10.1. CONCEPT OF PSYCHROMETRY AND PSYCHROMETRICS

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1 10 Psychromerics 11. Concep of psychromery and psychromerics. 12. Definiions. 13. Psychromeric relaions. 14. Psychromeers. 15. Psychromeric chars. 16. Psychromeric processes : Mixing of air sreams Sensible heaing Sensible cooling Cooling and dehumidificaion Cooling and humidificaion Heaing and dehumidificaion Heaing and humidificaion Highlighs Objecie Type Quesions Theoreical Quesions Unsoled Examples. 11. CONCEPT OF PSYCHROMETRY AND PSYCHROMETRICS Air comprises of fixed gases principally, nirogen and oxygen wih an admixure of waer apour in arying amouns. In amospheric air waer is always presen and is relaie weigh aerages less han 1% of he weigh of amospheric air in emperae climaes and less han 3% by weigh under he mos exreme naural climaic condiions, i is neerheless one of mos imporan facors in human comfor and has significan effecs on many maerials. Is effec on human aciiies is in fac alogeher disproporionae o is relaie weighs. The ar of measuring he moisure conen of air is ermed psychromery. The science which inesigaes he hermal properies of mois air, considers he measuremen and conrol of he moisure conen of air, and sudies he effec of amospheric moisure on maerial and human comfor may properly be ermed psychromerics. 12. DEFINITIONS Some of he more imporan definiions are gien below : 1. Dry air. The inernaional join commiee on Psychromeric Daa has adoped he following exac composiion of air expressed in mole fracions (Volumeric) Oxygen 2095, Nirogen 7809, Argon 0093, Carbon dioxide Traces of rare gases are negleced. Molecular weigh of air for all air condiioning calculaions will be aken as Hence he gas consan, R air kj/kg K Dry air is neer found in pracice. Air always conains some moisure. Hence he common designaion air usually means mois air. The erm dry air is used o indicae he waer free conens of air haing any degree of moisure. 2. Sauraed air. Mois air is said o be sauraed when is condiion is such ha i can co-exis in naural equilibrium wih an associaed condensed moisure phase presening a fla surface o i. For a gien emperaure, a gien quaniy of air can be sauraed wih a fixed quaniy of moisure. A higher emperaures, i requires a larger quaniy of moisure o saurae i. A sauraion, apour pressure of moisure in air corresponds o he sauraion pressure gien in seam ables corresponding o he gien emperaure of air. 3. Dry-bulb emperaure (DBT). I is he emperaure of air as regisered by an ordinary hermomeer ( db ). 449

2 450 ENGINEERING THERMODYNAMICS 4. We-bulb emperaure (WBT). I is he emperaure regisered by a hermomeer when he bulb is coered by a weed wick and is exposed o a curren of rapidly moing air ( wb ). 5. Adiabaic sauraion emperaure. I is he emperaure a which he waer or ice can saurae air by eaporaing adiabaically ino i. I is numerically equialen o he measured we bulb emperaure (as correced, if necessary for radiaion and conducion) ( wb ). 6. We bulb depression. I is he difference beween dry-bulb and we bulb emperaures ( db wb ). 7. Dew poin emperaure (DPT). I is he emperaure o which air mus be cooled a consan pressure in order o cause condensaion of any of is waer apour. I is equal o seam able sauraion emperaure corresponding o he acual parial pressure of waer apour in he air ( dp ). 8. Dew poin depression. I is he difference beween he dry bulb and dew poin emperaures ( db dp ). 9. Specific humidiy (Humidiy raio). I is he raio of he mass of waer apour per uni mass of dry air in he mixure of apour and air, i is generally expressed as grams of waer per kg of dry air. For a gien baromeric pressure i is a funcion of dew poin emperaure alone. 1 Relaie humidiy (RH), (φ). I is he raio of he parial pressure of waer apour in he mixure o he sauraed parial pressure a he dry bulb emperaure, expressed as percenage. 11. Sensible hea. I is he hea ha changes he emperaure of a subsance when added o or absraced from i. 12. Laen hea. I is he hea ha does no affec he emperaure bu changes he sae of subsance when added o or absraced from i. 13. Enhalpy. I is he combinaion energy which represens he sum of inernal and flow energy in a seady flow process. I is deermined from an arbirary daum poin for he air mixure and is expressed as kj per kg of dry air (h). Noe. When air is sauraed DBT, WBT, DPT are equal. 13. PSYCHROMETRIC RELATIONS Pressure Dalon s law of parial pressure is employed o deermine he pressure of a mixure of gases. This law saes ha he oal pressure of a mixure of gases is equal o he sum of parial pressures which he componen gases would exer if each exised alone in he mixure olume a he mixure emperaure. Precise measuremens made during he las few years indicae ha his law as well as Boyle s and Charle s laws are only approximaely correc. Modern ables of amospheric air properies are based on he correc ersions. For calculaing parial pressure of waer apour in he air many equaions hae been proposed, probably Dr. Carrier s equaion is mos widely used. (s ) wb [ p ( ps ) wb ]( db wb ) wb where Parial pressure of waer apour, s Parial pressure of waer apour when air is fully sauraed, p Toal pressure of mois air, db Dry bulb emperaure (ºC), and wb We bulb emperaure (ºC)....(11)

3 PSYCHROMETRICS 451 Specific humidiy W : Specific humidiy Mass of waer apour Mass of dry air or W m m Also, a m a p a V R T and m V R T where p a Parial pressure of dry air, Parial pressure of waer apour, V Volume of mixure, R a Characerisic gas consan for dry air, and R Characerisic gas consan for waer apour. From equaions (12) and (13) a...(12)...(13) W V R T R p a a R T pa V R pa Bu R a R 0 F kj/kg K in SI unis M a HG R R 0 F kj/kg K in SI unis M 18 where R 0 Uniersal gas consan, M a Molecular weigh of air, and M Molecular weigh of waer apour. W p 622 pa p p p i.e., W (14) p p The masses of air and waer apour in erms of specific olumes are gien by expression as HG I KJ I K J m a V a and m V where a Specific olume of dry air, and Specific olume of waer apour. Degree of sauraion (µ) : W a Degree of sauraion Mass of waer apour associaed wih uni mass of dry air Mass of waer apour associaed wih sauraed uni mass of dry sauraed air...(15)

