Consider a hydroelectric turbine. The water enters at 1 atm at 10 C and the flow

Question

Consider a hydroelectric turbine. The water enters at 1 atm at 10 C and the flow rate through the turbine is 40 m3/s. The water is discharged from the turbine 200 m below the intake at 1 atm and the temperature of the water at the discharge is 10.2 C. You may assume the water is incompressible. Consider the turbine to be adiabatic and the process to be steady. Neglect the change of kinetic energy. Determine the power output of the turbine. Determine the power, if the discharge water temperature is 10 C. Ans. 44.9 MW; 78.5 MW.

Explanation / Answer

flow rate = 40m3/s and density 1000 so mass flow rate = 40000 kg/s , and total loss in potential = mgH = 40000*9.8*200 = 78.5 MW when discharge temp = 10 C then Power output = 78.5 MW, and when discharge temp = 10. 2 C then power output = 78.5 MW - C*m*temp change = 78500000 - 4200*40000*0.2 = 78500000- 33600000 = 44900000 W = 44.9MW

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