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# A lake 30 km long and 20 km wide is held up by a dam 50 meters tall.

A lake 30 km long and 20 km wide is held up by a dam 50 meters tall. The water is discharged into a second lake half a mile downstream from the first lake, which is 50 m lower than the lake level of the first lake. The first lake is on average 20 meter deep. How much energy is stored in the first lake?

How big a power plant could the lake support if it is not to run dry over the course of a year even without being replenished by precipitation or stream flow?

If precipitation in the area amounts to 50cm/year, how big is the watershed area that is required to maintain the lake level roughly unchanged while still supporting the power plant size you calculated?

The downstream lake opens the opportunity for energy storage. (Assume it has no electric power potential.) We use a second power plant turbine of equal size to the first one to pump water back from the lower lake to the upper lake with wind power. At times of high power demand the second turbine produces additional hydro-power. For simplicity assume that the first turbine cannot act as a pump and that the second turbine can run either way with equal power and if running as a generator it doubles the power output of the dam. How many 100m diameter windmills would you need, to provide as much power as can be absorbed by the second turbine in the pumped storage device? Assume peak power is achieved at 10m/sec wind speed with 40% efficiency in transforming the wind’s kinetic energy into electric power? (The density of air is 1.2kg/m3).

When would it make sense to invest by: a/ adding more windmills? b/ adding another water turbine-generator? c/ raising the dam another 5m?

1. A lake 30 km long and 20 km wide is held up by a dam 50 meters tall. The water is discharged
into a second lake half a mile downstream from the first lake, which is 50 m lower than the...

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