Heating, ventilating, and air conditioning  analysis and design

Tai ngay!!! Ban co the xoa dong chu nay!!! FrontMatter.qxd 6/15/04 4:06 PM Page i Heating, Ventilating, and Air Conditioning Analysis and Design FrontMatter.qxd 6/15/04 4:06 PM Page iii Heating, Ventilating, and Air Conditioning Analysis and Design Sixth Edition Faye C McQuiston Oklahoma State University Jerald D Parker Oklahoma Christian University Jeffrey D Spitler Oklahoma State University John Wiley & Sons, Inc FrontMatter.qxd 6/15/04 4:06 PM Page iv Acquisitions Editor Joseph Hayton Senior Production Editor Valerie A Vargas Marketing Manager Jennifer Powers New Media Editor Thomas Kulesa Senior Design Manager Harry Nolan Production Services Argosy Publishing Cover Image Photo by Eric Stoltenberg, P2S Engineering, Inc Reproduced with permission This book was set in 10/12 Times Roman by Argosy Publishing and printed and bound by Hamilton Printing The cover was printed by Phoenix Color Corporation This book is printed on acid-free paper © 2005 JohnWiley & Sons, Inc All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600 Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, (201) 748-6011, fax (201) 748-6008 Mail: PERMREQ@WILEY.COM To order books or for customer service, please call 1-800-CALL-WILEY (225-5945) Library of Congress Cataloging in Publication Data McQuiston, Faye C Heating, ventilating, and air conditioning : analysis and design / Faye C McQuiston, Jerald D Parker, Jeffrey D Spitler.–6th ed p cm Includes bibliographical references and index ISBN 0-471-47015-5 (cloth/CD-ROM : alk paper) Heating Ventilation Air conditioning I Parker, Jerald D II Spitler, Jeffrey D III Title TH7222.M26 2005 697–dc22 ISBN 0-471-47015-5 ISBN 0-471-66132-5 (WIE) Printed in the United States of America 10 2004048331 FrontMatter.qxd 6/15/04 4:06 PM Page v Contents Preface xi About the Authors Symbols xv Introduction xiii 1-1 Historical Notes 1-2 Common HVAC Units and Dimensions 1-3 Fundamental Physical Concepts 1-4 Additional Comments 18 References 18 Problems 19 Air-Conditioning Systems 22 2-1 The Complete System 22 2-2 System Selection and Arrangement 26 2-3 HVAC Components and Distribution Systems 2-4 Types of All-Air Systems 29 2-5 Air-and-Water Systems 36 2-6 All-Water Systems 37 2-7 Decentralized Cooling and Heating 39 2-8 Heat Pump Systems 41 2-9 Heat Recovery Systems 44 2-10 Thermal Energy Storage 45 References 46 Problems 46 Moist Air Properties and Conditioning Processes 28 49 3-1 Moist Air and the Standard Atmosphere 49 3-2 Fundamental Parameters 51 3-3 Adiabatic Saturation 53 3-4 Wet Bulb Temperature and the Psychrometric Chart 55 3-5 Classic Moist Air Processes 56 3-6 Space Air Conditioning—Design Conditions 65 3-7 Space Air Conditioning—Off-Design Conditions 75 References 79 Problems 79 v FrontMatter.qxd 6/15/04 4:06 PM Page vi vi Contents Comfort and Health—Indoor Environmental Quality 4-1 Comfort—Physiological Considerations 4-2 Environmental Comfort Indices 86 4-3 Comfort Conditions 89 4-4 The Basic Concerns of IAQ 92 4-5 Common Contaminants 93 4-6 Methods to Control Humidity 95 4-7 Methods to Control Contaminants 98 References 115 Problems 116 Heat Transmission in Building Structures 85 119 5-1 Basic Heat-Transfer Modes 119 5-2 Tabulated Overall Heat-Transfer Coefficients 5-3 Moisture Transmission 153 References 154 Problems 154 Space Heating Load Solar Radiation 138 158 6-1 Outdoor Design Conditions 158 6-2 Indoor Design Conditions 159 6-3 Transmission Heat Losses 160 6-4 Infiltration 160 6-5 Heat Losses from Air Ducts 173 6-6 Auxiliary Heat Sources 175 6-7 Intermittently Heated Structures 175 6-8 Supply Air For Space Heating 175 6-9 Source Media for Space Heating 176 6-10 Computer Calculation of Heating Loads References 178 Problems 179 181 7-1 Thermal Radiation 181 7-2 The Earth’s Motion About the Sun 7-3 Time 185 7-4 Solar Angles 187 7-5 Solar Irradiation 190 7-6 Heat Gain Through Fenestrations 7-7 Energy Calculations 212 References 213 Problems 213 85 184 197 177 FrontMatter.qxd 6/15/04 4:06 PM Page vii Contents The Cooling Load 216 8-1 Heat Gain, Cooling Load, and Heat Extraction Rate 216 8-2 Application of Cooling Load Calculation Procedures 219 8-3 Design Conditions 220 8-4 Internal Heat Gains 221 8-5 Overview of the Heat Balance Method 226 8-6 Transient Conduction Heat Transfer 228 8-7 Outside Surface Heat Balance—Opaque Surfaces 231 8-8 Fenestration—Transmitted Solar Radiation 237 8-9 Interior Surface Heat Balance—Opaque Surfaces 240 8-10 Surface Heat Balance—Transparent Surfaces 246 8-11 Zone Air Heat Balance 249 8-12 Implementation of the Heat Balance Method 254 8-13 Radiant Time Series Method 255 8-14 Implementation of the Radiant Time Series Method 266 8-15 Supply Air Quantities 273 References 273 Problems 275 Energy Calculations and Building Simulation 9-1 Degree-Day Procedure 279 9-2 Bin Method 282 9-3 Comprehensive Simulation Methods 9-4 Energy Calculation Tools 293 9-5 Other Aspects of Building Simulation References 295 Problems 297 10 Flow, Pumps, and Piping Design 279 289 294 299 10-1 Fluid Flow Basics 299 10-2 Centrifugal Pumps 310 10-3 Combined System and Pump Characteristics 10-4 Piping System Fundamentals 317 10-5 System Design 335 10-6 Steam Heating Systems 343 References 358 Problems 359 11 Space Air Diffusion 366 11-1 Behavior of Jets 366 11-2 Air-Distribution System Design References 391 Problems 391 374 314 vii FrontMatter.qxd 6/15/04 4:06 PM Page viii viii Contents 12 Fans and Building Air Distribution 394 12-1 Fans 394 12-2 Fan Relations 394 12-3 Fan Performance and Selection 399 12-4 Fan Installation 407 12-5 Field Performance Testing 414 12-6 Fans and Variable-Air-Volume Systems 12-7 Air Flow in Ducts 418 12-8 Air Flow in Fittings 425 12-9 Accessories 437 12-10 Duct Design—General 439 12-11 Duct Design—Sizing 444 References 454 Problems 454 416 13 Direct Contact Heat and Mass Transfer 461 13-1 Combined Heat and Mass Transfer 13-2 Spray Chambers 464 13-3 Cooling Towers 472 References 479 Problems 479 461 14 Extended Surface Heat Exchangers 482 14-1 The Log Mean Temperature Deficiency (LMTD) Method 483 14-2 The Number of Transfer Units (NTU) Method 484 14-3 Heat Transfer–Single-Component Fluids 485 14-4 Transport Coefficients Inside Tubes 492 14-5 Transport Coefficients Outside Tubes and Compact Surfaces 496 14-6 Design Procedures for Sensible Heat Transfer 504 14-7 Combined Heat and Mass Transfer 513 References 524 Problems 525 15 Refrigeration 529 15-1 The Performance of Refrigeration Systems 529 15-2 The Theoretical Single-Stage Compression Cycle 15-3 Refrigerants 534 15-4 Refrigeration Equipment Components 540 15-5 The Real Single-Stage Cycle 553 15-6 Absorption Refrigeration 560 15-7 The Theoretical Absorption Refrigeration System 15-8 The Aqua–Ammonia Absorption System 572 15-9 The Lithium Bromide–Water System 576 References 578 Problems 579 531 570 FrontMatter.qxd 6/15/04 4:06 PM Page ix Contents Appendix A Thermophysical Properties Table A-1a Table A-1b Table A-2a Table A-2b Table A-3a Table A-3b Table A-4a Table A-4b Table B-1b Table B-2 Table B-3 Table B-4 Table B-5 596 Heating and Cooling Design Conditions—United States, Canada, 597 and the World—English Units Heating and Cooling Design Conditions—United States, Canada, 600 and the World—SI Units Annual BinWeather Data for Oklahoma City,OK 603 Annual Bin Weather Data for Chicago, IL 603 Annual Bin Weather Data for Denver, CO 604 Annual Bin Weather Data for Washington, DC 604 Appendix C Pipe and Tube Data Table C-1 Table C-2 605 Steel Pipe Dimensions—English and SI Units 606 Type L Copper Tube Dimensions—English and SI Units Appendix D Useful Data Table D-1 583 Properties of Refrigerant 718 (Water–Steam)— 584 English Units Properties of Refrigerant 718 (Water–Steam)—SI Units 585 Properties of Refrigerant 134a (1,1,1,2-Tetrafluoroethane)— 586 English Units Properties of Refrigerant 134a (1,1,1,2-Tetrafluoroethane)— 588 SI Units Properties of Refrigerant 22 (Chlorodifluoromethane)— 590 English Units Properties of Refrigerant 22 (Chlorodifluoromethane)— 592 SI Units Air—English Units 594 Air—SI Units 595 Appendix B Weather Data Table B-1a ix 608 Conversion Factors 609 607 FrontMatter.qxd 6/15/04 4:06 PM Page x x Appendixes Appendix E: Charts Chart 1a Chart 1b Chart 1Ha Chart 1Hb Chart Chart Chart Chart ASHRAE Psychrometric Chart No (IP) (Reprinted by 611 permission of ASHRAE.) ASHRAE Psychrometric Chart No (SI) (Reprinted by 611 permission of ASHRAE.) ASHRAE Psychrometric Chart No (IP) (Reprinted by 612 permission of ASHRAE.) ASHRAE Psychrometric Chart No (SI) (Reprinted by 612 permission of ASHRAE.) Enthalpy–concentration diagram for ammonia–water solutions (From Unit Operations by G G Brown, Copyright ©1951 613 by John Wiley & Sons, Inc.) Pressure–enthalpy diagram for refrigerant 134a (Reprinted by 613 permission.) Pressure–enthalpy diagram for refrigerant 22 (Reprinted by 614 permission.) Enthalpy-concentration diagram for Lithium Bromide–water solutions (Courtesy of Institute of Gas Technology, Chicago IL.) 614 Index 615 611 AppendixD.qxd 6/15/04 4:09 PM Page 609 Appendix D Useful Data 609 Table D-1 Conversion Factors Length ft = 30.48 cm in = 2.54 cm m = 39.37 in micron = 10-6 m = 3.281 x 10-6 ft mile = 5280 ft Area m2 = 1550.1472 in.2 m2 = 10.76392 ft2 Volume ft3 = 7.48 U.S gallons = 1728 in.3 m3 = 6.1 x 104 in.3 m3 = 35.3147 ft3 m3 = 264.154 U.S gallons Mass kg = 2.20462 lbm lbm = 7000 grams = 453.5924 g Force N = 0.224809 lbf lbf = 4.44822 N Energy Btu = 778.28 ft-lbf Kilocalorie = 103 calories = 3.968 Btu J = 9.48 x 10-4 Btu = 0.73756 ft-lbf kW-hr = 3412 Btu = 2.6552 x 106 ft-lbf Power hp = 33.000 (ft-lbf)/min hp = 745.7 W W = 3.412 Btu/hr = 0.001341 hp = 0.0002843 tons of refrigeration Pressure atm = 14.6959 psia = 2116 lbf/ft2 = 101325 N/m2 in wg = 249.08 Pa in of