Evaluate the power output of turbine:
Q: A turbine in steam power plant operating under steady state conditions receives the superheated steam at 3MPa and 350ºC at the rate of 1kg/s and having velocity of 50m/s at an elevation of 2m above the ground level. The steam leaves turbine at 10kPa with a quality of 0.95 at an elevation of 5m above ground level. The exit velocity of steam is 120m./s. The energy losses as heat from turbine are estimated at 5kJ/s. Estimate the power output of turbine. How much error will be introduced, if kinetic energy and the potential energy terms are ignored?
Sol.: Given that; the turbine is running under steady state condition. At inlet:
P1 = 3MPa; T1 = 350°C; m_{f} = 1 kg/sec; V_{1} = 50 m/s; Z_{1}=2mAt exit: P_{2} = 10kPa; x = 0.95; Z_{2} = 5 m; V_{2} = 120 m/s Heat exchanged during expansion = Q = - 5 kJ/sec From superheat steam which is given as table, at 3MPa and 350ºC h_{1} = 3115.25 kJ/kgh2 = h_{f2} + xh_{fg2} From saturated steam table; at 10kPa h_{2} = 191.81 + 0.95(2392.82) = 2464.99 kJ/kg
From the steady flow energy equation:
If the changes in kinetic and potential energies are neglected; then
SFEE as; Q - W_{s} = m_{f} (h_{2} - h_{1}) - 5 - 1W_{2} = 1 × (2464.99 - 3115.25) _{1}W_{2 }= 645.26KJ/sec
% Error introduced if kinetic energy and potential energy terms are ignored: