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COOLING TOWERS Selection, Design and Practice

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I

I

COOLING TOWERS Selection, Design and Practice

by Nicholas P. Cheremisinoff Paul N. Cheremisinoff

Copyright © 1981 by Ann Arbor Science Publishers, Inc. P.O. Box 1425,230 Collingwood, Ann Arbor, Michigan 48106 Library of Congress Card Catalog Number 81-65711 ISBN 0-250-40407-9 Manufactured in the United States of America All Rights Reserved

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PREFACE As the least expensive and most efficient alternative, once-through cooling has historically been the preferred method for cooling hot process waters in industrial operations and power plants. However, since thermal pollution has become a major environmental problem, the unlimited use of water for cooling purposes has become one of the major social and political issues constraining plant siting in many parts of the country. As an example, a WOO-megawatt power plant utilizing once-through cooling requires 300,000 to 700,000 gallons per minute of water consumption. Plant sites have drastically diminished near water sources where such water usage is possible. Consequently, closed-cycle cooling methods thaFrattempt to make maximum use of limited water supplies have become the primary cooling option. Cooling tower technology progressed slowly until very recently. New developments aim at improving the thermal efficiencies and minimizing maintenance of existing designs to save large capital investments. When sound engineering principles are applied to upgrade existing designs or new installations, cooling towers can produce colder process water and save input energy, while at the same time can minimize pollution impacts. To meet these objectives, design and process engineers' must thoroughly understand the operating principles and the limitations of the best technology that is presently available. Equally important is some insight into how technology needs are likely to change in the near future. ' This book gives state-of-the-art evaporative cooling tower techniques. Design practices and applications of modern cooling tower technology are presented. A design basis can be established through the detailed calculation procedures outlined and with selected use of the nearly 400 references compiled at the end of the book. Detailed abstracts of more than half of these references have been prepared so that the reader can readily obtain the most useful information for his or her specific problems, Nicholas P. Cheremisinoff Paul N. Cheremisinoff iii

Nicholas P. Cheremisinoff is Senior Project Engineer with : Exxon Research & Engineering Co. in Florham Park, N.J. He received his BS, MS and PhD degrees in Chemical , Engineering from Clarkson College of Technology, where he was an instructor from 1976 to 1977. Dr. Cheremisinoff is the author of a number of books and has contributed to the industrial press. He is a member of a number of professional and honor societies including Tau Beta Pi, Sigma Xi and AIChE. His special research interests, include heat and mass transfer phenomena and new energy technology.

Paul N. Cheremisinoff is Associate Professor of Environmental Engineering at the New Jersey Institute of Technology. A consultant and registered professional engineer, he has more than 30 years of practical design, development and manufacturing engineering experience in a wide range of organizations, specifically in chemical processing. He is the author/editor of many Ann Arbor Science Publishers handbooks, including Pollution Engineering Practice Handbook, Carbon Adsorption Handbook and Environmental Impact Data Book.

iv

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CONTENTS 1.

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Historical Developments. . . . . . . . . . . . . . . . . . . . . . . . Operating Principles. . . . . . . . . . . . . . . . . . . . . . . . . . . Cooling Tower Terminology . . . . . . . . . . . . . . . . . . . . . Design Overview . . . . . . . . . . . . . . .' . . . . . . . . . . . . . .

. . . . . .

1 2 3 5 8

2.

Properties and Definitions for the Air-Water System. . . . . . . . Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vapor Pressure . . . . . . . . . . . . . . . . . . . . . .". . . . . . . Saturated Condition . . . . . . . . . . . . . . . . . . . '. . . . . . . Definitions in Thermodynamics . . . . . . . . . . . . . . . . . . Wet Bulb Temperature. . . . . . . . . . . . . . . . . . . . . . . . Humidity Charts . . . . . . . . . . '. . . . . . . . . . . . . . . . . . Notation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Problems . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . .

.. .. .. .. " .. " .. ..

13 13 13 16 18 26 29 31 33

3.

Heat and Mass Transfer Principles. . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . '. . . . . . . . . . . . . . . . . . The General Energy Balance Equation. . . . . . . . . . . . . . Principles of Energy and Material Balances. . . . . . . . . . . Principles of Direct-Contact Transfer. . . . . . . . . . . . . . . Heat and Mass Transfer Analogies . . . . . . . . . . . . . . . . . Mass Transfer Theory. . . . . . . . . . . . . . . . . . . . . . . . . Transfer Units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lewis Number Relationship. . . . . . . . . . . . . . . . . . . . . Notation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.. .. .. .. .. " .. .. .. .. ..

35 35 35 39 43 44 46 51 52 53 55

4.

Cooling Tower Classifications . . . . . . . . . . . . . . . . . . . . . . .. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Cooling Tower Subclassifications and Configurations. . . . ..

59 59 59

v

Fill Arrangements . . . . . . . . . . . . . . . . . . . . . Distribution Systems . . . . . . . . . . . . . . . . . . . Mechanical-Draft Cooling Towers. . . . . . . . . . . Factory-Assembled Towers. . . . . . . . . . . . . . . Fan Assisted Hyperbolic Towers. . . . . . . . . . . . New Tower Designs. . . . . . . . . . . . . . . . . . . . Dry Cooling Towers. . . . . . . . . . . . . . . . . . . . Wet/Dry Tower Systems . . . . . . . . . . . . . . . . :

. . . . . . . :

. . . . . . . .

.. .. .. .. .. .. .. ..

70 70 70 74 75 77 79 83

5.

Theory and Design Principles. . . . . . . . . . . . . . . . . . . . . . Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gas-Liquid Contacting. . . . . . . . . . . . . . . . . . . . . . . Application of Psychrometric Chart. . . . . . . . . . . . . . Application of the Energy Balance . . . . . . . . . . . . . . . Construction of Equilibrium Curves . . . . . . . . . . . . . . Guidelines for Tower Specification. . . . . . . . . . . . . . . General Design Considerations and Packing Coefficients. Correcting for Liquid Film Resistance. . . . . . . . . . . . . Integrating Procedures for Tower Sizing. . . . . . . . . . . . Notation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . .

.. .. .. .. .. .. .. .. .. .. .. ..

87 87 87 91 96 102 104 108 112 113 119 120

6.

Operation and Design Practices . . . . . . . . . . . . Introduction. . . . . . . . . . . . . . . . . . . . . . Tower Coefficients . . . . . . . . . . . . . . . . . Tower Characteristics and Performance. . . . Power Conditions . . . . . . . . . . . . . . . . . . Considerations in Cooling Tower Selection. . Empirical Approach to Tower Sizing. . . . . . Problems Related to Outside Installation. . . Winter Operation. . . . . . . . . . . . . . . . . . . Problems with Fog Formation. . . . . . . . . . Blowdown . . . . . . . . . . . . . . . . . . . . . . . Water Consumption and Recirculation Rates Gas Cooling Operations . . . . . . . . . . . . . . Fire Hazard and Safety Precautions with Cooling Towers. . . . . . . . . . . . . . . . . . Cooling Tower Plumes . . . . . . . . . . . . . . . Cooling Tower Specification Guide. . . . . . . Notation. . . . . . . . . . . . . . . . . . . . . . . . Problems. . . . . . . . . . . . . . . . . . . . . . . .

vi

.. .. .. .. .... .... .. .. ... . .... ....

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . . .

.. 125 .. 125 .. 125 .. 127 .. 130 .. 134 .. 136 .. 138 .. 141 .. 143 .. 146 .. 149 .. 150

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

.. 153 .. 154 .. 158 .. 159 .. 160

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7.

Mechanical Components of Cooling Towers . . . . . . . . . . . . . Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Circulating Pumps. . . . . . . . . . . . . . . . . . . . . . . . . . . Fans. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Speed Reducers . . . . . . . . . . . . . . . . . . '. . . . . . . . . . . Drive Shafts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Instrumentation, Valves and Flowsheets . . . . . . . . . . . . Example of Cooling Tower Requisition. . . . . . . . . . . . . Cooling Tower Testing. . . . . . . . . . . . . . . . . . . . . . . . Bids Evaluation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cooling Tower Economics. . . . . . . . . . . . . . . . . . . . . .

" 163 .. 163 .. 163 .. 165 .. 167 .. 167 .. 168 .. 169 .. 179 .. 179 .. 183

8.

Cooling Tower Water Treatment. . . . . . . . . . . . . . . . . . . . . Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Problems Inherent to Water Contaminants. . . . . . . . . . . Pretreatment of Cooling Water Systems. . . . . . . . . . . . . Corrosion Detection . . . . . . . . . . . . . . . . . . . . . . . . . . Methods of Evaluating Cooling Water Inhibitors. . . . . . . Langelier and Ryznar Equations: Saturation and Stability Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . Organic Growths . . . . . . . . . . . . . . . . . . . . ,", . . . . . . Legionnaires' Disease . . . . . . . . . . . . . . . . . .'. . . . . . . Water Analysis and Treatment. . . . . . . . . . . . . . . . . . . Plastic Cooling Towers ...... : . . . . . . . . . . . . . . . . .

.. .. .. .. " ..

185 185 186 188 190 191

.. .. .. .. ..

191 192 193 194 198

Guidelines for Winter Operation. . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Overall Ice Prevention System Design . . . . . . . . . . . . . . Mechanics of the Fill Bypass and Ice Prevention Ring Sections. . . . . . . . . . .'. . . . . . . . . . . . . . . . . . Supplemental Ice Control: Fill Zoning. . . . . . . . . . . . . . Guidelines for Integrated System Operation. . . . . . . . . . Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.. 207 " 207 .. 207

9.

Appendix A': Steam Tables . . . . . . . . . . . . . . . . . . . . . . . Appendix B: Conversion Factors . . . . . . . . . . . . . . . . . . . Appendix C: Solutions to Selected Chapter Problems ...... Appendix D: Source Listing and Abstracts of the Cooling Tower Literature . . . . . . . . . . . . . . . . . . . . . Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vii

.. .. .. ..

209 211 212 213

. . .

215 225 245

. . .

259 335 341

FIGURES

1.1 1.2 2.1 2.2 2.3 2.4 2.5 2.6 3.1 3.2 3.3

Cooling tower operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . Countercurrent and crossflow cooling towers . . . . . . . . . . . . . , Vapor pressure curve for water. . . . . . . . . . . . . . . . . . . . . . .. Heat capacity curves for air and water vapor. . . . . . . . . . . . . .. Graphic representation of enthalpy change. . . . . . . . . . . . . . .. The principle of wet-bulb temperature. . . . . . . . . . . . . . . . . .. Psychrometric chart for the air-water vapor system . . . . . . . . .. Humidity chart example. . . . . . . . . . . . . . . . . . . . . . . . . . .. Energy, balance for an open system . . . . . . . . . . . . . . . . . . . . , Energy balance for a closed system . . . . . . . . . . . . . . . . . . . " Process operations or equipment can be represented by a generalized flow process known as the black box technique. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3.4 Generalized flow process considered in Example 1. . . . . . . . . .. 3.5 The action of diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . , 3.6 The Arnold diffusion cell. . . . . . . . . . . . . . . . . . . . . . . . . .. 3.7 Water tank for problem 3.7 . . . . . . . . . . . . . . . . . . . . . . . . .. 3.8 Adiabatic gas-liquid contact system for problem 3.9. . . . . . . . .. 4.1 Subclassifications of cooling towers . . . . . . . . . . . . . . . . . . .. 4.2 Atmospheric spray tower. . . . . . . . . . . . . . . . . . . . . . . . . .. 4.3 Hyperbolic natural draft tower. . . . . . . . . . . . . . . . . . . . . . .. 4.4 Counterflow tower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.5 Crossflow tower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.6 Single-structure type wet/dry cooling tower. . . . . . . . . . . . . .. 4.7 Wet/dry cooling tower. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.8 Coil shed cooling tower . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.9 Cross section of a simple cooling tower formed by enclosing a spraypond with louvered walls . . . . . . . . . . . . . . . . . . . , 4.10 Various geometries employed in constructing redwood fill for cooling towers. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.11 Power plant installation where multiple tower arrangement is

viii

4 10 14 22 23 27 30 31 36 37

39 41 47 55 56 57 60 61 61 62 63 64 64 65 66 67

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4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.20 4.21 4.22 4.23 4.24 5.1 5.2 5.3 5.4 5.5

5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14 5.15 5.16 6.1

utilized (towers are operated in parallel). Cooling towers are placed in a row at right angles to the prevailing winds Differences between crossflow and counterflow hyperbolic cooling towers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Operating principles behind splash-packing and. film-packing ... . Gravity and splash-type water distribution systems employed in cooling towers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Large mechanical-draft cooling towers . . . . . . . . . . . . . . . . . . . Design elements of mechanical-draft cooling towers . . . . . . . . . . Factory-assembled units are shipped in modular package form and erected in the field. . . . . . . . . . . . . . . . . . . . . . . . . . Forced draft tower curves and manufacturer's design procedure .. Fan-assisted hyperbolic tower . . . . . . . . . . . . . . . . . . . . . . . . Cooling tower design developed by Baltimore Aircoil Co. The system is designed to operate without fill packing ....... . Direct, dry-type cooling tower condensing system utilizing a mechanical-draft tower . . . . . . . . . . . . . . . . . . . . . . . . . . Indirect, dry-type cooling tower condensing system employing a natural-draft tower . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic of advanced dry cooling system proposed by McHale et al. . . . . . . . . . . . . . . . . . . . . . . ":1 • • • • • . • • Design features of the wet! dry cooling tower ..... ' . . . . . . . . . Free and interrupted flow through a column . . . . . . . . . . . . . . . Tower packing configurations . . . . . . . . . . . . . . . . . . . . . . . . Cross-sectional view of commonly used cooling tower fill arrangements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example of adiabatic humidification . . . . . . . . . . . . . . . . . . . . Cooling tower operation for Example 2 . . . . . . . . . . . . . . . . . . Countercurrent cooling tower operation . . . . . . . . . . . . . . . . . General operating diagram for a cooling tower . . . . . . . . . . . . . Daily and annual variations in ambient air wet-bulb temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of flow variance on cooling tower size factor . . . . . . . . . . Effect of range variance on tower size factor. . . . . . . . . . . . . . . Variation in tower size factor with approach . . . . . . . . . . . . . . . Important design parameters for the countercurrent cooling tower operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cooling tower operation for Example 3 . . . . . . . . . . . . . . . . . . Equilibrium curve and operating line for Example 3 . . . . . . . . . . Evaluation ofNTU' for Example 3 . . . . . . . . . . . . . . . . . . . . . Cooling tower operation for problem 5.5 . . . . . . . . . . . . . . . . . Countercurrent cooling diagram for constant conditions, variable L:G ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

