters offering a detailed description of those selected unit operations To facilitate the understanding of all the studied unit operations, each chapter concludes with a set of solved problems We hope this book will be useful as a reference for food engineers and as a text for advanced undergraduate and graduate students in food engineering We also hope this book will be a meaningful addition to the literature dealing with food processing operations Albert Ibarz Gustavo V Barbosa-Cánovas © 2003 by CRC Press LLC TX69299 fm frame Page Friday, September 20, 2002 7:41 AM Acknowledgments The authors wish to express their gratitude to the following institutions and individuals who contributed to making this book possible: Interministerial Commission of Science and Technology (CICYT) of Spain for supporting the preparation of this book through project TXT96-2223 The University of Lleida and the Washington State University (WSU) for supplying the facilities and conducive framework for the preparation of this book Dr Jorge Vélez-Ruiz, Universidad de las Américas-Puebla, México for his very important contributions in the preparation of Chapter María Luisa Calderón (WSU) for her professionalism and dedication in revising the Spanish version of the book from beginning to end Her commentaries and suggestions were very valuable José Juan Rodríguez and Federico Harte (WSU) for their decisive participation in the final review of the Spanish version Both worked with great care, dedication, enthusiasm, and professionalism The “translation team:” Lucy López (Universidad de las AméricasPuebla, México), Jeannie Anderson (WSU), Fernanda San Martín (WSU), and Gipsy Tabilo (WSU) for their incredible dedication to transforming this book into the English version All the students who attended our unit operations in food engineering courses; they provided a constant stimulus for conceiving and developing the finished work Albert Ibarz, Jr for his careful collaboration in preparing many of the figures in the book and Raquel Ibarz for her invaluable help and encouragement for making this book a pleasant reality © 2003 by CRC Press LLC TX69299 fm frame Page 11 Tuesday, September 10, 2002 1:42 PM Authors Albert Ibarz earned his B.S and Ph.D in chemical engineering from the University of Barcelona, Spain He is a Professor of Food Engineering at the University of Lleida, Spain and the Vice-Chancellor for Faculty Affairs His current research areas are: transport phenomena in food processing, reaction kinetics in food systems, physical properties of foods, and ultra high pressure for food processing Gustavo V Barbosa-Cánovas earned his B.S in mechanical engineering from the University of Uruguay and his M.S and Ph.D in food engineering from the University of Massachusetts at Amherst He is a Professor of Food Engineering at Washington State University and Director of the Center for Nonthermal Processing of Food His current research areas are: nonthermal processing of foods, physical properties of foods, edible films, food powder technology, and food dehydration © 2003 by CRC Press LLC TX69299 fm frame Page 13 Tuesday, September 10, 2002 1:42 PM CONTENTS 