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; V₁ = 50 m/s; Z₁=2mAt exit: P₂  = 10kPa; x = 0.95; Z₂  = 5 m;  V₂  = 120 m/s Heat exchanged during expansion = Q = - 5 kJ/sec From superheat steam which is given as table, at 3MPa and 350ºC h₁ = 3115.25 kJ/kgh2 = h_f2  + xh_fg2 From saturated steam table;  at 10kPa h₂  = 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 (h₂ - h₁) - 5 - 1W₂ = 1 × (2464.99 - 3115.25) ₁W₂ = 645.26KJ/sec

% Error introduced if kinetic energy and potential energy terms are ignored: