teoria parctica 3 lab. aero

8/16/2019 Teoria Parctica 3 Lab. Aero

1/20

REPÚBLICA BOLIVARIANA DE VENEZUELA

MINISTERIO DEL PODER POPULAR PARA LA DEFENSAUNIVERSIDAD NACIONAL EXPERIMENTAL

POLITECNICA DE LA FAUERZA ARMADA NACIONALNÚCLEO ARAGUA-SEDE MARACAY

INGENIERÍA AERONÁUTICA

LABORATORIO DE AERODINÁMICA 1PRACTICA Nº 3:

DESCARGA A LA ATMOSFERA DE UN

CHORRO TURBULENTO

PROF: CARLOSLOPEZ INTEGRANTES:

DAILI GUEVARA

C.I: !"1#"$!

DEYVID ARAMBURU

C.I: %$&"#!&

M'(')'*+ A,( %1/


2/20

INTRODUCCIÓN

E 0 2 4 (, 564 57 897 ) 8 685645 ;57'(( '; ;5, ; ' < 5 '6'4 (' 5=' 4 565 456;56) ' >') ' 5 ;57 (;56 * 574 56 4?(8 6 7 ;5 0 2 77 @6 0 )' 456;56) ' >') ' ' 4 (, 56) '. E745 4 ;5 0 2 75 )'(')45( =' (4('*5)4 ( '7 ) () '(57 5((94 )'7+ 75852'6457 ' (58 6 7.

P ( 4' 8 4 + ' 4 (, 56) ' 5;5 ( @ 6'(75 ( ' (5756) ' ;5'(5;57 56 ) 64')4 ) 6 5 0 ; ( ' 5 7456) ' ;5 )' '7 < 5 75

8 5 '6 ' ; 05(56457 5 ) ;';57+ )'(')45( =96; 75 (< 5 5 0 ;) 64 6 '85645 75 85=) '+ ;5 0 (8' )' 4 )'+ ) 8 ) 675) 56) ' ;5 '( 4 (' ;5 6 0 2 (;56'; ;5 (4 )57+ < 5 '05)4'6 = 6'7 56 ; (5)) 6 ;58 8 564 .

EN ESTE SENTIDO+ S5 (5' ='(9 6 574 ; ;5 * '69 7 7 ;5 )> (( 74 (, 564 7 ; 6;5 75 ;(9 ' (5) '( 7 ; 05(56457 )'8, < 5 5745 4 565.R505(5645 7 7 5 ) ;';57 ;5 ') 5(; ' 7 7 '( ') 6. E6 5 ) ' 75505)4 '('6 )9 ) 7 ; 6;5 75 ;545(8 656 7 (57 4'; 7 ;5 ' 8 78'+ ) '6;75 >', ' ;5 6 )> (( 4 (, 564 75 ;57)( ,5 6 0 2 8 (4'645 ;5

564 ') 6 ;5 6 9(5' ;545(8 6';' ;50 6 ?6; 75 ) 8 6' ',5(4 (' '645( ( ;5 6 (5) 64 . S5 5;56 ;50 6 ( ;5 ; 7 8'65('7 56 5 ) ' 45658 7

5 0 2 ( 8'( * 5 0 2 75) 6;'( + 5 0 2 ( 8'( 57 5 ' (5 < 5 56 5 (5) 64 + 6 0 2 75) 6;'( ;5 57 ;5 5 ) ;'; 856 ( < 5 5 0 2

( 8'( ) '6; 6' 8'* ( 5 4567 6.


3/20

MARCO TEÓRICO

L' 4 (, 56) ' 56 7 8 8 564 7 '48 70?( ) 7 4 565 6' 8 (4'6) '8 * ;574')';'+ ) 8 75 >' (5) 6 ) ; + ( 7 ) 564 0 ) 7 ;5; )'; 7 '574 ; ;5 ' A48 705('+ *' < 5 5749 (575645 56 4 ; 7 7 8 8 564 7)5()'6 7 ' 7 5 * 56 4('7 )' '7 < 5 5;'6 574'( 7 854 ;'7 '

8 (4'6457 ) =' '7 056 856 7 ;5 4 4?(8 ) .

