(a) Explanation Write the expression for the saturated temperature at state 2. T 2 s = T 1 ( p 2 p 1 ) k − 1 / k (I) Here, the specific heat ratio is k , the temperature at state 1 is T 1 , the saturated temperature at state 2 is T 2 s , the pressure at inlet of turbine is p 1 and the pressure at exit of turbine is p 2 . Write the expression for the saturated temperature at state 4. T 4 s = T 3 ( p 4 p 3 ) k − 1 / k (II) Here, the temperature at state 3 is T 3 , the saturated temperature at state 4 is T 4 s , the pressure at state 3 is p 3 and the pressure at state 4 is p 4 . Write the expression for the temperature at state 4. T 4 = T 3 − η t ( T 3 − T 4 s ) (III) Here, the temperature at state 4 is T 4 and the turbine efficiency is η t . Write the expression for the temperature at state 2. T 2 = T 1 + ( T 2 s − T 1 η c ) (IV) Here, the temperature at state 2 is T 2 and the compressor efficiency is η c . Write the expression for the specific enthalpy at saturated state 7. h 7 = h f + x 7 ( h g − h f ) (V) Here, the dryness fraction at state 7 is x 7 the specific enthalpy for saturated liquid is h f , the specific enthalpy for saturated vapor is h g and the specific enthalpy at state 7 is h 7 . Write the expression for the specific enthalpy at saturated state 9. h 9 = h 8 + V 8 ( p 9 − p 8 ) (VI) Here, the specific enthalpy at state 9 is h 9 , the pressure at state 8 is p 8 , the pressure at state 9 is p 9 and the specific enthalpy for saturated state 8 is h 8 . Write the expression for the mass flow rate for steam. m ˙ s = m ˙ g c p ( T 4 − T 1 ) ( h 5 − h 9 ) (VII) Here, the rate of the mass flow of steam is m ˙ s , the specific enthalpy at state 5 is h 5 , the specific heat constant at constant pressure is c p and the mass flow rate of the gas is m ˙ g . Write the expression for the mass flow rate for water. m ˙ w = m ˙ s ( h 7 − h 8 ) ( h 11 − h 10 ) (VIII) Here, the rate of the mass flow of water is m ˙ w , the specific enthalpy at state 7 is h 7 , the specific enthalpy at state 10 is h 10 , the specific enthalpy at state 11 is h 11 . Conclusion: Convert temperature from degree Fahrenheit to degree Rankin. 180 ° F + 460 = 640 ° R Substitute 640 ° R for T 1 , 1.67 for k , 200 lbf / in 2 for p 1 and 800 lbf / in 2 for p 2 in Equation (I). T 2 s = ( 640 ° R ) ( 800 lbf / in 2 200 lbf / in 2 ) 1.67 − 1 1.67 = ( 640 ° R ) ( 4 ) 0.401 ≈ 1116.16 ° R Convert unit of temperature 1400 ° F to degree Rankin. 1400 ° F = 1400 ° F + 460 = 1860 ° R Substitute 1860 ° R for T 3 , 1.67 for k , 200 lbf / in 2 for p 4 and 800 lbf / in 2 for p 3 in Equation (II). T 4 s = ( 1860 ° R ) ( 200 lbf / in 2 800 lbf / in 2 ) 1.67 − 1 1.67 = ( 1860 ° R ) ( 0.25 ) 0.401 ≈ 1066.80 ° R Substitute 1860 ° R for T 3 , 0.8 for η t and 1066.80 ° R for T 4 s in Equation (III). T 4 = 1860 ° R − 0.8 ( 1860 ° R − 1066.80 ° R ) = 1860 ° R − 634.56 ° R =1225 .44 ° R Substitute 640 ° R for T 1 , 0.8 for η c and 1116.16 ° R for T 2 s in Equation (IV). T 2 = 640 ° R + ( 1116.16 ° R − 640 ° R 0.8 ) = 640 ° R + 595.2 ° R =1235 .2 ° R Refer to table A-3E “properties of saturated water (liquid-vapor): pressure table” to obtain the specific enthalpy at pressure p 5 = 1200 lbf / in 2 as 1183.9 Btu / lb . Refer to table A-4E “properties of superheated water vapor” to obtain the specific enthalpy at temperature T 6 = 800 ° F and pressure p 6 = 1200 lbf / in 2 as 1378 (b) To determine The net power developed by the gas turbine. The net power developed by the vapor cycle. (c) To determine The overall thermal efficiency of the plant.

8th Edition

ISBN: 9781119391630

Author: MORAN

Publisher: WILEY

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Chapter 9.14, Problem 94P

(a)

To determine

The mass flow rate of the steam.

The mass flow rate of the cooling water.

(b)

To determine

The net power developed by the gas turbine.

The net power developed by the vapor cycle.

(c)

To determine

The overall thermal efficiency of the plant.

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Chapter 9.14, Problem 93P

Chapter 9.14, Problem 95P

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The mass flow rate of the steam. The mass flow rate of the cooling water.

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The mass flow rate of the steam. The mass flow rate of the cooling water.

The net power developed by the gas turbine. The net power developed by the vapor cycle.

The overall thermal efficiency of the plant.

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Chapter 9 Solutions

The mass flow rate of the steam.

The mass flow rate of the cooling water.

The net power developed by the gas turbine.

The net power developed by the vapor cycle.