ME 354 Tutorial, Week#11 Non-Reacting Mixtures Psychrometrics Applied to a Cooling Tower

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1 ME 5 Tutoril, Week# Non-Recting Mixtures Psychroetrics Applied to Cooling Toer Wter exiting the condenser of poer plnt t 5 C enters cooling toer ith ss flo rte of 5000 kg/s. A stre of cooled ter is returned to the condenser fro the cooling toer ith the se flo rte. Mke-up ter is dded in seprte stre t 0 C. Atospheric ir enters the cooling toer t 0 C nd et bulb teperture of 0 C. The voluetric flo rte of ir into the cooling toer is 8000 /s. Moist ir exits the toer t 0 C nd 90% reltive huidity. Assue n tospheric pressure of 0. kp. Deterine: ) the ss flo rte of dry ir, b) the ss flo rte of ke-up ter, nd c) the teperture of the cooled liquid ter exiting the cooling toer. Step : Dr digr to represent the syste Exhust Air T db,0 C φ 90% Wr Condenser Wter, T? C,5000 kg/s T 5 C Cooled Condenser Wter, Inlet Air V,8000 /s T db,0 C T b,0 C 5 Mke-up Wter? kg/s T 0 C 5 Step : Prepre property tble H 0 T ( C) (kg/s) h (/kg) (st. liq) (st. liq) (st. liq) 0

2 Air T db ( C) T b ( C) φ (%) (kg v /kg ) v ( /kg ) h (/kg ) Step : Stte your ssuptions Assuptions: ) The cooling toer opertes under stedy conditions ) ΔKE, ΔPE 0 ) Cooling toer is rigid nd dibtic W cv 0 & Q cv 0. ) Assue ll liquid ter is sturted 5) The pressure is constnt throughout the cooling toer t 0. kp. Step : Clcultions Prt ) The ss flo rte of dry ir cn be deterined using the voluetric flo rte of ir into the cooling toer (given in the proble s 8000 /s) nd the specific volue of this ir s shon in Eq., V, (Eq) v, We cn deterine the specific volue of the ir entering the cooling toer by deterining the stte point of loction on the psychroetric chrt using T db, 0 C nd T b, 0 C. Fro the psychroetric chrt, v, 0.87 /kg Substituting this vlue nd the given voluetric flo rte into Eq e cn deterine the ss flo rte of dry ir., V, v, 8000 s 96.8 kg /s Anser ) 0.87 Prt b) To deterine the ss flo rte of the ke-up ter, denoted s, e cn perfor ss blnce on the ter entering/exiting our cooling toer control volue. At loction e hve the stre of ter entering the cooling toer

3 fro the condenser, hich e ill denote s,. At loction e hve the stre of ter exiting the cooling toer to be returned to the condenser, hich e ill denote s,. We re told in the proble stteent tht,,. At loction, e hve the oisture entering the cooling toer control volue crried in by the incoing ir. We ill denote this s v,. At loction, e hve the oisture leving the cooling toer control volue crried out by the exiting ir. We ill denote this s v,. The ss blnce on the ter is perfored in Eq. + v, v, + 0 v, v, (Eq) Note: We could hve developed Eq ieditely by resoning tht the ount of ter tht needs to be de-up for ill be equl to the ount of oisture tht is picked up in the cooling toer by the ir nd exhusted. We cn express v, & v, in ters of the corresponding ss flo rtes of dry ir t loction & nd their respective huidity rtios & s shon in Eq nd Eq. v,, (Eq) v,, (Eq) Substituting Eq nd Eq into Eq e obtin Eq5. v, v,,, (Eq5) Fro our ssuption tht the cooling toer opertes in stedy nner, the ss flo rte of ir ill be constnt i.e.,,. Eq5 cn be reritten s Eq6. ( ) (Eq6) Recll tht e deterined the ss flo rte of dry ir in prt ). We cn deterine the huidity rtio of the ir entering the cooling toer by using stte point on the psychroetric chrt. Fro the psychroetric chrt, 0.6 g v /kg kg v /kg

4 Unfortuntely, stte point (T db, 0 C & φ90%) is off the psychroetric chrt so e ill hve to clculte the vlue of using eqution -b fro Cengel nd Boles s shon belo. Fro Tble T 0 C, P g 7.8 kp. 0.6φ Pg 0.6(0.9)(7.8) kg P φpg (7.8) v Substituting these vlues into Eq6, e cn deterine the ss flo rte of the ke-up ter. kg v ( ) kg ( ) s 0. kg v /s Anser b) Prt c) We cn deterine the teperture of the cooled liquid ter exiting the cooling toer by first deterining its enthlpy. Since e re ssuing it is sturted liquid e cn use the enthlpy to interpolte in Tble A- to deterine its teperture. To find the enthlpy of the ter exiting the cooling toer e ust perfor n energy blnce on the cooling toer control volue. At loction, the rte of energy entering the control volue crried in by the stre of ter coing fro the condenser is h,, here h is used to denote enthlpy. At loction e hve the stre of ter leving the cooling toer crrying y energy t rte of h,. At loction, the oist ir crries energy t rte of h into the control volue. At loction, e hve oist ir leving the cooling toer control volue crrying energy out t rte of h. The ke-up ter crries energy into the control volue t rte of h. Cobining ll of these stteents into one expression e obtin Eq7. Note: We hve de use of our list of ssuptions in developing Eq7. h, h, + h h + h 0 (Eq7) We cn isolte the enthlpy of the ter t loction by rerrnging Eq7 s shon in Eq8.

5 ( h h + h h + ),, (Eq8) h We hve previously deterined proble stteent. nd, nd e re given in the h, Since e hve ssued sturted liquid ter t loction e cn deterine h, fro Tble A- using T 5 C. h, h Using stte point on the psychroetric chrt e cn deterine h. h 58 h As stted previously, stte point is off the psychroetric chrt so e ust clculte h. Using eqution - fro Cengel nd Boles, e cn clculte the enthlpy of DRY AIR lone. h,.005 (0 C) 0. C We cn clculte the enthlpy of the MOISTURE in the ir using Tble A- for h T 0 C. hg, 57. v To cobine the dry ir nd oisture enthlpies t loction into one ter, h, e need to convert the enthlpy of the oisture to be on per kg of dry ir bsis by ultiplying it by the huidity rtio,. kg v h h, + hg, v 5

6 h Since e hve ssued sturted liquid ter t loction 5 e cn deterine h fro Tble A- using T 5 0 C. h Substituting these vlues into Eq8, e cn deterine the enthlpy of the ter t loction. h, 88.5 kg kg 96.8 s + (58 5.7) + kg 5000 s (0.) kg s (8.96) kg h, As stted previously, since e hve ssued sturted liquid ter t loction e cn use h, to find the corresponding teperture in Tble A-. Fro Tble A- e find tht h, lies in beteen the enthlpies corresponding to tepertures of 0 C nd 5 C. We cn interpolte in beteen the to find the teperture of the ter exiting the cooling toer T 0 C C 0 C T.6 C Anser c) Step 5: Sury ) the ss flo rte of dry ir is 96.8 kg/s b) the ss flo rte of ke-up ter is 0. kg/s, nd c) the teperture of the cooled liquid ter exiting the cooling toer is.6 C. 6