E7 ( 5 + < 5 7 7 505)4 7 7 6 5 ;56457 56 ' (5; 74( , ) 6 ;5 565(@ ' ;57;5 '7 @('6;57 57)' '7 ' '7 5< 5 '7+ '6457 ;5 ' ; 7 ') 6 56)' (. A;5897+ 5 4('67 (45 ;5 8'@6 4 ;57 0 7 )'7 4' 57 ) 8 5 8 8564 +)' (+ > 85;';+ 54).+ 5749 ; 8 6'; ( 0 2 7 4 (, 564 7+ * ' 85=) '+ ;5

'7 ( 5;';57 0 7 )'7 * < 8 )'7+ 75 5 0' (5) ;' ,'2 ) 6; ) 657 ;58 8 564 4 (, 564 . L' ; 7 5(7 6 ;5 56;5 0 5(4585645 ;5 '7

( 5;';57 574'; 74 )'7 ;5 0 2 + 4' 57 ) 8 ' (57 ( 85; + '( '6='7 *

;567 ;';57 57 5)4(' 57.

E 574 ; ;5 ' 4 (, 56) ' 56 ' A48 705(' 57 ) 8 )'; * (5< 5(5 '4 =') 6 ;5 7 0 74 )'; 7 5< 7 ;5 85; ;'+ < 5 6 6)' 5@'6 ' 75(

7 0 ) 564585645 ) 8 54 7 ( '7 ; 8567 657 ;5 ?74'. P ( 4( '; + '8 7 , ;'; ;5 ) 64( '( '7 ) 6; ) 657 897 ' ( ';'7 56 '

5 5( 8564') 6 ; (5)4'+ >')5 ; 0 ) 5 4(','2 . S 6 58,'(@ + ' 8 ;5 =') 6;5 '7 5)4 7 ) 6)(54 7 (5 '4 7 ' 056 856 7 4 (, 564 7+ 4'64 56 5', ('4 ( + ) 8 85; '645 7 8 ') 6 6 8?( )'+ 5(8 45 7 574 ; ;5

0 (8' ;54' ';'+ ;57)( , 56; 5 ) 8 (4'8 564 ;5 0 2 * 7 , 4'6; 5'645'8 564 ;5 > 457 7 < 5 2 74 0 < 56 5 8 78 .


4/20

P ( 574' ('= 6+ '(' 5 4'( (5) 7'85645 8'* (57 ) 8 )') 657+ 754 ='6+ ) 8 6 (8' @565(' + '7 4?)6 )'7 ;5 '69 7 7 ; 8567 6' ; 6;5 '7'( ', 57 8'652';'7 56 4 ; 7 7 574 ; 7 75 (57564'6 56 0 (8'

'; 8567 6' + 5(8 4 56; + ( 4'64 + ' ) 8 '(') 6 564(5 ; 05(56457 57)' '7* ) 6; ) 657 ;5 ( , 58'. E6 '(4 ) '(+ ' ; 6;5 5 74' 6 @('; 56457 @6 0 )'4 56 ' 5 ) ;'; ;5 0 2 + ( 5258 )> (( 7+ ; 6;5; 05(56) '7 ;5 ;567 ;'; 75'6 8 (4'6457+ 5;5 @565('(75 6 0 24 (, 564 *+ ( 4'64 + ' 85=) ' ;5 '7 ( 5;';57 75 5(9 0' (5) ;'.

P ( ) 67 @ 5645+ 5 8 8 564 4 (, 564 57 0 5(4585645 ( 4') 65 (5) (( ; ;5 7 5 58564 7 0 ; 7 57 5 4(58';'85645 4 (4 7 + 6) 7) '6; 5 0 ; 56 7 ) 62 64 75 8 5 5 ;5 0 (8' 574') 6'( '. S 658,'(@ + ) 64 565 7) ') 657 ;5 4'8' 0 6 4 ) 8 '(', 57 ) 6 6@ 4 ;57< 5 ;545(8 6'6 ' ) 65894 )' ;5 8 8 564 85; .

CHORRO O FLUJO TUBULENTO

D5 ') 5(; ' ' 7) 7 ;'; ;5 0 ; + 6 0 2 75 ) '7 0 )' 56 '8 6'( *4 (, 564 .

