1.1. Pumped hydroelectric systems store large bodies of water behind a dam. When electricity is needed in the grid, the dam is lifted, allowing water to flow from the upper reservoir.

One such power station, known as the Cruachan power station, is shown in Fig. 1.1. This facility has been producing hydroelectric power since 1965.

The vertical distance between the base of the upper reservoir and the turbine is 396 m. This arrangement allows Cruachan power station to produce a power output of 0.62 GW with an efficiency of 76%.

Determine the energy transferred by the water each second in order to achieve this power output.

1.2. Water is made to flow out of the upper reservoir through connecting pipes at a rate of 200 m³ per second. The density of water is 1.0 × 10³ kg m⁻³. 

(i) Use this flow rate to determine the energy transferred by the water each second.

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(ii) Explain why this value is not consistent with the energy transfer rate calculated in (a).

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1.3. Estimate the depth of the water held in the upper reservoir. State any assumptions made.