UNIVERSIDAD DE LA COSTA CUC
LABORATORIO LABORATORIO DE HIDRAULICA
FLUJO SOBRE UNA UN A COMPUERTA
PRESENTADO POR: CRISTIAN PERTUZ PEREA JAFFET RAMOS CABARCAS JUAN NAVARRO MERCADO JOSE RINCONES Grupo: AM
PROFESOR: ING. GERALD MESTRA MESTR A RODRIGUEZ
ABRIL DE 201 BARRAN!UILLA " ATLANTICO
UNI VERSI DAD DE LA COS OSTA,CUC
F A CUL T A D DE I NGENI ERI A
Contenido 1. INTRODUCCIÓN............. INTRODUCCIÓN...................... .................. .................. .................. ................. ................. .......................................3 ..............................3 2. OBJETIVOS............... OBJETIVOS........................ .................. .................. .................. .................. ................. ................. ....................................4 ...........................4 2.1. 2.1. OBJ BJET ETIIVO GEN GENER ERA AL.................................................................................4 2.2. 2.2. OBJE OBJETI TIVO VOS S ESPEC ESPECIF IFIC ICOS OS........................................................................4 3. MARCO TEORICO.............. TEORICO...................... ................. .................. .................. .................. ................. ................. .................. ...................5 ..........5 4. PROCEDIMIENTO........... PROCEDIMIENTO.................... .................. .................. ................. ................. .................. .................. ..............................7 .....................7 5. CALCULO Y RESUSTADOS......... RESUSTADOS................. ................. .................. .................. ............................. ..................................8 ..............8 6. ANALISIS DE RESULTADOS.... RESULTADOS............. .................. .................. ................. ................. .................. .............................8 ....................8 7. CONCLUSIONES............... CONCLUSIONES........................ ................. ................. .................. .................. .........................................13 ................................13 2 8. BIBLIOGRAFIA.............. BIBLIOGRAFIA....................... ................. ................. .................. .................. .................. .....................................14 ............................14 4
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UNI VERSI DAD DE LA COSTA,CUC
F A CUL T A D DE I NGENI ERI A
1. INTRODUCCI#N E !"#$ %&#$ "'& ($)*"+,-& *"++ /+, 0/-$ ($)$ "'& &%+,-",& ("&,&& $ ,+(-&'"&, "+ /+ &#"/-& + &("+,$ & & &%+,-",& + & ($)*"+,-& ("&'$ /-& +/ *+"+& ($)*&,&& ($' + !"#$ &"&/ &,,%&. L&/ ($)*"+,-&/ *"++' -,&%&#&, + $/ )&'+,&/ $ & $/ /-"&($'+/ F"#$ %,+ !"#$ /")+,$. E' +/-& +*+,+'(& 0&)$/ & -,&%&#&, + $/ !$,)&/9 & *,)+,& &%,+'$ & ($)*"+,-& (&& 5)) )&'-+'+'$ "' (&"& ($'/-&'-+ ",&'-+ -$& & +*+,+'(& &/: +-+,)'&, & &-",& &'-+/ + & ($)*"+,-& #"'-$ ($' & &-",& +/*"/ + & )/)&; & /+"'& +/ -+'+'$ & &-",& &'-+/ + & ($)*"+,-& ($'/-&'-+ 0&,&'$ + (&"& *&,& &/: )&'-+'+, & )/)& &-",&. T$$ $ &'-+,$, $ ,+&<&)$/ +/*+(:!(&)+'-+ *&,& (&("&, + ($+!(+'-+ + +/(&,& "+ +/-+ & 0&,&, & &%+,-",& + & ($)*"+,-& + (&"&.
3
UNI VERSI DAD DE LA COSTA,CUC
F A CUL T A D DE I NGENI ERI A
2. OBJETIVOS 2.1.
OBJETIVO GENERAL
E/-&%+(+, & ,+&(=' >& +'-,+ & *,$!"'& + !"#$ + "'& ($)*"+,-& + (&"& "+ *&/& *$, +%&#$ + +&.