E6 )> (( 7 4 (, 564 7 '7 5< 5 '7 '(4 ) '7 < 5 57496 645(')4 '6;505)4 '6 6 8 8 564 7 6 75@ ( 6 (;56 574', 5) ; + 56 4('*5)4 ( '7) 8 54'85645 5((';'7. C'(')45( =96; 75 ( 5 85=)' ;5 0 ; ) 64 6;5 0 (8' )' 4 )'+ ( ) 675) 56) ' ;5 ( 4 ('7 ;5 6 0 2 (;56'; ;5

(4 )57.


5/20

TIPOS:

De pared: 505)4 7 7) 7 7

Libre: ' 756) ' ;5 '(5;+ 56 ) ' 75 505)4 '6 8 8 564 7 ;5 )' '7 ;50 ; ' ; 74 64'7 5 ) ;';57.

C '6; 6 7 (505( 8 7 ' 4 (, 56) ' 56 5745 )'7 5 0 ; )> (( < 575 (57564' 6 7 56) 64('8 7 < 5 75 5;5 (505( ( ' ' ) ' ;'; ;5 4 (, < 575 ) 675( ' 56 ' @ ' @ 56+ 6 7 5(8 45 ' (5) '( 5 ' , ( 4 + ' ) 60 7

5(4 (,') 6 < 5 75 5 5;' '8'( 5745 4 ;5 056 856 < 5 75(57564'.

E258 7 ;5 ' )') 6 56 564(5 ( 7 ;( ' 75( 574 ; '( ''8, 564') 6 56 )( ';5( 7 ;5 '(' 7 ) 6'( 5 ( , 58' ;5 574(?74?(8 ) + '6' ='( * 4 8 ='( ) 6 8 8 564 ;5 0 ; 7 6 ' @ 6' ;5 '7) 7'7 < 5 75 56) 564('6 * 75 (5 ') 6'6 ) 6 ' 6@56 5( ' 8 ;5(6' *' < 556 ' ;' ; '( ' 6 7 56) 64('8 7 ( ;5'; 7 ;5 ) 674'6457 0 ; 7 < ; 7 @'757. P ( 4' 8 4 + 7 458'7 (5 ') 6'; 7 ) 6 '7 ; 74 64'7 6@56 5() 8 ( 5258 ' 85)96 )'+ < 8 )'+ 854' (@ '+ ( 856) 6'( ' @ 6'7+'7 ) 8 ' 85; ) 6' 0 7 )' * , @ '. E6 7 9(5'7 ;5 ' ) 56) '. N 5;575( '6' ='; 7 6 6 ;54' '; ) 6 ) 8 564 ;5 8 8 564 ;5 7 0 ; 7 ; 698 )' ;5 7 0 ; 7.

TUNEL DE VIENTO

U6 4 65 ;5 564 57 6' 674' ') 6 ; 6;5 @(') '7 ' ' 45)6 @ '897 ' '6=';' * ' ! 4 (, 6'7 ;5 ' 4' 456) ' 75 @565(' 6 0 2 ) 64 6 ;5' (5 5(4 )' (5@ ', 5. E74 5(8 45 ' ) ' < 5( 5(7 6'+ (5)(5'( ' 7567') 6;5 ' )' ;' ,(5+ 56 6 57 ') 75@ ( * 7 5( 7'; 56 4 ; 8 8564 (

674( )4 (57 ' 4'85645 ) ' 0 )'; 7.


6/20

TÚNEL DE VIENTO VERTICAL

E74 7 75 6 564'( 6 '(' 5 5(05)) 6'8 564 ;5 ; 75 ;5 '7, 8,'7 ;5 )' ;'+ ' 6 574 @') 6 '5( ; 698 )' ;5 ) 5(4 7 '7 5)4 7 ;5

5 , 8,'(;5 56 )'; H '(' 852 ('( 7 ' 657 56 ) 6; ) 657 ;5?(; ;' 74' H *+ 0 6' 85645+ ) 8 56 6 574( )'7 + '(' 5 564(56'8 564 ;5'(')' ; 74'7.

C',5 ;574')'(+ < 5 56 5 4 65 ;5 564 5(4 )' 5 0 2 ;5 ' (5 75@565(' * ; ( @5 ;5 8'65(' < 5 '7' ( ' )98'(' 56 7564 ; 5(4 )' * >') ''(( ,'+ ;5 8'65(' < 5 ) ' < 5( ,254 7 4 '; 56 ' )98'(' ) 8 567'(9 '@(' 5;'; ) 6 ' 5 ) ;'; '7)56;5645 ;5 0 2 ;5 ' (5+ 5(8'65) 56;57494 ) 56 5 '. A7 57+ ' )98'(' (5) ,5 5 6 8,(5 ;5 )98'(' ;5 5 J.

NÚMERO DE REYNOLDS

E7 5 6 85( '; 8567 6' ' '(4 ( ;5 ) ' 75 5;5 574 ; '( 5)'(9)45( 4 (, 564 ;5 0 2 . E6 574 ; 7 (5' ='; 7 7 ,(5 0 2 7 4 (, 56475 >'6 56) 64('; )> (( 7 4 (, 564 7 ) 6 6 6 85( ;5 R5*6 ;7 ;5 (;56;5 K 1%3 ' 6< 5 5 7456 4(','2 7 56 7 < 5 75 65 ;5 8'6 0 574 7 < 5 '4 (, 56) ' 6 5749 4 4' 85645 ;57'(( ';' >'74' ' (57 ;5 6 85( ;5R5*6 ;7 ;5 ' (5;5; ( ;5 ! K 1%3.

S5@ 6 5 )( 45( ;5 R5*6 ;7 75 5;5 7 65( < 5 5 0 2 4 (, 5

) 67 745 56 6 8 8 564 85; + (5 '4 '85645 7 8 5+ 7 ,(5 5 < 5 77 5( 65 6 8 8 564 75) 6;'( ;5 )'(9)45( 7) '4 ( + 5( 6

5( ; ) + ) 6 6 8 (4'645 57 ' 5'4 ( .


7/20

SENSOR DE PRESIÓN

L' (57 6 57 6' 0 5(=' < 5 525()5 7 ,(5 6 9(5' ;545(8 6';'+ * 758 ;5 56 6 ;';57 ;5 0 5(='7 ( 6 ;';57 ;5 9(5'. E74' 0 5(=' 75 5;5' )'( ' 6 64 56 6' 7 5(0 ) 5 ; 74( , (75 7 ,(5 574'. C';' 5= < 575 525()5 75 ( ; )5 6' ;50 5 6+ 6' ; 74 (7 6 6 )'8, ;5 856 ; 8567 6.

L 7 ( 6) 7 < 5 75 ' )'6 ' ' 85; ) 6 ;5 (57 6 75 4 ='64'8, ?6 56 ' ;545(8 6') 6 ;5 458 5('4 ('7+ 0 2 7 * 6 5 57 ;5 < ; 7.

P'(' 85; ( ' (57 6 75 4 ='6 7567 (57 < 5 57496 ; 4'; 7 ;5 6 5 585647567 , 5 ' ' (57 6 * < 5 58 456 6' 75 ' 5 ?)4( )' ' '( '( ' (57 6 < 5 ( )'6 5(') 657 ;5 ) 68 4') 6 7 574' 7 5(' 6 ;545(8 6';

' ( 8 45.

E7 8 (4'645 4565( 56 ) 564' ' (57 6 < 5 75 8 ;5+ *' < 5 5;56; 74 6@ (75 7 7 @ 56457 4 7: P(57 6 ',7 4'+ P(57 6 ; 05S ,(5 (57 6+ U6 ;';57 ;5 M5; ;'. E6 5 7 7458' 645(6') 6' ;5 85; ;'7+

5749 574'6;'( =';' 56 P'7)' 57. E6 7 ' 757 ;5 >', ' 6@ 57' 75 4 ='PSI.

MATERIALES E!UIPOS"


8/20

B'6) '5( ; 698 ) ;5 0 2 5(4 )'S5)) 6 ;5 ( 5,' '(' ;57)'(@'( 5 )> (( ' ' '48 705('.C567 ( ;5 (57 6M'6 854( 8 4I674( 8564 ;5 85; ) 6 56 8 854( 7

PROCEDIMIENTO E#PERIMENTAL

Se e$e%&'( )* +i,'ie-&e:

S5 4 8 '7 5)4 ('7 ;5 ' (57 6 '48 70?( )' * ' 458 5('4 ('

'8, 5645.S5 8 ;5 5 ; 9854( ;5 4 , ;5 ;57)'(@'+ * 75 7 4 ' 5 7567 ( ;5

(57 6 ;57 ='645 56 5 )564( ;5 )> (( .S5 56) 56;5 5 ,'6) * 75 75 5)) 6' ' 5 ) ;'; < 5 75 6; )'+ ) 6

' 5( ' < 5 75 56) 564(' 56 5 ; )4 ;5 7' ;' ;5 564 '; (.S5 4 8' ' (57 6 56 5 )564( ;5 )> (( .S5 4 8'6 '7 5)4 ('7 ;5 (57 6.S5 (5 45 * 75 ;57 '=' ' 7 6;' 56 7564 ; ;5 0 2 .P'(' 0 6 < 4'( 75 , )' 5 64 56 ; 6;5 ' 5 ) ;'; 57 ) 674'645.

