Cal Poly Pomona



CHAPTER 5

RENEWABLE ENERGY SOURCES II: ALTERNATIVES

Questions and Problems

1. Calculate the pressure in Newtons per square centimeter at the bottom of a static column of water 300 meters high.

1 ATM = 760 mm Hg; ρHg = 13.6 g/cc, ρH20 = 1 g/cc

1 ATM = 760 mm Hg (13.6/1) = 10.3 meters of H20

1 ATM at surface + 300/10.3 = 30 ATM (101325 Pa/ATM) = 3.04e6 Pascals

3.04e6 N/m2 (1m/100cm)2 = 304 N/cm2

Just for fun: 304 N/cm2 = 441 psi

2.

a) How much electric energy can be generated by the water in a lake 2000 meters wide by 8000 meters long by 100 meters deep if all the water falls through a vertical distance of 500 meters? Assume that the generator is 90% efficient. Express your answer in joules.

b) What would the electric power output be if the lake were drained over a period of one year? Express your answer in megawatts.

c) How large a community would this serve at the typical rate of 1 MWe per 1000 people (per year)?

d) At $0.05/ KWhr, what is the value in dollars of this electrical energy?

(a) 8000x100x2000 (1000 kg/m3) = 1.6e12 Kg of water

Work = Fweight Δy eff= mgh eff= 1.6e12”g” 500m 0.9= 7.2e15 Joules

(b) Power = Work / time = 7.2e15 Joules / (365d*24h*3600s) = 2.3e8 W or 228 MW

(c) 228,000 people

(d) 1 KW-hr = 1000 J/s (3600s) = 3.6e6 J or $0.05 / 3.6e6J

$0.05 / 3.6e6J (7.2e15 Joules) = $100 million

3.

a) Calculate the energy in joules made available when 1 kg of water falls 30 meters if 90% of the energy can be converted to a useful form.

b) Calculate the energy in joules made available when 1 kg of water is cooled by 2°C if 3% of this energy can be converted to a useful form.

c) Compare these two numbers. Does this say something about the relative amounts of water that must pass through a hydroelectric plant and an OTEC plant?

4. If a windmill produces 23 kW of electric power at a wind velocity of 10 miles per hour, how much power will it produce at a wind velocity of 20 miles per hour?

5. A windmill has a diameter of 2 meters. It converts wind energy to electrical energy at an efficiency of 60% of the theoretical maximum when connected to an electrical generator.

a) What is the electric power output at a wind velocity of (1) 10 mph? (2) 20 mph? (3) 30 mph?

b) How many 60 watt lightbulbs can be supplied with electricity under conditions of (1), (2), and (3)?

6. How much thermal energy in joules is made available by cooling 1 cubic meter of rock from 240°C to 100°C? The specific heat is 2.4 J/cm3⋅°C.

7. A geothermal-powered steam turbine operates between a steam temperature of 210°C and an environmental temperature of 25°C. What is its maximum (ideal) efficiency? What percentage of the total steam energy must be discharged as a waste heat?

8. Calculate the overall efficiency of an OTEC plant that operates with the ideal Carnot efficiency between the temperatures of 20°C and 5°C, but which uses two-thirds of the energy extracted to run pumps and make up other losses.

9.

a) Starting from the results of Examples 5.4 and 5.5, estimate the number of cubic meters of water that would flow each second through an OTEC plant large enough (1000 MWe) to provide electricity for Miami. Use the approximation of an ideal heat engine as in the examples.

b) If this water flows at a velocity of 4 m/s, what would be the necessary diameter of the pipes?

10. A tidal basin with an area of 14 square kilometers and a depth of 12 meters empties in 6 hours with the water passing through turbines.

a) How many cubic meters per second must flow on average during this six-hour period?

b) How many square meters of cross-sectional area must the turbine pipes have if the flow velocity is 7 m/s?

11. Estimate the number of Btu that would be generated annually in the United States if all the municipal waste were incinerated. Assume 1000 pounds per year per person of burnable waste at 4300 Btu/lb. How does this compare with the total energy consumption of the United States?

12. Estimate the forest area needed to supply fuel continuously for a 1000 MWe power plant. Note that this requires about three times as much thermal power as electric power.

Multiple Choice Questions

1. Fifteen kilograms of water 90 meters above a generator represents ___ joules of potential energy. 15(g)90 = H

a) 2102

b) 60

c) 980

d) 9.8

e) 29,160

f) 1350

g) 1380

h) 13,230

2. If a 90-meter high waterfall has a flow rate of 15 kilograms per 0.1 second, what is the power in watts in the stream of water as it hits the bottom? H

a) 210.2

b) 600

c) 98

d) 9.8

e) 291,600

f) 135

g) 13,800

h) 132,300

3. Hydroelectricity accounts for approximately ___ percent of the electrical energy consumption in the United States. B

a) 1

b) 7

c) 40

d) 70

4. How much electric power could be obtained from a small hydroelectric station if the elevation change was 150 meters and if 10,000 kg of water passed through the turbines every second, with the overall efficiency being 85%? 150(10^5)*.85 = C

a) 1.3 MWe

b) 25 MWe

c) 12.5 MWe

d) 12.5 kWe

5. A windmill system which produces 5 kW of electric power when the wind is blowing at 3 m/s, will produce ___ kilowatts when the wind is at 9 m/s. 5 (93 / 33) = (D)

a) 1.67

b) 15

c) 45

d) 135

6. A wind of 30 m/s produces ___ times as much power per square meter as does a wind of 10 m/s. A

a) 27

b) 9

c) 3

d) 36

7. If the wind blows for one year at a steady 10 m/s, the energy we could get in this year per square meter of cross section through the use of a windmill would be about ___ kWh.

a) 2200 ................
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