Question 6.CSGP.79: A steam turbine receives water at 15 MPa, 600°C at a rate of......
A steam turbine receives water at 15 MPa, 600°C at a rate of 100 kg/s, shown in Fig. P6.79. In the middle section 20 kg/s is withdrawn at 2 MPa, 350°C, and the rest exits the turbine at 75 kPa, and 95% quality. Assuming no heat transfer and no changes in kinetic energy, find the total turbine power output.
C.V. Turbine Steady state, 1 inlet and 2 exit flows.
Continuity Eq.6.9: \dot{ m }_1=\dot{ m }_2+\dot{ m }_3 ; \quad \Rightarrow \quad \dot{ m }_3=\dot{ m }_1-\dot{ m }_2=80 \,kg / s
Energy Eq.6.10: \dot{ m }_1 h _1=\dot{ W }_{ T }+\dot{ m }_2 h _2+\dot{ m }_3 h _3
Table B.1.3
\begin{aligned}& h _1=3582.3 \,kJ / kg , \\& h _2=3137\, kJ / kg\end{aligned}
Table B.1.2 :
\begin{aligned}h _3 & = h _{ f }+ x _3 h _{ fg }=384.3+0.95 \times 2278.6 \\& =2549.1 \,kJ / kg\end{aligned}
From the energy equation, Eq.6.10
\Rightarrow \quad \dot{ W }_{ T }=\dot{ m }_1 h _1-\dot{ m }_2 h _2-\dot{ m }_3 h _3=91.565 \,MW
