Heat Flow Question

The thermal resistance
R
of insulation is given by the
expression:
Q
h
=
A
(T
high
– T
low
)/
R, where
Q
h
is the flow
rate of heat
(btu/hr) across a wall with cross-sectional area
A
(ft
2). The heat flow
from the
side of the wall with the higher temperature T
high
(o
F) to
the side with the
lower temperature T
low (o F). Estimate the flow rate of heat across a wall that
is 8.0 ft high
and 10.0 ft long. The temperature difference on a winter day is: T
high – T
low = 50
oF, and the
R-value is 13 [
oF – ft
2/(btu/hr)

Mark whether the statements as written are “true” or “false”. If the statement is
false, make minor changes to the statement so that the statement is true.
T
1. ____
Heat transfers in the direction from hot to cold.
More
F
2. ____
Less than 5% of the world’s oil reserves is located in the United States. (It’s actually 18%)
F
3. ____
Resources such as wind, solar energy, and hydropower, are considered
nonrenewable resources because they cannot be replenished as they are
used up.
T
4. ____
Energy generated by hydropower produces nearly 10% of the electricity
in the U.S.
F
5. ____
Because a hydropower plant uses water, hydropower is considered a
nonrenewable resource.
T
6. ____
The largest utility costs for UAB’s operation is for electricity (based on
2018 data).
F
7. ____
The theoretical efficiency indicated by the Carnot cycle, states that:
 = 1 – (T H/T C).
plant
F
8. ____
The largest operational hydropower pant in the world is located at
Hoover Dam, located in Clark County, Nevada. Yichang, Hubei province. China
T
9. ____
Overall efficiency of hydroelectric power stations are typically 80% to
95%.
T
10.____
Driving gasoline-powered vehicles and burning coal to generate
electricity both contribute to global warming.
Only one I’m not sure
of. Found Data at:
https://www.uab.edu/f
inancialaffairs/images
/documents/reporting/
2018-financial-report.
pdf
1
MULTIPLE CHOICE: (40 points; 4 points each) Choose the most appropriate
answer to the following (for those problems requiring short calculations, you need
to show your work to receive full credit):
11. ____ The joule is a unit of:
(a)
(b)
(c)
(d)
Work
Weight
Power
Force
12. ____ Kinetic energy refers to:
(a)
(b)
(c)
(d)
Energy of position
Energy of motion
Energy stored in fossil fuels
Electrical energy
13. ____ Roughly, what fraction of our nation’s current energy needs is supplied
by coal?
(a)
(b)
(c)
(d)
(e)
10 %
20 %
30 %
40 %
80 %
14. ____ Which of the following is a nonrenewable resource?
(a)
(b)
(c)
(d)
(e)
Solar
Hydroelectric
Methane
Coal
Wind
15. ____ Which of the following is not a method of heat transfer?
(a)
(b)
(c)
(d)
Conduction
Convection
Condensation
Radiation
16. ____ How much power does the U.S. produce from hydroelectricity?
(a)
(b)
(c)
(d)
7%
36 %
57 %
10 %
2
17. ____ How much does it cost UAB to operate on an annual basis (based on
costs from FY 2018 – 2019)?
Only one I’m not sure
of. Found Data at:
https://www.uab.edu/f
inancialaffairs/images
/documents/reporting/
2018-financial-report.
pdf
(a)
(b)
(c)
(d)
(e)
~$48,000,000
~$100,000,000
~$52,000,000
~$62,000,000
~$30,000,000
18. ____ The following is not an advantage for hydropower:
(a)
(b)
(c)
(d)
It is renewable;
It has low maintenance costs;
It costs very little to make;
Fuel is not burned.
19. ____ What pulls water into the penstock?
(a)
(b)
(c)
(d)
Gravity
The force of all the water
The turbine
None of the above.
20. ____ Which of the following statements about hydropower dams is untrue?
(a) Hydropower dams impede or prevent the migration of fish.
(b) Hydropower dams and large reservoirs displace large numbers of
people.
(c) Dam building can cause downstream changes such as increased
water temperature and fluctuating water levels.
(d) Hydropower is an unreliable and nonrenewable source of power.
(e) All of the above.
(f) None of the above.
SHORT ANSWER
21.
Describe the difference between energy and power.
Energy is the total amount of work done whereas power is how fast you can complete the work.
3
22.
Why is the Pelton wheel considered an impulse device?
Because It extracts energy from the impulse of moving water, unlike the traditional water wheel that uses the
water’s dead weight.
23.
Why is the Francis turbine classified as a radial-flow device?
Because the flow of water is radial at entry and then turned into axial at discharge.
24.
The Mississippi River has an immense flow rate
(~593,000 ft³/sec) driven by small elevation difference. Would a Pelton wheel
(impulse device), a Francis turbine, or a Kaplan turbine be the best choice for
generating power from the Mississippi River? Why?
Kaplan because it allows efficient power production in low head applications. The head ranges from 10-70 meters
and the output from 5 to 200MW. The Pelton turbine is used at high elevation differences or heads of greater than
25 metres.and the Francis is most suitable in very large storage hydropower systems with medium flow rates.
4
ANALYTICAL PROBLEMS
25.
The Glen Canyon Dam in Arizona dams the Colorado River creating
Lake Powell behind it. The dam is 710 feet tall. Total (maximum
continuous) generating capacity for the power plant is approximately 1.0
GW (1 million kilowatts). Assume the effective head of the hydroelectric
plant is 700 feet, and it has a generating efficiency of 90%.
(a)
At maximum capacity, determine what flow is required
through the hydroelectric plant’s turbines to generate its generating
capacity (nameplate power). Express the flow in cubic meters/sec.
(b)
If the dam operates at 60% of capacity on average, determine
how much energy it produces on an annual basis. Express your answer in
watt units (e.g., W, kW, MW, GW, etc.).
26. The thermal resistance R of insulation is given by the
expression: Q h = A (T high – T low)/R, where Q h is the flow rate of heat
(btu/hr) across a wall with cross-sectional area A (ft 2). The heat flow from the
side of the wall with the higher temperature T high (o F) to the side with the
lower temperature T low (o F). Estimate the flow rate of heat across a wall that
is 8.0 ft high and 10.0 ft long. The temperature difference on a winter day is:
T high – T low = 50 oF, and the R-value is 13 [oF – ft 2/(btu/hr)].
5