Lesson 28 Psychrometric Processes

Transcription

1 1 Lesson 28 Psychrometrc Processes Verson 1 ME, IIT Khrgpur 1

2 2 The specfc objectves of ths lecture re to: 1. Introducton to psychrometrc processes nd ther representton (Secton 28.1) 2. Importnt psychrometrc processes nmely, sensble coolng nd hetng, coolng nd dehumdfcton, coolng nd humdfcton, hetng nd humdfcton, chemcl dehumdfcton nd mxng of r strems (Secton 28.2) 3. Representton of the bove processes on psychrometrc chrt nd equtons for het nd mss trnsfer rtes (Secton 28.2) 4. oncept of Sensble Het Fctor, By-pss Fctor nd pprtus de pont temperture of coolng cols (Secton 28.2.) 5. Prncple of r shers nd vrous psychrometrc processes tht cn be performed usng r shers (Secton 28.3) 6. oncept of enthlpy potentl nd ts use (Secton 28.4) At the end of the lecture, the student should be ble to: 1. Represent vrous psychrometrc processes on psychrometrc chrt 2. Perform clcultons for vrous psychrometrc processes usng the psychrometrc chrts nd equtons 3. Defne sensble het fctor, by-pss fctor, contct fctor nd pprtus de pont temperture 4. Descrbe the prncple of n r sher nd ts prctcl use 5. Derve equton for totl het trnsfer rte n terms of enthlpy potentl nd expln the use of enthlpy potentl Introducton: In the desgn nd nlyss of r condtonng plnts, the fundmentl requrement s to dentfy the vrous processes beng performed on r. nce dentfed, the processes cn be nlyzed by pplyng the ls of conservton of mss nd energy. All these processes cn be plotted esly on psychrometrc chrt. Ths s very useful for quck vsulzton nd lso for dentfyng the chnges tkng plce n mportnt propertes such s temperture, humdty rto, enthlpy etc. The mportnt processes tht r undergoes n typcl r condtonng plnt re dscussed belo Importnt psychrometrc processes: ) Sensble coolng: Durng ths process, the mosture content of r remns constnt but ts temperture decreses s t flos over coolng col. For mosture content to remn Verson 1 ME, IIT Khrgpur 2

3 constnt, the surfce of the coolng col should be dry nd ts surfce temperture should be greter thn the de pont temperture of r. If the coolng col s 100% effectve, then the ext temperture of r ll be equl to the col temperture. Hoever, n prctce, the ext r temperture ll be hgher thn the coolng col temperture. Fgure 28.1 shos the sensble coolng process -A on psychrometrc chrt. The het trnsfer rte durng ths process s gven by: 3 c = m (h h ) = m c (T T ) (28.1) A pm A h o h A A W DBT Fg.28.1: Sensble coolng process -A on psychrometrc chrt b) Sensble hetng (Process -B): Durng ths process, the mosture content of r remns constnt nd ts temperture ncreses s t flos over hetng col. The het trnsfer rte durng ths process s gven by: h = m (h h ) = m c (T T ) (28.2) B pm B Verson 1 ME, IIT Khrgpur 3

4 here c pm s the humd specfc het ( kj/kg dry r) nd m s the mss flo rte of dry r (kg/s). Fgure 28.2 shos the sensble hetng process on psychrometrc chrt. 4 h B h W B DBT Fg.28.2: Sensble hetng process on psychrometrc chrt c) oolng nd dehumdfcton (Process -): When most r s cooled belo ts de-pont by brngng t n contct th cold surfce s shon n Fg.28.3, some of the ter vpor n the r condenses nd leves the r strem s lqud, s result both the temperture nd humdty rto of r decreses s shon. Ths s the process r undergoes n typcl r condtonng system. Although the ctul process pth ll vry dependng upon the type of cold surfce, the surfce temperture, nd flo condtons, for smplcty the process lne s ssumed to be strght lne. The het nd mss trnsfer rtes cn be expressed n terms of the ntl nd fnl condtons by pplyng the conservton of mss nd conservton of energy equtons s gven belo: By pplyng mss blnce for the ter: m. = m. + m (28.3) Verson 1 ME, IIT Khrgpur 4