68 69 71 72

73 74 75 76 77

79 80 81 83 84 89 90 90 92 94 97 102 106 108 108 109 110

115 116 118

122 126

6.2 6.3 6.4 6.5 6.6 6.7

6.8 6.9 6.10 6.11 6.12 6.13 6.14 6.15 6.16 6.17

7.1 7.2 7.3 7.4 7.5 8.1 9.1 9.2

9.3 9.4

Crossflow tower cooling diagram. . . . . . . . . . . . . . . . . . . . .. Generalized tower characteristic curves. . . . . . . . . . . . . . . . .. Countercurrent cooling tower rating chart for 15° range . . . . . .. The effects of varying process conditions on a cooling tower's enthalpy temperature diagram. . . . . . . . . . . . . . .. The effect of variations in performance requirement on tower ground area for a fixed tower design with constant G . . . . .. Catwalks are an essential part of the cooling tower package. Shown here is a small cooling tower with a walkway around the entire unit for inspection and maintenance purposes. . .. Interface and recirculation problems. . . . . . . . . . . . . . . . . . .. Proper tower orientation can avoid interference from multiple tower arrangements .. '. . . . . . . . . . . . . . . . . . . . . . . . .. Heat balance about a cooling tower. . . . . . . . . . . . . . . . . . . .. Equation 6.8 correlated mechanical-draft performance data .... , Portion of psychrometric chart illustrating fog formation. . . . .. Fog formation assisted by wake formation and hourly variations in ambient air humidity . . . . . . . . . . . . . . . . .. Chart for estimating cooling tower makeup requirements. . . . .. Chart for estimating cooling tower blowdown. . . . . . . . . . . . .. Lewis number correlation for the air-water system. . . . . . . . . .. Typical pl~t comparing relative ground concentration in the cooling tower stack direction. Ground-level concentrations are normally averaged over the year . . . . . . . . . . . . . . . .. Recommended minimum submergence depths versus velocity. .. Various methods to prevent vortex formation. . . . . . . . . . . . .. Centrifugal fan configurations. . . . . . . . . . . . . . . . . . . . . . .. Typical flowsheet for a cooling tower system . . . . . . . . . . . . .. Typical cooling tower performance curves for different water loadings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Modular constructed plastic cooling towers . . . . . . . . . . . . . .. Illustrates the danger of freezing for normal cooling tower operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Diagram showing the proper flow allocations during low heat load operation, with water flow diverted from the fill section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . " Typical fill water ,distribution pattern in the zoned mode of operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Operating regions for the winter operating modes for ice prevention. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

x

127 129 130 133 136

139 139 140 141 142 144 145 148 149 151

157 164 164 167 170 180 199 208

210 212 213

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TABLES 2.1 2.2 4.1 4.2 5.1 5.2 5.3 5.4 5.5 6.1 6.2 6.3 7.1 7.2 8.1 8.2 8.3 8.4

Constants for Heat Capacity Equation 2.28 for Air and Water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Enthalpy Values for Air and Water. . . . . . . . . . . . . . . . . .. Comparison Between Characteristics of Mechanical- and Natural-Draft Cooling Towers . . . . . . . . . . . . . . . . . . . . , Design Considerations and Characteristics of Dry Cooling. . .. Heat Absorbed by Cooling Water for Various Operations. . .. Humidification Characteristics of Packing Materials. . . . . . .. Guide to Packing Height Specification. . . . . . . . . . . . . . . .. Air-Water Mixtures-Enthalpies and Humidities. . . . . . . . . .. Computations for Construction of Figure 5.15 . :\ . . . . . . .. Maximum Temperatures and Maximum Wind Velocities for Different Cities in the United States. . . . . . . . . . . . . . . .. Fill Packing Factors at 120°F .. ',' . . . . . . . . . . . . . . . . . .. Specification List for Cooling Towers. . . . . . . . . . . . . . . .. Economic Considerations of Wet Cooling Systems. . . . . . . .. Procedure for Estimating Potential Water Cost and Sewer Taxes Savings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , Pretreatment Procedures. . . . . . . . . . . . . . . . . . . . . . . . .. Chemical Treating Agents for Cooling Water Towers ..... " High-Impact Polyethylene Properties. . . . . . . . . . . . . . . . .. Plastics Chemicals Resistance Chart. . . . . . . . . . . . . . . . . ..

xi

23 24 78 82 105 112 112 115 117 131 137 158 181 182 190 197 200 201

CHAPTER 1 OVERVIEW INTRODUCTION

In the light of the ecological renaissance of the last two decades, thermal pollution is now receiving serious attention. It is environmentally unacceptable to directly discharge hot water back to its source after it has been used to cool chemical process equipment, electrical generating turbines or refrigeration and air conditioning equipment. Hot process waters must either be cooled before discharge, or cooled and recyoled. Purchasing and then discarding large quantities of water into sewage systems is cost prohibitive in many parts of the country, and even if favorable economics were to exist, environmental concerns would forbid such practices. In the past, abundant resources made' it possible to use cold water on a once-through basis. Where topographical considerations were accounted for, large ponds, lakes or canals were used to contain, cool and recirculate or discharge process waters. To facilitate cooling and reduce land requirements, spray systems were often employed to aerate the water in the ponds. In today's economic framework, however, energy conservation matches the importance of our ecology. Consequently, utilizing cooling water efficiently is a vital engineering consideration. As examples, by using colder water, a chemical plant can condense more salable condensate, refrigeration/ air conditioning machinery will consume less power, and power plants can significantly reduce energy generation debits. Cooling tower technology has progressed slowly until recently. A large portion of the recent advances is aimed at improving existing cooling towers to save large capital investments. When sound modern engineering principles are applied to upgrading existing designs or to "grass-roots" installations, cooling towers can produce colder water and save input energy, while at the same time eliminating potential pollution problems. To meet these objectives, both design and process engineers must have a thorough understanding of the principles of operation and the limitations

2

COOLING TOWERS

of the best available technology that presently exists. Equally important is some insight into how technology needs are likely to change in the near future. This book is intended as a state-of-the-art review of the design and application of modern-day cooling tower technology.

HISTORICAL DEVELOPMENTS The technique of evaporative cooling can be traced back to ancient times when rivers, seas, lakes, ponds, etc., were utilized as a medium of water supply. With limited industrial activities of the past ages and plentiful resources, cold water could be used "once-through," discharged and forgotten. Where topographical corisiderations were taken into account in plant site selection, large ponds or canals were employed to hold, cool, recirculate or discharge process waters. This type of an approach required large land areas. To reduce the amount of real estate needed, spray systems were installed to aerate the water in holding ponds and to promote faster cooling by generating more water' surface to the atmosphere in the form of spray. This early development eliminated the need to rely on top layer evaporation and sensible heat exchange. The next logic~ development of cooling tower technology came when it was discovered that by spraying downwards in a box, instead of upwards, lower temperatures could be achieved. Shortly after this observation was made, instead of relying on prevailing winds for air movement in spray ponds and atmospheric spray towers, aerodynamically designed fans or air movers were incorporated into designs. As the mechanics and hydrodynamics of water cooling became better understood, fill or packing material was included in designs to slow the vertical fall of water and to provide greater air/water interfacial contact for more difficult cooling. Today, everyone of these techniques is utilized in some form or another. Cooling tower technology appears to have made an entire circle, as emphasis is once again directed toward atmospheric cooling. However, there are significant differences in these modern designs compared to early prototypes. Hyperbolic cooling towers are being constructed without the use of fans or air movers. These structures measure about 980-1700 meters in diameter at the base a~d 980-1700 meters in height. With structures of this magnitude, detailed and reliable engineering design practices are essential. Presently, the United States accounts for 50% of the world cooling tower market. About 25% of the U.S. market is with the petrochemical industry, 15% involved in personal comfort and 60% with electric power generation [1]. More than twice as many of these towers are mechanical draft, as opposed to natural draft, units. The former type are employed nationwide,

---~~--

~-

--~--

OVERVIEW

3

while the latter are concentrated in the Appalachian area because of favorable climatic conditions. This balance, however, is likely to change in the light of developing technology.