mercury = 3376.85 Pa lbf/in.2 = 6894.76 Pa Pa = N/m2 = 1.4504 x 10-4 lbf/in.2 continues AppendixD.qxd 6/15/04 4:09 PM Page 610 610 Appendixes Table D-1 Conversion Factors (continued) Temperature degree R difference = degree F difference = degree C difference = degree K difference degrees F = (degrees C) + 32 degrees C = (degrees F – 32) Thermal Conductivity W calorie hr Btu -ft -F = 0.004134 s -cm -C = 1.7307 m -C mW-C = 0.5778 hr Btu -ft -F Btu-in W = 0.1442 m -C hr-ft -F Btu-in mW-C = 6.933 hr-ft -F Heat Transfer Coefficient Btu2 = 5.678 W m -C hr-ft -F W = 0.1761 Btu2 m -C hr-ft -F Viscosity Absolute poise = 100 centipoises lbm = 1490 centipoises = 1.49 N -2 s m sec - ft lbf - sec = 47,800 centipoises ft centipoise = 0.001 N -2 s m Viscosity Kinematic ft2/sec = 0.0929 m2/s m2/s = 10.764 ft2/sec Specific Heat calorie = Btu g-C lbm - F Btu = 4486.8 kg J- C lbm - F kg J- C = 0.2388 Btu lbm - F AppendixE.qxd 6/15/04 2:40 PM Page 611 Appendix E Chart 1b ASHRAE Psychrometric Chart No (SI) (Reprinted by permission of ASHRAE.) Charts 36 ASHRAE PSYCHROMETRIC CHART NO 30 NORMAL TEMPERATURE–SEA LEVEL Chart 1a ASHRAE Psychrometric Chart No (IP) (Reprinted by permission of ASHRAE.) BAROMETRIC PRESSURE 101.325 kPa COPYRIGHT 1981 0.2 3.0 % −∞ −200 −100 80 % % 60 65 60 14 50 60 55 15 016 15 014 45 18 90 0.75 0.80 12 0.85 80 40 DRY BULB TEMPERATURE – F IDITY E HUM ATIV % REL 60 15 20 95 90 85 80 75 70 65 60 55 50 45 40 12.5 10 002 25 ENTHALPY (h) BTU PER POUND OF DRY AIR 120 ELATIVE 10% R 10 20 30 DRY BULB TEMPERATURE °C 004 115 30 ITY HUMID 35 110 13.0 35 006 105 20% 40 100 45 35 25 13 40 30 0.90 0.95 70 20% 0.70 14 % 30 50 0.65 16 45 15 0.60 % 010 0.5 100 1.0 30 10 012 20 10 40 10 20 008 55 % 30 0.7 50 % 50 % 40 40 018 0.5 0.8 % 20 20 0.8 HUMIDITY RATIO (W) – POUNDS MOISTURE PER POUND DRY AIR F RE RA TU PE TE TU SA 50 % 60 110 22 0.8 0% 70 % 0.1 90 0.2 IR DR YA OF ND PE RP OU BT U ON 90 % 70 65 25 35 HUMIDITY RATIO (W) POUNDS MOISTURE PER POUND DRY AIR DE VIA TIO N PY AL TH EN RA TI SA TU 14 M 70 20 0.8 TH EN TE TI RA °C IR 75 RE YA DR ( AL 40 70 90 50 60 WET BULB OR WATER TEMPERATURE F M ON RA TU RAM R PE 020 75 35 PE R D EM 0.8 PE N BT U AT EN TU U 80 R UL OG RE TH 022 °C TB KIL AL WE ER 60 EP PY (h 25 ETR IL )K 55 15 PY B h) PO OF AI IC M U JO 50 Y DR 25 O 024 RE 70 UB RA TU 40 KI EC PE M OLU V 80 ENTHA ∆h LPY = ∆W HUM IDITY RATIO EM S LE IR 1000 BT R PE 0.9 UL 2.0 TB YA DR WE LO 2.5 LB 85 F AI A GR ENTHALPY = ∆h HUMIDITY RATIO ∆W PER 45 50 80 R Y DR M FT N TIO RA TU SA 004 32 = −0 −0 − .012 ∆H S ∆H T −0.1 016 NS I TO BLE H EA T TAL HEAT −0.2 15 00 −1 .026 U 00 SE 85 EC 20 0.4 60 UM 0.5 020 008 4.0 8.0 −8 ∞ −4 .0 −2 0 028 −4 −2 −1 0 SENSIBLE HEAT = ∆H TOTAL HEAT ∆H 2.0 0.6 50 0.4 −0 0.8 5.0 90 0.4 24 0.9 1.0 VOL ∞ 5000 3000 1.0 120 30 −5.0 −2.0 2.0 4.0 ∞ 0.6 HUMIDITY RATIO (W) GRAMS MOISTURE PER KILOGRAM DRY AIR 10.0 90 0.4 28 26 −∞ 1.0 % 1.0 0.8 80 ∞ AMERICAN SOCIETY OF HEATING, REFRIGERATING AND AIR-CONDITIONING ENGINEERS, INC .024 30 SEA LEVEL COPYRIGHT 1963 028 40 50 SENSIBLE HEAT = ∆HS TOTAL HEAT ∆HT NORMAL TEMPERATURE BAROMETRIC PRESSURE 29.921 INCHES OF MERCURY ENTHALPY OF WATER-BTU-PER LB DRY AIR 1.01.11.2 10 AMERICAN SOCIETY OF HEATING, REFRIGERATING AND AIR-CONDITIONING ENGINEERS, INC 0.9 ASHRAE PSYCHROMETRIC CHART NO AppendixE.qxd 6/15/04 2:40 PM Page 612 Chart 1Ha ASHRAE Psychrometric Chart No (IP) (Reprinted by permission of ASHRAE.) ASHRAE PSYCHROMETRIC CHART NO 5000 FT BAROMETRIC PRESSURE 24.89 INCHES OF MERCURY Chart 1Hb ASHRAE Psychrometric Chart No (SI) (Reprinted by permission of ASHRAE.) COPYRIGHT 1965 39 0 0.4 AMERICAN SOCIETY OF HEATING, REFRIGERATING AND AIR-CONDITIONING ENGINEERS, INC ASHRAE PSYCHROMETRIC CHART NO −∞ AI R DR Y AM GR LO KI R PE S LE °C % RA TU AL PE TH 90 )K DRY BULB TEMPERATURE F M % TE 80 ON RA TI 70 % SA TU 006 35 90 10% 0.85 0.90 12 002 120 115 110 25 ENTHALPY (h) BTU PER POUND OF DRY AIR 0.95 80 10 ITY UMID IVE H RELAT 60 10 20 30 30 40 0.75 0.80 14 004 105 100 95 90 85 80 75 70 65 60 55 50 45 HUMIDITY RATIO (W) GRAMS MOISTURE PER KILOGRAM DRY DR AIR % (h PY % 70 EN HUMIDITY RATIO (W) – POUNDS MOISTURE PER POUND DRY AIR % 80 60 RE % 90 F RE RA TU PE M TE ON RA TI OU R OF D N U PO R PE TU )B PY AL TH EN SA TU AIR RY 40 MD 35 RA 20 0.70 16 1.0 15 0.65 20% DRY BULB TEMPERATURE °C 10 18 70 15 25 0.60 100 0.9 IDITY HUM 20 % 15 10% 30 TIVE RELA 0.5 30 0.9 13 40 35 OG 10 20 40 35 110 22 % 20% 45 40 010 0.4 0.5 10 0.9 16 40 % 50 30 012 50 15 KIL 15 008 45 PER 55 TRE % 30 45 50 % 60 1.0 16 60 15 40 014 20 % 40 20 ME 55 60 °C BIC 0% RA TU RE 50 016 PE 1.0 25 EM 65 50 018 BT 1.0 17 60 UL CU ENTHALPY = ∆h HUMIDITY RATIO ∆W 020 70 65 TB ME 70 WE 35 25 70 1.0 (h 022 75 30 20 55 AIR DR Y AI ATU RE 24 OJ OF ND TU 40 ER 120 25 80 OLU V MP 2.5 EN TH AL PY DE VIA TIO NB TE IL LB .024 26 1.1 BU SENSIBLE HEAT = ∆HS TOTAL HEAT ∆HT 2.0 PE RP OU ET 0.4 −5.0 2.0 −2.0 4.0 ∞ − −24.0 −1 0 FW 5.0 −0 80 75 50 60 40 70 80 WET BULB OR WATER TEMPERATURE F 0.6 0.2 0.1 45 −∞ 1.0 026 17 32 1.0 0.8 10.0 ENTH ∆h ALPY = ∆W M I D IT Y RATIO N TIO RA TU SA ∞ 60 80 50 3.0 0.2 IR DR YA 1000 HU 90 028 DRY 004 85 LB .008 50 ER T P U F EC 18 UM 012 −1 28 COPYRIGHT 1981 AMERICAN SOCIETY OF HEATING, REFRIGERATING AND AIR-CONDITIONING ENGINEERS, INC VOL = −0.1 00 −0.2 15 ∆H S ∆H T −0 −0 −0 NS T O IB L E H EA TAL HEAT BAROMETRIC PRESSURE 84.556 kPa SE 10 NORMAL TEMPERATURE ELEVATION: 1500 METRES 60 1.1 00 20 .020 016 4.0 8.0 −8 ∞ −4 −2 0 0.5 024 − 100 0−200 0 HUMIDITY RATIO (W) POUNDS MOISTURE PER POUND DRY AIR 1.0 2.0 0.6 55 028 1.0 0.8 1.1 1.0 ∞ 5000 300 ENTHALPY OF WATER-BTU-PER LB DRY AIR 1.01.11.2 30 30 50 1.00 SENSIBLE HEAT = ∆HS TOTAL HEAT ∆HT NORMAL TEMPERATURE–HIGH ALTITUDE (5000 FT) Density=1 38 300 PSIA 45 50 55 10 20 100 200 (psia) 400 40 PRESSURE 1000 −20 220 20 −20 95 -0.04 2000 -0.02 3000 quid ed li satu rat T=100 F 90 0.00 0.1 -60 100 60 85 R-134a 0.02 -20 0.2 20 0.04 Chart Pressure–enthalpy diagram for refrigerant 134a (Reprinted by permission.) 0.06 1.0 20 0.3 0.9 80 0.8 0.08 0.7 60 0.4 0.6 0.10 0.5 X=0.5 0.4 CONCENTRATION, LB AMMONIA/LB SOULTION /ft 0.3 lbm 0.2 75 0.1 0.12 T=100 F 0.6 ⫺400 70 SOLIDS 0.14 ⫺300 140 0.7 ⫺80 F ⫺200 0.16 F 180 0.8 ⫺80 65 F 0.18 ⫺40 ⫺40 F 0.9 SIA 60 IA PS IA PS IA PS 1P ⫺100 PSIA 0.20 14.7 sa 0.22 SIA 30 P turated vapor 10 20 32 0F 20 220 -60 60 40 32 20 0F 14 40 PSIA 80 50 30 60 100 0.2 120 F 100 PSIA PSIA 200 -20 250 140 160 0.2 100F 80 F 100 140 120 180 150 60 180 160 100 AT 300 P 250 SIA 200 20 S UID 0.2 LIQ 220 200F 100 SA TU RA TE D 140 0.3 S= 300F 140 360 340 320 100 40 140 -R /lbm 0B tu 400 180 ENTHALPY, BTU/LB SOLUTION 0.3 400 60 35 220 500 240 0.012 0.3 14.7 1.0 260 300 PSIA 100 600 (Btu/lbm) S ENTHALPY 30 LINE T=300 F ION 180 180 UCT 36 STR CON 340 IUM 260 380 IBR 200 0.024 UIL 280 260 0.018 0.036 0.048 10 0.12 0.096 0.18 0.24 0.48 0.36 0.72 1.2 0.96 1.8 2.4 3.6 4.8 7.2 12 9.6 lbm/ft 0.072 20 40 100 200 400 1000 2000 3000 260 220 24 420 EQ 300 700 30 20 S= 10 40 20 10 30 0P 50 SIA 15 00 10 0 50 800 50 30 14 900 460 OR SA T3 00 PS 10 00 IA 500 VAP ATE D UR 42 SAT 1000 10 A 540 PSI 100 30 50 300 1100 580 1200 620 Chart Enthalpy–concentration diagram for ammonia–water solutions (From Unit Operations by G G Brown, Copyright ©1951 by John Wiley & Sons, Inc.) AppendixE.qxd 6/15/04 2:40 PM Page 613 AppendixE.qxd 6/15/04 2:40 PM Page 614 Chart Enthalpy-concentration diagram for Lithium Bromide–water solutions (Courtesy of Institute of Gas Technology, Chicago IL Chart Pressure–enthalpy diagram for refrigerant 22 (Reprinted by permission.) 270 PRESSURE-ENTHALPY DIAGRAM SCALE CHANGE 250 -20 -10 10 20 30 40 50 60 70 12 REFRIGERANT 4000 TEMPERATURE in °F ENTROPY in tu/(lb)(°R) VOLUME in cu ft/lb QUALITY in Wt % 3000 100 110 17 18 0.0 1 0 120 130 140 150 0.2 0.1 0.020 160 0.2 170 0.2 0.022 0.2 0.01 0.01 E.I DUPONT DE NEMOURS & COMPANY, INC WILMINGTON, DELAWARE 19898 0.025 180 160°F 1400 190 48 50 52 230 5000 60 26 80 56 54 27 0 0.04 2000 0.07 1400 R UID VAP O ATE D LIQ ATE D UR SAT SAT UR 10.0 Y UALIT CONS TANT Q -80 14 20 -60 30 -80 3.0 CONSTANT VOLUME 40 50 -100 1.4 40 50 60 70 80 90 0.2 -20 -10 10 20 30 40 50 60 70 80 90 31 30 20 30 10 -120 0.8 0.6 -30 30 18 30 15 10 MM 10 5M M 8.0 6.0 −10 16 14 MM MM Hg Hg F 20 F F F 12 Hg 10 Hg 77 Hg F F F 4.0 −30 3.0 -100 -100 2.0 -120 50 MM -40 -80 4.0 50 10 -20 6.0 70 Hg F 8.0 -60 M 14 20 -60 M 20 10 F 14 7.0 40 -40 -40 10 90 5.0 60 20 F -20 30 Hg 22 4.0 Hg F 40 M 110 3.0 80 -20 60 M 24 -0 80 2.0 100 30 1.4 M M F 20 120 40 100 140 20 140 1.0 160 60 180 80 40 200 20 40 300 0.7 200 100 0.4 30 130 26 60 60 400 150 220 140 0.3 0.5 260 80 240 80 600 28 280 100 100 200 0.2 30 120 300 120 800 34 32 140 0.14 160 1000 36 160 140 170 0.10 180 400 300 38 180 190 0.05 40 200 3000 F 0.2 42 204.81 200 600 44 800 210 4000 46 1000 1.0 200 0.03 25 200 2000 ABSOLUTE PRESSURE (LBS PER SQUARE INCH) 180 0.11 5000 90 T E AN UR ST T N RA CO PE M TE "FREON" 22 80 ENTHALPY, BTU/LB SOLUTION -30 100 32 110 3 34 120 35 36 0 2.0 40 70 130 140 −50 1.4 T AN ST OPY N R CO NT E ENTHALPY (BTU PER LB ABOVE SATURATED LIQUID AT -40 F) SCALE CHANGE 38 1.0 −70 0.8 150 160 170 180 190 0.6 200 −90 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 CONCENTRATION, LB LITHIUM BROMIDE/LB SOLUTION 0.60 0.65 0.70 0.75 0.80 Index.qxd 6/15/04 4:10 PM Page 615 Index A Absorptance, 182 Absorption refrigeration, 560, 570 LiBr-water, 576 aqua-ammonia, 572 Absorption, air cleaning, 108 Adiabatic equivalent temperature, 87 Adiabatic humidification, 62 Adiabatic mixing, 63 Adiabatic saturation, 53 ADPI, 375 Adsorption, 108 Aerosol, 95 Affinity laws, pumps, 316 Air cleaning, 13, 108 Air data, 594 Air diffusers, 369, 374 Air diffusion in spaces, 366 Air distribution performance index, 375 Air distribution system design, 374 Air ducts, heat loss, 173 Air elimination in liquid system, 329 Air filtering, 109 Air flow, accessories, 