Physics 12: Homework #5: due May 17



Part of this week's assignment is adapted from Chapter 5 of the book.

  1. The UCSD campus has installed 1.2 MW of solar PV (peak) capacity. Given five hours of full-sun-equivalent hours per day, how many MWh (big brother to the kWh) would you expect campus to generate in a year from the PV array? Compared to an annual energy appetite in the neighborhood of 200,000 MWh, what fraction of the campus' needs are met by the PV setup?

  2. Campus measures approximately 1.5 km by 2.0 km. If using 15% efficient PV panels, what fraction of campus would have to be covered in order to meet the total demand of 200,000 MWh in a year, assuming that each panel would be exposed to 5 hours of 1000 W/m² incident sunlight per day? (hint: first work out the peak power of the PV panels in full sun, which should several times higher than the average campus demand of about 25 MW, due to day/night/weather impediments)

  3. How many showers per day could be supported by a single hot water panel with an area of 1 m²? Assume 5 hours of full-sun equivalent per day. It's up to you to make up reasonable numbers for everything else you need.

  4. (Adapted from MC 5.2) If a 50-meter high waterfall has a flow rate of 300 kg per second (about 2000 showers), what is the power, in Watts, of the stream of water as it hits the bottom?

  5. (Adapted from Q&P 5.4) If a windmill produces 25 kW of electric power at a wind velocity of 5 meters per second, how much power will it produce at a wind velocity of 10 m/s? I'll bet you can do this without a calculator, if you use scaling relations!

  6. (Adapted from Q&P 5.5) A windmill has a diameter of 10 meters. It converts wind energy into electrical energy at an efficiency of 60% of the theoretical maximum when connected to an electrical generator.
    1. What is the electric power output at a wind velocity of (1) 5 m/s? (2) 10 m/s? (3) 15 m/s?
    2. How many households would be satisfied under conditions of (1), (2), and (3), if a typical household runs at an average power of 1000 W (24 kWh per day)?

  7. Considering typical windmill efficiencies, if we found a site with a steady wind always at 10 m/s throughout the year, how much energy, in kWh, would we be able to collect per square meter of windmill area? If a house uses 20 kWh every day, how many square meters of windmill will it take to satisfy the house in this magically windy place (careful to account for year vs. day)?

  8. So far in the class, we have talked about solar, hydroelectric, and wind as renewable schemes for producing energy. Make some informed/thoughtful statements about the advantages and limitations of each, and articulate a strategy that you would advocate in a role as adviser to the President of the U.S.


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