4 452 ENGINEERING THERMODYNAMICS i.e., µ W W s...(16) where, W s Specific humidiy of air when air is fully sauraed F p I 622 HG p ( ) pkj p p ps µ F ps I ps( p p ) 622 p p where p p s HG L F1 HG F1 NM HG p p s p p skj IO KJ I KJ QP...(17) s Parial pressure of waer apour when air is fully sauraed (s can be calculaed from seam ables corresponding o he dry bulb emperaure of he air). Relaie humidiy (RH), φ : or Relaie humidiy, φ Mass of waer apour in a gien olume Mass of waer apour in he same olume if sauraed a he same emp. p T m R T p m p T s s ps R T Insering he alue of equaion (18) ino equaion (17), we ge L M ps 1 p µ φ φ p M P 1 p N O P Q L NM p 1 p φp 1 p s s O P Q φ P F HG p p p φ p φ(p s ) µ(p φ s ) φ(p s + µs ) µp µ p µ φ p p + µ p p s s s 1 ( 1 µ ) p Since s << p φ ~ µ Insering he alue of he from equaion (14) ino equaion (18), we ge s s I KJ...(18)...(19) φ p a W W p a...(110) ps ps Noe 1. Relaie humidiy as compared o specific humidiy plays a ial role in comfor air-condiioning and indusrial air-condiioning. Relaie humidiy signifies he absorpion capaciy of air. If iniial relaie humidiy of air is less i will absorb more moisure. 2. W, µ and φ canno be conenienly measured as hey require measuremen of and s. The alue of can be obained from he measuremen of he we bulb emperaure and he alue of s can be calculaed from seam ables corresponding o gien air emperaure.

5 PSYCHROMETRICS 453 Enhalpy of mois air I is he sum of enhalpy of dry air and enhalpy of waer apour associaed wih dry air. I is expressed in kj/kg of dry air h h air + W. h apour c p db + W. h apour where h Enhalpy of mixure/kg of dry air, h air Enhalpy of 1 kg of dry air, h apour Enhalpy of 1 kg of apour obained from seam ables, W Specific humidiy in kg/kg of dry air, and c p Specific hea of dry air normally assumed as kj/kg K. Also h apour h g + c ps ( db dp ) where h g Enhalpy of sauraed seam a dew poin emperaure, and c ps 1.88 kj/kg K. h c p db + W[h g + c ps ( db dp )]...(111) (c p + c ps W) db + W(h g c ps dp ) c pm db + W(h g c ps dp )...[111(a)] where c pm (c p + c ps W) is he specific hea of humid air or humid specific hea. The alue of c pm is aken as kj/kg dry air per K. I is he hea capaciy of (1 + W) kg of moisure per kg of dry air. h apour ~ h g a dry bulb emperaure. So, h c p db + W h g....(112) Howeer, a beer approximaion is gien by he following relaionship : h apour db kj/kg of waer apour...[112 (a)] where db is dry bulb emperaure in ºC, and he daum sae is liquid waer a 0ºC. h db + W( db ) kj/kg dry air....[112 (b)] Adiabaic sauraion process In an insulaed chamber when unsauraed air flows oer a long shee of waer (Fig. 11), he waer eaporaes, and he specific humidiy of he air increases. As he eaporaion akes place Insulaed chamber 1 Unsauraed air 1 kg of dry air a db and + W kg of 1 db2 1 waer apour a and h db2 f 1 kg of dry air a db + W kg of 2 2S Waer h f (a db 2 ) waer apour a h Make-up waer 2 Sauraed air 2S a db2 Fig. 11. Adiabaic sauraion process. boh he air and waer are cooled. The process coninues unil he energy ransferred from he air o he waer is equal o he energy required o apourise he waer. When his poin is reached,

6 454 ENGINEERING THERMODYNAMICS hermal equilibrium exiss wih respec o waer, air and waer apour, and consequenly he air is sauraed. The equilibrium emperaure is called he adiabaic sauraion emperaure or he hermodynamic we bulb emperaure. The make-up waer is inroduced a his emperaure o make he waer leel consan. The adiabaic cooling process is shown in Fig. 12 for he apour in he air-apour mixure. Alhough he oal pressure of he mixure is consan, he parial pressure of he apour increases, and in he sauraed sae corresponds o he adiabaic sauraion emperaure. The apour is iniially a DBT db1 and is cooled adiabaically o DBT db2 which is equal o he adiabaic sauraion wb2. The adiabaic sauraion emperaure and we bulb emperaures are aken o be equal for all pracical purposes. The we bulb emperaure lies beween he dry bulb emperaure and dew poin emperaure. Fig. 12. Adiabaic cooling process. Le us now apply he firs law o he enire process. Considering he process o be seady sae seady flow, neglecing changes in kineic and poenial energies, we hae h 1 + (W 2s W 1 )h h...(113) f 2 2 The quaniies W 2s, h 2s and h f2 are he funcions of emperaure db2. The erm (W 2s W 1 )h f2 is quie small and if his erm is negleced, i can be seen ha he enhalpy remains consan in adiabaic sauraion. Equaion (113) may be rewrien as h 1 Wh 1 f2 h 2s W h s 2s f 2 The inle erm can be generalized and he expression can be wrien as follows : Σ h 2s W 2s h f h 2 1 Wh 1 f 2 h x W x h f2...(114) This means ha sigma funcion (Σ) as defined by he equaion, is consan for any we bulb emperaure. Also h 1 h 2s (W 2s W 1 ) h f2...(115)

7 PSYCHROMETRICS 455 Equaion (115) indicaes ha he enhalpy of an air-waer apour mixure is equal o he enhalpy of sauraed air a he same we bulb emperaure, less small correcion erm (W 2s W 1 ) h f2. This correcion erm is called enhalpy deiaion. h 1 h air (1) + W 1 h apour (1)...(116) h 2s h air (2) + W 2s h apour (2)...(117) or h air (1) + W 1 h g1 + (W 2s W 1 ) h f2 h air (2) + W 2s h g2 c p db1 + W 1 h g1 + (W 2s W 1 ) h f2 c p db2 + W 2s h g2...(118) Afer arranging, we ge cp( db db ) + W s( hg hf ) W 1 h h g1 f2 or W 1 c p( db db ) + W s h g2...[118(a)] hg h 1 f2 Noe. The we bulb emperaure is no a propery of mois air as i is influenced by hea and mass ransfer raes. Thus in psychromeric equaions and psychromeric chars where he we bulb emperaure appears, i is always he hermodynamic we bulb emperaure ha is considered. 14. PSYCHROMETERS A psychromeer is a deice which is used for measuring dry bulb and we bulb emperaures simulaneously. The psychromeers may be classified as follows : 1. Laboraory psychromeer 2. Sling psychromeer 3. Aspiraing psychromeer 4. Coninuous recording psychromeer. The descripion of a sling psychromeer is gien below : Refer Fig. 13. The sling psychromeer consiss of wo hermomeers mouned on a base plae. The one wih he sock is we-bulb hermomeer ; he oher is dry-bulb. The we bulb exiss Sock We bulb Dry bulb Insrumen is roaed abou 2 o 3 imes per second unil reading aains consan alues. Handle is firmly grasped and hermomeers are swung. Fig. 13. Sling psychromeer. below he dry-bulb. This is done purposely so ha sock can be dipped in waer wihou weing he dry-bulb. The handle of he frame helps for roaing he psychromeer o produce necessary air moion. As he psychromeer is roaed i proides necessary air elociy oer he hermomeer. Fas moemen of air pas he sock is necessary o bring he air a emperaure db always in immediae conac wih he we sock. The emperaure spread beween dry bulb and we bulb readings depends upon he amoun of moisure in he air. Dry air, or air ha has low moisure

