16.1 SECTION 16 HEATING, VENTILATING, AND AIR CONDITIONING ECONOMICS OF INTERIOR CLIMATE CONTROL 16.2 Equations for Heating, Ventilation, and Air-Conditioning Calculations 16.2 Determining Cooling-Tower Fan Horsepower Requirements 16.12 Choosing an Ice Storage System for Facility Cooling 16.13 Annual Heating and Cooling Energy Loads and Costs 16.22 Heat Recovery Using a Run-Around System of Energy Transfer 16.24 Rotary Heat Exchanger Energy Savings 16.26 Savings from ‘‘Hot-Deck’’ Temperature Reset 16.28 Air-to-Air Heat Exchanger Performance 16.29 Steam and Hot-Water Heating Capacity Requirements for Buildings 16.32 Heating Steam Required for Specialized Rooms 16.32 Determining Carbon Dioxide Buildup in Occupied Spaces 16.33 Computing Bypass-Air Quantity and Dehumidifier Exit Conditions 16.34 Determination of Excessive Vibration Potential in Motor-Driven Fan 16.36 Power Input Required by Centrifugal Compressor 16.37 Evaporation of Moisture from Open Tanks 16.38 Checking Fan and Pump Performance from Motor Data 16.40 Choice of Air-Bubble Enclosure for Known Usage 16.41 Sizing Hydronic-System Expansion Tanks 16.45 SYSTEM ANALYSIS AND EQUIPMENT SELECTION 16.53 Building or Structure Heat-Loss Determination 16.53 Heating-System Selection and Analysis 16.55 Required Capacity of a Unit Heater 16.58 Steam Consumption of Heating Apparatus 16.65 Selection of Air Heating Coils 16.67 Radiant-Heating-Panel Choice and Sizing 16.72 Snow-Melting Heating-Panel Choice and Sizing 16.75 Heat Recovery from Lighting Systems for Space Heating 16.77 Air-Conditioning-System Heat-Load Determination—General Method 16.78 Air-Conditioning-System Heat-Load Determination—Numerical Computation 16.85 Air-Conditioning System Cooling-Coil Selection 16.90 Mixing of Two Airstreams 16.97 Selection of an Air-Conditioning System for a Known Load 16.99 Sizing Low-Velocity Air-Conditioning- Systems Ducts—Equal Friction Method 16.102 Sizing Low-Velocity Air-Conditioning Ducts—Static-Regain Method 16.111 Humidifier Selection for Desire Atmospheric Conditions 16.114 Use of the Psychrometric Chart in Air- Conditioning Calculations 16.119 Designing High-Velocity Air- Conditioning Ducts 16.122 Air-Conditioning-System Outlet- and Return-Grille Selection 16.125 Selecting Roof Ventilators for Buildings 16.130 Vibration-Isolator Selection for an Air Conditioner 16.134 Selection of Noise-Reduction Materials 16.136 Choosing Door and Window Air Curtains for Various Applications 16.139 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Source: HANDBOOK OF MECHANICAL ENGINEERING CALCULATIONS 16.2 ENVIRONMENTAL CONTROL Economics of Interior Climate Control EQUATIONS FOR HEATING, VENTILATION, AND AIR-CONDITIONING CALCULATIONS A variety of calculation procedures are used in designing heating, ventilating, and air-conditioning systems. To help save time for design and application engineers, technicians, and consulting engineers, some 75 design equations are presented at the start of this section of the handbook. These equations are used in both manual and computer-aided design (CAD) applications. And since this handbook is de- signed for worldwide use, the first group of equations presents USCS and SI ver- sions to allow easy comparisons of the results. Abbreviations used in the equations follow this presentation. Btu ⅐ min H ϭ 1.08 ϫ CFM ϫ ⌬T (1) S 3 h ⅐ ft ⅐ ЊF kJ ⅐ min H ϭ 72.42 ϫ CMM ϫ ⌬T (2) SMM 3 h ⅐ m ⅐ ЊC Btu ⅐ min ⅐ lb DA H ϭ 0.68 ϫ CFM ϫ ⌬W (3) L 3 h ⅐ ft ⅐ grHO 2 kJ ⅐ min ⅐ kg DA H ϭ 177,734.8 ϫ CMM ϫ ⌬W (4) LMM 3 h ⅐ m ⅐ kgHO 2 lb ⅐ min H ϭ 4.5 ϫ CFM ϫ ⌬h (5) T 3 h ⅐ ft kg ⅐ min H ϭ 72.09 ϫ CMM ϫ ⌬h (6) TMM 3 h ⅐ m H ϭ H ϩ H (7) TSL H ϭ H ϩ H (8) TM SM LM Btu ⅐ min H ϭ 500 ϫ GPM ϫ ⌬T (9) h ⅐ gal ⅐ ЊF kJ ⅐ min H ϭ 250.8 ϫ LPM ϫ ⌬T (10) MM h ⅐ L ⅐ ЊC AC CFM ϫ 60 min/h ϭ (11) HR VOLUME AC CMM ϫ 60 min/h ϭ (12) HR VOLUME MM Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. HEATING, VENTILATING, AND AIR CONDITIONING HEATING, VENTILATING, AND AIR CONDITIONING 16.3 ЊF Ϫ 32 ЊC ϭ (13) 1.8 ЊF ϭ 1.8ЊC ϩ 32 (14) where H S ϭ sensible heat, Btu/h H SM ϭ sensible heat, kJ/h H L ϭ latent heat, Btu/h H LM ϭ latent heat, kJ/h H T ϭ total heat, Btu/h H TM ϭ total heat, kJ/h H ϭ total heat, Btu/h H M ϭ total heat, kJ/h ⌬T ϭ temperature difference, ЊF ⌬T M ϭ temperature difference, ЊC ⌬W ϭ humidity ratio difference, gr H 2 O/lb DA ⌬W M ϭ humidity ratio difference, kg H 2 O/kg DA ⌬h ϭ enthalpy difference, Btu / lb DA ⌬h ϭ enthalpy difference, kJ / lb DA CFM ϭ airflow rate, ft 3 /min CMM ϭ airflow rate, m 3 /min GPM ϭ water flow rate, gal/min LPM ϭ water flow rate, L/min AC/HR ϭ air change rate per hour, English AC/HR M ϭ air change rate per hour, SI AC/HR ϭ AC/HR M VOLUME ϭ space volume, ft 3 VOLUME M ϭ space volume, m 3 kJ/h ϭ Btu/h ϫ 1.055 CMM ϭ CFM ϫ 0.02832 LPM ϭ GPM ϫ 3.785 kJ/lb ϭ Btu/lb ϫ 2.326 m ϭ ft ϫ 0.3048 m 2 ϭ ft 2 ϫ 0.0929 m 3 ϭ ft 3 ϫ 0.02832 kg ϭ lb ϫ 0.4536 1.0 GPM ϭ 500 lb steam/h 1.0 lb steam / h ϭ 0.002 GPM 1.0 lb H 2 /h ϭ 1.0 lb steam/h kg/m 3 ϭ lb/ft 3 ϫ 16.017 (density) m 3 /kg ϭ ft 3 /lb ϫ 0.0624 specific volume kg H 2 O/kg DA ϭ gr H 2 O/lb DA/7000 ϭ lb H 2 O/lb DA Steam Pipe Pressure Drop and Flow Rate Equations 2 0.01306W (1 ϩ 3.6/ID) ⌬P ϭ (15) 5 3600 ϫ D ϫ ID 5 ⌬P ϫ D ϫ ID W ϭ 60 (16) Ί 0.01306 ϫ (1 ϩ 3.6/ID) Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. HEATING, VENTILATING, AND AIR CONDITIONING 16.4 ENVIRONMENTAL CONTROL W ϭ 0.41667VA D ϭ 60VA D (17) INCHES FEET 2.4WW V ϭϭ (18) AD60AD INCHES FEET where ⌬P ϭ pressure drop per 100 ft of pipe (psig/ 100 ft) W ϭ steam flow rate, lb/h ID ϭ actual inside diameter of pipe, in D ϭ average density of steam at system pressure, lb/ft 3 V ϭ velocity of steam in pipe, ft/min A INCHES ϭ actual cross-sectional area of pipe, in 2 A FEET ϭ actual cross-sectional area of pipe, ft 2 Condensate Piping Equations H Ϫ H SSS SCR FS ϭϫ100 (19) H LCR FS W ϭϫW (20) CR 100 where FS ϭ flash steam, % H SSS ϭ sensible heat at steam supply pressure, Btu/ lb H SCR ϭ sensible heat at condensate return pressure, Btu/lb H LCR ϭ latent heat at condensate return pressure, Btu/ lb W ϭ steam flow rate, lb/h W CR ϭ condensate flow based on percentage of flash steam created during condensing process, lb/h. Use this flow rate in steam equations above to determine condensate return pipe size. HVAC Efficiency Equations BTU OUTPUT EER COP ϭϭ (21) BTU INPUT 3.413 BTU OUTPUT EER ϭ (22) WATTS INPUT Turndown ratio ϭ maximum firing rateϺminimum firing rate (that is 5Ϻ1, 10Ϻ1, 25 Ϻ1) GROSS BTU OUTPUT OVERALL THERMAL EFF ϭ GROSS BTU INPUT ϫ 100% (23) BTU INPUT Ϫ BTU STACK LOSS COMBUSTION EFF ϭ BTU INPUT ϫ 100% (24) Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. HEATING, VENTILATING, AND AIR CONDITIONING HEATING, VENTILATING, AND AIR CONDITIONING 16.5 Overall thermal efficiency range 75%–90% Combustion efficiency range 85%–95% Equations for HVAC Equipment Room Ventilation For completely enclosed equipment rooms: 0.5 CFM ϭ 100 ϫ G (25) where CFM ϭ exhaust airflow rate required, ft 3 /min G ϭ mass of refrigerant of largest system, lb For partially enclosed equipment rooms: 0.5 FA ϭ G (26) where FA ϭ ventilation-free opening area, ft 2 G ϭ mass of refrigerant of largest system, lb Psychrometric Equations The following equations are from Carrier Corporation publications.* These equa- tions cover air mixing, cooling loads, sensible heat factor, bypass factor, temperature at the apparatus, supply air temperature, air quantity, and determination of air con- stants. Abbreviations and symbols for the equations are given below. Abbreviations adp apparatus dew point BF bypass factor (BF) (OALH) bypassed outdoor air latent heat (BF) (OASH) bypassed outdoor air sensible heat (BF) (OATH) bypassed outdoor air total heat Btu/h British thermal units per hour cfm, ft 3 /min cubic feet per minute db dry-bulb dp dew point ERLH effective room latent heat ERSH effective room sensible heat ERTH effective room total heat ESHF effective sensible heat factor ЊF degrees Fahrenheit fpm, ft/min feet per minute gpm, gal/min gallons per minute *Handbook of Air-Conditioning System Design, McGraw-Hill, New York, various dates. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. HEATING, VENTILATING, AND AIR CONDITIONING 16.6 ENVIRONMENTAL CONTROL gr/lb grains per pound GSHF grand sensible heat factor GTH grand total heat GTHS grand total heat supplement OALH outdoor air latent heat OASH outdoor air sensible heat OATH outdoor air total heat rh relative humidity RLH room latent heat RLHS room latent heat supplement RSH room sensible heat RSHF room sensible heat factor RSHS room sensible heat supplement RTH room total heat Sat Eff saturation efficiency of sprays SHF sensible heat factor TLH total latent heat TSH total sensible heat wb wet-bulb Symbols cfm ba bypassed air quantity around apparatus cfm da dehumidified air quantity cfm oa outdoor air quantity cfm ra return air quantity cfm sa supply air quantity h specific enthalpy h adp apparatus dew point enthalpy h cs effective surface temperature enthalpy h ea entering air enthalpy h la leaving air enthalpy h m mixture of outdoor and return air en- thalpy h oa outdoor air enthalpy hr m room air enthalpy h sa supply air enthalpy t temperature t adp apparatus dew point temperature t edb entering dry-bulb temperature t es effective surface temperature Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. HEATING, VENTILATING, AND AIR CONDITIONING HEATING, VENTILATING, AND AIR CONDITIONING 16.7 t ew entering water temperature t ewb entering wet-bulb temperature t ldb leaving dry-bulb temperature t lw leaving water temperature t lwb leaving wet-bulb temperature t m mixture of outdoor and return air dry- bulb temperature t oa outdoor air dry-bulb temperature t rm room dry-bulb temperature t sa supply air dry-bulb temperature W moisture content or specific humidity W adp apparatus dew point moisture content W ea entering air moisture content W es effective surface temperature moisture content W la leaving air moisture content W m mixture of outdoor and return air mois- ture content W oa outdoor air moisture content W rm room moisture content W sa supply air moisture content Air Mixing Equations (Outdoor and Return Air) cfm ϫ t ϩ cfm ϫ t oa oa ra rm t ϭ (27) m cfm sa (cfm ϫ h ) ϩ (cfm ϫ h ) oa oa ra rm h ϭ (28) m cfm sa (cfm ϫ W ) ϩ (cfm ϫ W ) oa oa ra rm W ϭ (29) m cfm sa Cooling Load Equations ERSH ϭ RSH ϩ (BF)(OASH) ϩ RSHS* (30) ERLH ϭ RLH ϩ (BF)(OALH) ϩ RLHS* (31) *RSHS, RLHS, and GTHS are supplementary loads due to duct heat gain, duct leakage loss, fan and pump horsepower gains, etc. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. HEATING, VENTILATING, AND AIR CONDITIONING 16.8 ENVIRONMENTAL CONTROL ERTH ϭ ERLH ϩ ERSH (32) TSH ϭ RSH ϩ OASH ϩ RSHS* (33) TLH ϭ RLH ϩ OALH ϩ RLHS* (34) GTH ϭ TSH ϩ TLH ϩ GTHS* (35) RSH ϭ 1.08† ϫ cfm ϫ (t Ϫ t ) (36) sa rm sa RLH ϭ 0.68† ϫ cfm ϫ (W Ϫ W ) (37) sa rm sa RTH ϭ 4.45† ϫ cfm ϫ (h Ϫ h ) (38) sa rm sa RTH ϭ RSH ϩ RLH (39) OASH ϭ 1.08 ϫ cfm (t Ϫ t ) (40) oa oa rm OALH ϭ 0.68 ϫ cfm (W Ϫ W ) (41) oa oa rm OATH ϭ 4.45 ϫ cfm (h Ϫ h ) (42) oa oa rm OATH ϭ OASH ϩ OALH (43) (BF)(OATH) ϭ (BF)(OASH) ϩ (BF)(OALH) (44) ERSH ϭ 1.08 ϫ cfm ‡ ϫ (t Ϫ t )(1 Ϫ BF) (45) da rm adp ERLH ϭ 0.68 ϫ cfm ‡ ϫ (W Ϫ W )(1 Ϫ BF) (46) da rm adp ERTH ϭ 4.45 ϫ cfm ‡ ϫ (h Ϫ h )(1 Ϫ BF) (47) da rm adp TSH ϭ 1.08 ϫ cfm ‡ ϫ (t Ϫ t )* (48) da edb ldb TLH ϭ 0.68 ϫ cfm ‡ ϫ (W Ϫ W )* (49) da ea la GTH ϭ 4.45 ϫ cfm ‡ ϫ (h Ϫ h )* (50) da ea la Sensible Heat Factor Equations RSH RSH RSHF ϭϭ (51) RSH ϩ RLH RTH ERSH ERSH ESHF ϭϭ (52) ERSH ϩ ERLH ERTH TSH TSH GSHF ϭϭ (53) TSH ϩ TLH GTH *RSHS, RLHS, and GTHS are supplementary loads due to duct heat gain, duct leakage loss, fan and pump horsepower gains, etc. †See below for the derivation of these air constants. ‡When no air is to be physically bypassed around the conditioning apparatus, cfm da ϭ cfm sa . Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. HEATING, VENTILATING, AND AIR CONDITIONING HEATING, VENTILATING, AND AIR CONDITIONING 16.9 Bypass Factor Equations t Ϫ ttϪ t ldb adp edb ldb BF ϭ 1 Ϫ BF ϭ (54) t Ϫ ttϪ t edb adp edb adp W Ϫ WWϪ W la adp ea la BF ϭ 1 Ϫ BF ϭ (55) W Ϫ WWϪ W ea adp ea adp h Ϫ hhϪ h la adp ea la BF ϭ 1 Ϫ BF ϭ (56) h Ϫ hhϪ h ea adp ea adp Temperature Equations at the Apparatus (cfm ϫ t ) ϩ (cfm ϫ t ) oa oa ra rm t * ϭ (57) edb cfm † sa t ϭ t ϩ BF(t Ϫ t ) (58) ldbadp edbadp Both t ewb and t lwb correspond to the calculated values of h ea and h la on the psychro- metric chart. (cfm ϫ h ) ϩ (cfm ϫ h ) oa o a ra rm h * ϭ (59) ea cfm † sa h ϭ h ϩ BF(h Ϫ h ) (60) la adp ea adp Temperature Equations for Supply Air RSH t ϭ t Ϫ (61) sa rm 1.08cfm † sa Air Quantity Equations ERSH cfm ϭ (62) da 1.08(1 Ϫ BF)(t Ϫ t ) rm adp ERLH cfm ϭ (63) da 0.68(1 Ϫ BF)(W Ϫ W ) rm adp ERTH cfm ϭ (64) da 4.45(1 Ϫ BF)(h Ϫ h ) rm ad p *When t m , W m , and h m are equal to the entering conditions at the cooling apparatus, they may be substituted for t edb , W ea , and h ea , respectively. †See footnote on page 16.9. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. HEATING, VENTILATING, AND AIR CONDITIONING 16.10 ENVIRONMENTAL CONTROL TSH cfm * ϭ (65) da 1.08(t Ϫ t ) edb ldb TLH cfm * ϭ (66) da 0.68(W Ϫ W ) ea la GTH cfm * ϭ (67) da 4.45(h Ϫ h ) ea la RSH cfm ϭ (68) sa 1.08(t Ϫ t ) rm sa RLH cfm ϭ (69) sa 0.68(W Ϫ W ) rm sa RTH cfm ϭ (70) sa 4.45(h Ϫ h ) rm s a cfm ϭ cfm Ϫ cfm (71) ba sa da Note: cfm da will be less than cfm sa only when air is physically bypassed around the conditioning apparatus. cfm ϭ cfm ϩ cfm (72) sa oa ra Derivation of Air Constants 60 1.08 ϭ 0.244 ϫ (73) 13.5 where 0.244 ϭ specific heat of moist air at 70ЊF db and 50% rh, Btu/(ЊF ⅐ lb DA) 60 ϭ min/h 13.5 ϭ specific volume of moist air at 70ЊF db and 50% rh 60 1076 0.68 ϭϫ 13.5 7000 where 60 ϭ min/h 13.5 ϭ specific volume of moist air at 70ЊF db and 50% rh 1076 ϭ average heat removal required to condense 1 db water vapor from the room air 7000 ϭ gr/lb 60 4.45 ϭ 13.5 *See footnote on page 16.9. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. HEATING, VENTILATING, AND AIR CONDITIONING