OPERATING PRINCIPLES Cooling tower operation is based on evaporative condensation and exchange of sensible heat. The mixing of two fluid streams at different temperatures (in this case air and water) releases latent heat of vaporization, causing a cooling effect to the warmer fluid (water). This cooling effect is accomplished by transforming a portion of the liqUid into a vapor state, thereby releasing the latent heat of vaporization. This effect can be simply demonstrated by wetting the back of your hand and blowing on it. The airstream releases the latent heat of vaporization, causing the temperature of the water on the skin to drop. As the water is transformed to the vapor state, it consumes heat, which it derives from the remaining water on the skin. The net effect is one of cooling. In a cooling tower's operation, sensible heat also plays a role. When warm water contacts cooler air, the air cools the water and its temperature rises as it gains the sensible heat of the water. Roughly 25% ,gf the sensible heat transfer takes place within the tower, with the bala~ce of the cooling phenomenon achieved from the evaporative effect of the latent heat of vaporization. In simple terms, a cooling tower is a device that transfers quantities of heat from one mass to another. As we will see in later chapters, a cooling tower is simply an air-mass heat exchanger. A more technical description of a cooling tower is that it represents a heat rejection solution to the chemical process, or correction of the heat penalty generation of compression equipment [2]. Regardless which definition is preferred, cooling towers simply move heat from point A to point B and ultimately discharge the heat to the atmosphere. The atmosphere thus represents the ultimate disposal site for waste thermal energy and is appropriately referred to as a "heat sink." During operation there is a loss of water. Water vapor passes through the cooling tower and is discharged into the atmosphere. For normal operation, water losses amount to approximately 0.2% of the total volume of water circulated for every 10° of cooling range, 1% for each 12° temperature differential in the area of 1000 Btu/lb of water evaporated. As an example, a 1O,000-gpm unit with a 20° temperature range (Le., water entering at 100°F) and exiting at 80°F) will lose an average of 167 gpm of water because of evaporation. Evaporation losses are due to a number of factors, principal ones being blowdown, splashing and drift. These will be discussed in detail later. When the temperature of the heated air is below 140°F, cooling towers

~~~-

4

COOLING TOWERS

generally represent the most economical atmospheric heat rejection system. Temperature differential is related to the ambient wet-bulb temperature. It is a function of natural conditions and is independent of tower design. In normal operations, continuously recirculating water picks up waste heat from a refrigeration compressor or process heat exchanger, and the hot water is pumped to the top of the tower and dropped over the cooling tower. Evaporative action removes the heat from the water and adds it to the air. The hot, moist air is ejected from the fan stack, and the cooled 'water returns to the compressor or exchanger to pick up more heat. Figure 1.1 illustrates the cooling tower operation. As noted, two principles of heat transfer are involved: evaporation and convection. The rate of heat transfer by both convection and evaporation increases with an increase in air-to-water interfacial surface, relative velocity, contact time and temperature differential. Packing and fill in a tower serve to increase the interfacial surface area; the tower chimney or fans create the relative air-to-water velocity; and contact time is a function of tower size. These three factors all may be influenced by the tower design. The ability of a tower to function is measured by how close it brings the cold water temperature to the wet-bulb temperature of the surrounding

FROM ENTERING TOWER AT TEMPERATURE TI

TO LEAVING TOWER AT T2

EXAMPLE:

AT A SPECIFIED WET-BULB

TEMPERATURE RANGE:::

(Twb )

OF 78°F -

~T ::: TI - T

2 ::: 20°F

APPROACH ::: T2 - Twb ::: 7 OF Figure 1.1

Cooling tower operation.

OVERVIEW

5

air. The lower the wet-bulb temperature (which indicates either cool air, low humidity or a combination), the colder the tower can make the water. The water temperature will never go below the temperature of the incoming air. In practice, the final water temperature will be several degrees above the wet-bulb temperature.

COOLING TOWER TERMINOLOGY There are a number of terms with rather rigorous definitions within the context of cooling tower technology. It is' worthwhile for the newcomer to this subject to learn these definitions early on in the discussions. In subsequent chapters we will apply the following definitions to establishing specific design guidelines. Acceptance Testing-Test procedures to determine the water cooling capacity of towers. Instrumentation used and measurement procedures should be those recommended by the Cooling Tower Institute (CT!) in its "Acceptant Text Procedures." Air Inlet-That portion of the cooling tower structure in which air is drawn into the system. Ambient Dry-Bulb Temperature-External outdoor te'l11perature as indicated by a dry-bulb thermometer and expressed in degrees ,Fahrenheit. Ambient Wet-Bulb Temperature- The temperature in degrees Fahrenheit to which air can be cooled, making it adiabatic to saturation by the addition of water vapor. In practical terms, the wet-bulb temperature is the temperature indicated by a thermometer, the bulb of which is kept moist by a wick and over which air is circulated. Approach or Approach to the Wet-Bulb-The difference in temperature CF) of the cold water leaving the tower and the wet-bulb temperature of the ambient air. Balancing Valve-Hand or mechanically operated valve installed in each riser pipe of a multicell tower to control water flow. Basin-The area at the bottom of the tower for collecting cold water. Crossflow towers have a hot water distribution basin at the top and, in some cases, 'a water basin between the top and bottom basins. Blowdown (Purge)-The continuous or intermittent wasting of small amounts of circulating water. Its purpose is to prevent an increase in the concentration of solids in the water due to evaporation, normally expressed as a percentage of the water being circulated. Capacity-The average amount of water circulating in the cooling system at any given time, expressed in gallons per minute. Casing-The vertical enclosing side- or endwall of a tower, exclusive of the air inlet louvers.

6

COOLING TOWERS

Cell-A unit consisting of a distribution system, mechanical equipment and partition walls. A single tower can have several independent cells. Individual cells can be shut down, or several cells can be run on partial capacity. Cellular Film-Asbestos fill packing that converts water droplets into a thin molecular filter for more efficient cooling. Less static pressure is encountered than with splash-bar fill, thus permitting the use of higher air velocities. Concentration Cycles-Comparison of dissolved solids in makeup water witli solids concentration in the circulating water. Cooling Factor-The ratio of the pounds of water circulated per unit of time to the pounds of dry air cooling the water per unit of time. Cooling Tower Institute-International organization of cooling tower engineers, manufacturers and users, dedicated to improving the professional and technical state of the art. Counterflow-A system in which air encounters the hot water at a 180 angle. Air enters near the base of the tower and moves upwards through the fill and falling water. Crossflow- A system in which air encounters the hot water at a 90 angle. Air enters through the entire sidewall and moves horizontally through the fill and falling water. Delta Temp~rature (Range)-Difference between entering and leaving water temperatures. Design Conditions-Thermal parameters for which the cooling tower is purchased. They consist of a given gpm flow of water entering the tower at a specific temperature, cooling through a given range, leaving the tower at the required temperature, and having a designated approach to a stated wet-bulb temperature. Diffusion (Redistribution) Deck-A device below the hot water distribution basin of a crossflow tower to break up the water going through the orifices before it goes through the fill. Distribution System-Mechanical method of passing hot water over the fill uniformly. Low-pressure spray-through piping and nozzles are usually used in counterflow towers; gravity drop is normally utilized in crossflow towers. Drift-Entrained water droplets that escape from the tower with the exhaust air, expressed as a percentage of water circulated. Drift Eliminator-Baffling that causes discharging hot air containing entraining water droplets to change direction a number of times. Droplets hit the eliminator surface and fall back into the tower. Enthalpy -Total heat content; the sum of the sensible heat of the air and water vapor and of the latent heat of vaporization. 0

0

OVERVIEW

7

Fill Packing-Specially designed baffling used to provide a large surface area for heat transfer. Two classes of materials are used: splash bars of wood, metal transite or plastic and film pack (cellular fill). The splash type cools the water as the droplets bounce down a series of bars in the air stream; film packing converts droplets into a thin film .. Fog-A mist formed where the ambient air cannot absorb all the plume's moisture. The intensity of the fog is a function of the heat rise of air passing through the tower and the temperature and humidity of the ambient air. Fog plumes are normally permissible since there are no droplets of water raining out of the discharge area; however, fog may cause icing of nearby roads and may restrict visibility. Forced Draft-Air introduced at the bottom of the tower is forced to the top by a centrifugal blower. Heat Load-Amount of heat (in Btu) dissipated in a cooling tower. It is equal to the weight of water circulated per unit of time multiplied by the cooling range. Induced Draft-Air mover, usually an aerial fan, on top of the tower pulls air up through the fill and out the stack. Latent Heat of Vaporization-The heat required to change a liquid into a vapor without a change in the temperature or pressure. Louvers-Baffles used for changing the direction of air flow into the tower in a uniform, parallel manner, and for preventing water droplets from splashing out of the tower as they fall through the structure. Makeup -This term refers to the water required to replace the circulating water that is lost by evaporation, drift, bl~wdown and leakage. It is expressed as a percentage of the water circulated and normally is automatically controlled by a float valve. Net Effective Volume-A portion of the total structural volume in which the circulating water is in intimate contact with the air flowing through the tower (expressed in cubic feet). Performance-The measure of the tower's ability to cool water. It is usually expressed in terms of cooling a quantity of water (gpm) from a specified hot water temperature to a specified cold water temperature at a stated wet-bulb temperature. Performance Curve-A graphic representation of the relationship of water temperature, approach, wet-bulb temperature, range, static pressure and air movement. Plenum-An enclosed chamber in which pressure is higher than atmospheric pressure. Plume-Visible manifestation of water vapor condensing as warm, moist air mixing with the cooler, outside air. Psychrometer-Instrument used to measure the wet-bulb temperature.

8

COOLING TOWERS

Pumping Head-The energy required to raise water to the distribution elevation and overcome friction losses through pipe, valves, fittings and nozzles. It is expressed in feet of liquid the pump must move and is equal to the total friction loss, static head and pressure drop through the distribution system. Range-The numerical difference between the temperature of the hot water entering the cooling tower at the distribution system and the ' temperature of the colder water leaving the sump basin. Recirculation (Recycle)-Hot exhaust air forced downward and back into the cooling tower raises the wet-bulb temperature of the entering air above dry-bulb temperature, impairing tower performance. It is usually caused by design, wind or placement problems. Sensible Heat-The heat requIred to change the temperature of air or water. Static Pressure Drop-The reduction of air movement through the tower resulting from resistance of internal components such as air-intake louvers, fill packing, water distribution system, internal supporting beams, drift eliminators and fan stack configuration. Sump-Depressed section of the cold water collecting basin, from which cooled water retlfrns to the heat source. TDS-Total di~solved solids contained in solution in the cooling water system. Water Load-Circulating rate of water over the tower, expressed in gallons per minute. Wet-Bulb Temperature-The temperature of saturated air. The lower the wet-bulb temperature, the more exchange of heat a cooling tower can do. A tower cannot cool the water to a temperature below the wet-bulb temperature of the entering air. Windage-The loss of water through the air-intake louvers as a result of malfunctioning of the wind check walls in the lower section of the tower.