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Introduction to Unit Operations: Fundamental Concepts Process .1 Food Process Engineering Transformation and Commercialization of Agricultural Products .2 Flow Charts and Description of Some Food Processes Steady and Unsteady States .3 Discontinuous, Continuous, and Semicontinuous Operations Unit Operations: Classification 1.7.1 Momentum Transfer Unit Operations 1.7.2 Mass Transfer Unit Operations .8 1.7.3 Heat Transfer Unit Operations .8 1.7.4 Simultaneous Mass–Heat Transfer Unit Operations 1.7.5 Complementary Unit Operations Mathematical Setup of the Problems Unit Systems: Dimensional Analysis and Similarity 11 Magnitude and Unit Systems 11 2.1.1 Absolute Unit Systems 11 2.1.2 Technical Unit Systems 12 2.1.3 Engineering Unit Systems .12 2.1.4 International Unit System (IS) 13 2.1.5 Thermal Units 14 2.1.6 Unit Conversion 15 2.2 Dimensional Analysis 17 2.2.1 Buckingham’s π Theorem 18 2.2.2 Dimensional Analysis Methods 20 2.2.2.1 Buckingham’s Method .20 2.2.2.2 Rayleigh’s Method 22 2.2.2.3 Method of Differential Equations 22 2.3 Similarity Theory 23 2.3.1 Geometric Similarity .24 2.3.2 Mechanical Similarity .25 2.3.2.1 Static Similarity 25 2.3.2.2 Kinematic Similarity .25 2.3.2.3 Dynamic Similarity 25 Problems 30 2.1 © 2003 by CRC Press LLC TX69299 ch01 frame.book Page 859 Wednesday, September 4, 2002 2:13 PM References 859 Heldman, D.R (1992), Food freezing, in Handbook of Food Engineering (D.R Heldman and D.B Lund, Eds.), New York: Marcel Dekker Heldman, D.R and Lund, D.B (1992), Handbook of Food Engineering, New York: Marcel Dekker Heldman, D.R and Singh, R.P (1981), Food Process Engineering, Westport, CT: AVI Herranz, J (1979), Procesos de Transmisión de Calor, Madrid: Castillo Higgs, S.J and Norrington, R.J (1971), Rheological properties of selected foodstuffs, Proc Biochem., 6(5), 52 Holdsworth, S.D (1971), 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Reverté Weltmann, R.N (1943), Breakdown of thixotropic structure as function of time, J Appl Phys., 14, 343 Welty, J.R., Wicks, Ch.E., and Wilson, R.E (1976), Fundamentals of Momentum, Heat and Mass Transport, New York: John Wiley & Sons White, G.W (1970), Rheology in food research, J Food Technol., 5, Wilkinson, W.L (1974), Chem Eng., 285, 289 Windsor, M and Barlows, S (1984), Introducción a los Subproductos de Pesquería, Zaragoza, Spain: Acribia Zimm, B.H and Grothers, D.M (1962), Simplified rotating cylinder viscometer for DNA, Proc Natl Acad Sci., 48, 905 Zitny, R et al (1978), Paper presented at 6th International CHISA Congress, Prague © 2003 by CRC Press LLC TX69299 ch01 frame.book Page 865 Wednesday, September 4, 2002 2:13 PM Appendix TABLE A1 Properties of Saturated Steam t (°C) Vapor Pressure (kPa) 0.01 12 15 18 21 24 27 30 33 36 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 0.611 0.758 0.935 1.148 1.402 1.705 2.064 2.487 2.985 3.567 4.246 5.034 5.947 7.384 9.593 12.349 15.758 19.940 25.03 31.19 38.58 47.39 57.83 70.14 84.55 101.35 120.82 143.27 169.06 198.53 232.1 270.1 313.0 316.3 415.4 475.8 543.1 Specific volume (m3/kg) Liquid Vapor 0.0010002 0.0010001 0.0010001 0.0010003 0.0010005 0.0010009 0.0010014 0.0010020 0.0010027 0.0010035 0.0010043 0.0010053 0.0010063 0.0010078 0.0010099 0.0010121 0.0010146 0.0010172 0.0010199 0.0010228 0.0010259 0.0010291 0.0010325 0.0010360 0.0010397 0.0010435 0.0010475 0.0010516 0.0010559 0.0010603 0.0010649 0.0010697 0.0010746 0.0010797 0.0010850 0.0010905 0.0010961 206.14 168.132 137.734 113.386 93.784 77.926 65.038 54.514 45.883 38.774 32.894 28.011 23.940 19.523 15.258 12.032 9.568 7.671 6.197 5.042 4.131 3.407 2.828 2.361 1.982 1.673 1.419 1.210 1.037 0.892 0.771 0.669 0.582 0.509 0.446 0.393 0.347 Enthalpy (kJ/kg) Liquid Vapor Entropy (kJ/kg K) Liquid Vapor 0.00 12.57 25.20 37.80 50.41 62.99 75.58 88.14 100.70 113.25 125.79 138.33 150.86 167.57 188.45 209.33 230.23 251.13 272.06 292.98 313.93 334.91 355.90 376.92 397.96 419.04 440.15 461.30 482.48 503.71 524.99 546.31 567.69 589.13 610.63 632.20 653.84 0.0000 0.0457 0.0912 0.1362 0.1806 0.2245 0.2679 0.3109 0.3534 0.3954 0.4369 0.4781 0.5188 0.5725 0.6387 0.7038 0.7679 0.8312 0.8935 0.9549 1.0155 1.0753 1.1343 1.1925 1.2500 1.3069 1.3630 1.4185 1.4734 1.5276 1.5813 1.6344 1.6870 1.7391 1.7907 1.8418 1.8925 2501.4 2506.9 2512.4 2517.9 2523.4 2528.9 2534.4 2539.9 2545.4 2550.8 2556.3 2561.7 2567.1 2574.3 2583.2 2592.1 2600.9 2609.6 2618.3 2626.8 2635.3 2643.7 2651.9 2660.1 2668.1 2676.1 2683.8 2691.5 2699.0 2706.3 2713.5 2720.5 2727.3 2733.9 2740.3 2746.5 2752.4 9.1562 9.0773 9.0003 8.9253 8.8524 8.7814 8.7123 8.6450 8.5794 8.5156 8.4533 8.3927 8.3336 8.2570 8.1648 8.0763 7.9913 7.9096 7.8310 7.7553 7.6824 7.6122 7.5445 7.4791 7.4159 7.3549 7.2958 7.2387 7.1833 7.1296 7.0775 7.0269 6.9777 6.9299 6.8833 6.8379 6.7935 865 © 2003 by CRC Press LLC TX69299 ch01 frame.book Page 866 Wednesday, September 4, 2002 2:13 PM 866 Unit Operations in Food Engineering TABLE A1 (continued) Properties of Saturated Steam t (°C) 160 165 170 175 180 190 200 225 250 275 300 Vapor Pressure (kPa) 617.8 700.5 791.7 892.0 1002.1 1254.4 1553.8 2548 3973 5942 8581 © 2003 by CRC Press LLC Specific volume (m3/kg) Liquid Vapor 0.0011020 0.0011080 0.0011143 0.0011207 0.0011274 0.0011414 0.0011565 0.0011992 0.0012512 0.0013168 0.0010436 0.307 0.273 0.243 0.217 0.194 0.157 0.127 0.078 0.050 0.033 0.022 Enthalpy (kJ/kg) Liquid Vapor Entropy (kJ/kg K) Liquid Vapor 675.55 697.34 719.21 741.17 763.22 807.62 852.45 966.78 1085.36 1210.07 1344.0 1.9427 1.9925 2.0419 2.0909 2.1396 2.2359 2.3309 2.5639 2.7927 3.0208 3.2534 2758.1 2763.5 2768.7 2773.6 2778.2 2786.4 2793.2 2803.3 2801.5 2785.0 2749.0 6.7502 6.7078 6.6663 6.6256 6.5857 6.5079 6.4323 6.2503 6.0730 5.8938 5.7045 TX69299 ch01 frame.book Page 867 Wednesday, September 4, 2002 2:13 PM Appendix 867 TABLE A2 Physical Properties of Water at Saturation Pressure Temp (˚C) Density (kg/m3) ␤ 10–4 (K–1) cp (kJ/kg K) k (W/m K) ␣ ·10–6 (m2/s) ␩ ·10–6 (Pa s) ␯ ·10–6 (m2/s) 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 999.9 1000.0 999.7 999.1 998.2 997.1 995.7 994.1 992.2 990.2 988.1 985.7 983.2 980.6 977.8 974.9 971.8 968.7 965.3 961.9 958.4 951.0 943.5 934.8 926.3 916.9 907.6 897.3 886.6 876.0 862.8 852.8 837.0 827.3 809.0 799.2 –0.7 4.226 4.206 4.195 4.187 4.182 4.178 4.176 4.175 4.175 4.176 4.178 4.179 4.181 4.184 4.187 4.190 4.194 4.198 4.202 