2.2. •
•
•
•
OBJETIVOS ESPECIFICOS
C&("&, + ($+!(+'-+ + +/(&,& + & ($)*"+,-& %&#$ &/ ($'($'+/ + !"#$ +'/&&&/. I)*+)+'-&, *,?(-(&/ + &%$,&-$,$ /$%,+ )+(=' + !"#$ +' ($)*"+,-&/. O%/+,0&, ("& +/ + ($)*$,-&)+'-$ + ($+!(+'-+ + +/(&,& +' "' (&'& $'+ + (&"& +/ ($'/-&'-+ & &-",& + & ($)*"+,-& 0&,&%+. C$'$(+, ("? +/ + ($)*$,-&)+'-$ + & &-",& @Y1 (&"& ($' ,+/*+(-$ & & &%+,-",& + & ($)*"+,-&.
4
UNI VERSI DAD DE LA COSTA,CUC
F A CUL T A D DE I NGENI ERI A
$. MARCO TEORICO F%u&o ' (r')*+ ,- o/pu-r('+ U'& C$)*"+,-& +/ "'& *&(& )=09 *&'& $ (",0&9 "+ & +0&'-&,/+9 !$,)& "' $,!($ +'-,+ /" %$,+ '!+,$, & +/-,"(-",& >,?"(& @*,+/&9 (&'&9 +-(. /$%,+ & ("& /+ '/-&&9 /+ "-<& +' & )&$,:& + $/ (&/$/ *&,& & ,+"&(=' + (&"&+/9 ($)$ +)+,+'(& (+,,+ *&,& )&'-+')+'-$ +' $/ $-,$/.
L&/ ($)*"+,-&/ -+'+' &/ *,$*+&+/ >,?"(&/ + $/ $,!($/ 9 ("&'$ +/-?' %+' (&%,&&/9 -&)%' *"++' +)*+&,/+ ($)$ )+$,+/ + !"#$.
Eu'o-+ p'r' -% 'u,'% ,- %u&o ' (r')*+ ,- o/pu-r('+: '.
A (r')*+ ,- o/pu-r('+ p%''+: *&,& +"(, & +*,+/='9 /+ ($'/+,& + (&/$ )?/ +'+,&9 $'+ & ($)*"+,-& +/-? '('&& "' ?'"$ θ ,+/*+(-$ & & >$,<$'-&9 -+'+ "' &'(>$ B "& & + (&'&.
5
UNI VERSI DAD DE LA COSTA,CUC
F A CUL T A D DE I NGENI ERI A
6
UNI VERSI DAD DE LA COSTA,CUC
F A CUL T A D DE I NGENI ERI A
E !"#$ & -,&0/ + $,!($ !$,)&$ *$, + &%$ '!+,$, + & ($)*"+,-& + !$'$ + (&'& *"++ ($'/+,&,/+ %)+'/$'&. N=-+/+ "+ & +/(&,& /"*+,(,:-(& %&#$ & ($)*"+,-& ,+"(+ *,$,+/0&)+'-+ /" *,$!"'& & $ &,$ + "'& ($,-& /-&'(& I9 &"&/ &%&#$9 >&/-& "'& /+((=' +' $'+ & ($'-,&((=' + (>$,,$ +/ ($)*+-&9 &)&& V-' o(r'('. 1 . 1>--*!"$/.+&.+".($>,&"(&&,-("$/+/!"#$+'(&'&+/!"#$($)*"+,-&/! "#$($)*"+,-&/.>-)
3. PROCEDIMIENTO MATERIALES B&'($ >,?"($. C,$'$)+-,$. C&'&+-& R+& )-,(& L:)')+-,$ + *"'-&
PROCEDIMIENTO E/-+ +'/&$ ($'/-& + $/ *&,-+/. L& *,)+,& *&,-+ $'+ Y$ ($'/-&'-+9 0&,&(=' + ; & /+"'& *&,-+ $'+ +/ ($'/-&'-+9 0&,&(=' + Y$. L& *,)+,& *&,-+ Y$ ($'/-&'-+9 0&,&(=' + . •
S+ ,& & *+,& + & ($)*"+,-& >&/-& $,&, &($)$&, & ($)*"+,-& & "'& &-",& + 95 ) *$, +'()& + !$'$ + (&'&. 7
UNI VERSI DAD DE LA COSTA,CUC
F A CUL T A D DE I NGENI ERI A
S+ &%,+ ,&"&)+'-+ & 0?0"& $'+ /+ ($'-,$& + !"#$ + %&'$ >,?"($ >&/-& -+'+, "' Y$ H 912 )9 +/- +/-&%+. Y& +/-&%+ + !"#$ /+ *,$(++ & )+, + Y1 + (&"& . D+/*"/ + -$)&, +/-&/ )+&/ /+ 0& '(,+)+'-&'$ + 95 ) & &-",& $ &%+,-",& + & ($)*"+,-& /+ 0& &")+'-&'$ + (&"& )&'-+'+'$ Y$ H 912 ). P&,& (&& &-",& + & &%+,-",& + & ($)*"+,-& /+ +%+ )+, + (&"& *,$!"'& + &"&/ +%&#$ + & ($)*"+,-& Y1. S+ ,+*-+ + *,$(+)+'-$ & )+'$/ 4 0+(+/. •
• •
•
L& /+"'& *&,-+ ($'/-&'-+9 V&,&(=' + Y$. •
•
• •
•
S+ ,+*-+ -$$ + *,$(+)+'-$ &'-+,$, *+,$ +/-& 0+< +/-&,? ($'/-&'-+ + (&"& +/-&,? 0&,&'$ + Y$. S+ &%,+ + ($'-,$ + !"#$ + %&'($ >,?"($ /+ )+ + (&"& *,+/+'-&$. S+ )+ "'& &-",& $ &%+,-",& + & ($)*"+,-& +' 95. S+ +/*+,& >&/-& "+ + !"#$ /+ +/-&%(+ /+ ,+/-,&' $/ 0&$,+/ + Y$ + Y1. P&,& !'&<&, /+ '(,+)+'-& & &%+,-",& + & ($)*"+,-& +' 95 /+ ,+*-+ + *,$(+)+'-$ & )+'$/ 4 0+(+/.
. C4LCULO 5 RESULTADOS A%(ur' o+('( Yg 0,005 0,01 0,015 0,02
A0
Y0 0,12 0,12 0,12 0,092
A1 V0 0,000262 0,05756666 0,009 5 7 0,09564444 0,009 0,000525 4 0,15211111 0,009 0,000975 1 0,006 0,001125 0,20869565
DATOS Y1 0,0035 0,007 0,013 0,015
Q 0,0005181 0,0008608 0,001369 0,00144
CALCULOS V1 Cd 1,97371428 0,90041391 6 9 1,63961904 0,74799874 8 7 1,40410256 0,79306868 4 4 1,28 0,71454209
B 0,075 0,075 0,075 0,075
H0 H1 0,12067562 19,1111633 1 4 0,12186500 13,1933598 7 0,12471718 9,68322717 5 2 0,10087948 8,051352
8
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2
9
3
5
Q: Caudal (m3/s) Cd: Coeficiente de descarga (adimensional) B: Base del canal (m) Yg: Abertura de la compuerta (m) g: Gravedad (m/s2) Yo: rofundidad del flu!o aguas arriba
= BY
A
A = ( 0.075∗0.12 ) =0.009 m 2
V =
V =
Q A 0.0005181
Cd =
0.009
=0.05756 m / s
Q BYg √ 2 gYo
Cd =
0.0005181
( 0.075∗0.005) √ ( 2∗9.81 ) 0.12
=0.9004
2
Vo Ho=Yo + 2g
2
(0.05756 ) Ho = 0.12 + =0.12006 2∗9.81 2
V 1 H 1 =Y 1 + 2g
2
(1.97 ) H 1 =0.035 + =19.11 2∗9.81
UNI VERSI DAD DE LA COSTA,CUC
F A CUL T A D DE I NGENI ERI A
Cd vs. Q 1 0.9 0.8 0.7 0.6 Cd
0.5 0.4 0.3 0.2 0.1 0 0
0
0
0
0
0
0
Q
Q vs. Yg 0 0 0 0 Q
0 0 0 0 0 0
0.01
0.01
0.01
0.01
0.01
0.02
0.02
0.02
0.02
Yg
1
UNI VERSI DAD DE LA COSTA,CUC
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Ho vs H1 0.14 0.12
f(x) 0x ! 0.1 "# 0.24
0.1 0.08
H1 0.06
$ine%& ()
0.04 0.02 0 6
8
10
12
14
16
18
20
Ho
