Question

As shown below, steam at 80 bars (8 MPa) and 450 degrees Centers a well-insulated turbine operating at steady state with a volumetric flow rate of 236 m/min. Twenty percent of the entering mass flow exits through a pipe of diameter 0.25 m at 60 bars (6 MPa) and 400 degrees C. The rest exits through a pipe of diameter 1.5 m with a pressure of 0.7 bars (70 kPa) and a quality of 90%. Find the velocity at each exit duct. Also determine the shaft power output of this turbine (a) neglecting changes in kinetic energy (b) including the changes in kinetic energy, and assuming low velocity at the inlet. Partial answers: Velocities at exits are 19.9 m/s and 101.6 m/s Turbine P1 = 80 bar Ti = 440°C (AV), = 236 m /min x3 = 0.90 Pz = 0.7 bar Dz = 1.5 m m2 = 0.20 m P2 = 60 bar T2 = 400°C D2 = 0.25 m

please answer specifically the second part of the problem, concerning the shaft power output of the turbine

Answer 1

Soln Pr = so bar T 1 my Pe = cobar Pi= sobar ૨, to x3=0.9 me m₂, Pz = 0.7 bar T: 4.40°c 9 = 236 mi/min Pa = 0.7 bar 3 D3= 1.5 m my=0,2 m P2 = 60 bar s To = 400°c De = 0.25m = for state : 1 Pi= go bas, T = 440°c, si = 936 m/min m²/leg 4 sp. sp. volume ma 0.037454 esb ... mis kg/min 0.036454 legls 236 60X 0.036454 I mi 107.9 kgls & Enthalpy ho = 3247.86 Kylieg. #for state: e me= 0.2m = 0.ex 107.9 = 21,58 legis for P₂ =60 bar T2=400°c enthalpy h₂ = 317.8.18 kJ/kg for state :3 3 = 0.9 P3=0.7 bar 2 m₂ = m,- m2 ... ha= hgt az chy-hf) at 0.7 bar 107.9 - 81-58 376.68 + 0.9 (26 59.41 - 376.68 ) mig = 86.32 Kyls uz = 243). 137 243). 137 kolky

@ shaft power output colo consider sidering changes in K.E. W = michi-h2) & mg (ha-ha) 10:7.9 (3247.p6 - 3178.18 ) + 86.321 3178.18 - 2431-137) 7453.73 + 64485 71938.48 KS Iw 71.94 mg Ans Considering kinetic energy changes in g-Ws mi[sh + Ske, tope.] cohere AKE. = APE change in in kinetic enengy. change in potential energy 3. = 0 ( same height)

- We loco velocity at inlet assuming very Vino mls. and V2 = 19.9 mls; V3 = 101.6 m/s given. So, Since Turbine is insulated So, steady flow energy aquation becomes, -W- {m, chahi) + m3 chy-has} + {m, (0, 1, tm. + 3 (ve-V3) 2 1000 1000 2 4. WE michi-hz) + m₂ lh2.43) (107.9)(1969-0) 15634) (101.6-1992) 2 1000 looo " Wa 71938.48 2-36 488.43 W = 71488.7 KI I wa #1-489 MJ And

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