5 5 h oolng col h h W o m h o W o m h W W c t m T s T T o Fg.28.3: oolng nd dehumdfcton process (-) By pplyng energy blnce: m.h = + m.h + m t. h (28.4) from the bove to equtons, the lod on the coolng col, s gven by: t t = m (h h ) m ( ) h (28.5) nd the 2 term on the RHS of the bove equton s normlly smll compred to the other terms, so t cn be neglected. Hence, t = m (h h ) (28.6) It cn be observed tht the coolng nd de-humdfcton process nvolves both ltent nd sensble het trnsfer processes, hence, the totl, ltent nd sensble het trnsfer rtes ( t, l nd s ) cn be rtten s: here l t s = l + s = m (h h ) = m.h = m (h h ) = m.c fg ( (T pm T ) ) (28.7) By seprtng the totl het trnsfer rte from the coolng col nto sensble nd ltent het trnsfer rtes, useful prmeter clled Sensble Het Fctor (SHF) s defned. SHF s defned s the rto of sensble to totl het trnsfer rte,.e., SHF = / /( + ) (28.8) s t = s s l ) From the bove equton, one cn deduce tht SHF of 1.0 corresponds to no ltent het trnsfer nd SHF of 0 corresponds to no sensble het trnsfer. A SHF of 0.75 to 0.80 s qute common n r condtonng systems n norml dry-clmte. A Verson 1 ME, IIT Khrgpur 5

6 loer vlue of SHF, sy 0.6, mples hgh ltent het lod such s tht occurs n humd clmte. From Fg.28.3, t cn be seen tht the slope of the process lne - s gven by: From the defnton of SHF, Δ tn c = (28.9) Δ T 6 1 SHF SHF = l s mh = m c fg pm Δ Δ T 2501Δ = Δ T Δ = 2451 Δ T (28.10) From the bove equtons, e cn rte the slope s: 1 1 SHF tn c = (28.11) 2451 SHF Thus e cn see tht the slope of the coolng nd de-humdfcton lne s purely functon of the sensble het fctor, SHF. Hence, e cn dr the coolng nd dehumdfcton lne on psychrometrc chrt f the ntl stte nd the SHF re knon. In some stndrd psychrometrc chrts, protrctor th dfferent vlues of SHF s provded. The process lne s drn through the ntl stte pont nd n prllel to the gven SHF lne from the protrctor s shon n Fg SHF ho-hc h-hc Wo-Wc c Fg.28.4: A psychrometrc chrt th protrctor for SHF lnes In Fg.28.3, the temperture T s s the effectve surfce temperture of the coolng col, nd s knon s pprtus de-pont (ADP) temperture. In n del stuton, hen ll the r comes n perfect contct th the coolng col surfce, then the ext temperture of r ll be sme s ADP of the col. Hoever, n ctul cse the ext temperture of r ll lys be greter thn the pprtus de-pont temperture due to boundry lyer development s r flos over the coolng col surfce nd lso due to Verson 1 ME, IIT Khrgpur 6

7 temperture vrton long the fns etc. Hence, e cn defne by-pss fctor (BPF) s: BPF T T S = (28.12) T TS It cn be esly seen tht, hgher the by-pss fctor lrger ll be the dfference beteen r outlet temperture nd the coolng col temperture. When BPF s 1.0, ll the r by-psses the col nd there ll not be ny coolng or de-humdfcton. In prctce, the by-pss fctor cn be ncresed by ncresng the number of ros n coolng col or by decresng the r velocty or by reducng the fn ptch. Alterntvely, contct fctor(f) cn be defned hch s gven by: 7 F = 1 BPF (28.13) d) Hetng nd Humdfcton (Process -D): Durng nter t s essentl to het nd humdfy the room r for comfort. As shon n Fg.28.5., ths s normlly done by frst sensbly hetng the r nd then ddng ter vpour to the r strem through stem nozzles s shon n the fgure. Hetng col Stem nozzles h D m T h m T D D h D h D D h m T T D Fg.28.5: Hetng nd humdfcton process Mss blnce of ter vpor for the control volume yelds the rte t hch stem hs to be dded,.e., m : m = m ( ) (28.14) D Verson 1 ME, IIT Khrgpur 7

8 8 here m s the mss flo rte of dry r. From energy blnce: h = m (h h ) m h (28.15) D here h s the het suppled through the hetng col nd h s the enthlpy of stem. Snce ths process lso nvolves smultneous het nd mss trnsfer, e cn defne sensble het fctor for the process n y smlr to tht of coolnd nd dehumdfcton process. e) oolng & humdfcton (Process -E): As the nme mples, durng ths process, the r temperture drops nd ts humdty ncreses. Ths process s shon n Fg As shon n the fgure, ths cn be cheved by spryng cool ter n the r strem. The temperture of ter should be loer thn the dry-bulb temperture of r but hgher thn ts de-pont temperture to vod condenston (T < T < T DPT ). old ter spry or etted surfce m T h m T E E h E E T T DPT T E T Fg.28.6: oolng nd humdfcton process It cn be seen tht durng ths process there s sensble het trnsfer from r to ter nd ltent het trnsfer from ter to r. Hence, the totl het trnsfer depends upon the ter temperture. If the temperture of the ter spryed s equl to the etbulb temperture of r, then the net trnsfer rte ll be zero s the sensble het trnsfer from r to ter ll be equl to ltent het trnsfer from ter to r. If the ter temperture s greter thn WBT, then there ll be net het trnsfer from ter to r. If the ter temperture s less thn WBT, then the net het trnsfer ll be from r to ter. Under specl cse hen the spry ter s entrely recrculted nd s nether heted nor cooled, the system s perfectly nsulted nd the mke-up ter s suppled t WBT, then t stedy-stte, the r undergoes n dbtc sturton process, durng hch ts WBT remns constnt. Ths s the process of dbtc sturton dscussed n hpter 27. The process of coolng nd humdfcton s encountered n de vrety of devces such s evportve coolers, coolng toers etc. Verson 1 ME, IIT Khrgpur 8

9 9 f) Hetng nd de-humdfcton (Process -F): Ths process cn be cheved by usng hygroscopc mterl, hch bsorbs or dsorbs the ter vpor from the mosture. If ths process s thermlly solted, then the enthlpy of r remns constnt, s result the temperture of r ncreses s ts mosture content decreses s shon n Fg Ths hygroscopc mterl cn be sold or lqud. In generl, the bsorpton of ter by the hygroscopc mterl s n exothermc recton, s result het s relesed durng ths process, hch s trnsferred to r nd the enthlpy of r ncreses. Hygroscopc mterl F W F W F T T F Fg hemcl de-humdfcton process g) Mxng of r strems: Mxng of r strems t dfferent sttes s commonly encountered n mny processes, ncludng n r condtonng. Dependng upon the stte of the ndvdul strems, the mxng process cn tke plce th or thout condenston of mosture. ) Wthout condenston: Fgure 28.8 shos n dbtc mxng of to most r strems durng hch no condenston of mosture tkes plce. As shon n the fgure, hen to r strems t stte ponts 1 nd 2 mx, the resultng mxture condton 3 cn be obtned from mss nd energy blnce. From the mss blnce of dry r nd ter vpor: m,1 1 + m,2 2 = m,3 3 = (m,1 + m,2 ) 3 (28.16) From energy blnce: m,1h 1 + m,2h2 = m,3h3 = (m,1 + m,2 ) h3 (28.17) From the bove equtons, t cn be observed tht the fnl enthlpy nd humdty rto of mxture re eghted verges of nlet enthlpes nd humdty rtos. A generlly vld pproxmton s tht the fnl temperture of the mxture s the Verson 1 ME, IIT Khrgpur 9

10 eghted verge of the nlet tempertures. Wth ths pproxmton, the pont on the psychrometrc chrt representng the mxture les on strght lne connectng the to nlet sttes. Hence, the rto of dstnces on the lne,.e., (1-3)/(2-3) s equl to the rto of flo rtes m,2/m,1. The resultng error (due to the ssumpton tht the humd specfc hets beng constnt) s usully less thn 1 percent. 10 m,1 m,1 +m,2 = m,3 m,2 Fg Mxng of to r strems thout condenston ) Mxng th condenston: As shon n Fg.28.9, hen very cold nd dry r mxes th rm r t hgh reltve humdty, the resultng mxture condton my le n the to-phse regon, s result there ll be condenston of ter vpor nd some mount of ter ll leve the system s lqud ter. Due to ths, the humdty rto of the resultng mxture (pont 3) ll be less thn tht t pont 4. orrespondng to ths ll be n ncrese n temperture of r due to the relese of ltent het of condenston. Ths process rrely occurs n n r condtonng system, but ths s the phenomenon hch results n the formton of fog or frost (f the mxture temperture s belo 0 o ). Ths hppens n nter hen the cold r ner the erth mxes th the humd nd rm r, hch develops tords the evenng or fter rns. Fg Mxng of to r strems th condenston Verson 1 ME, IIT Khrgpur 10

11 Ar Wshers: An r sher s devce for condtonng r. As shon n Fg.28.10, n n r sher r comes n drect contct th spry of ter nd there ll be n exchnge of het nd mss (ter vpour) beteen r nd ter. The outlet condton of r depends upon the temperture of ter spryed n the r sher. Hence, by controllng the ter temperture externlly, t s possble to control the outlet condtons of r, hch then cn be used for r condtonng purposes. Elmntor Pltes Ar n Ar out Mke-up ter Pump ooler/ heter Fg.28.10: Ar sher In the r sher, the men temperture of ter droplets n contct th r decdes the drecton of het nd mss trnsfer. As consequence of the 2 nd l, the het trnsfer beteen r nd ter droplets ll be n the drecton of decresng temperture grdent. Smlrly, the mss trnsfer ll be n the drecton of decresng vpor pressure grdent. For exmple, ) oolng nd dehumdfcton: t < t DPT. Snce the ext enthlpy of r s less thn ts nlet vlue, from energy blnce t cn be shon tht there s trnsfer of totl energy from r to ter. Hence to contnue the process, ter hs to be externlly cooled. Here both ltent nd sensble het trnsfers re from r to ter. Ths s shon by Process -A n Fg b) Adbtc sturton: t = t WBT. Here the sensble het trnsfer from r to ter s exctly equl to ltent het trnsfer from ter to r. Hence, no externl coolng or hetng of ter s requred. Tht s ths s cse of pure ter recrculton. Ths s Verson 1 ME, IIT Khrgpur 11

12 shon by Process -B n Fg Ths the process tht tkes plce n perfectly nsulted evportve cooler. c) oolng nd humdfcton: t DPT < t < t WBT. Here the sensble het trnsfer s from r to ter nd ltent het trnsfer s from ter to r, but the totl het trnsfer s from r to ter, hence, ter hs to be cooled externlly. Ths s shon by Process - n Fg d) oolng nd humdfcton: t WBT < t < t DBT. Here the sensble het trnsfer s from r to ter nd ltent het trnsfer s from ter to r, but the totl het trnsfer s from ter to r, hence, ter hs to be heted externlly. Ths s shon by Process -D n Fg Ths s the process tht tkes plce n coolng toer. The r strem extrcts het from the hot ter comng from the condenser, nd the cooled ter s sent bck to the condenser. e) Hetng nd humdfcton: t > t DBT. Here both sensble nd ltent het trnsfers re from ter to r, hence, ter hs to be heted externlly. Ths s shon by Process -E n Fg Thus, t cn be seen tht n r sher orks s yer-round r condtonng system. Though r sher s nd extremely useful smple devce, t s not commonly used for comfort r condtonng pplctons due to concerns bout helth resultng from bcterl or fungl groth on the etted surfces. Hoever, t cn be used n ndustrl pplctons. 12 D E B W A DBT Fg.28.11: Vrous psychrometrc processes tht cn tke plce n n r sher Verson 1 ME, IIT Khrgpur 12

13 Enthlpy potentl: As shon n cse of n r sher, henever ter (or etted surfce) nd r contct ech other, there s possblty of het nd mosture trnsfer beteen them. The drectons of het nd mosture trnsfer depend upon the temperture nd vpor pressure dfferences beteen r nd ter. As result, the drecton of the totl het trnsfer rte, hch s sum of sensble het trnsfer nd ltent het trnsfers lso depends upon ter nd r condtons. The concept of enthlpy potentl s very useful n quntfyng the totl het trnsfer n these processes nd ts drecton. The sensble ( S) nd ltent ( L) het trnsfer rtes re gven by: S L = h. = m A S.h (t fg t = h D ).A S ( ).h fg (28.18) the totl het trnsfer T s gven by: T = S + L = has (t t ) + hd.as ( ). hfg (28.19) here t t h c = dry-bulb temperture of r, o = temperture of ter/etted surfce, o = humdty rto of r, kg/kg = humdty rto of sturted r t t, kg/kg = convectve het trnsfer coeffcent, W/m 2 o. h D = convectve mss trnsfer coeffcent, kg/m 2 h fg = ltent het of vporzton, J/kg Snce the trnsport mechnsm tht controls the convectve het trnsfer beteen r nd ter lso controls the mosture trnsfer beteen r nd ter, there exsts relton beteen het nd mss trnsfer coeffcents, h c nd h D s dscussed n n erler chpter. It hs been shon tht for r-ter vpor mxtures, hd h hc or = Les number 1.0 (28.20) cpm hd.cpm here c s the humd specfc het kj/kg.k. pm Hence the totl het trnsfer s gven by: T has S + L = cpm [(t t ) + ( ). h ] = (28.21) fg Verson 1 ME, IIT Khrgpur 13

14 14 by mnpultng the term n the prenthess of RHS, t cn be shon tht: T has = S + L = [(h h )] (28.22) cpm thus the totl het trnsfer nd ts drecton depends upon the enthlpy dfference (or potentl) beteen ter nd r (h-h ). f h > h ; then the totl het trnsfer s from ter to r nd ter gets cooled f h < h ; then the totl het trnsfer s from r to ter nd ter gets heted f h = h ; then the net het trnsfer s zero,.e., the sensble het trnsfer rte s equl to but n the opposte drecton of ltent het trnsfer. Temperture of ter remns t ts et bulb temperture vlue The concept of enthlpy potentl s very useful n psychrometrc clcultons nd s frequently used n the desgn nd nlyss of evportve coolers, coolng toers, r shers etc. uestons nd nsers: 1. Whch of the follong sttements re TRUE? ) Durng sensble coolng of r, both dry bulb nd et bulb tempertures decrese b) Durng sensble coolng of r, dry bulb temperture decreses but et bulb temperture remns constnt c) Durng sensble coolng of r, dry nd et bulb tempertures decrese but de pont temperture remns constnt d) Durng sensble coolng of r, dry bulb, et bulb nd de pont tempertures decrese Ans.: ) nd c) 2. Whch of the follong sttements re TRUE? ) The sensble het fctor for sensble hetng process s 1.0 b) The sensble het fctor for sensble coolng process s 0.0 c) Sensble het fctor lys les beteen 0.0 nd 1.0 d) Sensble het fctor s lo for r condtonng plnts opertng n humd clmtes Ans.: ) nd d) Verson 1 ME, IIT Khrgpur 14

