1.1. The diagram below shows a possible design for a pumped storage system used to generate electricity. 

Figure 1

Water from the upper reservoir is to fall through a vertical distance of 120 m before reaching a powerplant chamber. The water rotates a turbine in the chamber that drives an electricity generator. After leaving the turbine, the water travels through an exit pipe to a lake.

Show that the maximum possible speed of the water as it arrives at the turbine is about 50 m s⁻¹.

1.2. The volume of water flowing into the turbine every second is 4.5 m³. 

Deduce the radius of the intake pipe that is required for the system.

1.3. The water leaves the powerplant chamber at a speed of 19 m s⁻¹. 

Calculate the maximum possible power output of the turbine and generator. 

Give an appropriate unit for your answer.

Density of water = 1000 kg m⁻³.

1.4. Energy losses are estimated to reduce the output power for the turbine and generator to 60% of the value you calculated in part (c). 

Explain two possible reasons for this energy loss.