ECUACIONES Y FÓRMULAS

E) ') 6 ;5 B5(6


9/20

V 5 ) ;'; ;5 0 ; .

;567 ;'; ;5 0 ;

P (57 6.

@ ')5 5(') 6 @(' 4'4 ( '

= ' 4 (' 56 ' ; (5)) 6 ;5 ' @(' 5;';.

E) ') 6 ;5 R5*6 ;7.

V5 ) ;'; P '48H

U =

√ P u− P a

1

2 ρ

V5 ) ;'; ;5 564(';' ;5 75)) 6 ;5 ( 5,'

P u− ¿ P w1

2 ρ

U w= √ ¿

P(57 6 8'6 8?4( )'


10/20


11/20

%+%%& %+1 %+1$ %+1! %+%1 %+1 %+1$ %+1/

%+%1& %+1 %+1$ %+1#" %+% %+1 %+1$ %+1" %+% & %+1 %+1$ %+1"& %+%3 %+1 %+1$ %+1"! %+%3& %+1 %+1$ %+1"! %+%! %+1 %+1$ %+1"! %+%!& %+1 %+1$ %+1"! %+%& %+1 %+1$ %+1#/ %+%&& %+1 %+1$ %+1&/ %+%/ %+1 %+1$ %+1!

%+%/& %+1 %+1$ %+13 %+%# %+1 %+1$ %+13 %+%#& %+1 %+1$ %+13 %+%" %+1 %+1$ %+13 P'('

%%88 Y 8H X 8HT , 8HR58'67 T , 8H P 4 4

% %+ %+1$ %+13/ %+%%& %+ %+1$ %+1! %+%1 %+ %+1$ %+1!! %+%1& %+ %+1$ %+1& %+% %+ %+1$ %+1/ %+% & %+ %+1$ %+1# %+%3 %+ %+1$ %+1#" %+%3& %+ %+1$ %+1" %+%! %+ %+1$ %+1" %+%!& %+ %+1$ %+1#! %+%& %+ %+1$ %+1/" %+%&& %+ %+1$ %+1/ %+%/ %+ %+1$ %+1& %+%/& %+ %+1$ %+1!! %+%# %+ %+1$ %+13" %+%#& %+ %+1$ %+13! %+%" %+ %+1$ %+13 %+%"& %+ %+1$ %+13 %+%$ %+ %+1$ %+13