DESIGN OVERVIEW One of the earliest cooling tower configurations was developed so that the water would pass through the distribution of piping or troughs and fall vertically through the Jill packing area. In this design, air was drawn to the bottom of the tower and then moved vertically upward through the fill packing. During the fluid-fluid mixing, both air and water flowed counter to each other, thus the term counterflow tower. To meet other requirements, such as increased water throughput, lower architectural profile demands and greater utilization of electrical energy, as well as to improve cooling efficiency, crossflow designs were developed.

....

OVERVIEW

9

In the crossflow design, hot water is brought to the top of the tower and pumped into basins or pans where it falls through specially designed orifices on top of the fill area. In crossflow designs, air travels horizontally through the fill region of the tower and at a 90° angle (Le., across the vertical falling water). Figure 1.2 illustrates both the counterflow,· or countercurrent, tower and the crossflow tower. Air movers on many industrial installations usually consist of propeller-type air foils. These induce air through the tower and discharge the hot moist air through cylinders that surround the propellers. Such systems generally consists of electric motors connected by flexible-shaft couplings and gearreducing trains to provide the driving force. Fan blade technology has advanced such that more efficient systems are now available in lightweight materials such as plastics. Due to this weight reduction as well as to the high strength associated with plastics and reinforced plastics, fan usage has been extended to larger diameter towers [3]. In the smaller cooling tower installations employed for refrigeration and air conditioning service, induced-draft propeller-type air movers are used. A favored design utilizes the rotary centrifugal squirrel cage blower, which is normally driven by electric motors connected to the rotors by V-belts. Because of lower fan efficiency, these often use more,,> electric power to achieve the same results as propeller fans. To ensure high performance, it is important that the water distribution system provide a uniform flow pattern through the fill material. Water flow maldistributions are very common, especially with units that have been operated for a number of years. This is caused by tower and fill deterioration, and nozzles undergoing fouling or clogging. When a nozzle becomes clogged, it naturally leaves a dry spot in the fill. Air, as any moving flUid, will follow the path of least resistance and thus channel through this dry spot. Consequently, a large amount of energy and 'cooling potential can be lost due to water maldistribution. Newer nonclogging, noncorroding ceramic nozzles have been introduced to the market. These generally help reduce maintenance requirements and are now replacing steel nozzles on existing installations. Drift was' defined earlier as entrained water droplets in the air stream, which pass through the tower and discharge along with the hot air through the plenum or fan stack. A drift eliminator, which is merely a specially designed baffling system, can be installed between the water distribution system and the air discharge to minimize entrainment. Older designs for drift eliminators consisted of zigzag slats, which abruptly change the air flow direction prior to discharge. This causes droplets to impinge on the baffles and fall back into the tower. This type of design is energy intensive as it requires significant energy to transport the air through the baffling.

-

(A)

0

("')

0 0

2 C') ~

0

~ t!'l

( F)

(F)

, ' ... AIR /

......

/

(F)

"'-1(- . - - - - - - - - - - - , iiE~=~ A. MECHANICAL EQUIPMENT B. WATER DISTRIBUTION C. FILL PACKING D. DRIFT ELIMINATORS E. COLD WATER BASIN F. AIR INLET LOUVRES G. REDISTRIBUTION AREA

COUNTERFLOW

Figure 1.2

.......~-

CROSSFLOW

Countercurrent and crossflow cooling towers.

~

F

OVERVIEW

11

Cellular eliminators (discussed later) can cause the air to change less abruptly and make multiple direction changes as well. This is a more efficient method of minimizing entrainment than the conventional wooden slat system. Cooling towers themselves can be sources of pollution since they do not destroy heat but merely move it from one plaoe to another, ultimately discharging it to the atmosphere. There are engineering principles that can assist in the selection of the method and area of discharge. We will examine these principles in more detail in the chapters to follow.

REFERENCES 1. Kolfat, T.D. "Cooling Tower Practices," Power Eng. (January 1975). 2. Burger, R. "Cooling Tower Technology," Poll. Eng. (May 1980). 3. Cheremisinoff, N. P., and P. N. Cheremisinoff, Fiberglass-Reinforced Plastics Deskbook (Ann Arbor, MI: Ann Arbor Science Publishers, Inc., 1978).

SUGGESTED READING 1. Burger, R. "Know Your Cooling Tower," Power (March 1979). 2. Burger, R. "Cooling Tower Retrofit," Chern. Eng. Prog:"(March 1979). 3. Dickey, 1. B. "Managing Waste Heat With the Water Cobling Tower," Combustion (May 1979). 4. Holzhauer, R. "Industrial Cooling Towers," Plant Eng. (July 1975). 5. Knuesch, T. "Keep Your Cool When Selecting the Right Tower," Process Eng. (September 1978). 6. Knuesch, T. "Environmental Aspects of Cooling Tower Selection," Process Eng. (November 1978). 7. Maze, R. W. "Air Cooler or Water Tower-Which for Heat Disposal," Chern. Eng. (January 1975). 8. McGraw, M. G. "Before-the-Fact Modeling Solves Tower Problem," Electrical World (October 1979).

CHAPTER 2 PROPERTIES AND DEFINITIONS FOR THE AIR-WATER SYSTEM

INTRODUCTION

In this chapter we will review some of the principles of thermochemistry, with particular attention to the air-water vapor system. Basic definitions in thermodynamics are reviewed along with important physical properties and definitions for gaseous mixtures. It is important that these definitions be learned early on. Note, however, that this chapter is only meant as a review. The references listed at the end of this chapter should be consulted for a detailed treatment of these subjects. Further, example problems are included at the end of the chapter to stress principles discussed.

VAPOR PRESSURE A gas existing below its critical temperature is generally referred to as a vapor because it can condense. If a pure gas is maintained at a constant temperature below its critical temperature and the pressure is increased, eventually the gas begins to condense into a liquid. This procedure can be reversed by decreasing the applied pressure and the liquid will be transformed back to its gaseous state. In our discussions, the term vapor will be used to refer to a gas below its critical point in a process where the phase change is of interest. The terms gas and noncondensable gas will refer to a gas above the critical point or to a gas that cannot condense. If both temperature and pressure are kept constant, then vaporization and condensation are equilibrium processes. The equilibrium pressure is referred to as the vapor pressure. There is only one pressure at which the liqUid and vapor phases of a pure substance can exist in equilibrium at a given temperature. Naturally, either phase may exist over a wide range of conditions.

13

14

COOLING TOWERS

A pressure-temperature diagram best illustrates the processes of vaporization and condensation. Figure 2.1 is such a diagram for pure water. From this plot, a corresponding pressure can be obtained at which water vapor and water liquid exist in equilibrium. Boiling water is a good example of an equilibrium condition. Any substance has an infinite number of boiling points. The "normal" boiling point, however, refers to the temperature at which boiling occurs at a pressure of 1 atm (760 mm). For water, the normal boiling point occurs when the vapor pressure of the water equals the pressure of the surrounding atmosphere. To illustrate the' vaporization process, let us assume that we begin heating a pan of water from an initial temperature of 150°F (Point A on Figure 2.1). If the pan is open to the atmosphere, then the water vapor above the liquid surface is at all times in eqUilibrium with the liquid. As the temperature rises (and the atmospheric pressure remains constant), nothing really occurs until the water reaches 212°F, at which temperature the water begins to boil or evaporate. Evaporating water molecules push back the atmosphere and completely change from liqUid into vapor (Point B on Figure 2.1). If we now cover the pan with a lid and continue heating the water vapor from point B

, D

go

-

A

:x::

760

0

::l

E E

0

11.1

500 11.1 (f) (f)

0

11.1

a.. a..

B

C

I

ICE (SOLID)

E TYPICAL CONSTANT VOLUME LINE (CHARLES' LAW)

LIQUID (SUBCOOLED)

F

..J

0::

---'I

z

15

0:: ::l

0:: 0

.J

I

dS

VAPOR (SUPERHEATED)

0

180

oct

>

5

150 SOLID a VAPOR IN EQUILIBRIUM Figure 2.1

190 212 TEMPERATURE

Vapor pressure curve for water.

(0 F)

L

PROPERTIES FOR THE AIR-WATER SYSTEM

15

(which is formed at constant pressure), then the gas laws become applicable in the region B-C and higher temperatures. To reverse this process, we would cool the liquid to point B where vapor condenses to form a liqUid. The temperature at point B represents the dew point for the case described. The process of vaporization/condensation at constant temperature can be explained by the points D, E and F on Figure 2.1. Water either would condense or vaporize at constant temperature as the pressure approaches point E on the vapor-pressure curve. Line G-H shows that when the solid form (ice) passes directly into the vapor phase without first becoming a liquid, then sublimation is said to occur. Water sublimes below 32°F. As an example, everyone has seen frost disappear in the winter, even though the thermometer might have read 25°F. The pressure-temperature plot of Figure 2.1 extends all the way to the critical temperature and pressure, which has not been shown. Above the critical temperature, water strictly exists as a gas. The term saturated is used to describe the vapor-liquid portion of the curve. Basically, it implies the same thing as saying that vapor and liqUid are in equilibrium with each other. The gas is said to be saturated if it is ready to condense the first drop of liqUid. Conversely, the liquid is saturated if it is just about to vaporize. For the gas, this condition is called the dew point; for the liquid, it is the bubble point. The term "wet gas" refers to a mixture of liquid and vapor at equilibrium (Le., both liqUid and vapor are saturated). The region to the right of the vapor-pressure curve in Figure 2.1 is the superheated region. The region to the left of the curve is the subcooled regfon. The temperatures in the superheated region, when measured as the difference (line K-L) between the actual temperature of the superheated vapor and the saturation temperature for the same pressure, are referred to as the degrees of superheat. Another term we will use in later discussions is "quality." Quality refers to the weight fraction of vapor. As we have already observed, the vapor-pressure-temperature curve is nonlinear. To reduce this curve to a linear form, a plot of log (p*) versus (l/T) can be made for moderate temperature intervals. The resultant straight line is described by the following expression, which can be derived from the Clausius-Clapeyron equation. log (p*) = m

1 T

+C

(2.1)

Equation 2.1 describes the change of a substance's vapor pressure with temperature. The intercept C depends on the specific substance. An equation for the change of vapor pressure with total pressure at constant temperature is as follows:

16

COOLING TOWERS

(2.2)

where V is the molal volume of saturated liquid or gas, and Pt is the total pressure. Under normal conditions this effect can be neglected.

SATURA TED CONDITION The molecules of water vapor are free to migrate randomly in all directions. If in a closed vessel, the molecules will eventually distribute themselves throughout the entire volume of the container. When any gas contacts a liquid, the gas acquires vapor from the liquid. If sufficient contact time is allowed, equilibrium will result. At equilibrium, the partial pressure of the vapor equals the vapor pressure of the liqUid at the temperature of the system. At equilibrium, the gas is said to be saturated with the vapor at the given temperature (Le., the gas is at its dew point). Both air and water vapor can be described by the ideal gas laws. We can use this fact to col1tpute the partial pressure of air at saturation conditions. From the perfect gas l~ws at constant temperature: (2.3)

and (2.4 )

when 7) is moles. This can be rearranged to give Pair Pair PH,O - Pt - Pair

Yair Vt - Yair

where P t is total pressure. Equation 2.5 can be generalized for any two components:

Subscripts indicate component 1 and 2.

(2.5)

f"'

PROPERTIES FOR THE AIR-WATER SYSTEM

17

The most useful form of Equation 2.6 is:

(2.7)