4.206 4.211 4.224 4.232 4.250 4.257 4.270 4.285 4.396 4.396 4.480 4.501 4.560 4.605 4.690 4.731 4.857 0.558 0.568 0.577 0.587 0.597 0.606 0.615 0.624 0.633 0.640 0.647 0.652 0.658 0.663 0.668 0.671 0.673 0.676 0.678 0.680 0.682 0.684 0.685 0.686 0.684 0.684 0.680 0.679 0.673 0.670 0.665 0.655 0.652 0.637 0.634 0.618 0.131 0.135 0.137 0.141 0.143 0.146 0.149 0.150 0.151 0.155 0.157 0.158 0.159 0.161 0.163 0.164 0.165 0.166 0.167 0.168 0.169 0.170 0.171 0.172 0.172 0.173 0.173 0.172 0.172 0.171 0.170 0.168 0.167 0.164 0.162 0.160 1793.64 1534.74 1296.44 1135.61 993.41 880.64 792.38 719.81 658.03 605.07 555.06 509.95 471.65 435.42 404.03 376.58 352.06 328.52 308.91 292.24 277.53 254.97 235.36 211.82 201.04 185.35 171.62 162.29 152.00 145.14 139.25 131.41 124.54 119.64 113.76 109.83 1.79 1.54 1.30 1.15 1.01 0.88 0.81 0.73 0.66 0.61 0.56 0.52 0.48 0.44 0.42 0.37 0.36 0.34 0.33 0.31 0.29 0.27 0.24 0.23 0.21 0.20 0.19 0.18 0.17 0.17 0.16 0.15 0.15 0.15 0.14 0.14 0.95 2.1 3.0 3.9 4.6 5.3 5.8 6.3 7.0 7.5 8.0 8.5 9.1 9.7 10.3 10.8 11.5 12.1 12.8 13.5 14.3 15.2 16.2 17.2 18.6 β is the volumetric thermal expansion coefficient, Cˆ P is the specific heat, k is the thermal conductivity, α is the thermal diffusivity, η is the absolute viscosity, and ν is the kinematic viscosity © 2003 by CRC Press LLC TX69299 ch01 frame.book Page 868 Wednesday, September 4, 2002 2:13 PM 868 Unit Operations in Food Engineering TABLE A3 Properties of Liquid and Saturated Vapor of Ammonia t (ºC) p (kPa) Enthalpy (kJ/kg) ˆ Liquid hˆ Vapor H Liquid sˆ Vapor Sˆ Liquid vˆ Vapor Vˆ –60 –55 –50 –45 –40 –35 –30 –28 –26 –24 –22 –20 –18 –16 –14 –12 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 10 11 12 13 14 15 16 17 18 19 20 21 21.99 30.29 41.03 54.74 72.01 93.49 119.90 132.02 145.11 159.22 174.41 190.74 208.26 227.04 247.14 268.63 291.57 303.60 316.02 328.84 342.07 355.71 369.77 384.26 399.20 414.58 430.43 446.74 463.53 480.81 498.59 516.87 535.67 555.00 574.87 595.28 616.25 637.78 659.89 682.59 705.88 729.79 754.31 779.46 805.25 831.69 858.79 886.57 –69.5330 –47.5062 –25.4342 –3.3020 18.9024 41.1883 63.5629 72.5387 81.5300 90.5370 99.5600 108.599 117.656 126.729 135.820 144.929 154.056 158.628 163.204 167.785 172.371 176.962 181.559 186.161 190.768 195.381 200.000 204.625 209.256 213.892 218.535 223.185 227.841 232.503 237.172 241.848 246.531 251.221 255.918 260.622 265.334 270.053 274.779 279.513 284.255 289.005 293.762 298.527 –0.10909 –0.00717 0.09264 0.19049 0.28651 0.38082 0.47351 0.51015 0.54655 0.58272 0.61865 0.65436 0.68984 0.72511 0.76016 0.79501 0.82965 0.84690 0.86410 0.88125 0.89835 0.91541 0.93242 0.94938 0.96630 0.98317 1.00000 1.01679 1.03354 1.05024 1.06691 1.08353 1.10012 1.11667 1.13317 1.14964 1.16607 1.18246 1.19882 1.21515 1.23144 1.24769 1.26391 1.28010 1.29626 1.31238 1.32847 1.34452 6.6592 6.5454 6.4382 6.3369 6.2410 6.1501 6.0636 6.0302 5.9974 5.9652 5.9336 5.9025 5.8720 5.8420 5.8125 5.7835 5.7550 5.7409 5.7269 5.7131 5.6993 5.6856 5.6721 5.6586 5.6453 5.6320 5.6189 5.6058 5.5929 5.5800 5.5672 5.5545 5.5419 5.5294 5.5170 5.5046 5.4924 5.4802 5.4681 5.4561 5.4441 5.4322 5.4204 5.4087 5.3971 5.3855 5.3740 5.3626 1.4010 1.4126 1.4245 1.4367 1.4493 