8 456 ENGINEERING THERMODYNAMICS conen has a low we bulb emperaure ; humid air ha has a high moisure conen, has a high we-bulb emperaure. When dry and we bulb emperaures are known he oher psychromeric properies like relaie humidiy, dew poin emperaure, degree of sauraion, humidiy raio, and olume of airapour mixure per kg of dry air are deermined by calculaions. 15. PSYCHROMETRIC CHARTS The psychromeric chars are prepared o represen graphically all he necessary mois air properies used for air condiioning calculaions. The alues are based on acual measuremens erified for hermodynamic consisency. For psychromeric chars he mos conenien co-ordinaes are dry bulb emperaure of air apour mixure as he abcissa and moisure conen (kg/kg of dry air) or waer apour pressure as he ordinae. Depending upon wheher he humidiy conens is abcissa or ordinae wih emperaure co-ordinae, he chars are generally classified as Mollier char and Carrier char. Carrier char haing db as he abcissa and W as he ordinae finds a wide applicaion. The char is consruced as under : 1. The dry bulb emperaure (ºC) of uni mass of dry air for differen humidiy conens or humidiy raios are indicaed by erical lines drawn parallel o he ordinae. 2. The mass of waer apour in kg (or grams) per kg of dry air is drawn parallel o he abcissa for differen alues of dry bulb emperaure. I is he major erical scale of he char. 3. Pressure of waer apour in mm of mercury is shown in he scale a lef and is he absolue pressure of seam. 4. Dew poin emperaures are emperaures corresponding o he boiling poins of waer a low pressures of waer apour and are shown in he scale on he upper cured line. The dew poins for differen low pressures are read on diagonal co-ordinaes. Vapour pressure in mm of Hg Enhalpy of sauraion We Bulb Dew poin Volume We bulb, dew poin or sauraion emp. Relaie humidiy Alignmen circle Moisure conen Sensible hea facor Kg of moisure per kg of dry air Dry bulb emp., º C Fig. 14. Skeleon psychromeric char.

9 PSYCHROMETRICS Consan relaie humidiy lines in per cen are indicaed by marking off erical disances beween he sauraion line or he upper cured line and he base of he char. The relaie humidiy cure depics quaniy (kg) of moisure acually presen in he air as a percenage of he oal amoun possible a arious dry bulb emperaures and masses of apour. 6. Enhalpy or oal hea a sauraion emperaure in kj/kg of dry air is shown by a diagonal sysem of co-ordinaes. The scale on he diagonal line is separae from he body of he char and is indicaed aboe he sauraion line. 7. We bulb emperaures are shown on he diagonal co-ordinaes coinciding wih hea coordinaes. The scale of we bulb emperaures is shown on he sauraion cure. The diagonals run downwards o he righ a an angle of 30º o he horizonal Enhalpy (h) k cal/ kg dry air % 80% 70% Sauraion emp.c % % % 91 30% 20% 92 10% Relaie humidiy Volume m /kg dry Air Humidiy raio (W) kg/kg dry air Dry bulb emperaure º C Enhalpy (h) k cal/kg dry air Fig. 15. Carrier char. 8. The olume of air apour mixure per kg of dry air (specific olume) is also indicaed by a se of diagonal co-ordinaes bu a an angle of 60º wih he horizonal. The oher properies of air apour mixures can be deermined by using formulae (already discussed). In relaion o he psychromeric char, hese erms can quickly indicae many hings abou he condiion of air, for example : 1. If dry bulb and we bulb emperaures are known, he relaie humidiy can be read from he char. 2. If he dry bulb and relaie humidiy are known, he we bulb emperaure can be deermined. 3. If we bulb emperaure and relaie humidiy are known, he dry bulb emperaure can be found.

10 458 ENGINEERING THERMODYNAMICS 4. If we bulb and dry bulb emperaures are known, he dew poin can be found. 5. If we bulb and relaie humidiy are known, dew poin can be read from he char. 6. If dry-bulb and relaie humidiy are known, dew poin can be found. 7. The quaniy (kg) of moisure in air can be deermined from any of he following combinaions : (i) Dry bulb emperaure and relaie humidiy ; (ii) Dry bulb emperaure and dew poin ; (iii) We bulb emperaure and relaie humidiy ; (i) We bulb emperaure and dew poin emperaure ; () Dry bulb emperaure and we bulb emperaure ; and (i) Dew poin emperaure alone. Figs. 14 and 15 show he skeleon psychromeric char and lines on carrier char respeciely. 16. PSYCHROMETRIC PROCESSES In order o condiion air o he condiions of human comfor or of he opimum conrol of an indusrial process required, cerain processes are o be carried ou on he ouside air aailable. The processes affecing he psychromeric properies of air are called psychromeric processes. These processes inole mixing of air sreams, heaing, cooling, humidifying, dehumidifying, adiabaic sauraion and mosly he combinaions of hese. The imporan psychromeric processes are enumeraed and explained in he following ex : 1. Mixing of air sreams 2. Sensible heaing 3. Sensible cooling 4. Cooling and dehumidificaion 5. Cooling and humidificaion 6. Heaing and dehumidificaion 7. Heaing and humidificaion Mixing of Air Sreams Refer Figs. 16 and 17. Mixing of seeral air sreams is he process which is ery frequenly used in air condiioning. This mixing normally akes place wihou he addiion or rejecion of Air m, W, h m, W, h m 3, W 3, h3 Air Air Fig. 16. Mixing of air sreams. eiher hea or moisure, i.e., adiabaically and a consan oal moisure conen. Thus we can wrie he following equaions : m 1 + m 2 m 3...(119) m 1 W 1 + m 2 W 2 m 3 W 3...(120) m 1 h 1 + m 2 h 2 m 3 h 3...(121)

11 PSYCHROMETRICS 459 h 3 h 1 h h W W h 2 h h W W W 1 W 2 W 3 W m 1 m 2 W W 3 2 W W 1 3 h h 3 2 h h 1 3 db2 D B T db3 db1 or where Fig. 17 Rearranging of las wo equaions gies he following : m 1 (W 1 W 3 ) m 2 (W 3 W 2 ) m 1 (h 1 h 3 ) m 2 (h 3 h 2 ) m1 W 3 W 2 h 3 h 2 m2 W1 W3 h1 h3 m M ass of dry air O W Specific humidiy a paricular sae poins. h Enhalpy P Q On he psychromeric char, he specific humidiy and enhalpy scales are linear, ignoring enhalpy deiaions. Therefore, he final sae 3 lies on a sraigh line connecing he iniial saes of he wo sreams before mixing, and he final sae 3 diides his line ino wo pars ha are in he same raio as were he wo masses of air before mixing. If he air quaniies are known in olume insead of mass unis, i is generally sufficienly accurae o unis of m 3 or m 3 /min. in he mixing equaions. The inaccuracy inroduced is due o he difference in specific olume a wo iniial saes. This difference in densiies is small for mos of he comfor air condiioning problems Sensible Heaing When air passes oer a dry surface which is a a emperaure greaer han is (air) dry bulb emperaure, i undergoes sensible heaing. Thus he heaing can be achieed by passing he air oer heaing coil like elecric resisance heaing coils or seam coils. During such a process, he specific humidiy remains consan bu he dry bulb emperaure rises and approaches ha of he surface. The exen o which i approaches he mean effecie surface emperaure of he coil is conenienly expressed in erms of he equialen by-pass facor. The by-pass facor (BF) for he process is defined as he raio of he difference beween he mean surface emperaure of he coil and leaing air emperaure o he difference beween he mean surface emperaure and he enering air emperaure. Thus on Fig. 18, air a emperaure db1, passes oer a heaing coil wih an aerage surface emperaure db3 and leaes a emperaure db2.

12 460 ENGINEERING THERMODYNAMICS The by-pass facor is expressed as follows : BF db 3 db2 db3 db1...(122) 3 h 2 h 3 h Air in Air ou Heaing coil W db1 db2 db3 D B T Fig. 18. Sensible heaing. Fig. 19 Or in erms of lenghs on he char (Fig. 19) i is lengh 2-3. The alue of he by-pass lengh 1-3 facor is a funcion of coil design and elociy. The hea added o he air can be obained direcly from he enering and leaing enhalpies (h 2 h 1 ) or i can be obained from he humid specific hea muliplied by he emperaure difference ( db2 db1 ). In a complee air condiioning sysem he preheaing and reheaing of air are among he familar examples of sensible heaing. Noe. By-pass facor can be considered o represen he fracion of air which does no come ino conac wih coil surface Sensible Cooling Refer Fig. 11 Air undergoes sensible cooling wheneer i passes oer a surface ha is a a emperaure less han he dry bulb emperaure of he air bu greaer han he dew poin emperaure. Thus sensible cooling can be achieed by passing he air oer cooling coil like eaporaing coil of he refrigeraion cycle or secondary brine coil. During he process, he specific humidiy remains consan and dry bulb emperaure decreases, approaching he mean effecie surface emperaure. On a psychromeric char he process will appear as a horizonal line 1 2 (Fig. 111), where poin 3 represens he effecie surface emperaure. For his process : By-pass facor BF db db db 2 3 db (123) The hea remoed from air can be obained from he enhalpy difference (h 1 h 2 ) or from humid specific hea muliplied by he emperaure difference ( ). db db 1 2

13 PSYCHROMETRICS 461 h 1 3 h 3 h Air in Air ou W Cooling coil db2 db3 DBT db1 Fig. 11 Sensible cooling. Fig Cooling and Dehumidificaion Refer Fig Wheneer air is made o pass oer a surface or hrough a spray of waer ha is a a emperaure less han he dew poin emperaure of he air, condensaion of some of he waer apour in air will occur simulaneously wih he sensible cooling process. Any air ha h 1 h 1 h 4 1 db3 < dp 4 h 3 ADP w 4 1 W db Cooling coil db3 db4 db1 D B T Fig Cooling and dehumidificaion. comes ino sufficien conac wih he cooling surface will be reduced in emperaure o he mean surface emperaure along a pah such as in Fig. 112, wih condensaion and herefore dehumidificaion occurring beween poins 2 and 3. The air ha does no conac he surface will be finally cooled by mixing wih he porion ha did, and he final sae poin will somewhere on he sraigh line connecing poins 1 and 3. The acual pah of air during he pah will no be sraigh line shown bu will be somehing similarly o he cured dashed line 1 4. I will resul

14 462 ENGINEERING THERMODYNAMICS from a coninuous mixing of air which is connecing a paricular par of he coil and air which is by passing i. I is conenien, howeer o analyse he problem wih he sraigh line shown, and o assume ha he final air sae resuls from he mixing of air ha has compleely by passed he coil wih air ha has been cooled o he mean effecie surface emperaure. If here is enough conac beween air and surface for all he air o come o he mean surface emperaure, he process is one of zero by pass. In any pracical sysem, complee sauraion is no obained and final sae will be a poin such as 4 in Fig. 112 wih an equialen by pass facor equal o lengh 3-4. For processes inoling condensaion, he effecie surface emperaure, e.g. db3 in Fig. 112 is called lengh 3-1 apparaus dew poin (ADP). The final sae poin of air passing hrough a cooling and dehumidifying apparaus is in effec a mixure condiion ha resuls from mixing he fracion of he air, which is equal o he equialen by-pass facor (BF) and is a iniial sae poin and he remaining fracion which is equal o one minus by pass facor (1 BF) and is sauraed a he apparaus dew poin (ADP). Toal hea remoed from he air is gien by Q h 1 h 4 (h 1 h 1 ) + (h 1 h 4 ) Q L + Q S where, W L Laen hea remoed (h 1 h 1 ), and Q S Sensible hea remoed (h 1 h 4 ) The raio Q S is called sensible hea facor (SHF) Or QL sensible hea raio (SHR) Q SHF S...(124) QL + QS The raio fixes he slope of he line 1 4 on he psychromeric char. Sensible hea facor slope lines are gien on he psychromeric char. If he iniial condiion and SHF are known for he gien process, hen he process line can be drawn hrough he gien iniial condiion a a slope gien by SHF on he psychromeric char. The capaciy of he cooling coil in onnes of refrigeraion is gien by, Capaciy in TR m a ( h 1 h 4 ) 60,...(125) where m a mass of air, kg/min and h enhalpy in kj/kg of air Cooling and Humidificaion If unsauraed air is passed hrough a spray of coninuously recirculaed waer, he specific humidiy will increase while he dry bulb emperaure decreases. This is he process of adiabaic sauraion or eaporaie cooling. This process is one of consan adiabaic-sauraion emperaure and for all pracical purposes, one of consan we bulb emperaure. The process is illusraed as pah 1-2 on Fig. 113, wih we bulb emperaure of air being ha of poin 3, which is also equilibrium emperaure of he recirculaed waer if here is sufficien conac beween air and spray, he air will leae a a condiion ery close o ha of poin 3. The concep of equialen by pass can be applied o his process bu anoher erm is more used o describe he performance of a humidifying apparaus. I is he sauraing or humidifying efficiency which is defined as he