C'u,'% o+('( Yg 0,005 0,01 0,015 0,02 0,025
Y0 0,16 0,067 0,03 0,032 0,021
DATOS Y1 0,004 0,0075 0,012 0,026 0,026
Q 0,000665 0,000665 0,000665 0,000665 0,000665
B 0,075 0,075 0,075 0,075 0,075
CALCULOS A0 A1 V0 V1 Cd H0 H1 0,055416 2,216666 1,000877 0,160626 24,10526 0,012 0,0003 67 67 4 1 25 0,0050 0,00056 0,132338 1,182222 0,773345 0,070570 6,862970 25 25 31 22 35 53 22 0,0022 0,295555 0,738888 0,770475 0,047808 2,689918 0,0009 5 56 89 78 99 06
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0,00195
0,277083 0,341025 0,559507 0,047652 0,596444 33 64 48 43 08
0,0024 0,0015 0,422222 0,341025 0,552536 0,057344 0,596444 0,00195 75 22 64 82 87 08
Q: Caudal (m3/s) Cd: Coeficiente de descarga (adimensional) B: Base del canal (m) Yg: Abertura de la compuerta (m) g: Gravedad (m/s2) Yo: rofundidad del flu!o aguas arriba
= BY
A
A = ( 0.075∗0.16 )=0.012 m 2 V = V =
Q A 0.000665
Cd = Cd =
0.012
=0.0554 m/ s
Q BYg √ 2 gYo
0.000665
(0.075∗0.005) √ ( 2∗9.81 ) 0.16
=1.0008
2
Vo Ho=Yo + 2g
2
( 0.0554 ) Ho=0.16 + = 0.1606 2∗ 9.81 2
V 1 H 1 =Y 1 + 2g
2
(2.21 ) H 1 =0.04 + =24.10 2∗9.81
12
UNI VERSI DAD DE LA COSTA,CUC
F A CUL T A D DE I NGENI ERI A
Cd vs. Yo 1.2 1 0.8 Cd
0.6 0.4 0.2 0 0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Yo
Cd vs. Yg 1.2 1 0.8 Cd
0.6 0.4 0.2 0 0
0.01
0.01
0.01
0.01
0.01
0.02
0.02
0.02
0.02
Yg
13
UNI VERSI DAD DE LA COSTA,CUC
F A CUL T A D DE I NGENI ERI A
Yo vs. Yg 0.18 0.16 0.14 0.12 0.1 Yo
0.08 0.06 0.04 0.02 0 0
0.01
0.01
0.01
0.01
0.01
0.02
0.02
0.02
0.02
Yg
Ho vs. H1 30 25 20 H1
f(x) 198.12x ' 7.62 "# 0.99
15
$ine%& ()
10 5 0 0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Ho
14
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DATOS TOMADOS POR GRUPO $ A%(ur' o+('(DATOS Yg 0,005 0,01 0,015 0,02
Y0 0,09 0,09 0,09 0,09
Y1 0,007 0,01 0,015 0,017
Q 0,00040094 0,00082812 0,00112641 0,00127395
B 0,075 0,075 0,075 0,075
C6%u%o+ ,-% 'u,'%
CAUDAL PARA Yg=0,005 0,00 T1 12,1 0,00041322 5 0,00 T2 12,6 0,00039683 5 0,00 T3 12,73 0,00039277 5 T 0,00 12,4766667 0,00040094 PROM 5 CAUDAL PARA Yg=0,01 T1 6,42 0,005 0,00077882 T2 5,32 0,005 0,00093985 T3 6,53 0,005 0,0007657 T PROM 6,09 0,005 0,00082812 CAUDAL PARA Yg=0,015 0,00 T1 4,81 0,0010395 5 0,00 T2 4,44 0,00112613 5 0,00 T3 4,12 0,00121359 5 T 0,00 4,45666667 0,00112641 PROM 5 CAUDAL PARA Yg=0,02
