SUPERFICIES-SUMERGIDAS.docx

7/23/2019 SUPERFICIES-SUMERGIDAS.docx

http://slidepdf.com/reader/full/superficies-sumergidasdocx 1/41

UNIVERSIDAD TÉCNICA DE AMBATO

FACULTAD DE INGENIERÍA CIVIL Y MECÁNICA

CARRERA DE INGENIERÍA MECÁNICA

MODALIDAD PRESENCIAL

INFORME DE LABORATORIO

PRÁCTICA N° 1

DETERMINACIÓN DEL CENTRO DE FUEZAS YPRESIONES

SEMESTRE: QUINTO

PARALELO: “B”

PERÍODO ACADÉMICO

OCTUBRE !1" # MARZO !1$



1. ÍNDICE

2.

3. 1 IDENTIFICACIÓN....................................................................2

4. 2. MARCO TEÓRICO....................................................................3

5. %1 D&'&()*+,-*.+ /&0 -&+'( /& 2(&3*+&3%......................................................4

6. % D&'&()*+,-*.+ /& 0, 45&(6, (&350',+'&%.......................................................8

7. %7 D&'&()*+,-*.+ /& 2(&3*+&3%...................................................................9

8. %8 S52&(4*-*& 20,+, 2,(-*,0)&+'& 35)&(9*/,%.................................................10

9. %8%1 D&'&()*+,( &0 -&+'( /& 2(&3*+&3 , ;<!° 2,(-*,0)&+'& 35)&(9*/%..........11

10. %8%...........D&'&()*+,( 0, 45&(6, (&350',+'& , ;<!° 2,(-*,0)&+'& 35)&(9*/%

1211. %8%7.. .D&'&()*+,( &0 -&+'( /& 2(&3*+&3 , =><!°C? 2,(-*,0)&+'& 35)&(9*/%

12

12. %"....................................................S52&(4*-*& 20,+, '',0)&+'& 35)&(9*/,%13

13. %"%1........D&'&()*+,( &0 -&+'( /& 2(&3*+&3 , ;<!°C '',0)&+'& 35)&(9*/%14

14. %"%..............D&'&()*+,( 0, 45&(6, (&350',+'& , ;<!° '',0)&+'& 35)&(9*/%14

15. %"%7...........D&'&()*+,( &0 -&+'( /& 2(&3*+&3 =><!° '',0)&+'& 35)&(9*/%15

16. %"%8..............D&'&()*+,( 0, 45&(6, (&350',+'& =><!° '',0)&+'& 35)&(9*/%15

17. 3..............................................................................................OBJETIVO16

18. 4..........................................................MATERIAL O EQUIPO A UTILIZAR 16

19.6.....DISCUSIÓN, OBSERVACIONES E INTERPRETACIÓN DE RESULTADOS37

20. 7................................................CONCLUSIONES RECOMENDACIONES37

21. !......................................................................................BIBLIO"RAFÍA38

22......................................................................................ANE#OS................................................................................................................39

23.

1



1 IDENTIFICACIÓN

ÁREA ACADÉMICA ENERGÍA

ASIGNATURA SISTEMAS @IDRÁULICOS I

UNIDAD TEMÁTICA FUERZAS DEBIDAS A FLUIDOS

ESTÁTICOSTÍTULO/ NOMBRE DE LA PRÁCTICA CENTROS DE FUERZA Y PRESIÓN

HORAS POR SEMANA DEL

CURSO:3 PRÁCTICA: N° 1

FECHA DE REALIZACIÓN DE LA PRÁCTICA:

P,(,0&0 B: DÉCIMA PRIMERA SEMANA

HORARIO DE LA PRÁCTICA:

P,(,0&0 “B” 05+&3: !! , <!!

NOMBRE DE LOS INTEGRANTES

MANOBANDA JORGE MANOSALVAS ERICK

NOMBRE DEL

PROFESOR/AYUDANTE

ING. LUIS ESCOBAR / EGRESADO

ANDREA GOYES

2. MARCO TEÓRICO

E0 &'* /& &3'& &5*2 &3 )&/*( 0, 45&(6, 5& &&(-& 5+ 405*/ 3(& 0,3 352&(4*-*&3

5& &3'+ &+ -+',-' -+ H0% P,(, &00 '),(&)3 5+, 9&)&'(, &+ 0, -5,0 0, 2(&3*.+

&&(-*/, 3(& 353 352&(4*-*&3 + 9&+&(,+ ))&+'3 -+ (&32&-' , 5+ 25+'? ,

2



&J-&2-*.+ /& &+ 5+, /& &00,3? 5& 3&( 0, 352&(4*-*& &+ 0, 5& +3 ,3,(&)3 2,(, 0,

(&,0*6,-*.+ /& 0, &J2&(*&+-*,%

C+-&2'3 *)2(',+'&3:

