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EE 132B Spring 2015 with Izhak Rubin at UCLA
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MAE108 Homework 2 Solutions - Spring 2015 April 19, 2015 Problem 2.7 Define • D1 = the event that the first weld is defective • D2 = the event that the second weld is defective • D3 = …Full description
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EE-3352: Fundamentals of Electric Power Engineering Prof. Gosney Spring 205 !omewor" #2 For $onday% &anuary 2'% 205% read ()apters *-5 +pages 53-, ()apter *: Power Plants ()apter 5: En/ironmental mpact of Power Plants For 1ednesday% 1ednesday% &anuary 2% 205: ()apter * uestions: *.3% *.*% *.5% *.'% *.% *.% *.,% *.20% *.2% *.3* +pages '-
4.13) a hydroelectric power plant has a synchronous generator whose speed must be fxed at 180r/min. The Turbine is rancis !should be "elton) type 10m runner diameter. #hen the $ow rate at the no%%le o& the penstoc' is 10 m 3/s( the generated electricity is 0 *#. +& the total e,ciency o& the generator( turbine( and hydro is 88-( compute the elocity o& water et. olution 2c wr 5&r 180
5
60
.
64. m/s 7ow( "w "in p 50
"in
0.88
9.8 *# "c & δ !2i : 2c) 2c 2i 2c ;
Pc 2 f ∂V c
6
2i 64. ;
56.8 × 10 3
( )( 10 )( 94.25 )
2 10
2i 14.4 m/s <+ 14.4 m/s x 3.8 &/m x 90 mph/88 &/s =8. mph 4.14) the physical head o& an impoundment power plant is 100m. #hen the penstoc' is &ully closed( the pressure at the outta'e end is 109 7/m. #hen the penstoc' is &ully open( the pressure is reduced to 6>10 7/m. ?ompute the e@ectie head. olution h H = Pr Pr 0
h
5
(
100 9 x 10
)
6
10
h 60m Alternatie solution !and better) The actual pressure at the outta'e end &or 100 m o& physical head is 6.81 x 10 7/m( rather than the 109 7/m reported in the problem. ?onseBuently( when the penstoc' is &ull open and the pressure is reduced to 6x10 7/m( the e@ectie head is C "r/g delta !6x10 7/m)/!6.81 m/sD1000 'g/m 3) 61.=4 meters.
4.1) a man owns a land that includes a low head water &all and wants to build a small hydroelectric plant. The e@ectie head o&
the reseroir is 0m. Ce used a tube o& 3 m length and 1 m diameter as a penstoc'. Ce computed the speed o& the water inside the penstoc' by dropping a small ball at the entrance o& the tube and measuring the time it too' to reach the other end o& the tube. The ball traelled the penstoc' in s. a. ?ompute the power at the outta'e o& the tube. b. +& the coe,cient o& per&ormance o& the turbine is 0.6( and the e,ciency o& the generator turbine and generator is 60-( compute the expected generation o& the site. c. +& the cost o& building the small hydroelectric system is E10*( compute the paybac' period i& the cost o& electricity &rom the neighboring utilities is E0./'#h. Assume that the water $ow is always constant. d. +s building this small hydroelectric system a good inestment. olution a.)"out fδgh 2
π r L δgh t
π ( 0.5
2
2
) ( 3)
( 1000 ) ( 9.8 ) ( 20 )
230.91 kW b.) ?oe,cient o& per&ormance 0.6 F,ciency !) 60"expected 0.6x0.6x30.61 16=.43 '# c.) ?ost o& building E10* ?ost o& Flectricity E0.'#h Assuming the water $ow is constant(
6
10 × 10
"aybac' period
0.2 × 197.43 × 24 × 365
8.61 ≅
28 years
d.) Guilding this small hydroelectric system is not a good inestment since the cost o& building the system is too high and the paybac' period &or the system is Buite long. 4.19) a hydroelectric dam creates a reseroir o& 10'm3. The aerage head o& the reseroir is 100m. ?ompute the "F o& the reseroir. olution PE r= mgh 13
¿ 10 × 9.8 × 100 15
¿ 9.8 × 10 J
4.1=) a penstoc' is used to bring water &rom behind a dam into a turbine. The e@ectie head is 0m and the $ow rate o& water is 0m3/s. ?ompute the power o& the water exiting the penstoc'. olution Pout = fδgh ¿ ( 50 ) (1000 ) ( 9.8 ) ( 20 ) ¿ 9.8 MW
4.18) the penstoc' o& a hydroelectric power plant is 4m in diameter. The water head is 90m. ?ompute the water $ow rate and the elocity o& water inside the penstoc' i& the power at the exit o& the penstoc' is 10*#. olution Pout = fδgh
10
7
= f ( 1000 ) ( 9.81 ) ( 60 ) 3
f =16.9 m / s
f = A V i V i=
16.9
π ( 2
2
)
V i=1.34 m / s
4.16) A hydroelectric dam has a penstoc' that discharges 10H 'g/s o& water. The head o& the dam is 80 m. a. ?ompute the olume o& the discharged water per second !$ow rate). b. ?ompute the power o& the water entering the turbine. c. Assume that hydro e,ciency is 0.6( the turbine e,ciency is 0.6 and the generator e,ciency is 6-( estimate the generated electrical power. olution 5
Pout = P¿ × ɳ h × ɳ t × ɳ g Pout =78.4 × 0.95 × 0.9 × 0.92 Pout =61.67 MW
4.0) A natural gas power plant has a condenser that extracts 8(000 Gtu/'g o& natural gas. ?ompute the mechanical energy o& the turbine and the oerall system e,ciency. olution W = # −# 2
1
W = ( 48000 ) ( 1.054 )− (28000 ) ( 1.054 )
7ote 1 GTI 1.04 'J
W = 21096 kJ
ɳ i$eal
=
W 21080 = =41.67 #1 50592
4.1) an oilKfred power plant has a condenser that extracts 8(000Gtu/'g o& oil. ?ompute the mechanical energy o& the turbine and the oerall system e,ciency. olution W = # −# 2
1
W = ( 45000 ) ( 1.054 )− (28000 ) ( 1.054 ) W = 17918 kJ
ɳ i$eal =
W 17918 = =37.78 #1 47430
4.34) Fstimate the amount o& nuclear energy produced by 10 'g o& LMHI. olution
.6) +& a 100 *# coalKfred power plant is conerted into natural gas ( compute the annual percentage reduction o& NO. olution N &rom coal = 'g/*#h N &rom 7atural Pas g/*#h +n one year( N &rom coal =x4x399130 'g/year N &rom 7atural Pas 0.00x4x39 43.8 'g/year A!!ual re$uctio! erce!tage=
61320
− 43.8 ×
61320
100
=99.92
.10) in 009( the world consumed 19.8 x 10QL '#h o& electricityR estimate the maximum amount o& NO released &rom the coalKfred power plant worldwide. olution N released &rom coal ='g/*#h =x10 K3 'g/S#h 12
