Question 4.18: Problem: A gas turbine receives compressed air at 800 kPa an...
Problem: A gas turbine receives compressed air at 800 kPa and 300 °C, which leaves at 120 kPa and 60 °C. What should the mass flow rate of air be if a power output of 5 kW is required?
Find: Mass flow rate of air \dot{m} .
Known: Inlet pressure P_1 = 800 kPa, inlet temperature T_1 = 300 °C, outlet pressure P_2 = 120 kPa, outlet temperature T_2 = 60 °C, shaft work \dot{W} _{shaft} = −50 kW.
Assumptions: Negligible heat losses from the turbine, negligible changes in kinetic and potential energy between the turbine inlet and outlet, air is an ideal gas with constant specific heat.
Governing Equation:
Rate of shaft work (turbine) \dot{W} _{shaft}=\dot{m} (h_2-h_1)
Properties: Average temperature Tavg = (T2 + T1) / 2 = (300 °C + 60 °C) / 2 = 180 °C = 453.15 K ≈ 450 K, specific heat of air at 450 K cp = 1.020 kJ / kgK (Appendix 4).
\dot{W} _{shaft}=\dot{m} (h_2-h_1) = \dot{m} c_p(T_2-T_1)
-50 \ kJ/s = \dot{m} \times 1.020 \ kJ/kgK \times (60 \ ^\circ C-300 \ ^\circ C)
\dot{m} =0.20425 \ kg/s
Answer: The mass flow rate of air should be 0.20 kg / s.