A hydraulic turbine is fed with water from a reservoir whose free surface is at z₁ = 22 m a.s.l. (above sea level). Water enters the turbine inlet pipe, flows through the turbine and its diffuser, and is discharged downstream of the dam at z₂ = 14 m a.s.l.

Calculate the average power that the hydraulic turbine can generate over a year. The mean annual water mass flow rate is 200 m³/s. Choose carefully between control mass or control volume for your analysis.
Assume that the following idealizations hold: (a) One-dimensional flow at 1 and 2. (b) No energy transfer as heat occurs anywhere. (c) The flow kinetic energy at 1 and 2 is negligible. (d) Flow friction forces along the inlet pipe and the diffuser are negligible, except for those acting on the blades of the turbine, which reduce the amount of kinetic energy of the water that is converted into mechanical power at the shaft. Take into account this thermodynamic loss by assuming that the hydraulic efficiency of the turbine is 94%. Is the control mass concept useful in this case? Justify your answer.

Transcribed Image Text:

turbine dx₁ P₁ 1 high inlet power shaft control mass at time t control mass at time t + dt control volume at all times 2 low outlet dx₂ Z1