437 circular equivalent ducts, 424 duct friction factors, 434 fittings, 425 friction loss in ducts, 420 hydraulic grade line, 441 in ducts, 418 pressure gradient diagrams, 441 sizing ducts, 444 Air handlers, Air handling equipment, 28 Air mass, effect on solar radiation, 192 Air quality, indoor air quality procedure, 106 Air quality, indoor, 85 Air return grilles, performance, 384 Air speed, effect on comfort, 91 Air systems, dual-duct, 33 multizone, 34 primary, 36 reheat, 31 single-zones, 29 variable-volume, 32 Air washers, 464 Air washing, 108 Air, adiabatic mixing, 63 behavior of jets, 366 composition of dry air, 50 effectiveness in using outdoor air, 101 makeup, 99 moist air processes, 56 moist air properties, 49 outdoor, 99 outdoor, requirements for ventilation, 103 properties of moist air 52 recirculated, 99 removal in steam systems, 347 solubility in water, 330 standard atmosphere, 49 Air-and-water systems, 36 fan-coils, 37 Air-change method, infiltration, 161 Air-conditioning systems, 22 Air-flow resistance of filters, 109 All-air systems, 7, 22, 29 All-water systems, 37 Angle of incidence, solar, 189 Anticipator, 15 Apparatus dew point, 69 Approach, cooling towers, 472 Aqua-ammonia absorption systems, 572 ASHRAE clear sky model, 192 ASHRAE thermal sensation scale, 89 ASHRAE, Atmospheric clearness number, 192 Auxiliary heat sources, effect on heat load, 175 Azeotropes, 538 B BACnet, 13 Balanced-capacity method of duct design, 446 615 Index.qxd 6/15/04 4:10 PM Page 616 616 Index Basement wall heat transfer, 142 Beam radiation, solar, 191 Below grade heat transfer, 142 Bin method, 282 Bin data, 603 Binary mixtures, refrigerants, 561 Blackbody, 182 Blends, refrigerant, 538 Blow-through air handler, 10 Boilers, 23 Brines, in fluid flow, 302 Building air distribution, 394 Building automation systems, 2, 13 Building envelope, definition, 119 Building materials, thermal properties, 123 Building modeling, 290 Building simulation, 279, 294 Buried pipe, heat transfer, 152 Bypass factor, coil, 69 occupied zone, 102 C Capacity, Capilliary tubes, 552 Carbon dioxide, 93 Carnot refrigeration cycle, 530 Catalysis, 108,109 Ceiling spaces, 141 Central plants, 27 Central systems, 26 Centrifugal fans, 394 Centrifugal pumps, 310 Chemisorption, 108, 109 Chillers, 23 Chilled water storage systems, 45 Chlorofluorocarbons, CFCs, 538 Circular equivalent ducts, 424 Clean rooms, 100 Cleaning, air, 13, 108 Clear sky model, ASHRAE, 192 Clearness number, 192 Clo, definition, 86 Closed loop systems, 14 Closed-loop heat pumps, 42 Clothing insulation effect on comfort, 91 Coefficient of performance (COP), 529 Coil by-pass factor, 69 Coil refrigeration load, 69 Coils, flow control, 331 Colebrook’s equation, 302 Comfort and health, 85 Comfort conditions, 89 Comfort indices, 86, 87 Commissioning, new buildings, Common contaminants, 93 Common pipe, fluid systems, 336 Components, HVAC, 28 Compression refrigeration cycle, 531 Compressor control, 549 Compressor loading, 548 Compressors, 540 Computer calculation of heating loads, 177 Concrete floors, below grade, 143 Condensate return, steam systems, 344 Condensation, inside tubes, 494 Condensers and evaporators, refrigeration, 549 Condensing units, 26 Condition line, 67 Conductance, thermal, 121 Conduction transfer functions (CTFs), 228 Conduction, 119 Configuration factor, radiation, 193 Conservation of mass equation, 299 Constant volume fan powered terminal, 389 Contaminant concentration, 100 Contaminants, 93 method to control, 98 source elimination, 98 Control actions, 14 Control point, 15 Control valves, 333 Control, direct digital, 13 proportional, 16 Controls and instrumentation, 13 Convection, 121, 129 Convective heat transfer coefficient, 129 Conversion factors, *note please furnish Converter, 23 Cooling and dehumidifying, 58 Cooling load, 216 Cooling load, 69 absorbed solar heat gain, 233 calculation procedures, 219 design conditions, 220 exterior convection, 233 exterior radiation, 234 fenestrations, 237 Index.qxd 6/15/04 4:10 PM Page 617 Index heat balance method, 216, 224 heat extraction rate, 216, 218 heat gain from occupants, 222 heat gain, 216 infiltration, 250 internal heat gains, 221,244 lights, 218, 223 mass effect, 218 miscellaneous equipment, 224 people effect, 222 radiant time series method, 216,255 supply air, 273 transient conduction, 228 zone air heat balance, 249 Cooling tower, 23, 472 Cooling, basic concepts, Crack method, infiltration, 161 Crawl spaces, heat transfer, 151 Cross flow outside tubes, 497 Curtain walls, infiltration, 165 D Daily range, 220 Dalton’s law for mixtures, 51 Dampers, 437 DDC, direct digital control, 13 Decentralized systems, 39 Declination of the sun, 188 Dedicated outdoor air systems (DOAS), 107 Degree day procedure, 279 Degree days, selected cities, 280 Degree of saturation, 52 Dehumidification, basic concepts, 10 Demand charges, Desiccants, 97 Design-build, Dew point, 52 Diffuse radiation, solar, 191 Diffuser, high sidewall, performance, 381 basic flow patterns, 369 linear, performance data, 378 noise, 373 round ceiling, performance, 379 T-Bar, performance, 383 Diffusion of air in spaces, 366 Diffusion of moisture, 153 Dilution, with outdoor air, 98 Direct action control, 16 617 Direct contact heat and mass transfer, 461 Direct digital control, 13 Direct exchange (DX) systems, 27 Direct expansion (DX) systems, 27 Discount, future value of money, Displacement ventilation, 107, 374 Distribution systems, 28 Diversity factor, 27 Doors, heat transfer through, 143, 147 Drapery fabrics, characterization, 209 indoor shading properties, 211 Draw-through configuration, 28 Dry air, composition, 50 Dry bulb temperature, 55 Dry condensing units, 26 Dual-duct systems, 33 Duct design, balanced-capacity method, 446 equal-friction method, 444 general, 439 optimization, 453 return air systems, 453 sizing, 444 static regain method, 450 Duct Fitting Database, 433, 407 Ductless systems, 41 Dust-holding capacity of filters, 109 DX systems, 27 E Earth’s motion about sun, 184 Earth’s tilt, effect of, 185 Economizer, 32, 34 EER, 529 Effective draft temperature (EDT), 375 Effective emittance of air spaces, 132 Effective temperature, 87 Effectiveness in using outdoor air, 101 Effectiveness-NTU method, 482, 484 Elevation head, 300 Emittance of various surfaces, 132 Emittance, 183 Energy calculations, 279 bin method, 282 solar radiation, 212 tools, 293 Energy efficiency ratio (EER), 529 Energy management systems, 13 Energy recovery systems, 44 Index.qxd 6/15/04 4:10 PM Page 618 618 Index Energy service companies (ESCOs) , Energy storage systems, 45 Energy, versus power, English engineering system of units, Enthalpy of air, 52 Enthalpy potential, 516 Envelope, building, definition, 119 Environmental comfort indices, 86 Environmental effect of refrigerants, 535 Environmental quality, 85 Environmental tobacco smoke (ETS), 95 Equal friction method of duct design, 444 Equation of time, solar, 186 Equivalent length, duct fittings, 433, 435 fittings, steam, 354 piping, 321, 323 ESCOs, Ethylene glycol, properties, 303, 493 Evaporation, inside tubes, 494 Evaporative cooling, 71 Exfiltration, definition, 99 Expansion tanks, 327 Expansion valves, 550 Extended surface heat exchangers, 482 External shading, windows, 199 F Face and bypass control, 76 Fan Application Manual, 407 Fan laws, 398 Fan powered terminal, 389 Fan-coil systems, 37 Fans, 394 centrifugal, 394 characteristics, 396 efficiency, 396 field performance testing, 414 general performance, 396 installations, 407 laws, 398 performance and selection, 399 relations, 394 static power, 395 system effect, 407 total power, 395 tubeaxial, 394 vaneaxial, 394 variable air volume systems, 416 Feedback control systems, 14 Feedforward systems, 14 Fenestrations, heat transfer in, 143,144 solar heat gain, 197 solar radiation, 237 with internal shading, 207 without internal shading, 203 Fick’s law, 153 Filter efficiency, 109 Filter pressure loss, 115 Filtering, filters,109 Filters, data on high performance filters, 114 Fin efficiency, 486 Fin surface effectiveness, 487 Finned surface heat transfer, 499 Fins, efficiency with mass transfer, 518 Fire dampers, 438 Fitting pressure loss coefficients, 426 Floating control action, 15 Floors and walls below grade, 143 Floors, grade level, 150 Flow measurement, 306 Fluid capacity rates, 485 Fluid flow, 299 air elimination, 329 combined pump and system characteristics, 314 common pipe principle, 336 control through coils, 331 control valves, 333 equivalent length of piping, 321, 323 expansion tanks, 327 four-pipe systems, 336 friction factor, 301 friction loss, water, 320 measurement, 306 parallel circuits, 305, 314 pumps, 310 resistance coefficients, fittings, 322 series circuits, 314 system characteristic, 305 system design, 335 total pressure, 300 two-pipe systems, 336 Forced convection, 129 Fourier equation, 119 Free convection, 129 Free cooling, 559 Friction factor, 301 Friction factors, galvanized steel ducts, 434 Index.qxd 6/15/04 4:10 PM Page 619 Index Friction loss charts, water, 320 Fundamental physical concepts, Furnaces, G Gas constant, 51 Gas contaminants, 93 Gas mixtures, 51 Gas removal, 108 Gateway, 14 Glide, refrigerant, 539 Global irradiation, 181 Global warming potential, GWP, 538 Globe thermometer, 87 Greenhouse warming potential, 538 Grey surfaces, 130 Ground-coupled heat pumps, 42 GWP, 538 H Halocarbons, 538 HBM, 216 Head, fluid flow equations, 300 Health and comfort, 85 Heat and mass transfer, 461 Heat and mass transfer, combined, 513 Heat balance method, 216 Heat balance method, implementation, 254 Heat balance method, overview, 226 Heat balance, interior surface, 240 Heat exchanger effectiveness, 484, 486 Heat exchangers, 482 Heat exchangers, design procedures, 504 Heat extraction rate, 216, 218 Heat gain, 216 Heat gains through fenestrations, solar, 197 Heat losses, air ducts, 173 Heat losses, transmission, 160 Heat pump systems, 41 Heat pump types, 42 Heat pump, typical operating characteristics, 285 Heat pumps, closed-loop, 42 Heat pumps, ground-coupled, 42 Heat recovery systems, 44 Heat stress index, 87 619 Heat transfer modes, basic, 119 Heat transfer, convective coefficients, 492 Heat transfer, convective, 121, 129 Heat transfer, finned surfaces, 499 Heat transfer, single component fluids, 485 Heat transfer, transient conduction, 228 Heat transmission, 119 Heating and humidifying, 60 Heating load, space, 158 Heating loads, computer calculation, 177 Heating systems, steam, 343 Heating, basic concept, Henry’s law, 329 High velocity duct design, 450 Historical notes, Hour angle, definition, 188 Humidification, 98 Humidification, adiabatic, 62 Humidifying, 12 Humidity ratio, 51 Humidity, methods to control, 95 HVAC components, 28 HvacLoadExplorer, 177 Hydraulic diameter, 301 Hydraulic grade line, 441 Hydrochlorofluorocarbons, HCFCs, 538 Hydrofluorocarbons, HFCs, 538 I Ice storage systems, 45 Indoor air quality (IAQ) procedure, 106 Indoor air quality, 85, 92 Indoor design conditions, heating, 158 Indoor environmental quality (IEQ), 85 Induction ratio, diffuser, 367 Infiltration, air change method, 161 calculation aids, 165 cooling load, 250 crack method, 161 curtain walls, 165 definition, 99 effect on heating load 160 stack effect, 163 windows and doors, 162 Instrumentation, 13 Integral control, 17 Intermittently heated structures, 175 Index.qxd 6/15/04 4:10 PM Page 620 620 Index Internal heat gains, 221 International system of units, Multizone system, 34 Mycotoxins, 94 J N Jets, behavior, 366 j-factor analogy, 463 Joule equivalent, National primary ambient air quality standards, 97 Natural convection, 129 Net positive suction head, 312 Noise in diffuser outlets, 373 Number of transfer units, NTU, 484 Nusselt number, 461 L Latent cooling, 10 Latent heat transfer, 12, 60 Lewis number, 462 Lights, effect on cooling load, 218, 223 Lithium bromide-water systems, 576 LMTD, 482 Load, cooling, 69 Localized ventilation, 107 Log mean temperature difference, 482 Lost head, due to friction, 300 Lost head, fluid flow, 301 Low temperature systems, 46 M Makeup air, definition, 99 Mass and heat transfer, combined, 513 Mean radiant temperature, 87 Mean solar constant, 190 Met, definition, 86 Metabolic rate, 86 Micron, definition, 181 Mini-split systems, 41 Miscellaneous equipment, cooling load, 224 Modeling, buildings, 290 strategies, 293 systems, 291 Modulating control action, 14 Moist air processes, 56 Moist Air Properties, 49 Moisture concentration in wall spaces, 153 Moisture transmission in buildings, 153 Mold poisons, 94 Monochromatic radiation properties, 183 Motor load factor, 224 Motor use factor, 224 O Occupant heat gain, 222 Occupied zone bypass factor, 102 Occupied zone, definition, 101 Odor, 109 Offset, control point shift, 16 Open loop systems, 14 Open networks, 14 Operative temperature, 87, 91 Orifices, for flow measurement, 308 Outdoor air, dedicated systems (DOAS), 107 definition, 99 dilution with, 98 effectiveness in using, 101 quality standards, 97 requirements for ventilation, 103 Outdoor design conditions, heating, 158 Outlets, air diffusers, 369 Overall heat transfer coefficient, 138 Overall heat transfer coefficient, 482 Ozone depletion potential, ODP, 535, 537 P Packaged units, 39 Parallel flow circuits, 305, 314 Particle dispersoids, 96 Particulate air cleaners, types, 111 Particulate air filters, types, 111 Particulate characteristics, 96 Particulate matter, 94 Particulate removal, 109 Part-load factor, energy calculations, 286 Index.qxd 6/15/04 4:10 PM Page 621 Index Peak demand, People, effect on cooling load, 222 Performance contracting, Physiological considerations, 85 PI and PID control, 18 Pipe and tube data, 608 Pipe sizing, 319 Pipe, buried, heat transfer, 152 Piping design, 299 Piping systems, closed loops, 319 fundamentals, 317 open loops, 318 refrigerant, 556 Pitot tube, 306 Power, charges, Prandtl number, 462 Predicted mean vote index, 89 Predicted percent dissatisfied, 89 Pressure coefficient, infiltration, 162 Pressure loss in duct fittings, 426 Pressure loss, filters 115 Pressurization of rooms, 100 Pressurization, effect of infiltration, 162 Primary air, 36 Proportional control, 16 Proportional plus integral control, 17 Protocol, control systems, 13 Psychrometric charts, 55 Psychrometrics, 49 Psychrometrics, fundamental parameters, 51 PTAC units, 39 Pump control, 343 Pumps and piping, 28 Pumps, 299 affinity laws, 316 multiple arrangement, 317 net positive suction head, 312 R Radiant exchange, 129 Radiant temperature, 87 Radiant time series method, 216, 255, 266 Radiation configuration factor, 193 Radiation, solar, 181 Radiation, thermal, 129 Radon, 94 Recirculated air, definition, 99 