Example Problem – Calculation of Turbine Shaft Power Given: Water (ρ= 998. kg/m3, µ= 1.00 ×10-3kg/m⋅s) flows from one large reservoir to another, and through a turbine as sketched. The elevation difference between the two reservoir surfaces is Hgross= 120.0 m. The pipe is 5.0 cm I.D. cast iron pipe. The total pipe length is 30.8 m. The entrance is slightly rounded; the exit is sharp. There is one regular flanged 90-degree elbow, and one fully open flanged angle valve. The turbine is 81% efficient. The volume flow rate through the turbine is 0.0045 m3/s. D2 1 Turbine turbine shaftW±Control volume Hgross To do: Calculate the shaft power produced by the turbine in units of kilowatts. Solution: •First we draw a control volume, as shown by the dashed line. We cut through the surface of both reservoirs (inlet 1 and outlet 2), where we know that the velocity is nearly zero and the pressure is atmospheric. We also slice through the turbine shaft. The rest of the control volume simply surrounds the piping system.
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