(a) Explanation Write the expression for the saturated pressure at ambient state. p r a s = ( p a p 1 ) p r 1 (I) Here, the pressure at state 1 is p 1 , the reduced pressure at state 1 is p r 1 , the pressure at ambient state is p a and the saturated pressure at ambient state is p r a s . Write the expression for the specific enthalpy in terms of compressor efficiency at ambient state. h a = h 1 + ( h a s − h 1 η c 1 ) (II) Here, the compressor efficiency at state 1 is η c 1 , the specific enthalpy at state 1 is h 1 , the specific enthalpy at ambient state is h a and the saturated specific enthalpy at ambient state is h a s . Write the expression for the saturated pressure at state 2. p r 2 s = ( p 2 p b ) p r b (III) Here, the average pressure is p b , the reduced pressure at average pressure is p r b , the pressure at state 2 is p 2 and the saturated pressure at state a is p r 2 s . Write the expression for the specific enthalpy in terms of compressor efficiency at state 2. h 2 = h b + ( h 2 s − h b η c 2 ) (IV) Here, the compressor efficiency at second stage is η c 2 , the specific enthalpy at average temperature is h b , the specific enthalpy at state 2 is h 2 and the saturated specific enthalpy at state 2 is h 2 s . Write the expression for the specific enthalpy at regenerator. h x = η r e g ( h 4 − h 2 ) + h 2 (V) Here, the efficiency of the regenerator is η r e g , the specific enthalpy at regenerator is h x and the specific enthalpy at state 4 is h 4 . Write the expression for the net power developed. W ˙ c y c l e = m ˙ [ ( h 4 − h 3 ) − ( h a − h 1 ) − ( h 2 − h b ) ] (VI) Here, the mass flow rate is m ˙ , the net power developed for the cycle is W ˙ c y c l e , the specific enthalpy at state 3 is h 3 . Write the expression for the rate of heat transfer for the cycle. Q ˙ i n = m ˙ ( h 3 − h x ) (VII) Here, the rate of heat transfer for the combustor is Q ˙ i n . Write the expression for the thermal efficiency of the cycle. η = W ˙ c y c l e Q ˙ i n (VIII) Here, the thermal efficiency is η , Write the expression for the reduced pressure at saturated at state 4. p r 4 s = p 4 p 3 p r 3 (IX) Here, the pressure at state 3 is p 3 , the pressure at state 4 is p 4 , the reduced pressure at state 3 is p r 3 and the reduced pressure at saturated state 4 is p r 4 s . Write the expression for the specific enthalpy in terms of turbine efficiency at state 4. h 4 = h 3 − η t ( h 3 − h 4 s ) (X) Here, the turbine efficiency is η t , the specific enthalpy at state 4 is h 4 . Conclusion: Refer to table A-22E “ideal gas properties of air” to obtain the specific enthalpy and reduced pressure at temperature T 1 = 530 ° R as 126.66 Btu / lb and 1.2997 . Since, the average temperature and inlet temperature are same. Hence, the enthalpy at average temperature and inlet temperature are also same h b = 126.66 Btu / lb . Substitute 50 lbf / in 2 for p a , 14.7 lbf / in 2 for p 1 and 1.2998 for p r 1 in Equation (I). p r a s = ( 50 lbf / in 2 14.7 lbf / in 2 ) ( 1.2997 ) = ( 3.4013 ) ( 1.2997 ) = 4.4207 Refer to table A-22E “ideal gas properties of air” to obtain the saturated specific enthalpy at reduced pressure p r a s = 4.4207 as 179.90 Btu / lb . Substitute 179.90 Btu / lb for h a s , 126.66 Btu / lb for h 1 and 0.84 for η c 1 in Equation (II). h a = 126.66 Btu / lb + ( 179.90 Btu / lb − 126.66 Btu / lb 0.84 ) = 126.66 Btu / lb + 63.3809 Btu / lb = 328.34 Btu / lb ≈ 190.04 Btu / lb Calculate the ratio of pressure at state 1 and 2. p 2 p 1 = 10 p 2 = 10 ( 14.7 lbf / in 2 ) = 147 lbf / in 2 Substitute 50 lbf / in 2 for p b , 147 lbf / in 2 for p 2 and 1.2997 for p r b in Equation (III). p r 2 s = ( 147 lbf / in 2 50 lbf / in 2 ) ( 1.2997 ) = ( 2.94 ) ( 1.2997 ) = 3 (b) To determine The net power developed for the cycle. The thermal efficiency for the cycle.

8th Edition

ISBN: 9781119391630

Author: MORAN

Publisher: WILEY

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Chapter 9.14, Problem 83P

(a)

To determine

The net power developed for the cycle.

The thermal efficiency for the cycle.

(b)

To determine

The net power developed for the cycle.

The thermal efficiency for the cycle.

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Chapter 9.14, Problem 82P

Chapter 9.14, Problem 84P

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