If equilibrium has not been reached between a mixture of components, the condition is referred to as partial saturation. At partial saturation the gas mixture obeys real gas laws. There are several ways to express the concentration of a vapor in a mixture of gases. Most often, weight or mole fraction is used. Other definitions are relative saturation (relative humidity), molal saturation (molal humidity) and absolute saturation (absolute humidity). Relative humidity is defined by the following relation: Pvapor --=oR s Psatd

where

(2.8)

Rs relative saturation Pvapor partial pressure of the vapor in the gas mix ture Psatd = partial pressure of the vapor in the gas mixture if the gas were saturated at the given temperature of the mixture =0 =0

For the air-water system, %RH = PH,o/PH,o (100)_ A;,\OO% relative humidity, the partial pressure of the vapor is the same as the vapor pressure of the condensed vapor, Another way to express vapor concentration is by molal saturation, which is the ratio of the moles of vapor to the moles of vapor-free gas. (2.9)

where

Ms 7)v 7)'

=0 =0 =0

molal saturation moles of vapor the moles of vapor-free or dry gas

For a two-component system, , (2.10) (2.1l)

and 7),

P,

VI

7)1

P,

v,

-:::::-:;::-:::::--=--=0---

(2.12)

18

COOLING TOWERS

Multiplying by the ratio of the molecular weights, the weight of vapor per weight of dry gas can be computed: 7Jy

(MWy) = Wy

7J

(MW')

,

(2.13 )

W'

Subscript V refers to vapor and superscript prime (') refers to the dry gas. MW is molecular weight. Absolute saturation is defined as the ratio of the moles of vapor per mole of dry gas to the moles of vapor that would be present per mole of dry gas if the mixture were completely saturated at the existing temperature and total pressure. We can express this as

(2.14)

Note that PI saturated is really pi and that Pt ship becomes ' , \'.

PI . Pt- P, % SaturatIOn = (100)--*PI Pt -

=PI + P 2. Then the relation-

PI(pt-p;) =* -P _p 100 PI t I

(2.15)

pi

From Equation 2.8 we can write the following:

% Saturation

=

Pt- P

*)

RH ( Pt _ P:

100

(2.16)

The percent saturation is never greater than the relative saturation except at saturated conditions or at zero percent saturation (where % saturation =

%RH).

DEFINITIONS IN THERMODYNAMICS This section reviews some basic definitions and formulas in thermodynamics. These definitions will be used to develop energy balances to describe cooling tower operations. In our discussions we will use the following terms: system, property, extensive and intensive properties, and

L

PROPERTIES FOR THE AIR-WATER SYSTEM

19

state. The term system refers to any specified mass of material or piece of equipment under consideration. Any system enclosed by a boundary that prevents the exchange of mass with the surroundings is a nonflow or closed system. An open or flow system, such as a cooling tower, has exchange of both mass and energy with the surroundings. The term property refers to a characteristic of a material and can be measured. Examples are pressure, temperature and volume. Properties may also be computed, such as, for example, internal energy, which cannot be measured directly. An extensive property is one whose value is the sum of each of the subsystems comprising the entire system. An example is a gas mixture, in which each constituent (or subsystem) has masses or volumes different from the original system. Thus, mass or volume is an extensive property. An intensive property is one whose values are not additive and do not vary with the quantity of the sample in the system. Examples are temperature, pressure and density. The term state refers to material with a specified set of properties at a given time. It is not a function of the system configuration but only of its intensive properties.

Heat Heat can be defined as a portion of the total energy flo~ across a system boundary and is caused by a temperature difference between the system and the surroundings. Heat can be exchanged by conduction, convection and/or radiation. We can evaluate heat transfer by use of the energy balance, which will be discussed later.

Work Work can be defined as the energy transferred between the system and surroundingso It is often expressed as a vector force acting through a vector displacement on the system boundaries:

W= fFdX

(2.17)

where F is in the direction of dx. Work can be classified as energy that can be transferred to or from a mechanical state. This should not be confused with heat, which is the transfer of energy to atomic or molecular states. The former is macroscopically observable, whereas the latter is not.

20

COOLING TOWERS

Kinetic Energy Kinetic energy refers to the energy that a system possesses because of its velocity relative to the surroundings. Mathematically it is defined as follows: kE

=

1 2

-mY'

(2.18)

where v is fluid velocity.

Potential Energy Potential energy refers to the energy a system possesses due to the force exerted on its mass by a gravitational field with respect to some reference plane. Mathematically, it is' defined as follows: PE

= mgh

(2.19)

Internal Energy Internal energy refers to the macroscopic changes of molecular, atomic and subatomic energies. All these follow rigorous conservation laws for dynamic systems. Irlternal energy is an exact differential, which, for a pure substance, can be e~pressed exclusively in terms of temperature and specific volume, U = U(T,V), where the bar (-) refers to per unit mass. By taking a total derivative we can state the following:

dU=(au)_ aT v dT+ (a:Q) av TdV

(2.20)

The term (aU/aT)" is defined from thermodynamics as the heat capacity at constant volume (Cv). The second term on the right hand side (RRS) of Equation 2.20, (au/avh, is much less than Cv and can be neglected. By taking the integral of our differential expression we obtain a relation for internal energy:

- =fT, CvdT

t;U

(2.21)

T,

Engineers prefer to estimate internal energy changes from enthalpies.

Enthalpy Enthalpy is an exact differential, which is expressed as the sum of two variables:

PROPERTIES FOR THE AIR-WATER SYSTEM

H = U + pV

21

(2.22)

where p is pressure and V is volume. Enthalpy is a function of both temperature and pressure: H = H(T,P)-and can be expressed by the following differential expression:

dH=(aH) aT PdT+(aH') ap TdP

(2.23)

(aH/aT)p is the heat capacity at constant pressure (Cp). The second term on the RHS of Equation 2.23 can be neglected at modest pressures. Therefore, the integral of this expression gives the following: (2.24)

Enthalpy changes are most frequently computed with respect to a reference condition. In the steam tables, this reference condition is liquid water at 32°F and its vapor pressure. Thus, the left-hand side (LHS) of Equation 2.24 is FINAL STATE OF SYSTEM ENTHALPY

INITIAL STATE OF SYSTEM ENTHALPY

~~

t.H

= NET

ENTHALPY CHANGE = = Hz - H,

(H, - Href) (2.25)

Heat Capacity Previously, we defined the heat capacity t~rms as follows:

Cp =(aH') aT P

(2.26)

(2.27)

A simplified definition of heat capacity is the amount of energy needed to raise the temperature of a material by 1°. Various units for heat capacity include cal/(g-mole )CC), kcal/(kg-mole )(C), Btu/(lb-mole )CF), cal/(g)(C) or Btu/(lbm)CF). Heat capacity curves for water vapor and air are given in Figure 2.2.

22

COOLING TOWERS

0. .... (.)LI..

.....

0

p

16

....

>-11.1 1-...1 14 -0 (.):I!!

«. Q. m «...I (.) ..... 1 -' «;:)

~~

12 10

8 6

o o o N

o oII)

TEMPERATURE ( Figure 2.2

0 0

o o

N

It)

~

CD

°c )

Heat capacity curves for air and water vapor.

Most equations for heat ~apacities of substances are empirical. Heat capacity at constant pressure is generally expressed in terms of temperature with a power, series type formula: Cp = a + bT + CT' + dT3 + ...

(2.28)

or sometimes in the following form: Cp = a + bT + CT-lI' + .. . C p = a + bT -

cr' + .. .

(2.29a) (2.29b)

In general, heat capacity equations are valid only over a moderate range of temperatures. Table 2.1 gives constants to be used with Equation 2.28 for air and water gases. The units of heat capacity with these constants are cal/(g-mole )CK or °C) or Btu/ (lb -mole)(R or OF). Another useful term is specific heat, which is the ratio of the heat capacity of one substance to the heat capacity of a reference material. The heat capacity of water is approximately unity in cgs and American engineering units. Heat capacity is used to compute enthalpy changes. Note that the definition given by Equation 2.24 is really the area under the heat capacity curve between temperatures Tl and T2 (Figure 2.3). We can also obtain an exact integral by substituting an expression for Cp (such as Equation 2.28) into Equation 2.24 and performing the following integration:

-PROPERTIES FOR THE AIR-WATER SYSTEM

23

Table 2.1 Constants for Heat Capacity Equation 2.28 for Air and Water

State

T

a

Air

Gas

°C

Water

Gas

°C

6.917 6.713 6.900 6.713 7.880

oK of oR

10 2 b 0.09911 0.04697 0.02884 0.02609 0.3200 -

109 d

lOSc 0.07627 0.1147 0.02429 0.03540 0.04833

-

0.4696 0.4696 0.08052 0.08052

Applicable Temperature Range CK) 0-1500 273-1800 32-2700 492-3200 0-3500

AREA UNDER CURVE REPRESENTS

L\R HEAT CAPACITY,

Cp

T,

T2

TEMPERATURE, T

Figure 2.3

Graphic representation of enthalpy change.

(2.30)

For estimates, a mean heat capacity is used, which is defined as the enthalpy change divided by the temperature differential for that change. This can be stated as follows: (2.31)

Note also that if the heat capacity expression is a power series (e.g., Cp == a + bT + cT2 + ... ), then,

==

PROPERTIES FOR THE AIR-WATER SYSTEM Ab

l/J = Tb

25

(2.34)

where Ab is the molal heat of vaporization in cal/g-mole and Tb is the normal boiling point in oK. For water, the constant ljJ has a value of 26. The Clausius-Clapeyron equation is an exact thermodynamic relationship between the slope of the vapor pressure curve and the molal heat of vaporization:

where

dP*

A

dT

T(VG - VI)

(2.35)

p* = vapor pressure T = absolute temperature , A =molal heat of vaporization at temperature T V,G = molal volume of gas VI = molal volume ofliquid

Equation 2.35 can be rearranged to a simpler form by neglecting VI to give dlnP*

(2.36)

d(1/T) = -AIR

where R is the ideal

~ga:;.s_l_a_w_c~o_n_s_ta_n_t_.~",!","

On integrating this I?xprl?ssion,

log,op*

=

WI?

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __

obtain

A +a 2.303 RT

(2.37)

where a is a constant of the integration.

Dry-Bulb Temperature This is the'temperature of a vapor-gas mixture as ordinarily determined by immersion of a thermometer in the gas mixture. Dew Point Dew Point, as waS defined earlier, is the temperature at which a vapor-gas mixture becomes saturated when cooled at a constant total pressure out of contact with a liquid.

L

24

COOLING TOWERS

ff

TZ

aCT z - T ,) + ~

CpdT

T,

CPm

=

Tz

_ T,

(T~ - T~) + ~

(T; -

T~) (2.32)

(T z -T,)

dT

where T 1 in this expression is a reference temperature. For example, if T = O°C or O°F, then Equation 2.32 reduces to the following: b C Cp m = a + -2 T 2 + -3 T Zz

(2.33)

With regard to enthalpy changes, the simplest manner for computing is via tabulated enthalpy data. Data can be found in the literature [1,2]. Typical enthalpy data for air and water are given in Table 2.2. The Steam Tables are the most frequently used sources of enthalpy data for water. Heat of Vaporization There are several expressions that have developed, but our primary interest is with wat~i. Trouton's rule states that the ratio of the molal heat of vaporization of a,material at its normal boiling point (Le., at 1 atm) to the absolute temperature is a constant:

Table 2.2 Enthalpy Values for Air and Water (Btujlb-mole) Temperature °C

oK

of

oR

0.0 4.4 15.6 25.0 60.0 115.6 171.1

273. 277.4 288.6 298 333 388.6 444.1

32 40 60 77 140 240 340

492 500 520 537 600 700 800

226.7 282.2 393.3 504.4 615.6 726.7 837.8

499.7 555.2 666.3 777.4 888.6 999.7 1110.8

440 540 740 940 1140 1340 1540

900 1000 1200 1400 1600 1800 2000

Air

Water

0.0 55.57 194.6 312.7 751.2 1450.0 2153.0

0.0 64.02 224.2 360.5 867.5 1679.0 2501.0

2861.0 3579.0 5035.0 6540.0 8068.0 9623.0 11224.0

3336.0 4184.0 5925.0 7730.0 9602.0 11540.0 13550.0

26

COOLING TOWERS

Humid Volume The humid volume of a gas-vapor mixture is the volume, in ft3, of 1 lb of dry gas and its accompanying vapor at the prevailing temperature and pressure_ From the ideal gas law we can write the following: 1

.JI a )

vH= ( MW +MWA (359) B

where

TG+460 1 492

( l . J 1 a )TG+460

P =0.730 MWB +MWA t

'

P

t

(2.38)

~H = humid volume, ft3 T G = temperature of the gas, 0 F Pt = total pressure, atm MW A B = molecular weight of constituent A, B ila = absolute humidity

Humid Heat This is the heat capacity, of an air-water vapo~ mixture expressed on the basis of a unit weight of bone dry air. For a mixture of absolute humidity, Jl a , (2.39)

If neither vaporization nor condensation occurs, then the heat required to raise the temperature of WA lb of dry gas and its accompanying vapor AT is (2.40)

where Q is the heat quantity (Btu).

WET-BULB TEMPERATURE

The wet-buH temperature is the steady-state temperature achieved by a small quantity of liquid evaporating into a large quantity of unsaturated gasvapor mixture. The wet-bulb temperature is essentially a measure of the humidity of a gaseous mixture. We can describe the usefulness of this parameter by examining the behavior of a liquid particulate surrounded by a moving stream of unsaturated gas-vapor mixture. Figure 2.4 illustrates the system under consideration.

