Question

Steam enters a well-insulated turbine operating at steady state at 4 MPa with a specific enthalpy of 3015.4 kJ/kg and a velocity of 10 m/s. The steam expands to the turbine exit where the pressure is 0.07 MPa, specific enthalpy is 2400 kJ/kg, and the velocity is 90 m/s. The mass flow rate is 30 kg/s. Neglecting potential energy effects, determine the power developed by the turbine, in kW.

Answer 1

Answer:

power developed by the turbine = 18342 kW  

Explanation:

given data

pressure = 4 MPa

specific enthalpy h1 = 3015.4 kJ/kg

velocity v1 = 10 m/s

pressure = 0.07 MPa

specific enthalpy h2 =   2400 kJ/kg

velocity v2 = 90 m/s

mass flow rate = 30 kg/s

solution

first we apply here  thermodynamic equation that is express as energy equation is  

$h1 + \frac{v1}{2} + q = h2 + \frac{v2}{2} + w$      .......................1

we know turbine is insulated so q is  0

put here value we get

$3015.4 \times 1000 + \frac{10^2}{2} = 2400 \times 1000 + \frac{90^2}{2} + w$    

w =  611400 J/kg = 611.4 kJ/kg  

and  now we get power developed by the turbine W is

W = mass flow rate × w     ................2

put here value

W = 30 × 611.4

W = 18342 kW  

power developed by the turbine = 18342 kW