The water height from the Hoover Dam turbine inlets to the s

The water height from the Hoover Dam turbine inlets to the surface of Lake Powell is approximately 180 m. The water enters the turbines at approximately 140 km/hr at a temperature of about 8 degree C What is the water specific internal energy at the turbine inlet? Report your answer in kJ/kg. If the water temperature rose by 0.1 degree C during its pass through the turbine, how would the specific internal energy change compare to the water kinetic energy at the turbine inlet? How would it compare to the specific potential energy change associated with the water depth. Report your answers as ratios.

Solution

1unit mass of water is considered.

It has PE,KE and internal energy. the total is the internal energy of water at the inlet of the turbine

PE at 180 meter below the surface of water level is mgh = 1765.8 kj/kg

The internal energy of water at 8 degree centigrade = 33.727 kj/kg

the KE ( 1/2 mV*V ) = 2721444.5 kj/kg

Hence the total internal energy at inlet is = sum, of the above = 2723244 kj/kg

as the temperature increases by 0.1 degree, only the internal energy increases and the internal energy at 8.1 degree C = 108.34kj/kg

there fore the total internal energy at 8.1 degree C is sum of the above = 272333318.6kj/kg

Ratio of specific internal energy toIE = 2721444/2723244.5 = 0.10004

Ratio of PE to water depth = 1765.8/180 = 9.81