r PROPERTIES FOR THE AIR-WATER SYSTEM

J:

P.*

27

VAPOR

w P-A-R-T-I-A-L----l~!..--- LATENT H~AT PRESSURE

I

I

I

I

I

I

PA

I

/'

/

LIQUID DROP

/ {

\

\

/1 "

...... - - ....... 1

I

tw

I

T

P+--SENSI~LE I

TEMPERATURE

Figure 2.4

II

I

HEAT

The principle of wet-bulb temperature.

If the liquid droplet is initially at a higher temperature than the gas dew point, then the liquid's vapor pressure would be greater at the gas-liquid interface than the partial pressure of the vapor in the gas. Under these conditions, the liquid will evaporate and water vapor molecules will diffuse into the gas stream. The latent heat needed for evaporation will first be derived from the sensible heat of the liquid drop, causing it to cool down. When the liquid temperature has dropped below the dry-bulb temperature of the gas, heat begins to flow from the gas to the liquid. The rate at which this heat transfer occurs increases as the temperature differential becomes greater. After sufficient time, the heat transfer rate from gas to liquid matches the rate of heat requirement for the evaporation. Here, the temperature of the liquid remains at some constant low value known as the wet-bulb temperature. We can describe this process by a simple mathematical model developed for steady-state conditions. The total heat release at the interface, q, can be expressed in terms of the latent heat of vaporization and heat of solution, qs: (2.41)

where A. is the molar-heat of evolution and NAB is the mass rate of diffusion or mass flux. In the example given by Figure 2.4, there is no heat transfer across the gas-liquid interface (Le., q = 0), and we can assume that air does not diffuse into the liquid droplet (Le., NB= 0).

28

COOLING TOWERS

By asswning the rate of mass transfer is small and using principles of the film theory [3], the following expressions can be developed:

qs =

N MW C /1 (TG 1 - e- A A A lG

- tW) "" hG(TG - tW)

(2.42)

(2.43)

where

CA = heat capacity, Btu/(lb)CF)

hG == heat transfer coefficient of the gas, Btu/(hr)(ft'WF) TG == temperature of the gas, of tw = wet-bulb temperature, of F' = overall mass transfer coefficient, Ib-mol/(hr)(ft2) kG = gas phase mass transfer coefficient, Ib-mole/(hr)(ft2)(atm) Pt = total pressure, atm P 1,B = partial pressure, atm PAW = vapor pressure of component A at the wet-bulb temperature, atm

Equations 2-42, 2-43 and 2-41 can be combined and, through some algebraic acrobaNcs, the following expression derived:

TG -tw

(2.44 )

The quantity TG - tw is known as the wet-bulb depression. kH is the redefined mass transfer coefficient defined by

(2.45)

where PGM is the average partial pressure of the gas . .Ha and .HaW are the molal absolute humidity at TG and tw, respectively (Ib-mole vapor/lb-mole gas). hG/kH is known as the psychrometric ratio. The wet-bulb temperature is measured with a device called a psychrometer. . A simple one can be made by attaching a wick or porous cotton cloth to the mercury bulb of a thermometer and then wetting the wick. As long as the gas flow past the wick is turbulent, readings are not affected by gas velocity and the psychrometric ratio is constant. Dropkin [4] showed that for the air-water system hG/kH "'" 0.227.

r PROPERTIES FOR THE AIR-WATER SYSTEM

29

HUMIDITY CHARTS The humidity chart or psychrometric chart is a convenient plot for representing the properties of mixtures of a permanent gas and a condensable vapor. There are a number of forms in which this chart has been presented. One form, proposed by Grosvenor [5], is shown in Figure 2.5 for the airwater system at 1 atm. On the humidity chart of Figure 2.5, temperatures are plotted as abscissas and humidities as ordinates. Any point on the plot represents a specific mixture of air and water. The curve marked 100% humidity refers to saturated air and is a function of air temperature. Any point to the left of the saturation curve represents a mixture of saturated air and liquid water (this portion of the plot is useful in determining fog formation). Any point to the right of the saturation curve represents undersaturated air. Any point on the temperature axis represents bone-dry air. The curves between the two limits (saturated line and the temperature axis) represent mixtures of air and water of definite percentage humidities. Linear interpolation between the saturation curve and the temperature axis locates lines of constant percentage humidity. The diagonal lines that run upward and to the left of the saturation curve in Figure 2.5 are referred to as adiabatic cooling curves. Li'nes for the specific volume of dry air and the saturated volume are also shown. Coordinates of points on these lines are computed by use of Equation 2.38. The humid volume of unsaturated air can be determi!1ed by linear interpolation between the two lines, based on percentage humidity. Use of the humidity chart is best illustrated by examples. Let us consider just a portion of the psychrometric chart (Figure 2.6). Consider an unsaturated stream of air at some temperature, T b and a percentage humidity, Jl a , represented by point A on Figure 2.6 (this point is the intersection of the constant temperature line, T1, and - a constant percentage-humidity curve, Jl a1 ). The humidity of this air is fi1 (point B on Figure 2.6). The dew point can be determined by tracing the constant-humidity line through point A to the left to point C on the saturation curve. The dew point temperature is the abscissa value for point C (point D on the temperature axis). The adiabatic s;turation temperature is that temperature applying to the adiabatic-cooling curve through point A. The humidity value at adiabatic saturation is determined by following the adiabatic line through point A to point E on the saturation curve and reading the value Jl s on the humidity scale. The adiabatic saturation temperature is the abscissa value of point E, Le., Ts. The humid volume of the air stream is determined by locating points F and G on the saturated and dry-volume curves, respectively, which correspond to

w

0

2500

24

130

23

120

150011::

ENTHALPY OF SATURATED II::

< >-

1000>100

BOO

SPECIFIC VOLUME OF DRY AIR ENTHALPY OF DRY AIR PERCENT HUMIDITY CURVE

II::

c 20

III ..J


::::: --l

> t:e t'"' i:'1

CIl

N N

N N N

Table 3 (continued) Abs. Press Lb/Sq In. (Sat. Temp)

Sat. Stearn

Sh v 0.01693 16.30.1 h 208.52 1160.6 0.3535 1.7141 Sh v 0.01701 13.744 h 218.93 1164.1 0.3682 1.6995 Sh v 0.01708 11.896 h 228.03 1167.1 03809 1.6872 Sh v 0.01715 10.497

25 (240.07)

30 (250.34)

35 (259.29)

40

(l{lJn1i'

Sat. Water

~ d?6 14

'if,@ Q

0.3921 1.6765 ""tJ

.-

(281.02)

60 (292.71)

70 (302.93)

-- • h

b.l12,"'",

~O-:J~q.

250.21 1174.1 0.4112 1.6586

Sh v 0.1738 h 262.21 0.4273 Sh v 0.01748 h 272.74 0.4411

7.174 1177.6 1.6440 6.205 1180.6 1.6316

("')

Temperature-Degrees Fahrenheit 200 250 300 350 400 9.93 59.93 109.93 159.93 16.558 17.829 19.076 20.307 1165.6 1190.2 1214.5 1238.5 1.7212 1.7547 1.7856 1.8145 49.66 99.66 149.66 14.810 15.859 16.892 1189.0 1213.6 1237.8 1.7334 1.7647 1.7937 40.71 90.71 140.71 12.654 13.562 14.453 1187.8 1212.7 1237.1 1.7152 1.7468 1.7761 32.75 82.75 l32.75 11.036 11.838 12.624 1

i'fL\lWiiF 1??E •

1.6992 1.7312 1.7608 "-'--(j.iO~ ~."t2'"

1184.1 1.6720 7.29 7.257 1181.6 1.6492

1209.9 1.7048 57.29 7.815 1208.0 1.6934 47,07 6.664 1206.0 1.6640

450

500

600

700

800

900

1000

1100

209.93 21.527 l;262.5 1.8415 199.66 17.914 1261.9 1.8210 190.71 15.334 1261.3 1.8035 182.75 13.398

259.93 22.740 1286.4 1.8672 249.66 18.929 1286.0 1.8467 240.71 16.207 1285.5 1.8294 232.75 14.165

359.93 25.153 1334.6 1.9149 349.66 20.945 1334.2 1.8946 340.71 17.939 1333.9 1.8774 332.75 15.685

459.93 27.557 1383.3 1.9588 449.66 22.951 1383.0 1.9386 440.71 19.662 1382.8 1.9214 432.75 17.195

559.93 29.954 1432.7 1.9997 549.66 24.952 1432.5 1.9795 540.71 21.379 1432.3 1.9624 532.75 18.699

659.93 32.348 1483.0 2.0381 649.66 26.949 1482.8 2.0179 640.71 23.092 1482.7 2.0009 632.75 20.199

759.93 34.740 1534.2 2.0744 749.66 28.943 1534.0 2.0543 740.71 24.803 1533.9 2.0372 732.75 21.697

859.93 37.130 1586.2 2.1089 849.66 30.936 1586.1 2.0888 840.71 26.512 1586.0 2.0717 832.75 23.194

tU'lC

1'lQ1..£

lt1?'l.:1

14..21

1

Z"C

0

m£g

~

1~::I:2"'L--....l.c::Q~Q

1.7883 1.8143 1.8624 1.9065 1.9476 1.9860 2.0224

1O.v02O

1O.UOO

,L.1 • .:JUQ

J.,I;; • .J,I;;;7

1.":}.I"t.1

.1"t~~r"'.i'b:.1-.JU

1234.9 1.7349 107.29 8.354 1233.5 1.7134 97.07 7.l33 1232.0 1.6951

1259.6 1.7628 157.29 8.881 1258.5 1.7417 147.07 7.590 1257.3 1.7237

1284.1 1.7890 207.29 9.400 1283.2 1.7681 197.07 8.039 1282.2 1.7504

1332.9 1.8374 307.29 10.425 l332.3 1.8168 297.07 8.922 l331.6 1.7993

l382.0 1.8816 407.29 11.438 l381.5 1.8612 397.07 9.793 l381.0 1.8439

1431.7 1.9227 507.29 12.446 1431.3 1.9024 497.07 10.659 1430.9 1.8852

1482.2 1.9613 607.29 l3.450 1481.8 1.9410 597.07 11.522 1481.5 1.9238

2.0569

.1/ • .:J.JU

J.t..3~

1533.4 1.9977 707.29 14.452 lS33.2 1.9774 697.07 12.382 1532.9 1.9603

1585.6 2.0322 807.29 15.452 1585.3 2.0120 797.07 l3.240 1585.1 l.9949

0 0

1200 959.93 39.518 1639.2 2.1418 949.66 32.927 1639.0 2.1217 940.71 28.220 1638.9 2.1046 932.75 24.689 1.-'20

Q

2.0899

1638.6 2.0652 907.29 16.450 1638.4 2.0450 897.07 14.097 1638.2 2.0279

r ~ C'l --l

0

~ ~

Table 3 (continued) Abs. Press LbjSq In. (Sat. Temp) 80 (312.04)

90 (320.28)

100 (327.82)

110 (334.79)

120 (341.27)

140 (353.04)

Sat. Water

Sat. Stearn

Sh v 0.01757 5.471 h 282.15 1183.1 0.4534 1.6208 Sh v 0.01766 4.895 h 290.69 1185.3 0.4643 1.6113 Sh v 0.01774 4.431 h 298.54 llB7.2 0.4743 1.6027 Sh v 0.01782 4.048 h 305.80 1188.9 s 0.4834 l.5950 Sh v 0.01789 3.7275 h 312.58 1190.4 0.4919 1.5879 Sh v 0.01803 3.2190 h 324.96 1193.0 0.5071 1.5752

Temperature-Degrees Fahrenheit 550 350 400 450 500 37.96 5.801 1204.0 1.6473 29.72 5.128 1202.0 1.6323 22.18 4.590 1199.9 1.6187 15.21 4.149 1197.7 1.6061 8.73 3.7815 1195.6 1.5943

87.96 6.218 1230.5 1.6790 79.72 5.505 1228.9 1.6646 72.18 4.935 1227.4 1.6516 65.21 4.468 1225.8 1.6396 58.73 4.0786 1224.1 1.6286 49.96 3.4661 1220.8 1.6085

137.96 6.622 1256.1 1.7080 129.72 5.869 1254.9 1.0940 122.18 5.266 1253.7 1.6814 115.21 4.772 1252.5 1.6698 108.73 4.3610 1251.2 1.6592 96.96 3.7143 1248.7 1.6400

187.96 237.96 7.018 7.408 1281.3 1306.2 1.7349 1.1602 179.72 229.72 6.223 6.572 1280.3 l305.4 1.7212 1.7467 172.18 222.18 5.588 5.904 1279.3 1304.6 1.7088 1.7344 165.21 215.21 5.068· 5.357 1278.3 1303.8 1.6975 1.7233 158.73 208.73 4.6341 4.9009 1277.4 1302.9 1.6872 1.7132 146.96 196.96 3.9526 4.1844 1275.3 1301.3 1.6686 1.6949

600

700

BOO

900

1000

1100

1200

1300

1400

287.96 7.794 1330.9 1.1842 279.72 6.917 1330.2 1.7707 272.18 6.216 1329.6 1.7586 265.21 5.642 1328.9 1.7476 258.73 5.1637 1328.2 1.7376 i· 246.96 4.4119 1326.8 1.7196

387.96 8.560 1380.5 1.8289 379.72 7.600 1380.0 1.8156 372.18 6.833 1379.5 1.8036 365.21 6.205 1379.0 1.7928 358.73 5.6813 1378.4 1.7829 346.96 4.8588 1377.4 1.7652

487.96 9.319 1430.5 1.8702 479.72 8.277 1430.1 1.8570 472.18 7.443 1429.7 1.8451 465.21 6.761 1429.2 l.8344 458.73 6.1928 1428.8 1.8246 446.96 5.2995 1428.0 1.8071

587.96 10.075 1481.1 1.9089 579.72 8.950 1480.8 1.8957 572.18 8.050 1480.4 l.8839 565.21 7.314 1480.1 1.8732 558.73 6.7006 1479.8 1.8635 546.96 5.7364 1479.1 l.8461

687.96 10.829 1532.6 1.9454 679.72 9.621 1532.3 1.9323 672.18 8.655 1532.0 1.9205 665.21 7.865 1531.7 1.9099 658.73 7.2060 1531.4 1.9001 646.96 6.1709 1530.8 l.8828

787.96 11.581 1584.9 1.9800 779.72 10.290 1584.6 1.9669 772.18 9.258 1584.4 l.9552 765.21 8.413 1584.1 1.9446 758.73 7.7096 1583.9 1.9349 746.96 6.6036 1583.4 1.9176

887.96 12.331 1638.0 2.0131 879.72 10.958 1637.8 2.0000 872.18 9.860 1637.6 1.9883 865.21 8.961 1637.4 1.9777 858.73 8.2119 1637.1 19680 846.96 7.0349 1636.7 1.9508

987.96 13.081 1692.0 2.0446 979.72 11.625 1691.8 2.0316 972.18 10.460 1691.6 2.0199 965.21 9.507 1691.4 2.0093 958.73 8.7130 1691.3 1.9996 946.96 7.4652 1690.9 1.9825

1087.96 13.829 1746.8 2.0750 1079.72 12.290 1746.7 2.0619 1072.18 11.060 1746.5 2.0502 1065.21 10.053 1746.4 2.0397 1058.73 9.2134 1746.2 2.0300 1046.96 7.8946 1745.9 2.0129

-

CIl

--l

i:"l

>

:::::

--l

> !:Xi

r;;

CIl

N N

IN

N N

Table 3 (continued) Abs. Press Lb/Sq In. (Sat. Temp) 160 (363.55)

180 (373.08)

200 (381.80)

Sat. Water Sh v 0.01815 h 336.07 0.5206 Sh v 0.01827 h 346.19 0.5328 Sh v 0.01839 h 355.51 0.5438

.j::..

Sat. Steam 2.8336 1195.1 1.5641 1.5312 1196.9 1.5543 2.2873 1198.3 1.5454

Temperature-Degrees Fahrenheit 350 400 200 250 300 36.45 3.0060 1217.4 1.5906 26.92 2.6474 1213.8 1.5743 18.20 2.3598 1210.1 1.5593

86.45 3.2288 1246.0 1.6231 76.92 2.8508 1243.4 1.6078 68.20 2.5480 1240.6 1.5938

136.45 3.4413 1273.3 1.6522 126.92 3.0433 1271.2 1.6376 118.20 2.7247 1269.0 1.6242

186.45 3.6469 1299.6 1.6790 176.92 3.2286 1297.9 1.6647 168.20 2.8939 1296.2 1.6518

("'J

450 236.45 3.. 8480 1325.4 1.7039 226.92 3.4093 1324.0 1.6900 218.20 3.0583 1322.6 1.6773

500

600

336.45 4.2420 1376.4 1.7499 326.92 3.7621 1375.3 1.7362 318.20 3.3783 1374.3 1.7239

436.45 4.6295 1427.2 1.7919 426.92 4.1084 1426.3 1.7784 418.20 3.6915 1425.5 1.7663

Sh = superheat, F; v = specific volume, cu ft per lb; h = enthalpy, Btu per lb; s = entropy. Btu per F per lb.

700 536.45 5.0132 1478.4 1.8310 526.92 4.4508 1477.7 1.8176 518.20 4.0008 1477.0 1.8057

800 636.45 5.3945 1530.3 1.8678 626.92 4.7907 1529.7 1.8545 618.20 4.3077 1529.1 1.8426

900 736.45 5.7741 1582.9 1.9027 726.92 5.1289 1582.4 1.8894 718.20 4.6128 1581.9 1.8776

1000

1100

1200

836.45 6.1522 1636.3 1.9359 826.92 5.4657 1635.9 1.9227 818.20 4.9165 1635.4 1.9109

936.45 1036.45 6.5293 6.9055 1690.5 1745.6 1.9676 1.9980 926.92 1026.92 5.8014 6.1363 1690.2 1745.3 1.9545 1.9849 918.20 1018.20 5.2191 5.5209 1689.8 1745.0 1.9427 1.9732

0 0

t""'

Z

C'l --l

0

~

i:"l

::tI

CIl

APPENDIXB CONVERSION FACTORS

By

Multiply Acres Acres Acres Acres Acre-feet Acre-feet Angstrom units Atmospheres Atmospheres Atmospheres Atmospheres Atmospheres Atmospheres Barrels (British, dry) Barrels (British, dry) Barrels (British, dry) Barrels, cement Barrels, cement Barrels, oil' Barrels, (U.S., liquid) Barrels, (US., liquid) Barrels (U.S., liquid) Bars Bars Bars Bars Bars

43.560 4,047 1.562 x 10- 3 4840 43.560 3.259 x 10 5 3.937 x 10- 9 76.0 29.92 33.90 10,333 14.70 1.058 5.780 0.1637 36 170.6 376 42 4.211

0.1192 31.5 0.9869 1 x 10 6 1.020 x 10 4 2.089 x 10 3 14.50

225

To Obtain Square feet Square meters Square miles Square yards Cubic-feet Gallons Inches Centimeters of mercury Inches of mercury Feet of water Kilograms/square meter Pounds/square inch Tons/square foot Cubic feet Cubic meters Gallons (British) Kilograms Pounds of cement Gallons (U.S.) Cubic feet Cubic meters Gallons (U.S.) Atmospheres Dynes/square centimeter Kilograms/square meter Pounds/square foot Pounds/square inch

226

COOLING TOWERS

Multiply Board-feet British thermal units British thermal units British thermal units British thermal units British thermal units British thermal units Btu (mean) Btu (mean) Btu (mean) Btu/minute Btu/minute Btu/minute Btu/minute Btu/square foot/ minute Btu (mean)/hour (ft2tF Btu (mean)/hour (ft2 tF Btu (mean)/hour (ft2tF Btu (mean)/hour (ft2tF Btu (mean)/hour (ft 2 tF Btu (mean)/pound/ of Bushels Bushels Bushels Bushels Bushels Bushels Calories, gram (mean) Calories, gram (mean) Calories, gram (mean) Calories, gram (mean) Calories, (thermochemical)

By 144 square inches x 1 inch 0.2520 777.5 3.927 x 10-4 1054 107.5 2.928 x 10-4 251.98 0.55556 6.876 x 10- 5 12.96 0.02356 0.01757 17.57 0.1220 4.882

To Obtain Cubic inches Kilogram-calories Foot-pounds Horsepower-hours Joules Kilogram-meters Kilowatt-hours Calories, gram (mean) Centigrade heat units Pounds of carbon to CO 2 Foot-pounds/second Horsepower Kilowatts Watts Watts/square inch

3.94 x 10-4

Kilogram-calorie / (m 2 tC Gram-calorie/second (cm 2tC 0 Horsepower / ( ft 2 ) F

5.682 x 10-4

Watts/( cm 2tc

2.035 x 10- 3

Watts/(in. 2tc

1

Calories, gram/gramtC

1.244 2150 0.03524 4 64 32 3.9685 x 10- 3 0.001469 3.0874 0.0011628 0.999346

Cubic feet Cubic inches Cubic meters Pecks Pints (dry) Quarts (dry) Btu (mean) Cubic feet-atmospheres Foot-pounds Watt-hours Calories (int. steam tables)

1.3562 x 10-4

CONVERSION FACTORS

Multiply Calories, gram (mean)/gram Centigrams Centiliters Centimeters Centimeters Centimeters Centimeters Centimeters Centimeter-dynes Centimeter-dynes Centimeter-dynes Centimeter-grams Centimeter-grams Centimeter-grams Centimeters of mercury Centimeters of mercury Centimeters of mercury Centimeters of mercury Centimeters of mercury Centimeters/second Centimeters/second Centimeters/second Centimeters/second Centimeters/second Centimeters/ second Centimeters/ second/ second Centimetels/ second/ second Centimeters/ second/ second Circular mils Circular mils Circular mils Cord-feet

227

By

To Obtain

1.8 0.01 0.01 0.0328083 0.3937 0.01 393.7 10 1.020 x 10- 3 1.020 x 10- 8 7.376 x 10- 8 980.7 10-5 7.233 x 10-5 0.01316

Btu (mean)/pound Grams liters Feet (U.S.) Inches Meters Mils Millimeters Centimeter-grams Meter-kilograms Pound-feet Centimeter-dynes Meter-kilograms Pound-feet Atmospheres

0.4461

Feet of water

136.0

Kilograms/square meter

27.85

Pounds/square foot

0.1934

Pounds/square inch

1.969 0.03281 0.036 0.6 0.02237 3.728 x 10-4 0.03281

Feet/minute Feet/second Kilometers/hour Meters/minute Miles/hour Miles/minute Feet/second/second

0.036

Kilometers/hour/second

0.02237

Miles/hour/second

5.067 x 10- 6 7.854 x 10- 7 0.7854 4 feet x 4 feet x 1 foot

Square centimeters Square inches Square mils Cubic feet

228

COOLING TOWERS

Multiply Cords Cubic centimeters Cubic centimeters Cubic centimeters Cubic centimeters Cubic centimeters Cubic centimeters Cubic centimeters Cubic centimeters Cubic centimeters Cubic feet Cubic feet Cubic feet Cubic feet Cubic feet Cubic feet Cubic feet Cubic feet Cubic feet of water{60°F) Cubic feet/minute Cubic feet/minute Cubic feet/minute Cubic feet/minute Cubic feet/second Cubic feet/second Cubic feet/second Cubic feet-atmospheres Cubic foot-atmospheres Cubic foot-atmospheres Cubic foot-atmospheres Cubic foot-atmospheres Cubic inches Cubic inches Cubic inches Cubic inches Cubic inches Cubic inches Cubic inches Cubic inches Cubic inches (U.S.)

By 8 feet x 4 feet x 4 feet 3.531 x 10- 5 6.102 x 10- 2 10- 6 1.308 x 10- 6 2.642 x 10-4 10- 3 2.113 x 10- 3 1.057 x 10- 3 0.033814 2.832 x 10 4 1728 0.02832 0.03704 7.481 28.32 59.84 29.92 62.37 472.0 0.1247 0.4720 62.4 1.9834 448.83 0.64632 2.7203 680.74 2116.3 292.6 7.968 x 10-4 16.39 5.787 x 10-4 1.639 x 10- 5 2.143 x 10- 5 4.329 x 10- 3 1.639 x 10- 2 0.03463 0.01732 0.55411

To Obtain Cubic feet Cubic feet Cubic inches Cubic meters Cubic yards Gallons Liters Pints (liqUid) Quarts (Jiq uid) Ounces (U.S. fluid) Cubic centimeters Cubic inches Cubic meters Cubic yards Gallons Liters Pints (liquid) Quarts (liquid) Pounds Cubic centimeters/second Gallons/second Liters/second Pounds of water/minute Acre-feet/day Gallons/minute Million gallons/day Btu (mean) Calories, gram (mean) Foot-pounds Kilogram-meters Kilowatt-hours Cubic centimeters Cubic feet Cubic meters Cubic yards Gallons Liters Pints (liquid) Quarts (liquid) Ounces (U.S. fluid)

CONVERSION FACTORS

Multiply Cubic meters Cubic meters Cubic meters Cubic meters Cubic meters Cubic meters Cubic meters Cubic meters Cubic meters Cubic meters Cubic yards (British) Cubic yards Cubic yards Cubic yards Cubic yards Cubic yards Cubic yards Cubic yards Cubic yards Cubic yards/minute Cubic yards/minute Cubic yards/minute Days Days Decigrams Deciliters Decimeters Degrees (angle) Degrees (angle) Degrees (angle) Degrees/second Degrees/second Degrees/secord Dekagrams Dekaliters Dekameters Drams Drams Dynes Dynes Dynes

By 6

10 35.31 61,023 1.308 264.2 10 3 2113 1057 8.1074 x 10-4 8.387 0.9999916 7.646 x 105 27 46.656 0.7646 202.0 764.6 1616 807.9 0.45 3.367 12.74 1440 86,400 0.1 0.1 0.1 60 0.01745 3600 0.01745 0.1667 0.002778 10 10 10 1.772 0.0625 1.020 x 10- 3 7.233 x 10- 5 2.248 x 10- 6

229

To Obtain Cubic centimeters Cubic feet Cubic inches Cubic yards Gallons Liters Pints (liquid) Quarts (liquid) Acre-feet Barrels (U.S., liquid) Cubic yards (U.S.) Cubic centimeters Cubic feet Cubic inches Cubic meters Gallons Liters Pints (liquid) Quarts (liquid) Cubi~\ feet/ second Gallons/second Liters/second Minutes Seconds Grams Liters Meters Minutes Radians Seconds Radians/second Revolutions/minute Revolutions/second Grams Liters Meters Grams Ounces Grams Poundals Pounds

230

COOLING TOWERS

Multiply Dynes per square centimeter Ergs Ergs Ergs Ergs Ergs Ergs Ergs Ergs/second Ergs/second Ergs/second Ergs/second Ergs/second Ergs/second Fathoms Feet Feet Feet Feet Feet (U.S.) Feet of air (1 atmosphere 60°F) Feet of water Feet of water Feet of water Feet of water Feet of water Feet/minute Feet/minute Feet/minute Feet/minute Feet/minute Feet/second Feet/second Feet/second Feet/second Feet/second Feet/second

By

To Obtain Bars

9.486 x 1 7.376 x 1.020 x 10- 3 2.390 x 1.020 x 5.692 x

10- 1 I

4.426 x 10-6 7.376 x 10- 8 1.341 x 10- 10 1.434 x 10-9 10- 10 6 30.48 12 0.3048 1/3 1.893939 x 10-4 5.30 x 10-4

British thermal units Dyne-centimeters Foot-pounds Gram-centimeters Joules Kilogram-calories Kilogram-meters British thermal units/ minute Foot-pounds/minute Foot-pounds/second Horsepower Kilogram-calories/minute Kilowatts Feet Centimeters Inches Meters Yards Miles (statute) Pounds/square inch

0.02950 0.8826 304.8 62.43 0.4335 0.5080 0.01667 0.01829 0.3048 0.01136 30.48 1.097 0.5921 18.29 0.6818 0.Q1136

Atmospheres Inches of mercury Kilograms/square meter Pounds/square foot Pounds/square inch Centimeters/second Feet/second Kilometers/hour Meters/minute Miles/hour Centimeters/second Kilometers/hour Knots/hour Meters/minute Miles/hour Miles/minute

10- 8 1(f3 10- 1 I 10- 8 10- 9

CONVERSION FACTORS

Multiply

By

Feet/100 feet Feet/second/second

1 30.48

Feet/second/second Feet/second/second Feet/second/second Foot-poundals Foot-poundals Foot-pounds Foot-pounds Foot-pounds Foot-pounds Foot-pounds Foot-pounds Foot-pounds Foot-pounds Foot-pounds Foot-pounds/minute

1.097 0.304'8 0.6818 3.9951 x 10- 5 0.0421420 0.013381 3.7662 x 10-4 1.286 x 10- 3 1.356 x 10 7 5.050 x 10- 7 1.356 3.241 x 10-4 0.1383 3.766 x 10- 7 1.286 x 10- 3

Foot-pounds/minute Foot-pounds/minute Foot -pounds/minute Foot-pounds/minute Foot-pounds/second

0.01667 3.030 x 10- 5 3.241 x 10-4 2.260 x 10-5 , 7.717 x 10- 2

Foot-pounds/second Foot-pounds/second Foot-pounds/second Foot-pounds/second Foot-pounds/second Gallons (British) Gallons (British) Gallons (British)

1.818xlO- 3 1.945 x 10- 2 1.356 x 10- 3 4.6275 1.35582 4516.086 1.20094 10

Gallons (U.S.) Gallons Gallons Gallons Gallons Gallons Gallons

128 3785 0.1337 231 3.785 x 10-3 4.951 x 10-3 3.785

231

To Obtain Percent Grade Centimeters/second/ second Kilometers/hour/second Meters/second/second Miles/hour/second Btu (mean) Joules (abs) Liter-atmospheres Watt-hours (abs) British thermal units Ergs Horsepower-hours Joules Kilogram-calories Kilogram-meters Kilowatt-hours British thermal units/ minute Foot-pounds/second Horsepower Kilogram-calories/minute Kilowatts British thermal units/ minute Horsepower Kilogram-calories/minute Kilowatts Btu (mean)/hour Watts (abs) Cubic centimeters Gailons (U.S.) Pounds (avordupois) of of water at 62°F Ounces (U.S. fluid) Cubic centimeters Cubic feet Cubic inches Cubic meters Cubic yards Liters

232

COOLING TOWERS

Multiply Gallons Gallons Gallons/minute Gallons/minute Grains (troy) Grains (troy) Grains (troy) Grains (troy) Grains/U.S. gallons Grains/U.S. gallons Grains/Imperial gallons Grams Grams Grams Grams Grams Grams Grams Grams Gram-calories Gram-centimeters Gram -cen time te rs Gram-centimeters Gram-centimeters Gram-centimeters Gram-centimeters Gram-centimeters Gram-centimeters/ second Grams-centimeters 2 (moment of inertia) Grams-centimeters 2 Grams/cubic meters Grams/centimeter Grams/cubic centimeter Grams/cubic centimeter Grams/cubic centimeter Grams/ cubic centimeter Grams/liter Grams/liter Grams/liter

By

To Obtain

8 4 2.228 x 10-3 0.06308 1 0.06480 0.04167 2.0833 x 10- 3 17.118 142.86 14.286 980.7 15.43 10- 3 10 3 0.03527 0.03215 0.07093 2.205 x 10- 3 3.968 x 10-3 9.302 x 10-8 980.7 7.233 x 10- 5 9.807 x 10- 5 2.344 x 10- 8 10- 5 2.7241 x 10-8 9.80665 x 10- 5

Pints (liquid) Quarts (liquid) Cubic feet/second Liters/second Grains (average) Grams Pennyweights (troy) Ounces (troy) Parts/million Pounds/million gallons Parts/million Dynes Grains (troy) Kilograms Milligrams Ounces Ounces (troy) Poundals Pounds British thermal units British thermal units Ergs Foot-pounds Joules Kilogram-calories Kilogram-meters Watt-hours Watts (abs)

3.4172 x 10-4

Pounds-inch 2

2.37305 x 10- 6 0.43700 5.600 x 10- 3 62.43 0.03613 3.405 x 10- 7 8.34 58.417 9.99973 x 10-4 1000

Pounds-feet 2 Grains/cubic foot Pounds/inch Pounds/cubic foot Pounds/cubic inch Pounds/mil foot Pounds/ gallon Grains/gallon (U.S.) Grams/cubic centimeter Parts/million (ppm)

CONVERSION FACTORS

By

Multiply

233

To Obtain

0.06243 0.0142234

Pounds/cubic foot Pounds/square inch

100 100 100 100 0.5

Grams Liters Meters Watts Sphere

4

Spherical right angles

6.283

Steradians

42.44

British thermal units/ minute Foot-pounds/minute Foot-pounds/second Horsepower (metric) Kilogram calories/minute Kilowatts Watts British thermal unifs/hour Kilowatts Horsepower Horsepower British thermal units Foot-pounds Joules Kilogram-calories Kilo gram-meters Kilowatt-hours Minutes Seconds Centimeters Mils Atmospheres Feet of water Kilograms/square centimeters Kilograms/square meter Millimeters of mercury

Grams/liter Grams/square centimeter Hectograms Hectoliters Hectometers Hectowatts Hemispheres (sol. angle) Hemispheres (sol. angle) Hemispheres (sol. angle) Horsepower Horsepower Horsepower Horsepower Horsepower Horsepower Horsepower Horsepower (boiler) Horsepower (boiler) Horsepower, electrical Horsepower (me tric) Horsepower-hours Horsepower-hours Horsepower-hours Horsepower -hours Horsepower-hours Horsepower-hours Hours Hours Inches Inches Inches of mercury Inches of mercury Inches of mercury

33,000 550 1.014 10.70 0.7457 745.7 33,520 9.804 1.0004 0.98632 2547 1.98 x 10 6 1.684 x 10 6 641.7 2.737 x 10 5 0.7457 60 3600 2.540 10 3 0.03342 1.133 0.0345

Inches of mercury Inches of mercury

345.3 25.40

~.

234

COOLING TOWERS

Multiply

By