15 PSYCHROMETRICS 463 h W D B T db3 db2 db1 Fig Cooling and humidificaion. raio of dry-bulb emperaure decrease o he enering we bulb depression usually expressed as percenage. Thus, from Fig. 113, he sauraing efficiency is : F db db I 1 2 % η sa (126) HG db 1 db3kj As a fracion, i is equal o one minus he by pass facor for he process. This adiabaic process, for all pracical purposes, is line of consan enhalpy. The moisure added can be obained from he increase in specific humidiy Heaing and Dehumidificaion If air is passed oer a solid absorben surface or hrough a liquid absorben spray simulaneous heaing and dehumidificaion is accompanied. In eiher case he dehumidificaion resuls from adsorben or absorben haing a lower waer apour pressure han air. Moisure is condensed ou of he air, and consequenly he laen hea of condensaion is liberaed, causing sensible heaing of air. If hese were he only energies inoled, he process would be he inerse of he adiabaic sauraion process. There is, howeer, an addiional energy absorbed or liberaed by he acie maerial, ermed he hea of adsorpion or absorpion. For he solid adsorbens used commercially, such as silica gel or aciaed alumina, and for he more common liquid absorbens, such as soluions of organic sals or inorganic compounds like ehylene, glycol, hea is inoled and resuls in addiional sensible heaing. Thus he pah lies aboe a consan we bulb line on he psychromeric char such as pah 1-2 in Fig Heaing and Humidificaion If air is passed hrough a humidifier which has heaed waer sprays insead of simply recirculaed spray, he air is humidified and may be heaed, cooled or unchanged in emperaure. In such a process he air increases in specific humidiy and he enhalpy, and he dry bulb emperaure will increase or decrease according o he iniial emperaure of he air and ha of he spray. If sufficien waer is supplied relaie o he mass flow of air, he air will approach sauraion a waer emperaure. Examples of such processes are shown on Fig. 115.

16 464 ENGINEERING THERMODYNAMICS h 1 h W W db1 D B T db2 D B T db1 Fig Heaing and dehumidificaion. Fig Heaing and humidificaion. Process 1-2 : I denoes he cases in which he emperaure of he heaed spray waer is less han he air DBT. Process 1-3 : I denoes he cases in which he emperaure is equal o he air DBT. Process 1-4 : I denoes he cases in which a spray emperaure is greaer han air DBT. As in he case of adiabaic sauraion, he degree o which he process approaches sauraion can be expressed in erms of he by-pass facor or a sauraing efficiency. If he waer rae relaie o he air quaniy is smaller, he waer emperaure will drop significanly during he process. The resulan process will be a cured line such as he dashed 1-4 where 4 represens he leaing waer emperaure. Noe. I is possible o accomplish heaing and humidificaion by eaporaion from an open pan of heaed waer, or by direc injecion of heaed waer or seam. The laer is more common. The process line for i is of lile alue because he process is essenially an insananeous mixing of seam and he air. The final sae poin of he air can be found, howeer by making a humidiy and enhalpy balance for he process. The soluion of such a problem usually inoles cu-and-ry procedure. Example 11. The amospheric condiions are ; 20 C and specific humidiy of 0095 kg/kg of dry air. Calculae he following : (i) Parial pressure of apour (ii) Relaie humidiy (iii) Dew poin emperaure. Soluion. Dry bulb emperaure, db 20ºC Specific humidiy, W 0095 kg/kg of dry air (i) Parial pressure of apour, : The specific humidiy is gien by W 622 p p p p p 0095( ) 622

17 PSYCHROMETRICS bar. (Ans.) (ii) Relaie humidiy φ : Corresponding o 20ºC, from seam ables, s 0234 bar Relaie humidiy, φ or 65%. (Ans.) ps 0234 (iii) Dew poin emperaure, dp : The dew poin emperaure is he sauraion emperaure of waer apour a a pressure of bar, dp [from seam ables by inerpolaion] ( 14 13) 13 + [ ] ( ) C. (Ans.) Example 12. The air supplied o a room of a building in winer is o be a 17 C and hae a relaie humidiy of 60%. If he baromeric pressure is bar, find : (i) The specific humidiy ; (ii) The dew poin under hese condiions. Soluion. Dry bulb emperaure, db 17ºC Relaie humidiy, φ 60% Baromeric or oal pressure, p bar Specific humidiy, W : Corresponding o 17ºC, from seam ables, s 0194 bar Also, φ p p s i.e., bar. 622 p Specific humidiy, W p p kg/kg of dry air. (Ans.) Dew poin emperaure, dp : If he air is cooled a consan pressure he apour will begin o condense a he sauraion emperaure corresponding o bar. By inerpolaion from seam ables, he dew poin emperaure, dp is hen dp 9 + (10 9) 9.18 C. (Ans.) Example kg of waer apour per kg of amospheric air is remoed and emperaure of air afer remoing he waer apour becomes 20 C. Deermine : (i) Relaie humidiy (ii) Dew poin emperaure. Assume ha condiion of amospheric air is 30 C and 55% R.H. and pressure is bar.

18 466 ENGINEERING THERMODYNAMICS Soluion. Corresponding o 30ºC, from seam ables, s 0425 bar Relaie humidiy (R.H.), φ ps i.e., bar. Also he specific humidiy, 622 p W kg/kg of dry air. p p The specific humidiy afer remoing 004 kg of waer apour becomes, kg/kg of dry air and he emperaure db is gien as 20ºC. The parial pressure of waer apour,, a his condiion can be calculaed as follows : 622 p W p p 622 p p or, ( ) 622 or, bar Corresponding o 20ºC, from seam ables, s 0234 bar. (i) Relaie humidiy, φ or 73%. (Ans.) ps 0234 (ii) Dew poin emperaure, dp : Corresponding o 0171 bar, from seam ables, dp 15 C. (Ans.) Example 14. The sling psychromeer in a laboraory es recorded he following readings : Dry bulb emperaure 35 C We bulb emperaure 25 C. Calculae he following : (i) Specific humidiy (ii) Relaie humidiy (iii) Vapour densiy in air (i) Dew poin emperaure () Enhalpy of mixure per kg of dry air Take amospheric pressure bar. Soluion. For finding he parial pressure of apour, using he equaion : (s ) wb [ p ( ps ) wb ]( db wb ) wb Corresponding o 25ºC (from seam ables), (s ) wb 0317 bar Subsiuing he alues in he aboe equaion, we ge [ ]( 35 25) bar

