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C a l c u l a t e t h e p r e s s u r e i n N e w t o n s p e r s q u a r e c e n t i m e t e r a t t h e b o t t o m o f a s t a t i c c o l u m n o f w a t e r 3 0 0 m e t e r s h i g h .
1 A T M = 7 6 0 m m H g ; H g = 1 3 . 6 g / c c , H 2 0 = 1 g / c c
1 A T M = 7 6 0 m m 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
How much electricenergycan be generated by the water in a lake2000meterswide by8000meterslong by100metersdeep if all the water falls through a vertical distance of500meters? Assume that the generator is 90% efficient. Express your answer in joules.
What would the electricpoweroutput be if the lake were drained over a period of one year? Express your answer in megawatts.
How large a community would this serve at the typical rate of1MWeper 1000 people (per year)?
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 y e f f = m g h e f f = 1 . 6 e 1 2 g 5 0 0 m 0 . 9 = 7 . 2 e 1 5 J o u l e s
( b ) P o w e r = W o r k / t i m e = 7 . 2 e 1 5 J o u l e s / ( 3 6 5 d * 2 4 h * 3 6 0 0 s ) = 2 . 3 e 8 W o r 2 2 8 M W
( c ) 2 2 8 , 0 0 0 p e o p l e
( d ) 1 K W - h r = 1 0 0 0 J / s ( 3 6 0 0 s ) = 3 . 6 e 6 J o r $ 0 . 0 5 / 3 . 6 e 6 J
$ 0 . 0 5 / 3 . 6 e 6 J ( 7 . 2 e 1 5 J o u l e s ) = $ 1 0 0 m i l l i o n
Calculate the energy in joules made available when1kgof water falls30metersif 90% of the energy can be converted to a useful form.
Calculate the energy in joules made available when1kgof water is cooled by 2C if 3% of this energy can be converted to a useful form.
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?
If a windmill produces23kWof electric power at a wind velocity of10milesper hour, how much power will it produce at a wind velocity of 20 miles per hour?
A windmill has a diameter of2meters. It converts wind energy to electrical energy at an efficiency of 60%of the theoretical maximumwhen connected to an electrical generator.
What is the electric power output at a wind velocity of (1)10mph? (2)20mph? (3)30mph?
How many60wattlightbulbs can be supplied with electricity under conditions of (1), (2), and (3)?
How much thermal energy in joules is made available by cooling1 c u b i c m e t e r o f r o c k f r o m 2 4 0 C t o 1 0 0 C ? T h e s p e c i f i c h e a t i s 2 . 4 J / c m 3 " C .
A g e o t h e r m a l - p o w e r e d s t e a m t u r b i n e o p e r a t e s b e t w e e n a s t e a m t e m p e r a t u r e o f 2 1 0 C a n d a n e n v i r o n m e n t a l t e m p e r a t u r e o f 2 5 C . W h a t i s i t s m a x i m u m ( i d e a l ) e f f i c i e n c y ? W h a t p e r c e n t a g e of the total steam energy must be discharged as a waste heat?
Calculate the overall efficiency of an OTEC plant that operates with the ideal Carnot efficiency between the temperatures of 20C and 5C, but which uses two-thirds of the energy extracted to run pumps and make up other losses.
Starting from the results of HYPERLINK "https://jigsaw.vitalsource.com/books/9781119179238/epub/OPS/c05.xhtml" \l "c05-fea-0004" Examples 5.4and HYPERLINK "https://jigsaw.vitalsource.com/books/9781119179238/epub/OPS/c05.xhtml" \l "c05-fea-0005" 5.5, estimate the number of cubic meters of water that would flow each second through an OTEC plant large enough (1000MWe) to provide electricity for Miami. Use the approximation of an ideal heat engine as in the examples.
If this water flows at a velocity of4m/s, what would be the necessary diameter of the pipes?
A tidal basin with an area of14squarekilometersand a depth of12metersempties in 6 hours with the water passing through turbines.
How many cubic meters per second must flow on average during this six-hour period?
How many square meters of cross-sectional area must the turbine pipes have if the flow velocity is7m/s?
Estimate the number of Btu that would be generated annually in the United States if all the municipal waste were incinerated. Assume1000poundsper year per person of burnable waste at4300Btu/lb. How does this compare with the total energy consumption of the United States?
Estimate the forest area needed to supply fuel continuously for a1000MWepower plant. Note that this requires about three times as much thermal power as electric power.
Multiple Choice Questions
Fifteen kilograms of water90metersabove a generator represents ___ joules of potential energy. 15(g)90 = H
2102
60
980
9.8
29,160
1350
1380
13,230
If a90-meterhigh waterfall has a flow rate of15kilogramsper 0.1 second, what is the power in watts in the stream of water as it hits the bottom? H
210.2
600
98
9.8
291,600
135
13,800
132,300
Hydroelectricity accounts for approximately ___ percent of the electrical energy consumption in the United States. B
1
7
40
70
How much electric power could be obtained from a small hydroelectric station if the elevation change was150metersand if10,000kgof water passed through the turbines every second, with the overall efficiency being 85%? 150(10^5)*.85 = C
1.3 MWe
25 MWe
12.5 MWe
12.5 kWe
A windmill system which produces5kWof electric power when the wind is blowing at3m/s, will produce ___ kilowatts when the wind is at9m/s. 5 (93 / 33) = (D)
1.67
15
45
135
A wind of30m/sproduces ___ times as much power per square meter as does a wind of10m/s. A
27
9
3
36
If the wind blows for one year at a steady10m/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.
2200 <
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I t w i l l e a s i l y s u p p l y a l l t h e e n e r g y n e e d s o f the United States.
Since it basically comes from the sun, it is renewable.
It has its origins in the earth's radioactivity, and it can be exhausted locally.
The Geysers in California has a capacity of512GWe.
A geothermal-powered steam turbine operates between a steam temperature of 210C and an environmental temperature of 25C. What is its maximum (ideal) efficiency?
13%
18%
23%
28%
33%
38% 1 (273+25)/(273+210) = 38%
43%
48%
The normal geothermal gradient is _____
3C/km
30C/km normal geothermal gradient (30C/km)
3C/m
30C/m
3C/1000ft
1/16W/cm2
16W/m
3K/m
Tidal energy has its origin in _____ D
the phase of the moon.
just the oceans sloshing back and forth.
the decay of primordial radioactive nuclei within the earth.
the kinetic and gravitational potential energy of the earthmoonsun system.
trade winds acting on the earth's surface.
the hydrologic cycle.
the Carnot dynamics of ideal heat engines.
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