1. Offshore Wave Energy. An inventor approaches you with the design for a wave energy device that he claims will generate 50 GWh of energy annually. The device has a wave inlet 25 meters wide and converts wave energy to electricity by some secret process he won't reveal.
a. Might you be interested in investing in the development of this project? Discuss.
b. How high would waves need to be to generate this amount of power? Assume the average time between waves is T = 10s and that the wave energy generator works with 100% efficiency (all available wave energy is converted to electricity)
Hint:
a. Calculate the average power of the device per meter of wave inlet assuming continuous operation (24x365). Compare this value with the Global Wave Energy Averages shown in the lecture slides.
b. Use the wave energy formula P= (H 2)(T)/2 shown in class to calculate wave height H
2. Shoreline Wave Energy. The LIMPET OWC (oscillating water column) shoreline wave generator described in class has a nameplate rating of 500 kW with wave intensities of about 20 kW/m (https://www.wavegen.co.uk/what_we_offer_limpet_islay.htm)
a. How many household could one LIMPET OWC support assuming that an average household requires an average of 1 kW power? Assume a capacity factor of 40%.
b. How many LIMPET units would be required to support a community of 25,000 households (about the size of Boulder)?
c. Discuss the pros and cons of incorporating a series of LIMPET units in a new breakwater that is to be built to protect a large marina in a resort community.
3. 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?
4. Wave Power. A container ship having a displacement of 70,000 metric tons (70 million kg) is raised 1 meter in 5 seconds by an ocean wave. Compare the lift power of the wave to the ship's shaft horsepower of 50,000 hp (37,280 kW). Discuss.
Hints:
• Calculate the increase in potential energy when the ship is raised by 1 meter using the formula E=mgh, where E is energy expressed in Joules (J), m is mass (kg), g=9.8m/s2 is the gravitational constant, and h (meters) is the height to which the mass is raised.
- Convert Joules (J) to kWh using 1kWh = 3.6 MJ (million Joules)
• Calculate the power (energy per unit time) of the wave - note that the ship is raised in 5