5C2 : 
Heat Losses form a Steam Turbine 
5 pts 








Steam enters a turbine operating at steadystate with a mass flow rate of 4600 kg/h. The turbine develops a power output of 1000 kW. In the feed, the pressure is 60 bar, the temperature is 400^{o}C and the velocity is 10 m/s. For the effluent, the pressure is 0.1 bar, the quality is 90% and the velocity is 50 m/s. Calculate the rate of heat transfer between the turbine and the surroundings in kW. 
















Read : 
Apply the steadystate form of the 1st Law for open systems and solve for Q. Assume changes in potential energy are negligible. We know the values of two intensive variables for state 1, so we can look up H_{1}. We know the pressure and quality for state 2, so we can also determine H_{2}. Then, just plug back into the 1st Law to get Q ! 












Given : 
m 
4600 
kg/h 

v_{1} 
10 
m/s 


1.278 
kg/s 

P_{2} 
10 
kPa 

W_{s} 
1000 
kW 

x_{2} 
0.90 


P_{1} 
6000 
kPa 

v_{2} 
50 
m/s 

T_{1} 
400 
^{o}C 












Find : 
Q 
??? 
kW 












Diagrams : 






















































































































Assumptions: 







1  
The turbine operates at steadystate. 



2  
The change in the potential energy of the fluid from the inlet to the outlet is negligible. 










Equations / Data / Solve : 














Let's begin by writing the steadystate form of the 1st Law for open systems. 











Eqn 1 









Solve Eqn 1 for Q : 


Eqn 2 









We must use the Steam Tables to determine H_{2} and H_{1} : 














Eqn 3 









H_{1} 
3178.2 
kJ/kg 













At P_{2} = 10 kPa : 


H_{sat liq} 
191.81 
kJ/kg 





H_{sat vap} 
2583.9 
kJ/kg 





H_{2} 
2344.7 
kJ/kg 









Now, we can plug values into Eqn 2 to evaluate Q : 















Q 
63.51 
kW 








Verify : 
None of the assumptions made in this problem solution can be verified. 








Answers : 
Q 
63.5 
kW 