19 PSYCHROMETRICS 467 (i) Specific humidiy, 622 p W kg/kg of dry air. (Ans.) p p ( ) (ii) Relaie humidiy, φ ps 0563 [s 0563 bar corresponding o 35ºC, from seam ables] 447 or 44.7%. (Ans.) (iii) Vapour densiy : From characerisic gas equaion V m R T L N M m V where ρ ρ ρ R T ρ R T Uniersal gas consan apour densiy, R Molecular weigh of H O 5 ( ) kg/m (Ans.) (i) Dew poin emperaure, dp : Corresponding o 0252 bar, from seam ables (by inerpolaion), dp 21 + (22 21) ( ) 21.2 C. (Ans.) ( ) () Enhalpy of mixure per kg of dry air, h : h c p db + Wh apour [h g ( db dp )] [ ( )] (where h g kj/kg corresponding o 35ºC db ) kj/kg of dry air. (Ans.) Example 15. Adiabaic mixing : One kg of air a 35 C DBT and 60% R.H. is mixed wih 2 kg of air a 20 C DBT and 13 C dew poin emperaure. Calculae he specific humidiy of he mixure. Soluion. For he air a 35 C DBT and 60% R.H. : Corresponding o 35ºC, from seam ables, s 0563 bar Relaie humidiy, φ ps φ s bar 622 p W 0214 kg/kg of dry air p p Corresponding o 0338 bar, from seam ables, dp 26 + (27 26) ( ) 26.1ºC ( ) O Q P

20 468 ENGINEERING THERMODYNAMICS Enhalpy, h c p db + Wh apour db + W [h g ( db dp )] [ ( )] 943 kj/kg of dry air. For he air a 20 C DBT and 13 C dew poin emperaure : is he apour pressure corresponding o he sauraion pressure of seam a 13ºC bar 622 p W kg/kg of dry air p p Enhalpy, h c p db + Wh apour [h g ( db dp )] [ (20 13)] kj/kg of dry air Now enhalpy per kg of mois air 1 L O kj/kg of mois air 3 NM QP Mass of apour/kg of mois air 1 L O kg/kg of mois air 3 NM QP Specific humidiy of mixure kg/kg of dry air. (Ans.) Example 16. Sensible heaing : 90 m 3 of air per minue a 20 C and 75% R.H. is heaed unil is emperaure becomes 30 C. Calculae : (i) R.H. of he heaed air. (ii) Hea added o air per minue. Soluion. (i) For air a 20 C and 75% R.H. : s 0234 bar (from seam ables, a 20ºC) φ s bar dp 15 + (16 15) ( ) ~ 15.5ºC ( ) 622 p W kg/kg of dry air p p Enhalpy, h 1 c p db + Wh apour [h g ( db dp )] [ ( )] kj/kg of dry air (i) Relaie humidiy of heaed air : For air a 30 C DBT : Since he sauraion pressure of waer apour a 30ºC is higher han he sauraion pressure of waer apour a 20ºC so i is sensible heaing, where is same afer heaing. Relaie humidiy, φ or 41.2% ps 0425 (s 0425 bar, corresponding o 30ºC) i.e., Relaie humidiy of heaed air 41.2%. (Ans.)

21 PSYCHROMETRICS 469 (ii) Hea added o air per minue : Enhalpy, h 2 c p db + Wh apour [h g ( db dp )] [ ( )] kj/kg of dry air Mass of dry air in 90 m 3 of air supplied m a pv ( p p) V RT RT 5 ( ) kg/min. 287 ( ) Amoun of hea added per minue (h 2 h 1 ) ( ) ~ 1114 kj. (Ans.) Example 17. Sensible cooling : 40 m 3 of air a 35 C DBT and 50% R.H. is cooled o 25 C DBT mainaining is specific humidiy consan. Deermine : (i) Relaie humidiy (R.H.) of cooled air ; (ii) Hea remoed from air. Soluion. For air a 35 C DBT and 50% R.H. : s 0563 bar (A 35ºC, from seam ables) φ p p s φ s bar 622 p W 1 p p kg/kg of dry air h 1 c p db1 + W 1 [h g ( db1 dp1 ] dp1 ~ 23ºC (corresponding o bar) h [ (35 23)] 898 kj/kg of dry air For air a 25 C DBT : (i) R.H. of cooled air : Since he specific humidiy remains consan he apour pressure in he air remains consan. φ ps or 88.8% i.e., Relaie humidiy of he cooled air 88.8%. (Ans.) (ii) Hea remoed from air : h 2 c p db2 + W 2 [h g ( db2 dp2 )] [ (25 23)] 727 kj/kg of dry air. To find mass of dry air (m a ), using he relaion : LQ W1 W kg/kg of dry air O p a a m a R a T a NM dp dp 23 Csince p doesnochange 2 1 QP m a p 5 a a ( ) RT a a 287 ( ) kg Hea remoed from 40 m 3 of air m a (h 1 h 2 ) ( ) kj. (Ans.)

22 470 ENGINEERING THERMODYNAMICS Example 18. Cooling and dehumidificaion : 120 m 3 of air per minue a 35 C DBT and 50% relaie humidiy is cooled o 20 C DBT by passing hrough a cooling coil. Deermine he following : (i) Relaie humidiy of ou coming air and is we bulb emperaure. (ii) Capaciy of cooling coil in onnes of refrigeraion. (iii) Amoun of waer apour remoed per hour. Soluion. For he air a 35 C DBT and 50% R.H. : s 0563 bar (A 35ºC, from seam ables) φ s bar. W p kg/kg of dry air. p p h 1 c p db1 + W 1 [h g ( db1 dp1 )] dp1 23ºC (Corresponding o bar). h [ (35 23)] 898 kj/kg of dry dir. For he air a 20 C. As he sauraion apour pressure a 20ºC is 0234 bar, less han he apour pressure bar a 35ºC, so ha condensaion akes place and air will be sauraed a 20 C. (i) Relaie humidiy of exi air is 100 per cen. (Ans.) Since he air is sauraed, we bulb emperaure is equal o dry bulb emperaure 20 C. (Ans.) s 0234 bar. 622 p W kg/kg of dry air p p ( ) h 2 c p db2 + W 2 [h g ( db2 dp2 )] [ (20 20)] [Q When air is sauraed db dp ] kj/kg of dry air The weigh of waer apour remoed per kg of dry air kg/kg of dry air Hea remoed per kg of dry air h 1 h kj/kg of dry air Mass of dry air passing per minue m a pv 5 a a ( ) RT a a 287 ( ) kg/min (ii) Capaciy of he cooling coil in onnes of refrigeraion ma h h 1 2 ) TR. (Ans.) (iii) Amoun of waer remoed per hour m a (W 1 W 2 ) ( ) kg/h. (Ans.)

