(a)
The mass flow rate of air in the gas-turbine cycle.
(a)
Answer to Problem 109RP
The mass flow rate of air in the gas-turbine cycle is
Explanation of Solution
Show the T-s diagram as in Figure (1).
Express Prandtl number at state 8s.
Here, pressure at state 8s is
Express enthalpy at state 8.
Here, enthalpy at state 7 is
Express Prandtl number at state 10s.
Here, pressure at state 10s is
Express enthalpy at state 10.
Here, enthalpy at state 9 is
Express enthalpy at state 1.
Here, enthalpy of saturation liquid at pressure of
Express specific volume at state 1.
Here, specific volume of saturation liquid at pressure of
Express initial work input.
Here, pressure at state 2 and 1 is
Express enthalpy at state 2.
Express quality at state 4s.
Here, entropy at state 4s is
Express enthalpy at state 4s.
Here, enthalpy at saturation liquid and evaporation at pressure of
Express enthalpy at state 4.
Here, enthalpy at state 3 is
Express quality at state 6s.
Here, entropy at state 6s is
Express enthalpy at state 6s.
Here, enthalpy at saturation liquid and evaporation at pressure of
Express enthalpy at state 6.
Here, enthalpy at state 5 is
Express the mass flow rate of air in the gas-turbine cycle from energy balance equation.
Here, enthalpy at state 10 is
Conclusion:
Refer Table A-17, “ideal gas properties of air”, and write the enthalpy at state 7 and Prandtl number at state 7 corresponding to temperature at state 7 of
Substitute
Refer Table A-17, “ideal gas properties of air”, and write the enthalpy at state 8s corresponding to Prandtl number at state 8s of
Write the formula of interpolation method of two variables.
Here, the variables denote by x and y is Prandtl number at state8s and enthalpy at state 8s respectively.
Show the enthalpy at state 8s corresponding to Prandtl number as in Table (1).
Prandtl number at state 8s |
Enthalpy at state 8s |
9.684 | 523.63 |
9.849 | |
10.37 | 533.98 |
Substitute
Thus, enthalpy at state 8s corresponding to Prandtl number at state 8s of
Substitute
Refer Table A-17, “ideal gas properties of air”, and write the enthalpy at state 9 and Prandtl number at state 9 corresponding to temperature at state 9 of
Here, enthalpy at state 9 is
Substitute
Refer Table A-17, “ideal gas properties of air”, and write the enthalpy at state 10s corresponding to Prandtl number at state 10s of
Show the enthalpy at state 10s corresponding to Prandtl number as in Table (2).
Prandtl number at state 10s |
Enthalpy at state 10s |
52.59 | 843.98 |
56.3 | |
57.60 | 866.08 |
Use excels and substitutes the values from Table (II) in Equation (XVI) to get,
Here, enthalpy at state 10s is
Substitute
Refer Table A-17, “ideal gas properties of air”, and write the enthalpy at state 11 corresponding to temperature at state 11 of
Here, enthalpy at state 11 is
Refer Table A-5, “saturated water-pressure table”, and write the properties at pressure of
Substitute
Substitute
Substitute
Substitute
Refer Table A-6, “superheated water”, and write the properties corresponding to pressure at state 3 of
Here, enthalpy and entropy at state 3 is
Due to throttling process, entropy at state 3 is equal to entropy at state 4s.
Refer Table A-5, “saturated water-pressure table”, and write the properties corresponding to pressure of
Substitute
Substitute
Substitute
Refer Table A-6, “superheated water”, and write the properties corresponding to pressure at state 5 of
Here, enthalpy and entropy at state 5 is
Due to throttling process, entropy at state 5 is equal to entropy at state 6s.
Refer Table A-5, “saturated water-pressure table”, and write the properties corresponding to pressure of
Substitute
Substitute
Substitute
Substitute
Hence, the mass flow rate of air in the gas-turbine cycle is
(b)
The rate of total heat input.
(b)
Answer to Problem 109RP
The rate of total heat input is
Explanation of Solution
Express the rate of total heat input.
Conclusion:
Substitute
Hence, the rate of total heat input is
(c)
The thermal efficiency of the combined cycle.
(c)
Answer to Problem 109RP
The thermal efficiency of the combined cycle is
Explanation of Solution
Express the rate of total heat output.
Express the thermal efficiency of the combined cycle.
Conclusion:
Substitute
Substitute
Hence, the thermal efficiency of the combined cycle is
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