Chapter Applications of Energy Balance

Transcription

1 Capter 4 4. Appliation of Energy Balane We will diu exaple illutrating te analyi of erveral devie of interet in engineering, inluding nozzle and diffuer, turbine, opreor and pup, eat exanger, and trottling devie. In a nozzle, te fluid veloity inreae in te diretion of flow due to te redution in te flow area. In a diffuer, te fluid veloity dereae in te diretion of flow due to te inreae in te flow area. Exaple Stea enter a onverging-diverging nozzle operating at teady tate wit p 40 bar, T 400 o C, and a veloity of 0 /. Te tea flow troug te nozzle wit negligible eat tranfer and no ignifiant ange in potential energy. At te exit, p 5 bar, and te veloity i 665 /. Te a flow rate i kg/. Deterine te exit area of te nozzle, in. Apply te teady tate energy balane between () and () give V V Q W + g(z z ) + ( ) 0 V V + ( ) At p 40 bar (4 MPa), T 400 o C, 4 kj/kg (Table E4.-) 4 kj/kg + 0.5(0 665 ) N kg / kj 0 N 99 kj/kg Moran, M. J. and Sapiro H. N., Fundaental of Engineering Terodynai, Wiley, 008, pg. 6 4-

2 Table E4.- Stea propertie Speifi Internal Speifi Speifi Tep Preure Volue Energy Entalpy Entropy Quality Pae C MPa /kg kj/kg kj/kg kj/kg/k Dene Fluid (T>TC) Supereated Vapor At p 5 bar (.5 MPa), 99 kj/kg, v 0.68 /kg Te exit area i ten v A V ( kg)(0.68 /kg) 665 / Exaple Stea enter a turbine operating at teady tate wit a a flow rate of 4600 kg/. Te turbine develop a power output of 000 kw. At te inlet, te preure i 60 bar, te teperature i 400 o C, and te veloity i 0 /. At te exit, te preure i 0. bar, te quality i 0.9, and te veloity i 0 /. Calulate te rate of eat tranfer between te turbine and urrounding, in kw. Apply te teady tate energy balane between () and () give V V Q W + g(z z ) + ( ) Q Solving for wit g(z z ) 0,we obtain Q W V V + + ( ) Propertie of tea for tate () and () are lited in Table E4.- 4 Moran, M. J. and Sapiro H. N., Fundaental of Engineering Terodynai, Wiley, 008, pg

3 Table E4.- Stea propertie Speifi Internal Speifi Speifi Tep Preure Volue Energy Entalpy Entropy Quality Pae C MPa /kg kj/kg kj/kg kj/kg/k Dene Fluid (T>TC) Liquid Vapor Mixture Te ange in kineti energy i evaluated: ( ) V V 0.5(0 0 ) Te ange in entalpy i N kg / kj 0 N 0.4 kj/kg 45 kj/kg 77 kj/kg 8 kj/kg Q W Q W V V W + + ( ) 8.6 kj/kg 8 kj/kg kj/kg Q 000 kw 4600 kg (8.6 kj/kg) 600 Heat tranfer fro te turbine to te urrounding. kw kj/ 6.6 kw Exaple Air enter a opreor operating at teady tate at a preure of bar, a teperature of 90 K, and a veloity of 6 / troug an inlet area of 0.. At te exit, te preure i 7 bar, te teperature i 450 K, and te veloity i /. Heat tranfer fro te opreor to it urrounding our at a rate of 80 kj/in. Eploying te ideal ga odel, alulate te power input to te opreor, in kw. 5 Moran, M. J. and Sapiro H. N., Fundaental of Engineering Terodynai, Wiley, 008, pg

4 Apply te teady tate energy balane between () and () give Solving for V V Q W + g(z z ) + ( ) W wit g(z z ) 0,we obtain W Q + ( ) Te a flow rate i given by AV v V V + Te peifi veloity an be deterine fro ideal ga law R / M T v ( ) Te a flow rate i ten p 84 N (90 K) 8.97 kg K 0 N/ kg/ AV v ( 0. )( 6 / ) 0.84 kg/ kg/ Te ange in air entalpy an be obtained fro CATT progra 90.6 kj/kg 45. kj/kg 6.7 kj/kg Table E4.- Air propertie fro CATT Tep Preure Speifi Entalpy (Ma) K MPa kj/kg Te ange in kineti energy i evaluated: ( ) V V 0.5(6 ) Te power input to te opreor i ten N kg / kj 0 N 0.0 kj/kg 4-4