1.4623 1.4757 1.4811 1.4867 1.4923 1.4980 1.5037 1.5096 1.5155 1.5215 1.5276 1.5338 1.5369 1.5400 1.5432 1.5464 1.5496 1.5528 1.5561 1.5594 1.5627 1.5660 1.5694 1.5727 1.5762 1.5796 1.5831 1.5866 1.5901 1.5936 1.5972 1.6008 1.6045 1.6081 1.6118 1.6156 1.6193 1.6231 1.6269 1.6308 1.6347 1.6386 1.6426 4685.080 3474.220 2616.510 1998.910 1547.360 1212.490 960.867 878.100 803.761 736.868 676.570 622.122 572.875 528.257 487.769 450.971 417.477 401.860 386.944 372.692 359.071 346.046 333.589 321.670 310.263 299.340 288.880 278.858 269.253 260.046 251.216 242.745 234.618 226.817 219.326 212.132 205.221 198.580 192.196 186.058 180.154 174.475 169.009 163.748 158.683 153.804 149.106 144.578 © 2003 by CRC Press LLC 1373.19 1382.01 1390.64 1399.07 1407.26 1415.20 1422.86 1425.84 1428.76 1431.64 1434.46 1437.23 1439.94 1442.60 1445.20 1447.74 1450.22 1451.44 1452.64 1453.83 1455.00 1456.15 1457.29 1458.42 1459.53 1460.62 1461.70 1462.76 1463.80 1464.83 1465.84 1466.84 1467.82 1468.78 1469.72 1470.64 1471.57 1472.46 1473.34 1474.20 1475.05 1475.88 1476.69 1477.48 1478.25 1479.01 1479.75 1480.48 Entropy (kJ/kg·K) Specific volume (l/kg) TX69299 ch01 frame.book Page 869 Wednesday, September 4, 2002 2:13 PM Appendix 869 TABLE A3 (continued) Properties of Liquid and Saturated Vapor of Ammonia t (ºC) p (kPa) 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 915.03 944.18 974.03 1004.60 1035.90 1068.00 1100.70 1134.30 1168.60 1203.70 1239.60 1276.30 1313.90 1352.20 1391.50 1431.50 1472.40 1514.30 1557.00 1600.60 1645.10 1690.60 1737.00 1784.30 1832.60 1881.90 1932.20 1983.50 2035.90 2089.20 2143.60 2199.10 2255.60 2313.20 © 2003 by CRC Press LLC Enthalpy (kJ/kg) ˆ Liquid hˆ Vapor H 303.300 308.081 312.870 317.667 322.471 327.284 332.104 336.933 341.769 346.614 351.466 356.326 361.195 366.072 370.957 375.851 380.754 385.666 390.587 395.519 400.462 405.416 410.382 415.362 420.358 425.369 430.399 435.450 440.523 445.623 450.751 455.913 461.112 466.353 1481.18 1481.87 1482.53 1483.18 1483.81 1484.42 1485.01 1485.59 1486.14 1486.67 1487.18 1487.66 1488.13 1488.57 1488.99 1489.39 1489.76 1489.10 1490.42 1490.71 1490.98 1491.21 1491.41 1491.58 1491.72 1491.83 1491.88 1491.91 1491.89 1491.83 1491.73 1491.58 1491.38 1491.12 Entropy (kJ/kg·K) Specific volume (l/kg) Liquid sˆ Vapor Sˆ Liquid vˆ Vapor Vˆ 1.36055 1.37654 1.39250 1.40843 1.42433 1.44020 1.45604 1.47185 1.48762 1.50337 1.51908 1.53477 1.55042 1.56605 1.58165 1.59722 1.61276 1.62828 1.64377 1.65924 1.67470 1.69013 1.70554 1.72095 1.73635 1.75174 1.76714 1.78255 1.79798 1.81343 1.82891 1.84445 1.86004 1.87571 5.3512 5.3399 5.3286 5.3175 5.3063 5.2953 5.2843 5.2733 5.2624 5.2516 5.2408 5.2300 5.2193 5.2086 5.1980 5.1874 5.1768 5.1663 5.1558 5.1453 5.1349 5.1244 5.1140 5.1036 5.0932 5.0827 5.0723 5.0618 5.0514 5.0409 5.0303 5.0198 5.0092 4.9985 1.6466 1.6507 1.6547 1.6588 1.6630 1.6672 1.6714 1.6757 1.6800 1.6844 1.6888 1.6932 1.6977 1.7023 1.7069 1.7115 1.7162 1.7209 1.7257 1.7305 1.7354 1.7404 1.7454 1.7504 1.7555 1.7607 1.7659 1.7712 1.7766 1.7820 1.7875 1.7931 1.7987 1.8044 140.214 136.006 131.950 128.037 124.261 120.619 117.103 113.708 110.430 107.263 104.205 101.248 98.391 95.629 92.958 90.374 