15 15 3. Whch of the follong sttements re TRUE? ) As the by-pss fctor (BPF) of the coolng col ncreses, temperture dfference beteen r t the outlet of the col nd col ADP decreses b) The BPF of the col ncreses s the velocty of r through the col ncreses c) The BPF of the col ncreses s the fn ptch ncreses d) The BPF of the col decreses s the number of ros n the flo drecton ncrese Ans.: b), c) nd d) 4. Whch of the follong sttements re TRUE? ) Durng coolng nd humdfcton process, the enthlpy of r decreses b) Durng coolng nd humdfcton process, the enthlpy of r ncreses c) Durng coolng nd humdfcton process, the enthlpy of r remns constnt d) Durng coolng nd humdfcton process, the enthlpy of r my ncrese, decrese or remn constnt dependng upon the temperture of the et surfce Ans.: d) o 5. An r strem t flo rte of 1 kg/s nd DBT of 30 mxes dbtclly th nother r strem flong th mss flo rte of 2 kg/s nd t DBT of 15 o. Assumng no condenston to tke plce, the temperture of the mxture s pproxmtely equl to: ) 20 o b) 22.5 o c) 25 o d) nnot be found Ans.: ) 6. Whch of the follong sttements re TRUE? ) In n r sher, ter hs to be externlly cooled f the temperture t hch t s spryed s equl to the dry bulb temperture of r b) In n r sher, ter hs to be externlly heted f the temperture t hch t s spryed s equl to the dry bulb temperture of r c) In n r sher, f ter s smply recrculted, then the enthlpy of r remns nerly constnt t stedy stte Verson 1 ME, IIT Khrgpur 15

16 d) In n r sher, f ter s smply recrculted, then the mosture content of r remns nerly constnt t stedy stte Ans.: b) nd c) 7. Whch of the follong sttements re TRUE? ) When the enthlpy of r s equl to the enthlpy of sturted r t the etted surfce temperture, then there s no sensble het trnsfer beteen r nd the etted surfce b) When the enthlpy of r s equl to the enthlpy of sturted r t the etted surfce temperture, then there s no ltent het trnsfer beteen r nd the etted surfce c) When the enthlpy of r s equl to the enthlpy of sturted r t the etted surfce temperture, then there s no net het trnsfer beteen r nd the etted surfce d) When the enthlpy of r s equl to the enthlpy of sturted r t the etted surfce temperture, then the et bulb temperture of r remns constnt Ans.: c) nd d) 8. Wht s the requred ttge of n electrcl heter tht hets 0.1 m /s of r from 15 o nd 80% RH to 55 o? The brometrc pressure s kp. Ans.: Ar undergoes sensble hetng s t flos through the electrcl heter From energy blnce, the requred heter ttge (W) s gven by: W = m (h e h ) (V /ν).c pm (T e T ) Where V s the volumetrc flo rte of r n m 3 /s nd ν s the specfc volume of dry r. T e nd T re the ext nd nlet tempertures of r nd cpm s the verge specfc het of most r ( J/kg.K). Usng perfect gs model, the specfc volume of dry r s found to be: ν = (R.T/P ) = (R.T/( P t P v )) o At 15 nd 80% RH, the vpour pressure p v s found to be kp usng psychrometrc chrt or equtons. Substtutng the vlues of R, T, p nd p t v n the equton for specfc volume, e fnd the vlue of specfc volume to be m 3 /kg Heter ttge, W (V /ν).c pm (T e T )=(0.1/0.8274)x1021.6(55-15) = W 3 16 (ns.) Verson 1 ME, IIT Khrgpur 16

17 kg/s of most r t 45 o (DBT) nd 10% RH s mxed th 0.3 kg/s of most r t 25 o nd humdty rto of kg/kgd n n dbtc mxng chmber. After mxng, the mxed r s heted to fnl temperture of 40 o usng heter. Fnd the temperture nd reltve humdty of r fter mxng. Fnd the het trnsfer rte n the heter nd reltve humdty of r t the ext of heter. Assume the brometrc pressure to be 1 tm. Ans.: Gven: Strem 1: mss flo rte, m 1 = 0.2 kg/s; T = 45 o nd RH = 10%. 1 Usng psychrometrc equtons or psychrometrc chrt, the humdty rto nd enthlpy of strem 1 re found to be: W = kg/kgd & h = 61.0 kj/kgd 1 1 Strem 2: mss flo rte, m 2 = 0.3 kg/s; T = 45 o nd W = kg/kgd 2 2 Usng psychrometrc equtons or psychrometrc chrt, enthlpy of strem 2 s found to be: h = 71.0 kj/kgd 1 For the dbtc mxng process, from mss blnce: W m = + m 0.2x x0.018 = ,1 1,2 2 3 = m,1 + m, kg / kgd From energy blnce (ssumng the specfc het of most r to remn constnt): T m,1t1 + m,2t2 0.2x x25 o = = 33 (ns.) m + m =,1,2 From T nd W, the reltve humdty of r fter mxng s found to be: 3 3 RH 3 = 41.8% (ns.) For the sensble hetng process n the heter: s = m (h e h ) m.c pm (T e T ) = 0.5x1.0216(40-33) = kw (ns.) The reltve humdty t the ext of heter s obtned from the vlues of DBT (40 o ) nd humdty rto ( kg/kgd) usng psychrometrc chrt/equtons. Ths s found to be: 17 RH t 40 o nd kg/kgd = 28.5 % (ns.) Verson 1 ME, IIT Khrgpur 17

