# Homework Assignment #7 Problem #1 A windmill has a

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Homework Assignment #7:

Problem #1: A windmill has a diameter of 3 meters. It converts wind energy to
electrical energy with at efficiency of 40% of the theoretical maximum for windmills.
What is the electric power output at a wind velocity of 15 miles per hour?

(5 points) The amount of wind power (P = Energy/time) incident on an area (A) is given
in the textbook as:

P / A = 6.1 × 10−4 v 3

where if the velocity is input as meters/second, one gets kilowatts/meter^2. First one
converts 15 miles/hour = 6.7 meters/second. Thus, plugging into the equation above, one
gets P/A = 0.18 kiloWatts/meter^2. Then one has to account for the maximum (Betz)
efficiency of 0.59 and the 40% of the maximum (0.4), and so one gets 0.043
kiloWatts/meter^2.

To get the power output, one must multiply by the area of the windmill (i.e. the circle
swept out by the blades). Area = π R^2 = π (D/2)^2 = 7.0 meters^2. The total electrical
power output is 0.043 x 7.0 = 0.304 kilowatts or 304 Watts.

Problem #2: How many 60 Watt lightbulbs can be supplied with the electricity
described above?

(2 points) Since the above answer is ~ 300 Watts, one can supply electricity for 5
lightbulbs.

Problem #3: "The United States could triple our hydroelectric power capacity if we
ignored environmental issues." Write a paragraph detailing quantitatively whether this is
a true or false statement.

(4 points) See the lecture notes for details. The short answer is that we have already
developed a majority of our natural resources for hydroelectric and thus tripling the
capacity is not possible.

Problem #4: What percentage of Colorado's electricity currently comes from wind
energy?

(4 points) There is an interesting article at:

Also "As the 11th windiest state, there is a lot of interest in wind- generated electricity in

But not quite enough for the Senate Committee on Appropriations, which last Friday
voted 6-4 to table a bill mandating utilities to eventually produce 25 percent of the state's
electrical energy through renewable energy sources. Two earlier bills with similar
features also died this session.

SB 151 bore no fiscal note, meaning it would not have cost Colorado additional funds to
pass it. However, it would have required that 25 percent of the state's electricity come
from renewable sources by 2025, with 7 percent by 2010. Presently, about 1 percent of
Colorado's electricity is wind generated."

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