12/20

P-R Po-Pa ΔP1 ΔP2 U∞ Uₒ Re2,134165

5

1,482683

4

0,651482

1

93997,86

58

1,066752

08

405,2016

93

1933,664

062,1341655

1,4826834

0,6514821

93997,8658

1,06675208

405,201693

1933,66406

2,1341655

1,9319814

0,2021841

93997,8658

0,59427266

405,201693

1077,2172

2,1341655

2,0667708

0,0673947

93997,8658

0,34310348

405,201693

621,931643

2,1341655

2,0892357

0,0449298

93997,8658

0,28014282

405,201693

507,80506

2,1341655

2,0892357

0,0449298

93997,8658

0,28014282

405,201693

507,80506

2,134165

5

2,089235

7

0,044929

8

93997,86

58

0,280142

82

405,2016

93

507,8050

62,134165

52,089235

70,044929

893997,86

580,280142

82405,2016

93507,8050

62,134165

52,089235

70,044929

893997,86

580,280142

82405,2016

93507,8050

62,134165

52,089235

70,044929

893997,86

580,280142

82405,2016

93507,8050

62,134165

52,066770

80,067394

793997,86

580,343103

48405,2016

93621,9316

432,134165

52,066770

80,067394

793997,86

580,343103

48405,2016

93621,9316

432,134165

52,044305

90,089859

693997,86

580,396181

78405,2016

93718,1448

032,134165

51,909516

5 0,22464993997,86

580,626418

39405,2016

931135,486

632,134165

51,460218

5 0,67394793997,86

581,084988

48405,2016

931966,720

542,134165

51,460218

5 0,67394793997,86

581,084988

48405,2016

931966,720

54

P-R P-P ΔP1 ΔP2 U∞ Uₒ Re2,134165

5

1,482683

4

0,651482

1

93997,86

58

1,066752

08

405,2016

93

6445,546

872,134165

5 1,5725430,561622

593997,86

580,990454

44405,2016

935984,540

032,134165

5 1,7971920,336973

593997,86

580,767202

71405,2016

934635,604

772,134165

51,999376

10,134789

493997,86

580,485221

6405,2016

932931,813

88


13/20


14/20

2,1341655 2,021841

0,1123245

93997,8658

0,44294469

405,201693

5352,73533

2,1341655

1,9544463

0,1797192

93997,8658

0,56028564

405,201693

6770,73414

2,1341655

1,8870516

0,2471139

93997,8658

0,65699315

405,201693

7939,38952

2,1341655 1,797192

0,3369735

93997,8658

0,76720271

405,201693

9271,20954

2,1341655

1,7073324

0,4268331

93997,8658

0,86345816

405,201693

10434,4021

2,1341655

1,6174728

0,5166927

93997,8658

0,95001053

405,201693

11480,3383

2,1341655

1,5500781

0,5840874

93997,8658

1,0100693

405,201693

12206,1146

2,134165 5 1,505148 3 0,629017 2 93997,8658 1,04819845 405,201693 12666,88372,134165

51,482683

40,651482

193997,86

581,066752

08405,2016

9312891,09

372,134165

51,482683

40,651482

193997,86

581,066752

08405,2016

9312891,09

372,134165

51,482683

40,651482

193997,86

581,066752

08405,2016

9312891,09

37

.RAFICASEN E#CEL

0 0.02 0.04 0.06 0.080

0.2

0.4

0.6

0.8

1

1.2

U vs X

grafca develocidadre !ec"o#$30%%

X

U


15/20

0 0.020.040.060.080

500

1000

1500

2000

2500

RE vs X

&rafca re !ec"oal R'

X

RE

0 0.02 0.04 0.06 0.08 0.10

0.2

0.4

0.6

0.8

1

1.2

U vs X

grafca develocidadre !ec"o#$100%%

X

U


16/20

0 0.05 0.10

2000

4000

6000

8000

RE vs X

&rafca re !ec"oal R'

X

RE

AN/LISIS DE RESULTADOS


17/20

U6' 4 (, 56) ' '48 70?( )' 57 6' '@ 4') 6 ;5 ' '48 705('+ < 5 75' (5) ' 56 6' )' '+ ( 8' ' 7 5 * ;5 57 57 ( '( ', 5Q 75 )'(')45( ='( 6 )'8, (5 564 6 ;5 ; (5)) 6 5 64567 ;'; ;5 564 56 6' ) (4'

; 74'6) ' 56 7564 ; 5(4 )' . F(5) 564585645 75 ) '7 0 )'6 '7 4 (, 56) '775@ 6 ' )' 7' < 5 '7 ( @ 6' 56 5745 )'7 ,'796; 6 7 56 7) 6 ) 8 564 7 ';< ( ; 7 ; ('645 ' (9)4 )' ;58 7 ') 4'( < 5 ' 85; ;'< 5 75 ' 52' 5 )> (( ;5 ' 7 6;' 4 4 5 ) 6 ;5 ' 5745 ' ' ' 8564'6; +574 '7' ;5, ; ' < 5 ' 8'* ( ; 74'6) ' 4 565 5 )> (( ;5 ' '48 705('8'* ( 75(9 5 )'8, 56 5 ) 8 (4'8 564 ;5 )> (( 4 (, 564 >') ' ; )>''48 05('+ ( ) 67 @ 5645 ' 574 + 5 4(','2 75 >' )564('; 56 505)4 '( 6574 ; ;5 7 85)'6 78 7 ;5 645()'8, + 564(5 '7 8'@6 4 ;57 0 7 )'7)'(')45( 74 )'7 ;5 6' ) (( 5645 ;5 ' (5+ 4('7 ' 0 (8') 6 ;5 ' 0 @ (' '6457856) 6';' '(' '7 ;545(8 6'( )';' 6' ;5 '7 5 ) ;';57 ;5 56; 56; '

' ; 74'6) ' < 5 75 56) 564(5.

