EPS219 – Energy and the Environment
Homework#9 – Due in class, Thursday, April 11, 2013
1) The gradient of the Mississippi River is about 0.37 ft/mile as it passes through
New Orleans. Suppose that you dammed the river so that the reservoir extended
3 miles behind a hydroelectric dam. How much power could you theoretically
get out of the dam? (Hint: You will need to find on the web what the discharge of
the River is.)
Answer: (15 pts) (Can be done two different ways)
(From my powerpoint lecture) Power (kW) = 5.9 x Flow (m3/s) x Head (m)
Head = 0.37 ft/mi x 3 mi = 1.1 ft = 0.34 m
Average Flow = ~ 17,000 m3/s [Answer can vary]
Power = 5.9 x 17,000 x .34 = 34,000 kW = 34 MW [Answer can vary][In this case,
the “5.9” accounts for a loss in efficiency]
Or
E = mgh so Power = mgh/s = volume x density x g x h /s =
(17,000 m3/s)(1000 kg/m3)(9.8 m/s2)(0.34m)= 57 MW [This doesn’t take loss
of efficiency into effect]
2) Explain why coastlines tend to be good locations for wind energy?
(10 pts) Answer: Because there is often a breeze blowing perpendicular to the
coast because of differences between the land and ocean temperatures. In the
day time, the land is usually warmer, so breezes blow from the ocean to the land.
During the night time, this is reversed.
3) Suppose a wind turbine has blades with a radius of 50 m, and the wind is
blowing at 8 m/s. What is the theoretical maximum power that that turbine
could capture? What happens to the theoretical maximum power if you increase
the wind speed by 50%?
Answer: (15 pts)(Can be done 2 different ways)
If you just use E=.5mv2:
Power = E/s = 0.5 x A x rho x v3 = (0.5)(pi)(50m)2(1.2 kg/m)(8 m/s)3
= 2.4 MW
If you change the wind speed to 12 m/s, the power goes up to 8.1 kW
If you use the “Betz limit” equation from the book:
Power = 2.83 x 10-4 D2v3 kW = (2.83 x 10-4)(100m)2(8m/s)3 = 1.4 MW
If you change the wind speed to 12 m/s, the power goes up to 4.9 MW
4) Why are there two high tides and two low tides each day?
Answer: (10 pts) Because there are two bulges from the tides, one on the front
and back of the earth. So, as Earth rotates over a day, a point on Earth will pass
through both bulges, so will experience two high tides.
5) If you need a steady source of power, explain what the concerns are for
hydroelectric, wind, tidal, and ocean wave energy.
Answer: (20 pts)
Hydroelectric – mostly quite constant, but the amount of power can change over
longer periods of time (weeks to months) if the amount of rainfall changes
between seasons.
Wind – Very unpredictable. Can change over many different time scales, from
minutes to days. One day it can be very windy, the next, not windy at all.
Tidal – VERY predictable, but the magnitude varies significantly over both daily
and monthly cycles. But you know what they will be.
Ocean waves – Like wind, it can change over minutes to days.
6) Geothermal is a renewable form of energy. However, why is it that you could
expect to get not more than a few decades of power out of a deep rock
geothermal system?
Answer: (10 points) Because the water cools the rock off and the conduction of
heat is so slow, after a few decades the temperatures are too cool to efficiently
generate power.
HOWEVER, I originally had a typo here (I left out the “not”), so if someone
answers it the other way, give them full credit as well.