23 PSYCHROMETRICS 471 Example 19. Adiabaic humidificaion : 150 m 3 of air per minue is passed hrough he adiabaic humidifier. The condiion of air a inle is 35 C DBT and 20 per cen relaie humidiy and he oule condiion is 20 C DBT and 15 C WBT. Deermine he following : (i) Dew poin emperaure (ii) Relaie humidiy of he exi air (iii) Amoun of waer apour added o he air per minue. Soluion. For air a 35 C DBT and 20% relaie humidiy. s 0563 bar (A 35ºC from seam ables) φ s bar 622 p W kg/kg of dry air p p (i) The dew poin emperaure of air which is he sauraion emperaure of seam corresponding o he pressure bar is 8 + (9 8) ( ) ( ) 8.7ºC i.e., Dew poin emperaure 8.7 C. (Ans.) (ii) Relaie humidiy of he exi air : For air a 20ºC DBT and 15ºC WBT. (s ) wb [ p ( ps ) wb ]( db wb ) wb [ ]( 20 15) bar p W kg/kg of dry air p p ( ) p Relaie humidiy or 58.5%. (Ans.) ps 0234 (Q s 0234 bar, corresponding o 20ºC, from seam ables) The dew poin emperaure of air which is he sauraion emperaure of seam corresponding o 0137 bar is 11 C (from seam ables). (Ans.) The amoun of waer apour per kg of dry air W 2 W kg The mass of dry air in 150 m 3 of mixure m a pv 5 a a ( ) kg RT a a 287 ( ) (iii) The amoun of waer apour added o air per minue m a (W 2 W 1 ) kg/min. (Ans.) Example 11 Adiabaic sauraion process : An air-waer apour mixure eners an adiabaic sauraion chamber a 28 C and leaes a 18 C, which is he adiabaic sauraion emperaure. The pressure remains consan a 1.0 bar. Deermine he relaie humidiy and humidiy raio of he inle mixure. Soluion. The specific humidiy a he exi 622 ps W2s p p kg/kg of dry air (. 0206) s

24 472 ENGINEERING THERMODYNAMICS The specific humidiy a he inle (equaion 118) W 1 c ( ) + W ( h h ) p db2 db1 2s g2 f2 h h g1 f2 or or ( 18 28) ( ) ( ) kg/kg of dry air p 1 W 1 p p p 100. p ( ) or bar Relaie humidiy p p 1 s or 70%. (Ans.) Example 111. An air-waer apour mixure eners an air-condiioning uni a a pressure of 1.0 bar. 38 C DBT, and a relaie humidiy of 75%. The mass of dry air enering is 1 kg/s. The air-apour mixure leaes he air-condiioning uni a 1.0 bar, 18 C, 85% relaie humidiy. The moisure condensed leaes a 18 C. Deermine he hea ransfer rae for he process. Soluion. db1 38ºC, R.H., φ 1 75% b2 18ºC, R.H., φ 2 85% The flow diagram and he process are shown in Figs. 116 (a) and (b) respeciely. A 38 C From seam ables : s 0663 bar, h g kj/kg φ s bar W kg/kg of dry air A 18 C From seam ables : s 0206 bar, h g kj/kg h f kj/kg bar W kg/kg of dry air

25 PSYCHROMETRICS 473 (a) h 1 h 2 75% 1 W 1 W 85% 2 W 2 18º C 38º C D B T (b) Fig. 116 Hea ransfer rae, q ( Wh 2 g Wh 1 g ) + c 2 1 p ( db db ) + (W W 2 ) h f2 ( ) (18 38) + ( ) kj/kg of dry air. (Ans.) Example 112. Eaporaie Cooler : Amospheric air a 38ºC and 25% relaie humidiy passes hrough an eaporaor cooler. If he final emperaure of air is 18ºC, how much waer is added per kg of dry air and wha is he final relaie humidiy? Soluion. A 38ºC : s 0663 bar, h g kj/kg and φ s bar \M-herm\Th10-2.pm5

26 474 ENGINEERING THERMODYNAMICS A 18ºC : h g kj/kg, s 0206 bar W kg/kg of dry air Since enhalpy remains consan during he process c p db 1 + Wh 1 g c 1 p db 2 + Wh 2 g W (Q A 18ºC, h g kj/kg) i.e., W kg/kg of dry air Amoun of waer added W 2 W kg/kg of dry air. (Ans.) 622 p 2 Also, p 2 or ( ) bar Final relaie humidiy or 63%. (Ans.) 0206 Example 113. Sauraed air a 3ºC is required o be supplied o a room where he emperaure mus be held a 22ºC wih a relaie humidiy of 55%. The air is heaed and hen waer a 10ºC is sprayed o gie he required humidiy. Deermine : (i) The mass of spray waer required per m 3 of air a room condiions. (ii) The emperaure o which he air mus be heaed. Neglec he fan power. Assume ha he oal pressure is consan a bar. Soluion. (i) The flow diagram is shown in Fig. 117 (a) and he processes are shown in Fig. 117 (b). Spray Heaer Room 22º C, Sauraed air a 3º C 4 55 % R.H. (a) \M-herm\Th10-2.pm5

27 PSYCHROMETRICS % R. H. 3 55% 2 W 3C º D B T (b) Fig. 117 (i) Mass of spray waer required A 22ºC From seam ables : s 0264 bar φ 3 p 3 s3 55 P s bar W 3 ( ) A 3ºC From seam ables : s 0076 bar kg/kg of dry air φ 1 p p 1 s p p 0076 bar s W kg/kg of dry air W 3 W kg/kg of dry air a3 RT a ( ) p ( p ) a m 3 /kg of dry air Spray waer kg moisure/m 3. (Ans.) (ii) Temperaure o which he air mus be heaed db2 : Now h 2 + (W 3 W 2 ) h 4 h 3 \M-herm\Th10-2.pm5

28 476 ENGINEERING THERMODYNAMICS [c p db 2 + W 2 h apour (2) ] + (W 3 W 2 )h 2 c p db 3 + W 3 h apour (3) and c p ( db3 db2 ) + W 3 h apour (3) W 2 h apour (2) (W 3 W 2 )h 4 0 From he seam ables a bar : h g 2524 kj/kg dp sa 12.5ºC 1.005(22 db2 ) [ ( )] 0047 [ ( db2 12.5)] ( ) db db db db2 32.7ºC. (Ans.) Example 114. Cooling ower : A small-size cooling ower is designed o cool 5.5 lires of waer per second, he inle emperaure of which is 44ºC. The moor-drien fan induces 9 m 3 /s of air hrough he ower and he power absorbed is 4.75 kw. The air enering he ower is a 18ºC, and has a relaie humidiy of 60%. The air leaing he ower can be assumed o be sauraed and is emperaure is 26ºC. Calculae : (i) The amoun of cooling waer (make-up) required per second. (ii) The final emperaure of he waer. Assume ha he pressure remains consan hroughou he ower a bar. Soluion. The cooling ower is shown diagrammaically in Fig (i) Make-up waer required : A 18ºC s 0206 bar, φ s bar p a bar W i Air ou 26º C, φ 1 m, h, m, h a a2 2 2 Ho waer in (m, h ) w1 w1 Cold waer ou (m, h ) w2 w2 18º C, φ 60% m, h, m, h a a1 1 1 Fig. 118 \M-herm\Th10-2.pm5

