Steam enters a turbine operating at steady state with a mass

Steam enters a turbine operating at steady state with a mass flow of 10 kg/min, a specific enthalpy of 3100 kJ/kg, and a velocity of 30 m/s. At the exit, the specific enthalpy is 2300 kJ/kg and the velocity is 45 m/s. The elevation of the inlet is 3m higher than at the exit. Heat transfer from the turbine to its surroundings occurs at a rate of 1.1 kJ per kg of steam flowing. Let g= 9.81 m/s^2. Determine the power developed by the turbine, in kW.

Solution

from energy equation, we have

     (h1 + v1^2/2 + gz1) = (h2 + v2^2/2 +gz2) + (1.1) + (power output)

here, v1^2/2 = 0.45 kJ/kg

v2^2/2 = 1.0125 kJ/kg

   g(z1-z2) = 0.0294 kJ/kg

thus, the required result is,
     3100 + 0.45 + 0.0294 = 2300 + 1.0125 +1.1 + work output

                     workout put = 798.37 kJ/kg

given that, 10 kg/min,= 1/6 kg/s

hence, the required power is,

        P = 798.37* 1/6 = 133.06 kW