87.875 85.456 83.115 80.848 78.654 76.528 74.468 72.472 70.536 68.660 66.840 65.075 63.361 61.697 60.081 58.511 56.985 55.502 TX69299 ch01 frame.book Page 870 Wednesday, September 4, 2002 2:13 PM 870 Unit Operations in Food Engineering TABLE A4 Normalized Dimensions of Steel Tubing Catalog Number Nominal Diameter (in.) External Diameter (cm) Internal Diameter (cm) Wall Thickness (cm) 40 80 40 80 40 80 40 80 40 80 40 80 40 80 40 80 40 80 40 80 40 80 40 80 40 80 40 80 40 80 40 80 40 80 40 80 ⅛ ⅛ ẳ ẳ ẵ ẵ ắ ắ 1 1ẳ 1ẳ 1ẵ 1ẵ 2 2ẵ 2ẵ 3 3½ 3½ 4 5 6 8 10 10 12 12 1.029 1.029 1.372 1.372 1.715 1.715 2.134 2.134 2.667 2.667 3.340 3.340 4.216 4.216 4.826 4.826 6.033 6.033 7.303 7.303 8.890 8.890 10.16 10.16 11.43 11.43 14.23 14.13 16.83 16.83 21.91 21.91 27.31 27.31 32.39 32.39 0.683 0.546 0.925 0.767 1.252 1.074 1.580 1.387 2.093 1.885 2.664 2.431 3.505 3.246 4.089 3.810 5.250 4.925 6.271 5.900 7.793 7.366 9.012 8.545 10.226 9.718 12.819 12.225 15.405 14.633 20.272 19.368 25.451 24.287 30.323 28.890 0.173 0.241 0.224 0.302 0.231 0.320 0.277 0.373 0.287 0.391 0.338 0.455 0.356 0.485 0.368 0.508 0.391 0.554 0.516 0.701 0.549 0.762 0.574 0.808 0.602 0.856 0.655 0.953 0.711 1.097 0.818 1.270 0.927 1.509 1.031 1.748 © 2003 by CRC Press LLC TX69299 ch01 frame.book Page 871 Wednesday, September 4, 2002 2:13 PM Appendix 871 H=Enthalpy S=Entropy FIGURE A1 Mollier diagram for steam H = enthalpy; S = entropy © 2003 by CRC Press LLC 5.10 5.20 5.30 5.40 5.50 5.60 5.70 100 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 Pressure, kPa 30 1000 900 800 700 600 500 20 10 400 – 20 300 – 10 – 20 Temperature, °C– 40 300 400 500 600 700 800 900 1.000 6.7 6.8 6.9 – 20 100 90 80 70 200 – 20 20 40 60 80 1.500 7.0 2.000 7.1 7.2 30 100 120 1320 1340 1360 1380 1400 1420 1440 1460 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680 1700 1720 1740 Enthalpy, kJ/kg FIGURE A2 Diagram for ammonia © 2003 by CRC Press LLC Unit Operations in Food Engineering 200 150 Specific volume, m3/kg 40 TX69299 ch01 frame.book Page 872 Wednesday, September 4, 2002 2:13 PM Entropy kJ/kg K 2100 872 1320 1340 1360 1380 1400 1420 1440 1460 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680 1700 1720 1740 φ=0.15 φ=0.2 70 φ=0.5 60 sT(kJ/kg dry air) 50 φ=1 40 160 140 120 30 100 80 20 60 Isothermals in °C Isoenthalpics in kJ/kg dry air _Relative humidity 40 10 20 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 X (kg water/kg dry air) © 2003 by CRC Press LLC 873 FIGURE A3 Psychrometric chart sT–X TX69299 ch01 frame.book Page 873 Wednesday, September 4, 2002 2:13 PM φ=0.10 Appendix φ=0.05 80 ... 1.2 Food Process Engineering By analogy with other engineering branches, different definitions of food process engineering can be given Thus, according to one definition, food process engineering. .. September 4, 2002 2:13 PM Unit Operations in Food Engineering Food process engineering can also be defined as “the science of conceiving, calculating, designing, building, and running the facilities... Unit Operations in Food Engineering Albert Ibarz and Gustavo V Barbosa-Cánovas © 2003 by CRC Press LLC Unit Operations in Food Engineering Albert Ibarz, Ph.D University of Lleida Lleida, Spain