29 PSYCHROMETRICS 477 Then, m& a kg/s ( ) ( ) and m& 1 3 ( ) ( ) 0828 kg/s (Scrip denoes apour and he scrip a denoes he air). A exi a 26ºC, s 0336 bar and φ 1 s 0336 bar 622 p W 2 p p kg. Bu W m ma &m kg/s Hence, make-up waer required kg/s. (Ans.) (ii) Final emperaure of he waer : Also, &m w kg/s 5 and m& w m& 2 w (make-up waer) kg/s Applying he seady flow energy equaion and neglecing changes in kineic energy and poenial energy, we hae Wi + m& w hw + m& a ha + m& h a2 a2 2 2 w2 w2 Now, W i (i.e., work inpu) 4.75 kw 4.75 kj/s. Ealuaing he enhalpies from a daum of 0ºC, we hae : h w1 h f a 44ºC kj/kg, h a (18 0) kj/kg, h (18 10) kj/kg. [Corresponding o bar, s dp ~ 10ºC i.e., he apour is superheaed] h 1 h g a 26ºC 2549 kj/kg h a (26 0) kj/kg. Then, subsiuing, we ge h w2 or h w or h w kj/kg. By inerpolaion, h f kj/kg a 26.7ºC. Hence, final emperaure of waer 26.7ºC. (Ans.) \M-herm\Th10-2.pm5

30 478 ENGINEERING THERMODYNAMICS Example 115. A cooling ower used in power plan consiss of 10 big fans, &m waer 1000 kg/min. I is cooled from 35ºC o 30ºC. Amospheric condiions are 35ºC DBT, 25ºC WBT. Air leaes he ower a 30ºC, 90% RH. Find ou he quaniy of air handled per fan hour and he quaniy of make-up waer required per hour. (AMIE Winer, 1999) Soluion. Refer Fig Hea absorbed from he cooling ower m & waer c T ( ) (35 30) kj/h From psychromeric char, we hae A 35ºC DBT and 25ºC WBT : h kj/kg ; W kg/kg of air A 30ºC and 90% RH : h kj/kg ; W kg/kg of air Hea gained by air Hea los by waer m & air (h 2 h 1 ) Mass of air, m & air ( h h ) 2 1 Fig ( ) kg/h Quaniy of air handled per fan kg/h. (Ans.) Quaniy of make-up waer &m air (W 2 W 1 ) ( ) kg/h. (Ans.) SOLUTIONS USING PSYCHROMETRIC CHARTS Example 116. The following daa perain o an air-condiioning sysem : Uncondiioned space DBT 30ºC Uncondiioned space WBT 22ºC Cold air duc supply surface emperaure 14ºC. Deermine : (i) Dew poin emperaure. (ii) Wheher or no condensaion will form on he duc. Soluion. Refer Fig. 12 (i) To deermine he dew poin emperaure for he gien condiions, find he inersecion of 30ºC DBT and 22ºC WBT and moe horizonally (as shown by he arrow) o he dew poin emperaure scale. The dew poin ( dp ) is 18.6ºC. (Ans.) (ii) Since he duc emperaure (14ºC) is less han dp (18.6ºC) herefore moisure will condense on he duc surface. (Ans.) 3 \M-herm\Th10-2.pm5

31 PSYCHROMETRICS º C 18.6 C dp º W D B T 30º C Fig. 120 Example m 3 of air per minue a 15ºC DBT and 75% R.H. is heaed unil is emperaure is 25ºC. Find : (i) R.H. of heaed air. (ii) We bulb emperaure of heaed air. (iii) Hea added o air per minue. Soluion. Refer Fig l Locae poin 1 on he psychromeric char on inersecion of 15ºC DBT and 75% R.H. lines. l Through poin 1 draw a horizonal line o cu 25ºC DBT line and ge poin 2. l Read he following alues from he psychromeric char : h kj/kg h kj/kg s m 3 /kg. (i) R.H. of heaed air (read from char) 41%. (Ans.) (ii) WBT of heaed air (read from char) 16.1ºC. (Ans.) 200 (iii) Mass of air circulaed per min., m a kg Hea added o air/min. m a (h 2 h 1 ) ( ) 2376 kj. (Ans.) \M-herm\Th10-2.pm5

32 480 ENGINEERING THERMODYNAMICS h h h(kj/kg) 75% RH 41% RH W º C 25º C D B T Fig. 121 Example 118. I is required o design an air-condiioning plan for a small office room for following winer condiions : Oudoor condiions... 14ºC DBT and 10ºC WBT Required condiions... 20ºC DBT and 60% R.H. Amoun of air circulaion m 3 /min./person. Seaing capaciy of office... 6 The required condiion is achieed firs by heaing and hen by adiabaic humidifying. Deermine he following : (i) Heaing capaciy of he coil in kw and he surface emperaure required if he by pass facor of coil is 4. (ii) The capaciy of he humidifier. Sole he problem by using psychromeric char. Soluion. Refer Fig l Locae he poins 1 and 3 on he psychromeric char. l Draw a consan enhalpy line hrough 3 and consan specific humidiy line hrough 1. \M-herm\Th10-2.pm5

33 PSYCHROMETRICS 481 l Locae he poin 2 where he aboe wo lines inersec. h h(kj/kg) h % RH W(gm / kg of dry air) 1 W W º C 20º C 24.5º C D B T Fig. 122 From he psychromeric char : h kj/kg, h 2 h kj/kg db2 24.5ºC, s1 817 m 3 /kg The mass of air circulaed per minue, m a kg/min (i) Heaing capaciy of he heaing coil m a (h 2 h 1 ) ( ) kj/min kj/s or 4.77 kw. (Ans.) The by-pass facor (BF) of heaing coil is gien by : db 4 db2 BF db 4 db1 4 db db 12 4 ( db4 12) db i.e., db4 (coil surface emperaure) 32.8ºC. (Ans.) (ii) The capaciy of he humidifier ma W W 3 1 ) ( ) 60 kg/h kg/h. (Ans.) \M-herm\Th10-2.pm5