Answer:
[tex]\dot W_{out} = 3374.289\,\frac{BTU}{s}[/tex]
Explanation:
The model for the turbine is given by the First Law of Thermodynamics:
[tex]- \dot W_{out} + \dot m \cdot (h_{in} - h_{out}) = 0[/tex]
The turbine power output is:
[tex]\dot W_{out} = \dot m\cdot (h_{in}-h_{out})[/tex]
The volumetric flow is:
[tex]\dot V = \frac{\pi}{4} \cdot \left( \frac{2}{12}\,ft \right)^{2}\cdot (620\,\frac{ft}{s} )[/tex]
[tex]\dot V \approx 13.526\,\frac{ft^{3}}{s}[/tex]
The specific volume of steam at inlet is:
State 1 (Superheated Steam)
[tex]\nu = 1.33490\,\frac{ft^{3}}{lbm}[/tex]
The mass flow is:
[tex]\dot m = \frac{\dot V}{\nu}[/tex]
[tex]\dot m = \frac{13.526\,\frac{ft^{3}}{s} }{1.33490\,\frac{ft^{3}}{lbm} }[/tex]
[tex]\dot m = 10.133\,\frac{lbm}{s}[/tex]
Specific enthalpies at inlet and outlet are, respectively:
State 1 (Superheated Steam)
[tex]h = 1479.74\,\frac{BTU}{lbm}[/tex]
State 2 (Saturated Vapor)
[tex]h = 1146.1\,\frac{BTU}{lbm}[/tex]
The turbine power output is:
[tex]\dot W_{out} = (10.133\,\frac{lbm}{s} )\cdot (1479.1\,\frac{BTU}{lbm}-1146.1\,\frac{BTU}{lbm})[/tex]
[tex]\dot W_{out} = 3374.289\,\frac{BTU}{s}[/tex]
