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Final_Fall_2004 - FINAL EXAMINATION THERMO I OPEN BOOK...

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FINAL EXAMINATION THERMO I 5/15/2004 OPEN BOOK PORTION 1.) A pump takes 20 kg/sec of water at 25°C, 1 atm, through an inlet pipe of 10 cm diameter, and raises it to a final pressure of 1 MPa. The outlet pipe diameter is 1 cm. The pump efficiency is 90 percent. Find: a) The velocity of the water in the inlet pipe. b) The velocity of the water in the outlet pipe. c) The power required to drive the pump (kW). Conservation of mass: m in = m out First law: 2 2 IN IN IN c OUT OUT c W + m(h + /2g ) = m(h + /2g ) v v & & & (a): IN in m= A /v v & ; From Table 10s, v in = v l,sat (T in ) = v out = 0.001003 m 3 /kg so IN IN =mv/A v & = 0.001003(m 3 /kg)x20(kg/s)/( π x0.1 2 /4)(m 2 ) = 2.55 m/s (b): v out = v in (A in /A out ) = 2.55 x (10/1) 2 = 255 m/s (c): For an incompressible fluid, isentropic process, Eq. (6.58) gives (h out - h in ) s = v L (P out - P in ) = 0.001003x(1000-101.3) = 0.9014 kJ/kg, and first law becomes IN,S W & = m & [0.9014 + (1/2g c )( v 2 out - v 2 in )] = 20(kg/s)[0.9014 (kJ/kg) + (1/2x1000 (J/kJ))(255 2 -2.55 2 )] = 20x(0.9014+32.51) = 668.2 kW IN,A W & = IN,S W & / η P = 668.2/0.9 = 742.4 kW Note the Table or Figure number for all data used in your solution
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2.) A Rankine cycle operates at a boiler pressure of 800 kPa, and the superheater brings the exit temperature of the steam entering the turbine to 500°C. The condenser operates at 8 kPa.
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