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0,00 5 0,00 T2 3,81 5 0,00 T3 3,96 5 T 0,00 3,92666667 PROM 5
T1
A0 0,006 75 0,006 75 0,006 75 0,006 75
A1 0,0005 25 0,0007 5 0,0011 25 0,0012 75
V0 0,059398 59 0,122684 57 0,166875 03 0,188733 09
4,01
0,00124688 0,00131234 0,00126263 0,00127395
CALCULOS V1 Cd 0,763696 0,804596 2 07 1,104161 0,830924 16 78 1,001250 0,753480 19 22 0,999175 0,639130 17 88
H0 0,090719 31 0,093068 6 0,095677 32 0,097262 01
H1 2,867752 4 5,990038 4,932272 05 4,913911 73
Cd vs. Q 1 0.8 0.6
Cd 0.4 0.2 0 0
0
0
0
0
0
0
Q
16
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Q vs. Yg 0 0 0 0
Q 0 0 0 0 0
0.01
0.01
0.01
0.01
0.01
0.02
0.02
0.02
0.02
Yg
Ho vs. H1 7 6 5 4
f(x) 237.03x ' 17.65 "# 0.27
H1 3 2 1 0 0.09
0.09
0.09
0.09
0.09
0.1
0.1
0.1
0.1
Ho
C'u,'% o+('( Yg 0,005 0,01 0,015 0,02
Y0 0,095 0,038 0,023 0,02
DATOS Y1 0,007 0,01 0,019 0,02
Q 0,000357 0,000357 0,000357 0,000357
B 0,075 0,075 0,075 0,075
17
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C6%u%o+ ,-% 'u,'% CAUDAL T1 13,28 0,005 T2 12,31 0,005 T3 14,27 0,005 T4 16,16 0,005 T PROM 14,005 0,005
A0 0,0071 25 0,0028 5 0,0017 25
A1 0,0005 25 0,0007 5 0,0014 25
0,0015
0,0015
0,00037651 0,00040617 0,00035039 0,00030941 0,0003502
CALCULOS V0 V1 Cd 0,050105 0,697309 0,68 26 6 0,125263 0,551271 0,476 16 64 0,206956 0,250526 0,472391 52 32 72 0,379937 0,238 0,238 76
H0 H1 0,095511 2,275072 83 0,041198 1,121355 95 28 0,031732 0,326854 11 65 0,031548 0,297838 22 82
Cd vs. Yo 0.8 0.7 0.6 0.5 Cd
0.4 0.3 0.2 0.1 0 0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Yo
18
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Cd vs. Yg 0.8 0.7 0.6 0.5
Cd
0.4 0.3 0.2 0.1 0 0
0.01
0.01
0.01
0.01
0.01
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
Yg
Yg vs. Yo 0.1 0.09 0.08 0.07 0.06 Yo
0.05 0.04 0.03 0.02 0.01 0 0
0.01
0.01
0.01
0.01
0.01
Yg
1
UNI VERSI DAD DE LA COSTA,CUC
F A CUL T A D DE I NGENI ERI A
Ho vs. H1 2.5 f(x) 29.12x ' 0.45 "# 0.93
2 1.5 H1
