What is the power output of the turbine?

Question

Steam at 200(psia) and 600(°F) [state 1] enters a turbine through a 3-inch-diameter pipe with a velocity of . The exhaust from the turbine is carried through a 10-inch-diameter pipe and is at 5(psia) and 200(°F) [state 2].

Answer 1

The volumetric flow rate into the pipe is the velocity times the cross-sectional area so the volumetric flowrate is . Because the specific volume at these conditions is , the mass flowrate in is . At steady-state, the mass flow rate out must be the same as the mass flowrate in. So, if the specific volume at the outlet conditions is , then the volumetric flowrate out is The cross-sectional area of the 10-inch diameter exit pipe is , so the velocity is . Now, we can use this in the energy balance for an open

system.



We will assume that the heat loss from the turbine is negligible (Q = 0) and that the change in elevation from inlet to outlet is negligible (?z = 0), so the work output of the turbine is given by:



Our sign convention for W is that it is work done on the fluid, so the work output from the system is = 39.5 hp.