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6 - Prob 4.26 PROBLEM 4.26 PROBLEM STATEMENT Determine the...

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Prob 4.26 9/19/04 PROBLEM 4.26 PROBLEM STATEMENT: Determine the amount of power produced or consumed by the device below. The medium is air. DIAGRAM DEFINING SYSTEM AND PROCESS: P 3 = 100 kPa T 3 = 100°C v 3 = 150 m/s 3 m = 8 kg/s & P 1 = 5.0 MPa T 1 = 500°C 1 0 v P 2 = 500 kPa T 2 = 200°C v 2 = 200 m/s 2 m = 5 kg/s & & IN/OUT W = ? IN Q = 500 kW & P 4 = 300 kPa T 4 = 300°C 4 m = 3 kg/s & 4 3 2 1 GIVEN: Air, Q & IN = 500 kW State 1: P 1 = 5.0 MPa, T 1 = 500°C, 1 0 v State 2: P 2 = 500 kPa, T 2 = 200°C, v 2 = 200 m/s, m = 2 5 kg/s & State 3: P 3 = 100 kPa, T 3 = 100°C, v 3 = 150 m/s, m = 3 8 kg/s & State 4: P 4 = 300 kPa, T 4 = 300°C, m = 4 3 kg/s & FIND: Power, & IN/OUT W (kW) (determine direction) ASSUMPTIONS: Steady state steady flow, NPE at all states. Since direction of work is unknown, assume W (sign of result will confirm if correct) & OUT GOVERNING RELATIONS: Mass balance, IN OUT m = m & & Energy balance, & & IN IN Q + W + & 2 IN IN IN c c g m h + + z 2g g IN v & OUT - Q & & 2 OUT OUT OUT OUT c c g - W m h + + z 2g g OUT v = 0 QUANTITATIVE SOLUTION: From mass balance equation: m + 1 2 3 m = m +m & & & & 4 Substituting into the energy balance equation: [ ] & & & & & & & & & & & & & & 2 2 OUT 3 4 2 1 2 2 2 c 3 3 3 c 4 4 IN 2 2 2 2 1 3 1 3 4 1 4 2 2 c 3 3 c IN W = m +m - m h +m h + 2g - m h + 2g - m h +Q = m (h -h )+m (h -h )+m (h -h )+ 0.5m /g - 0.5m /g +Q v v v v Properties of air can be obtained from Table 5s as follows:
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Prob 4.26 9/19/04 1 3 2 4 h = 793.56 kJ/kg h = 374.60 kJ/kg h = 476.32 kJ/kg h = 579.79 kJ/kg Thus, the power is: [ ] × × & & OUT 2 2 2 2 2 OUT W = 5(476.32 - 793.56)+ 8(793.56 - 374.60)+3(793.56 -579.79) (kg/s)(kJ/kg) 1 1kJ + 2.5(200 ) - 4(150 ) (kg/s)(m /s ) + 500 (kW) 1kg m s N 1000J W = +2916.79 kW (+ sign means power is out as assumed) DISCUSSION OF RESULTS: Heat transfer and work terms in the energy balance can be arbitrarily assumed to be either in or out of the system. If the numerical result for had turned out to be negative, it simply would have indicated that the actual power was opposite to the assumed direction, i.e., into the system. & OUT W PROBLEM 4.27 PROBLEM STATEMENT: A nitrogen compressor in a chemical plant adiabatically compresses 600 ft 3 /s of N 2 from 15 psia and 77 °F to 300 psia and 900 °F. The nitrogen then passes through a heat exchanger, where it is cooled at constant pressure to an outlet temperature of 150 °F. Determine the power input (kW) to the compressor and the rate of heat transfer (Btu/hr) out of the nitrogen in the heat exchanger. Assume constant specific heats evaluated at the mean
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