5 W Q + ( ) V V + W kj + (0.709 kg/)( ) kj/kg 9.6 kw 4.4 Heat Exanger Heat exanger are devie for tranferring eat between two fluid trea. Heat exanger an be laified a indiret ontat type and diret ontat type. Indiret ontat type eat exanger ave no ixing between te ot and old trea, only energy tranfer i allowed a own in Figure Hot fluid Cold fluid Wall eparate trea Figure 4.4- Indiret ontat type eat exanger. Diret ontat type eat exanger ave no wall to eparate te old fro te ot trea a own in Figure Nonondenible bleed War water Stea Cold water Figure 4.4- Diret ontat type eat exanger. We will briefly diu two type of tubular eat exanger: onentri tube and ell-andtube eat exanger. A onentri tube or double pipe eat exanger i te iplet eat exanger for wi te ot and old fluid ove in te ae or oppoite diretion a own in Figure

6 Hot fluid Cold fluid Hot fluid Cold fluid Parallel flow Counter flow Figure 4.4- Conentri tube eat exanger. Sell-and-tube eat exanger i te ot oon onfiguration. Tere are any different for of ell-and-tube eat exanger aording to te nuber of ell-and-tube pae. A oon for wit one ell pa and two tube pae i own in Figure Baffle are uually intalled to inreae te eat tranfer oeffiient of te fluid by introduing turbulene and ro-flow in te ell ide. Baffle Sell inlet Tube oulet Tube inlet Sell outlet Figure 4.4-4a Sell-and-tube eat exanger wit one ell pa and two tube pae. Figure 4.4-4b Detail ontrution of a ell-and-tube eat exanger. 4-6

7 Exaple Saturated tea at 99.6 o C ondene on te outide of a 5- long, 4--diaeter tin orizontal opper tube by ooling liquid water tat enter te tube at 5 o C at an average veloity of / and leave at 45 o C. Liquid water denity i 997 kg/, p of liquid water i 4.8 kj/kg o C. (a) Deterine te rate of eat tranfer to water. (b) If te rate of eat tranfer to water i 00 kw, deterine te rate of ondenation of tea Condening tea Q T i T e (a) Te rate of eat tranfer to water i given by Q p (T e T i ) In ti equation, te a flow rate of water i given by ρv vel A tube Te eat tranfer rate i ten (997 kg/ )( /)(π 0.0 ).7586 kg/ Q (.7586 kg/)(4.8 kj/kg o C)(45 5) o C 4. kw (b) If te rate of eat tranfer to water i 00 kw, deterine te rate of ondenation of tea. We need te entalpy for aturated liquid and aturated vapor Speifi Tep Preure Entalpy Quality Pae C MPa kj/kg Saturated Vapor Saturated Liquid Te rate of eat tranfer to water an alo be deterined fro Q tea tea ( g f ) tea Q 00 kj/ kg/ ( ) kj/kg g f 4-7

8 Exaple A ligt oil i to be preeated before being fed to a ditillation tower. Te preeating i to be aoplied in a eat exanger in wi te eating ediu i ot oil. Te following data are available: Ma flow rate, kg/r Heat apaity, kj/kg K Entry teperature, K Ligt oil 60, Hot oil 0, ) If te ligt oil leave te eat exanger at 60 K, deterine te teperature of te exit ot oil. ) If te two fluid flow o-urrently troug te eat exanger, deterine te axiu attainable teperature of te ligt oil. ) If te two fluid flow ounter-urrently troug te eat exanger, deterine te axiu attainable teperature of te ligt oil. Q ) Deterine te teperature of te exit ot oil. p (T e T i ) p (T i T e ) T e T i T e 500 K (60,000)(.7) (60 00) K 44.4 K (0,000)(.8) p p (T e T i ) ) If te two fluid flow o-urrently troug te eat exanger, deterine te axiu attainable teperature of te ligt oil. For ourrent flow, te axiu attainable teperatrue of te ligt oil i T e T e p (T e T i ) p (T i T e ) T e T + T p i p i + p p T e (6)(.7)(00 K) + ()(.8)(500 K) (6)(.7) + ()(.8) 88.5 K Sine ) If te two fluid flow ounter-urrently troug te eat exanger, deterine te axiu attainable teperature of te ligt oil. p (60,000)(.7) 7,000 kj/r > p (0,000)(.8) 6,000 kj/r T e T i p (T e T i ) p (T i T i ) T e T i + p p ( T i T i ) T e 00 K + (0,000)(.8) (500 00) K K (60,000)(.7) 4-8