1 0.5 0 0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Ho
!. ANALISIS DE RESULTADOS
2
UNI VERSI DAD DE LA COSTA,CUC
F A CUL T A D DE I NGENI ERI A
P$, )+$ + &/ ,?!(&/ *$+)$/ ,+&($'&, &"'&/ 0&,&%+/ "+ +*+'+' + $-,&/ $%/+,0&, )+#$, + ($)*$,-&)+'-$ + "' !"#$ *&,& +$ 0)$/ & +*+,+'(& +' $/ *&,-+/ "'& ($' & &-",& '(& ($'/-&'-+ $-,& ($' "' (&"& ($'/-&'-+9 +' &)%&/ 0&,&'$ & &-",& + & ($)*"+,-&9 +' (&& "'& + &/ *&,-+/ >+)$/ ,+&($'&$ ,?!(&)+'-+ &"'&/ 0&,&%+/. E' & *,)+,& *&,-+ /+ ,+&($'= • C$+!(+'-+ + +/(&,& (&"& +/-&/ 0&,&%+/ /+ ,+&($'&' + !$,)& ,+(-& +%$ & )&$, (&"&9 )&$, ($+!(+'-+ + +/(&,& +' +/-+ (&/$ + (&"& +/ & 0&,&%+ '+*+'+'-+ & "+ '$/$-,$/ $ +-+,)'&)$/ /+' &/ ($'($'+/ ($' &/ "+ "+,+)$/ -,&%&#&, + ($+!(+'-+ + +/(&,& 0&,:& +*+'+'$ + (>$ (&"&. •
C&"& &-",& + & ($)*"+,-& +/-&/ 0&,&%+/ /+ ,+&($'&' ,+(-&)+'-+ +%$ & "+ + (&"& +*+'+ + & &-",& + & ($)*"+,-& / & &-",& + & ($)*"+,-& 0&,:&9 0&,&,& +'-$'(+/ + (&"& *&,& )&'-+'+, + ?,+& '(& ($)$ "'& ($'/-&'-+
•
E'+,:& '(& +'+,:& !'& +/ "'& ,+&(=' ,+(-&9 "+ /+ 0+ ,+&($'&& + "& !$,)& ($' &/ 0+$(&+/ &/ &-",&/9 +'("+'-,&' "' *"'-$ + +"%,$ +*+'+'$ + & &-",& + & ($)*"+,-&
E' & /+"'& *&,-+ /+ ,+&($'= •
C$+!(+'-+ + +/(&,& &-",& '(& +/ "'& ,+&(=' ,+(-&)+'-+ *,$*$,($'& +' & "+ + ($+!(+'-+ + +/(&,& +*+'+ ,+(-&)+'-+ + & &-",& & & "+ /+ +'("+'-,+ + !"$ &'-+/ + & ($)*"+,-&.
•
C$+!(+'-+ + +/(&,& &-",& + & ($)*"+,-& ,?!(&)+'-+ *$+)$/ $%/+,0&, "+ & )+& "+ &")+'-& & &-",& + & ($)*"+,-& &/: )/)$ 0&,&,& + ($+!(+'-+ + +/(&,& +/-+ /)'",? +%$ & "+ & 0+$(& /)'",? & )&$, &-",& + & ($)*"+,-&.
•
A-",& '(& &-",& + & ($)*"+,-& ($)$ +' +/-+ (&/$ /+ -,&%&#& ($' "' (&"& ($'/-&'-+9 & &-",& + & ($)*"+,-& '!"+ ,+(-&)+'-+ /$%,+ & &-",& '(&9 &/: +'-,+ )+'$, /+& & &-",& + & ($)*"+,-& )&$, /+,? & 21
UNI VERSI DAD DE LA COSTA,CUC
F A CUL T A D DE I NGENI ERI A
&-",& '(& / ($' + (&"& ($'/-&-+ /+ &")+'-& & &-",& + & ($)*"+,-&9 ')+&-&)+'-+ & &-",& &'-+/ + +/-& /)'",? >&/-& +&, & "' *"'-$ $'+ & &-",& '(& & & -",& !'& /+&' &/ )/)&/. •
E'+,:& '(& +'+,:& !'& +' & ,?!(& /+ *"++ $%/+,0&, "+ & +'+,:& !'& & '(& 0&' /)'"+'$ & )+& "+ & ($)*"+,-& 0& &'&'$ &-",&9 "+ & ($)*"+,-& >&(+ "+ + !"$ &"+,& )?/ 0+$(& & )+& "+ &")+'-& & &-",& &/: &/ +'+,:&/ /+ 0&' +"%,&'$.