Inches of mercury Inches of mercury Inches of water Inches of water Inches of water Inches of water Inches of water Inches of water Kilograms Kilograms Kilograms Kilograms Kilograms Kilogram-calories Kilogram-calories Kilogram-calories Kilogram-calories Kilogram-calories Kilogram-calories/ . minute Kilogram-calories/ minute Kilogram-calories/ minute Kilo gram -cen timeters 2 Kilogram-centimeters 2 Kilogram-meters Kilogram-meters Kilogram-meters Kilogram-meters Kilogram-meters Kilogram-meters Kilogram-meters Kilogram-meters Kilograms/cubic meter Kilograms,tubic meter Kilograms/cubic meter Kilograms/cubic meter Kilograms/meter

9.807 2.344 x 10-3 2.724 x 10- 6 10-3 0.06243 3.613 x 10- 5 3.405 x 10- 10 0.6720

To Obtain

70.73 0.4912 0.002458 0.07355 25.40 0.5781 5.204 0.03613 980,665 10 3 70.93 2.2046 1.102 x 10-3 3.968 3086 1.558 x 10- 3 426.6 1.162 x 10-3 51.43

Pounds/square foot Pounds/square inch Atmospheres Inches of mercury Kilograms/square meter Ounces/square inch Pounds/square foot Pounds/square inch Dynes Grams Poundals Pounds Tons (short) British thermal units Foot-pounds Horsepower -hours Kilogram-meters Kilowatt-hours Foot-pounds/second

0.09351

Horsepower

0.06972

Kilowatts

2.373 x 10- 3 0.3417 9.302 x 10- 3 9.807 x 10 7 7.233 3.6529 x 10- 6 9.579 x 10- 6

Pounds-feet 2 Pounds-inches 2 British thermal units Ergs Foot-pounds Horsepower-hours Pounds water evaporated at 212°F Joules Kilogram-calories Kilowa tt-hours Grams/cubic meter Pounds/cubic foot Pounds/cubic inch Pounds/mil foot Pounds/foot

CONVERSION FACTORS

Multiply

By

235

To Obtain

Kilograms/square centimeter Kilograms/square centimeter Kilograms/square centimeter Kilograms/square meter Kilograms/square meter Kilograms/square meter Kilograms/square meter

28.96

Inches of mercury

735.56

Millimeters of mercury

14.22

Pounds/square inch

9.678 x 10-5 3.281 x 10-3 2.896 x 10-3 0.07356

Kilograms/square meter Kilograms/square meter Kilograms/ square millimeter Kiloliters Kilometers Kilometers Kilometers Kilometers Kilometers Kilometers/hour Kilometers/hour Kilometers/hour Kilometers/hour Kilometers/hour Kilometers/hour Kilometers/hour / second Kilometers/hour/ second Kilometers/hour/ second Kilometers/hour/ second Kilometers/minute Kilowatts

0.2048 1.422 x 10-3 10 6 10 3 10 5 3281 10 3 0.6214 1093.6 27.78 54.68 0.9113 0.5396 16.67 0.6214 27.78 0.9113

Atmospheres Feet of water Inches of mercury Millimeters of mercury at O°C Pounds/square foot Pounds/square inch Kilograms/square meter Liters Centimeters Feet Meters Miles Yarlfs Centimeters/second Feet/minute Feet/second Knots/hour Meters/minute Miles/hour Centimeters/second/ second Feet/second/second

0.2778

Meters/second/second

0.6214

Miles/hour/second

60 56.92

Kilometers/hour British thermal units/ minute Foot-pounds/minute Foot-pounds/second Horsepower

Kilowatts Kilowatts Kilowatts

4.425 x 104 737.6 1.342

236

COOLING TOWERS

By

Multiply Kilowatts

14.34

Kilowatts Kilowa tt -hours Kilowatt-hours Kilowatt-hours Liters Liters Liters Liters Liters Liters Liters Liters Liters/minute Liters/minute Log, oN Log N or Ln N Meters Meters Meters Meters Meters Meters Meters Meters Meter-kilograms Meter-kilograms Meter-kilograms Meters/minute Meters/minute Meters/minute Meters/minute Meters/minute Meters/ second Meters/second Meters/second Meters/second Meters/ second Meters/second Meters/second/second

10 3 3415 2.655 x 10 6 1.341 10 3 0.03531 61.02 10- 3 1.308. x 10- 3 0.2642 2.113 1.057 5.885 x 10-4 4.403, x 10- 3 2.303 0.4343 100 3.2808 39.37 10- 3

10 3 1.0936 10'0 6.2137 x 104 9.807 x 10 7 10 5 7.233 1.667 3.281 0.05468 0.06 0.03728 196.8 3.281 3.6 0.06 2.237 0.03728 3.281

To Obtain Kilogram-calories/ minute Watts British thermal units Foot-pounds Horsepower, hours Cubic centimeters Cubic feet Cubic inches Cubic meters Cubic yards Gallons Pints (liquid) Quarts (liquid) Cubic feet/second Gallons/second LogEN or Ln N Log, oN Centimeters Feet Inches Kilometers Millimeters Yards Angstrom units Miles Centimeter-dynes Centimeter-grams Pound-feet Centimeters/second Feet/minute Feet/second Kilometers/hour Miles/hour Feet/minute Feet/second Kilometers/hour Kilometers/min ute Miles/hour Miles/minute Feet/second/second

CONVERSION FACTORS

Multiply

By

Meters/second/second Meters/second/second Micrograms Microliters Microns Miles Miles Miles Miles Miles (int. Nautical) Miles/hour Miles/hour Miles/hour Miles/hour Miles/hour Miles/hour/second

3.6 2.237 10- 6 10- 6 10- 6 1.609 x lOs 5280 1.6093 1760 1.852 44.70 88 1.467 1.6093 26.82 44.70

Miles/hour /second Miles/hour /second Miles/hour /second Miles/minute Miles/minute Miles/minute Miles/minute Milliers Milligrams Millili te rs Millimeters Millimeters Millimeters Millimeters of mercury Millimeters of mercury

1.467 1.6093 0.4470 2682 88 1.6093 60 103 10-3 10-3

Millimeters of mercury Mils Mils Mils Minutes (angle) Minutes (angle) Months Months

0.01934 0.002540 10-3

0.1 0.03937 39.37 0.0394 1.3595 X 10- 3

25.40 2.909 x 10-4 60 30.42 730

237

To Obtain Kilometers/hour/second Miles/hour/second Grams Liters Meters Centimeters Feet Kilometers Yards Kilometers Centimeters/second Feet/minute Feet/second Kilometers/hour Meters/minute Centimeters/second/ second Feet/second/second KiloIl)eters/hour /second

Met~rs/second/second

Centimeters/second Feet/second Kilometers/minute Miles/hour Kilograms Grams Liters Centimeters Inches Mils Inches of mercury Kilograms/square centimeter Pounds/square inch Centimeters Inches Microns Radians Seconds (angle) Days Hours

238

COOLING TOWERS

Multiply Months Months Myriagrams Myriameters Myriawatts Ounces Ounces Ounces Ounces Ounces (fluid) Ounces (fluid) Ounces (U.S. fluid) Ounces (U.S. fluid) Ounces (troy) Ounces (troy) Ounces (troy) Ounces (troy) Ounces/square inch Parts/million Parts/million Parts/million Pennyweights (troy) Pennyweights (troy) Pennyweights (troy) Pints (dry) Pints (liquid) Pints (U.S. liquid) Pints (U.S. liquid) Poundals Poundals Poundals Pounds Pounds Pounds Pounds Pounds Pound (troy) Pounds (troy) Pounds of carbon to CO 2 Pound-feet (torque)

By

43,800 2.628 x 10 6 10 10 10 16 437.5 28.35 0.0625 1.805 0.02957 29.5737 1/128 480 31.10 20 0.08333 0.0625 0.0584 0.7016 8.345 24 1.555 0.05 33.60 28.87 473.179 16 13,826 14.10 0.03108 444,823 7000 453.6 16 32.17 0.8229 373.2418 14,544 1.3558 x 10 7

To Obtain Minutes Seconds Kilograms Kilometers Kilowatts Drams Grains Grams Pounds Cubic inches liters Cubic centimeters Gallons (U.S.) Grains (troy) Grams Pennyweights (troy) Pounds (troy) Pounds/square inch Grains/U.S. gallon Grains/Imperial gallon Pounds/million gallons Grains (troy) Grams Ounces (troy) Cubic inches Cubic centimeters Cubic centimeters Ounces (U.S. flUid) Dynes Grams Pounds Dynes Grains Grams Ounces Poundals Pounds (av.) Grams Britith thermal units (mean) Dyne-centimeters

CONVERSION FACTORS

Multiply

239

To Obtain

By 7

Pound-feet Pound-feet Pound-feet Pounds-feet 2 Pounds-feee Pounds-inches 2 Pounds-inches 2 Pounds of water Pounds of water Pounds of water Pounds of water evaporated at 212°F Pounds of water / minute Pounds/cubic foot Pounds/cubic foot Pounds/cubic foot Pounds/cubic foot Pounds/cubic inch Pounds/cubic inch Pounds/cubic inch Pounds/cubic inch Pounds/foot Pounds/inch Pounds/square foot Pounds/square foot Pounds/square foot Pounds/square inch Pounds/square inch Pounds/square inch Pounds/square inch

1.356 x 10 13,825 0.1383 421.3 144 2,926 6.945 x 10-3 0.01602 27.68 0.1198 970.3

Centimeters-dynes Centimeter-grams Meter-kilograms Kilogram-centimeters 2 Pounds-inches 2 Kilogram-centimeters 2 Pounds-feet 2 Cubic feet Cubic inches Gallons British thermal units

2.699 x 10-4

Cubic feet/second

0.01602 16.02 5.787 x 10-4 5,456 x 10-9 27.68 2.768 x 10 4 1728 9.425 x 10- 6 1.488 178.6 0.01602 4.882 6.944 x 10- 3 0.06804 2.307 2.036 0.0703

Pounds/square inch Pounds/square inch Pounds/square inch Pounds/square inch

703.1 144 70.307 51.715

Quadrants (angle) Quadrants (angle) Quadrants (angle) Quarts (dry)

90 5400 1.571 67.20

Grams/cubic centimeter Kilograms/cubic meter Pounds/cubic inch Pounds/mil foot Grams/cubic centimeter Kilogl:ams/cubic meter Pounds/cubic foot Pounds/mil foot Kilograms/meter Grams/centimeter Feet of water Kilograms/square meter Pounds/square inch Atmospheres Feet of water Inches of mercury Kilograms/square centimeter Kilograms/square meter Pounds/square foot Grams/square centimeter Millimeters of mercury at O°C Degrees Minutes Radians Cubic inches

240

COOLING TOWERS

By

Multiply Quarts (liquid) QUarts (US. liquid) Quarts (US. liquid) Quarts (US. liquid) Radians Radians Radians Radians/second Radians/second Radians/second Radians/second/second

57.75 0.033420 32 0.832674 57.30 3438 0.637 57.30 0.1592 9.549 573.0

Radians/second/second

9.549

Radians/second/second

0.1592

Revolutions Revolu tions Revolutions Revolutions/minufe Revolutions/minute Revolutions/minute Revolutions/minute/ minute Revolutions/minute/ minute Revolutions/minute/ minute Revolutions/second Revolutions/second Revol utions/ second Revolutions/second/ second Revolutions/second/ second Revolutions/second/ second Seconds (angle) Spheres (solid angle) Spherical right angles Spherical right angles

360 4 6.283 6 0.1047 0.01667 1.745 x 10- 3 0.01667 2.778 x 10-4 360 6.283 60 6.283 3600 60 4.848 x 10- 6 12.57 0.25 0.125

To Obtain Cubic inches Cubic feet Ounces (US. fluid) Quarts (British) Degrees Minutes Quadrants Degrees/second Revolutions/second Revolutions/minute Revolutions/minute/ minute Revolutions/minute/ second Revolutions/second/ second Degrees Quadrants Radians Degrees/second Radians/second Revolutions/second Radians/second/second Revolutions/minute/ second Revolutions/second/ second Degrees/second Radians/second Revolutions/minute Radians/second/second Revolutions/minute/ minute Revolutions/minute/ minute Radians Steradians Hemispheres Spheres

CONVERSION FACTORS

Multiply

To Obtain

By

Spherical right angles Square centimeters Square centimeters Square centimeters Square centimeters Square centimeters Square centimeterscentimeters squared Square feet Square feet Square feet Square feet Square feet Square feet Square feet-feet squared

1.571 1.973 x 105 1.076 x 10- 3 0.1 550 10- 6 100 0.02420

Square inches Sq uare inches Square inches Square inches Square inches Square inches (U.S.) Square inches-inches squared Square kilometers Square kilometers Square kilometers Square kilometers Square kilometers Square meters Square meters Square meters Square meter,s Square miles Square miles Square miles Square miles Square millimeters Square millimeters Square millimeters Square mils

1.273 x 10 6 6.452 6.944 x 10- 3 10 6 645.2 7.71605 x 10-4 41.62

2.296 x 10- 5 929.0 144 0.09290 3.587 x 10- 8 1/9 2.074 x 104

247.1 10.76 x 10 6 0.3861 1.196 x 2.471 x 10.764 3.861 x 1.196 640 27.88 x 2.590 3.098 x 1.973 x 0.01 1.550 x 1.273

241

10 6

10 6 10-4 10- 7

10 6

10 6 10 3 10- 3

Steradians Circular mils Square feet Square inches Square meters Square millimeters Square inches-inches squared Acres Square centimeters Square inches Square meters Square miles Square yards Square inches-inches squared Circular mils Square centimeters Square feet Squar'emils Square millimeters Sq uare yards Square centimeterscentimeters squared Acres Square feet Square meters Square miles Square yards Acres Square feet Square miles Square yards Acres Square feet Square kilometers Square yards Circular mils Square centimeters Square inches Circular mils

242

COOLING TOWERS

Multiply Square mils Square mils Square yards Square yards Square yards Square yards Temperature CC) +273 Temperature CC) + 17.8 Temperature ("F) +460 Temperature CF) - 32 Tons (long) Tons (long) Tons (metric) Tons (metric) Tons (short) Tons (short) Tons (short)/square Tons (short)/square Tons (short)/square Tons (short)/square Watts Watts Watts Watts Watts Watts Watts Watt-hours Watt-hours Watt-hours Watt-hours Watt-hours Watt-hours Weeks Weeks Weeks

By

To Obtain 6

6.452 x 1010-6 2.066 x 10-4 9 0.8361 3.228 x 10- 7 1

feet feet inch inch

1.8

Square centimeters Square inches Acres Square feet Square meters Square milys Absolute temperature ("C) Temperature ("F)

5/9

Absolute temperature ("F) Temperature ("C)

1016 224.0 10 3 2205 907.2 2000 9765 13.89 1.406 x 10 6 2000 0.05692 10 7 44.26 0.7376 1.341 xlO- 3 0.01434 10-3 3.415 2655 1.341 x 10-3 0.8605 367.1 10-3 168 10,080 604,800

Kilograms Pounds Kilograms Pounds Kilograms Pounds Kilograms/square meter Pounds/square inch Kilograms/square meter Pounds/square inch British thermal units/ minute Ergs/second Foot-pounds/minute Foot-pounds/second Horsepower Kilogram-calories/minute Kilowatts British thermal units Foot-pounds Horsepower-hours Kilogram-calories Kilogram-meters Kilowatt-hours Hours Minutes Seconds

CONVERSION FACTORS

Multiply Yards Yards Yards Yards Years (common) Years (common)

By

91.44 3 36 0.9144 365 8760

To Obtain Centimeters Feet Inches Meters Days Hours

243

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APPENDIX C SOLUTIONS TO SELECTED CHAPTER PROBLEMS

SOLUTIONS TO PROBLEMS IN CHAPTER 2 2.1

The specific volume of the wet steam mixture is ft3/0.99 lb = 1.01 ft3/lb. From the Steam Tables, the specific volumes of saturated vapor and liquid are vG = 6.032 fe/lb and VI = 0.0175 ft3/lb, respectively. Let x = weight fraction of vapor. Then, from a mate'rial balance, solve for x: ' 00175 ft' (ft' ) ft' ib liquid (1 - x) Ib liquid + \6.03 21b vapor (x lb vapor) = 1.01 Th

where we have assumed a basis of I lb vapor-gas mixture. 0.0175 - 0.0175 x