Barrage Tidal System. You have a summer cabin on a remote island in the San Juan Islands of Peugeot Sound near Seattle. Currently, the only power you have at the cabin is a noisy and smelly gasoline generator that you would like to replace. On the shore of your island near your cabin is a natural cleft in the steep shoreline. If build a low dam across the cleft at the proper height, the dam would be flooded at high tide, but would create a pool or lagoon behind it at low tide. If you install a pipe through the bottom of the dam with a simple turbine and generator, you could generate electricity on the ebb flow of the tide. You do some quick measurements and find that the area of the lagoon behind the dam would be about 5m wide by 20m long, and the lagoon would be about 3m deep at high tide, and 1m deep at low tide.

a. As you think about going forward with this project, what environmental factors should you consider?
b. Assuming a capacity factor of 25%, how much energy could you generate from this setup with each tidal cycle? Recall that E=1397ηR 2A for each tidal cycle, where η is the capacity factor, R is the range of the tide in meters, and A is the area of the tidal pool in square kilometers.
c. How long could you light a 100W bulb with this energy if it all could be captured and used without loss?
d. Should you proceed with the project?