Barrage Energy Example

The area of morecambe bar at high water is approx. 200km^2. At low water most of the bay is exposed sand. for this exercise, we could assume that on average the sand slopes evenly so that half way between high and low tide the area of water is 100km^2.

The tidal range (between low and high tide) varies between 4m at neap tides and 8m at spring tides. To produce most energy we want to store the water at the highest level and then let it out when the tide is at its lowest, but this is not practicable as it would required very large turbines which would be used for only an hour or so per day. Therefore we decide to investigate a system that opens sluice gates whenever the sea is higher than the level of water in the bay and that allows the water to discharge though turbines whenever the level in the bay is more than 2m higher than the open sea.

A) Calculate the volume of water that is available for power generation at the extremes of spring and nap tides?
b) If during the time the turbines are running, the level of the water in the bay is 2m higher that that in the sea, what is the potential energy available from the scheme?
c) Assuming the turbines and associated machinery have an overall efficiency of 30% and the average bulk price for electricity is 2p/kWh, what annual income is available? (we can assume that the height of the tides varies evenly between neap and spring levels)
d) If investors are looking for a 15% return on capital employed, what is the maximum cost of the 17km barrage if it is to be privately financed and paid for by sales of electricity?