18 10. A coolng toer s used for coolng the condenser ter of refrgerton system hvng het rejecton rte of 100 kw. In the coolng toer r enters t 35 o (DBT) nd 24 o (WBT) nd leves the coolng toer t DBT of 26 o reltve humdty of 95%. Wht s the requred flo rte of r t the nlet to the coolng toer n m 3 /s. Wht s the mount of mke-up ter to be suppled? The temperture of mke-up ter s t 30 o, t hch ts enthlpy (h ) my be tken s kj/kg. Assume the brometrc pressure to be 1 tm. Ans.: At the nlet to coolng toer: DBT = 35 o nd WBT = 24 o From psychrometrc chrt/equtons the follong vlues re obtned for the nlet: Humdty rto, W = kg/kgd Enthlpy, h = kj/kgd Sp. volume, ν = m 3 /kgd At the outlet to coolng toer: DBT = 26 o nd RH = 95% From psychrometrc chrt/equtons the follong vlues re obtned for the outlet: Humdty rto, W o = kg/kgd Enthlpy, h = kj/kgd From mss nd energy blnce cross the coolng toer: c = m {(h o h ) (Wo W )h } = 100 kw Substtutng the vlues of enthlpy nd humdty rto t the nlet nd outlet of coolng toer nd enthlpy of mke-up ter n the bove expresson, e obtn: m = kg/s, hence, the volumetrc flo rte, V = m x ν = m 3 /s (ns.) Amount of mke-up ter requred m s obtned from mss blnce s: m = m (Wo - W ) = 18.97( ) = kg/s = grms/s (ns.) 11. In n r condtonng system r t flo rte of 2 kg/s enters the coolng col t 25 o nd 50% RH nd leves the coolng col t 11 o nd 90% RH. The pprtus de pont of the coolng col s 7 o. Fnd ) The requred coolng cpcty of the col, b) Sensble Het Fctor for the process, nd c) By-pss fctor of the coolng col. Assume the brometrc pressure to be 1 tm. Assume the condenste ter to leve the col t ADP (h = kj/kg) Ans.: At the nlet to the coolng col; T = 25 o nd RH = 50% From psychrometrc chrt; W = kg/kgd nd h = kj/kgd 18 Verson 1 ME, IIT Khrgpur 18

19 19 At the outlet of the coolng col; T = 11 o nd RH = 90% o From psychrometrc chrt; W o = kg/kgd nd h o = kj/kgd ) From mss blnce cross the coolng col, the condeste rte, m s: m = m (W W o ) = 2.0( ) = kg/s From energy blnce cross the coolng toer, the requred cpcty of the coolng col, c s gven by:; c = m (h h o) m.h = 2.0( ) x = kw (ns.) b) The sensble het trnsfer rte, s s gven by: s = m c pm (T T o ) = 2.0 x x (25 11) = kw The ltent het trnsfer rte, l s gven by: s = m h fg (W W o ) = 2.0 x x ( ) = kw The Sensble Het Fctor (SHF) s gven by: 1 SHF = /( + ) = /( ) = s s l (ns.) c) From ts defnton, the by-pss fctor of the col, BPF s gven by: BPF = (T o ADP)/(T ADP) = (11 7)/(25 7) = (ns.) 1 The smll dfference beteen c nd ( s + l) s due to the use of verge vlues for specfc het, c pm nd ltent het of vporzton, h fg. Verson 1 ME, IIT Khrgpur 19