ANALISIS DE .RAFICA

G565(' 85645 75 ; 7 65 '(' 5745 4 ;5 (9)4 )' ) 5(4'7 @('0 )'7+'7 ) ' 57 6 7 5(8 456 ,75( '6 897 ;54' ';'85645+ 5 ) 8 (4'8 564

;5 0 ; 4('7 7' ( ( 5 4 , ;5 ;57)'(@'. S 58 (5 4 8'6; 56 ) 564' '7; 74'6) '7 56 ' 4 ('7 '(' 7',5( 56 < ? 8 8564 ; )> 0 ; '( ' ) 6(57 5)4 ' 7 ; 9854( + < 5 56 5745 )'7 75 ) ) 3 85; ;'7 ) 6 (5 ') 6' J+ ; 6;5 75 ;56 4 < 5 ' 6 ) ) 6 6' ; 74'6) ' ;5 3%88 75 5;5

6; )'( < 5+ ' 6 5 ) 6 < 5 75 0 (8' 6 75 ,75( ' ' 7 8 5 74'7 ; (;7H+ 7 6 58,'(@ ' 85; ;' < 5 75 5 ' '; #%88 8'7+ ;52'6; '


18/20

4 , 4 4 56 6' ' 4 (' ;5 1%%88+ ; 6;5 ; )>' 0 @ (' 574' 0 (8';' 4('7 50 ; ;5 ' (5 + 5@ 75 5 ' 8564 1%%88 8'7 ) 8 ;545(8 6' 7

( )5; 8 564 7 ;5 ' (9)4 )'+ 57 8 (4'645 4 8'( 56 ) 564' < 5 ;564( ;55745 ) 6 75 0 (8' 6 0 2 '8 6'( < 5 75 5;5 856) 6'( ) 8 0 5(45 56)> (( ;5 4 ; 5 ) 6 + * 5 4( 0 2 75 5 ) 6 )5 ) 8 4('7 4 ( .


19/20

C*-%)'+i(-

T('7 ) 67 8'( ' 525) ) 6 ;5 574' (9)4 )' 5; ') 4'( < 5 577 8'85645 645(57'645 7 ; 5(7 7 ) 8 (4'8 564 < 5 5 7456 ;564( ;5

6 )> (( 4 (, 564 + 57 ( 5 < 5 5745 5 5( 8564 8 564('7 89; 74'6) ' ;5 )> (( ) 6 (57 5)4 ' ' '48 705(' 8'* ( 75( ' 5

) 8 (4'8 564 ;5 )> (( 56 4 (, 56) ' >') ' ' '48 705('. N ,74'645 '5 ) ;'; ;5 5745 57 0 6;'8564' '(' 5 574 ; ;5 ; )> 0 2 (< 5 '0 (8') 6 ;5 8 78 ;5 56;5(9 ;5 ; 9854( ;5 4 , ;5 ;57)'(@' * 5

7 ) 6'8 564 ;5 4 , 4 4 ) 6 (57 5)4 ' 6' ' 4 ('+ 57 5 ;5645 < 5 ) 6'7 @('0 )'7 ,456 ;'7+ 5745 0 2 4 565 6' 8'* ( 5 ) ;'; 56 5 )564( ;5

8 78 . D5* ; A('8, ( H

CONCLUSIÓN

E6 5 ( )5; 8 564 5 5( 8564' 75 ' (5) ) 8 75 ,75( ' 6'( ') 6 (57 5)4 ' 7 ;'4 7 4 8'; 7 ; ('645 5 ( )5; 8 564

5 5( 8564' + 75 ,75( ' ' @ 8 * '(5) ; ' 6 ) 6 ; 0 7 ( *' (5' =';


20/20

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(57 6 75 ( ; )5 6' '( ') 6 ( )';' 6' ;5 5 '7. T 8'6; 56 ) 564'< 5 ' )' ) '( '7 (57 657 ;58 7 ,75( '( < 5 '7 (57 6578'6 8?4( )'7 '( '6 75@ 6 ' ' 4 ('. D' G 5 '('H

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