T&)%' *$+)$/ ,+&($'&, $/ +!+(-$/ + "+ -+'+' Y$ @("&'$ +/ ($'/-&'-+ @("&'$ Y$ +/ ($'/-&'-+ *$+)$/ $%/+,0&, "+ ("&'$ Y$ +/ ($'/-&'-+ +/ )?/ + ($+!(+'-+ + +/(&,& & "+ + (&"& -+'+ "+ &")+'-&, & )+& "+ /+ &")+'-& & &-",& + & ($)*"+,-& *$, $ -&'-$ +/ )?/ !?( -,&%&#&, ($' "' (&"& ($'/-&'-+ 0&,&, & &-",& + & ($)*"+,-& >&/-& "+ + ($+!(+'-+ + +/(&,& /+& ):')$ *$, $ -&'-$ &/ *+,&/ *$, !,((=' -&)%' $ /+&' &($'&)+'-+ & +/$ *$+)$/ "&)+'-+ ($)*&,&, $/ 0&$,+/ "+ -+'+ K1 K$9 ("&'$ -+'+)$/ "'& &-",& ($'/-&'-+ $%/+,0&)$/ "+ & +'+,:& '(& -+'+ "'& 0&,&(=' ):')& +%$ & "+ /" 0+$(& +/ )" *+"+&9 *$, + ($'-,&,$ & +'+,:& !'& +/ )"(>$ )&$, +%$ & /" 0+$(& & ("& 0& /)'"+'$ & )+& "+ & &-",& + & ($)*"+,-& /+ >&(+ )&$,9 *$, $-,& *&,-+9 ("&'$ -+'+)$/ "' (&"& ($'/-&'-+ +'($'-,&)$/ "'& 0&,&(=' )"(>$ )&$, & )+& "+ & ($)*"+,-& &")+'-& /" &%+,-",&9 +/-$ +/ +%$ & "+ & (&'-& + !"$ +/ & )/)& /+)*,+9 +' ($'/+("+'(& +/ )"(>$ )?/ !?( ($'-,$&, & +'+,:& !'& ("&'$ + (&"& +' ($'/-&'-+ "+ ("&'$ & &-",& +/ ($'/-&'-+.
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7. CONCLUSIONES P&,& !'&<&,9 *$+)$/ ,+/&-&, & "-& + "'& ($)*"+,-& +' &' //-+)& >:,($ ($)$ +/-& '!"+ +' + ($)*$,-&)+'-$ + "' !"#$9 ($)$ *$, +#+)*$ +/ ($'-,$ + & 0+$(& & ("& +/ !"'&)+'-& ($'-,$&,&9 '$ /$$ *$, /+",& /'$ *&,& ($'-,$&, & !,((=' ($' & (&'& $ & -"%+,:& +' ($'/+("+'(& &/ *+,&/ *$, !,((='9 +' & *,?(-(& -"0)$/ $/ /-"&($'+/ -$-&)+'-+ !+,+'-+/ +' &)%&/ & ($)*"+,-& +,& + !&(-$, !"'&)+'-& +' + ($)*$,-&)+'-$ + !"$ *$, $ ("& *$+)$/ ($'(", "+ +*+'+'$ + & /-"&(=' + (=)$ "+,+)$/ "+ /+ ($)*$,-+ "' !"$ &/: *$,+)$/ "%(&, "'& ($)*"+,-& )&'*"&,& + -& !$,)& "+ + !"$ -+'& + ($)*$,-&)+'-$ "+ +/ ,+"+,$.
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". BIBLIOGRAFIA •
F"'&)+'-$/ *&,& &/ *,?(-(&/ + L&%$,&-$,$ + K,?"(&. F"#$ & -,&0/ + ($)*"+,-&/. R. M&,%+$ P,+<. T$)$ N8.
•
1 D$(")+'-$ +' :'+& ($'/"-&$ + 22 + &%, + 215 & &/ 3 *). D/*$'%+ +' >--*!"$/.+&.+".($>,&"(&&,-("$/+/!"#$+'(&'&+/!"#$($)*"+,-&/!"#$ ($)*"+,-&/.>-)
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