Reflectance of various surfaces, 132 621 Reflectance, 182 Reflectivity, 182 Refrigerant designation, 536 Refrigerant piping, 556 Refrigerant properties, 536 Refrigerant safety group, 535 Refrigerant system control, 556 Refrigerants, 534 R-22, 590 R-134a, 586 R-718, 584 Refrigerating efficiency, 531 Refrigeration control devices, 550 Refrigeration equipment components, 540 Refrigeration, 529 absorption, 560 real cycles, 553 single-stage cycle, 531 Reheat systems, 31 Relative humidity, 51 Relative roughness, pipe flow, 301 Relief air, 99 Reset rate, 17 Resistance coefficients for fittings, 322 Return air systems, 453 Return grilles, performance, 384 Reverse action control, 16 Reversible cycle, 530 Reynolds number, 302 Rooftop units, 40 Room air motion, 368 Room characteristic length, 375 Room criterion (RC) curves, 374 Room pressurization, 100 Roughness, absolute, pipe materials, 301 RTSM, 216 S Schmidt number, 462 Seasonal energy efficiency ratio (SEER), 529 Sensible cooling, 60, 66 Sensible heat factor SHF, 60, 66 Sensible heat transfer, 7, 60, 66 Shading, external, widows, 199 Sherwood number, 463 SI (International) system of units, Sick building syndrome, 93 Index.qxd 6/15/04 4:10 PM Page 622 622 Index Simulations, building, 279, 289 Single-zone systems, 29 Skin wettedness, 87 Solar absorptances, table of values, 183 altitude angle, 188 angle of incidence, 189 angles, 187 attenuation coefficients, interior, 210 azimuth angle, 189 beam radiation, 191 constant, 190 data, 212 data, table, 187 declination, 188 diffuse radiation, 191 heat gain coefficients (SHGC), 198 heat gain, absorbed, 233 irradiation, 190 radiation, 181 surface solar azimuth, 189 time, 185 zenith angle, 189 Solubility of air in water, 330 Source elimination of contaminants, 98 Source media for space heating, 176 Space air conditioning, 65 off design, 75 Space air diffusion, 366 Space air distribution, 107 Space cooling load, 69 Space heating load, 158 Space pressurization, 100 Special allowance factor, lights, 224 Spectral distribution of sunlight, 191 Split systems, 41 Spray chambers, 464 Spray dehumidifier, 464, 470 Stack effect, infiltration, 163 Standard atmosphere, 49 Static head, 300 Static regain method, 450 Steady flow energy equation, 299 Steam heating systems, 343 Steam, air removal from systems, 347 condensate return by gravity, 355 condensate return, 344 pipe sizing table, 353 separator, 345 sizing system components, 349 system operation, 348 table of flow rate and velocity, 350–351 traps, 346 Suction head, 312 Supply air, cooling, 273 definition, 98 for space heating, 175 Surface solar azimuth angle, 189 Surface unit conductances, table, 131 System characteristic, fluid flow, 305 System effect factors, fans, 407 System selection and arrangement, 26 T TAB, 18 Task conditioning systems, 107 Temperature, adiabatic equivalent, 87 daily range, 220 dry bulb, 55 effective, 87 operative, 87 radiant, 87 wet bulb globe, 87 wet bulb, 54 Terminal device, 36 Testing, adjusting and balancing, 18 Thermal bridge, definition, 138 Thermal comfort tool, 92 Thermal conductance, 121 Thermal conduction, 119 Thermal convection, 121 Thermal energy storage, TES, 45 Thermal properties, building materials, 123 Thermal radiation, 129, 181 Thermal resistance, 120 Thermal resistance, radiation, 130 Thermal resistance, table for plane air spaces, 133 Thermal sensation scale, ASHRAE 89 Thermal energy storage, 45 Thermodynamic wet bulb temperature, 54 Throttling range, 15 Throw, air diffuser, 367 Time value of money, Tobacco smoke, 95 Total dynamic head, pumps, 311 Total emissive power, 182 Index.qxd 6/15/04 4:10 PM Page 623 Index Total irradiation, 181 Total pressure, 300 Transmission heat losses, 160 Transmittance, 182 Transport coefficients inside tubes, 492 Transport coefficients outside tubes, 496 Turning vanes, 437 U Under-floor ventilation, 374 Unit resistances for air, table, 131 Unit thermal conductance, 121 Unit thermal resistance, 120 Unit ventilators, 38 Unitary systems, 39 Units and dimensions, Use factor, lights, 223 V Valve characteristic, 333 Valve selection, 333 Variable speed drives, fans, 416 Variable-volume systems, 32 VAV fan powered terminal, 389 VAV systems, 32 Ventilation air, definition, 98 Ventilation efficiency, 112 Ventilation rate procedure, 102 Ventilation, displacement, 107 Ventilation, room systems, 374 Volatile organic compounds (VOCs), 94 Volumetric efficiency of compressors, 542 W Walls and floors below grade, 143 Walls and roofs, heat conduction, 138 Water hammer, 344 Water systems, 37 Weather data, 212, 597 Web accessible control systems, Wet bulb globe temperature, 87 Wet bulb temperature, 54 Wien’s displacement law, 182 Wind, effect on infiltration, 162 WINDOW 5.2 software, 199, 246 Windows, heat transfer coefficients, 143 Z Zenith angle, solar, 189 Zeotropes, 539 Zone air heat balance, 249 Zone, definition, 26 Z-transform methods, 228 623