,K M)&+' &3 &0 2(/5-' /& 0, ,20*-,-*.+ /& 5+, 45&(6, , 5+, /*3',+-*, /,/,%

% M F d =

K L, 45&(6, 5& &&(-& &0 405*/ 3(& 5+, 352&(4*-*& 3.0*/, 5& &3' &+ -+',-'

-+ H0 &3 *95,0 ,0 2(/5-' /& 0, 2(&3*.+ &&(-*/, 3(& &00, 2( 35 (&,

% F P A=

-K E3', 45&(6,? 5& ,-', &+ -,/, (&, &0&)&+',0? 3& 25&/& (&2(&3&+',( 2( 5+,+*-, 45&(6, (&350',+'& 3(& 0, 352&(4*-*& -)20&', 5& ,-', &+ 5+ 25+'

00,),/ -&+'( /& 2(&3*+&3 &+ 0, 4*95(, -*+-*/&+'& -+ &0 -&+'( /& 9(,&/,/K%

F$%. 1

3



B,3+/+3 &+ &3'3 45+/,)&+'3 -,0-50,(&)3 0, 2(&3*.+ &&(-*/, 2( &0 405*/ 3(& 0,

352&(4*-*& 35)&(9*/,? 5& 3&9+ 0 -)&+',/ ,+'&(*()&+'&? 3&( *95,0 , 5+, 45&(6,

&5*,0&+'& ,20*-,/, &+ 5+ 25+' /&'&()*+,/%

1. S* 0, 352&(4*-*& 3.0*/, &3 20,+,? 0, 45&(6, (&350',+'& -*+-*/& -+ 0, 45&(6, '',0?

, 5& '/,3 0,3 45&(6,3 &0&)&+',0&3 3+ 2,(,0&0,3 &3 5+, 35), ,(*')H'*-, /& 0,3

45&(6,3K%2. S* 0, 352&(4*-*& &3 -5(,? 0,3 45&(6,3 &0&)&+',0&3 + 3+ 2,(,0&0,3 '&+/(+

-)2+&+'&3 25&3',3 /& 4(), 5& 0, 45&(6, (&350',+'& &3 )&+( 5& 0, 45&(6,

'',0 &3 5+, 35), &-'(*,0 /& 0,3 45&(6,3? ,( -)2+&+'&3 5& 3& 35)&+ 3&

(&3'&+K%

2.1 D&'&()$*+$-* &/ &*'(0 & (&$0*&.

S* '&+&)3 5+, 352&(4*-*& 35)&(9*/, 0, 2(&3*.+ 5& &0 405*/ &&(-& 3(& &00, &3

2(2(-*+,0 , 0, 2(45+/*/,/? &+ 0, 4*95(, &)3 5& 0, 2(&3*.+ “2” 3& ,

*+-(&)&+',+/ , )&/*/, 5& ,(, 0, /*3',+-*, , 0, 352&(4*-*& /&0 405*/ “”% L, 2(&3*.+

,(*,( /&3/& 0, 2(&3*.+ “21” ,3', “2”%

4



F$%. 2

D&*/ , &3', ,(*,-*.+ /& 0,3 2(&3*+&3 , 0 0,(9 /& 0, 352&(4*-*&? 0, Fuer!

E"u#$!%e&'eO O ( F

3& & /&320,6,/, /&0 Ce&'r) de Gr!$ed!dOC O *

/& 0, 352&(4*-*&? ,0

25+'

OC O (

? 00,),/ +e&'r) de (re,#)&e,- 5+, /*3',+-*,O&O

- F#*. 2

S* '),)3 5+, 352&(4*-*& /,/,? /**/*)3 0, /*3'(*5-*.+ /& 2(&3*+&3 &+ 5+, 6+,

(&-',+950,( /& 2(&3*.+ -+3',+'&

1O2 O

5+, '(*,+950,( /& ,3&

1O2 2 O−

,0'5(, “0”% E3',3

/3 /*3'(*5-*+&3 /& 2(&3*+&3 +3 9&+&(,+ /3 45&(6,3 &5*,0&+'&31O O F

O O F

5



F$%. 3

S* -,0-50,)3 03 ))&+'3 9&+&(,/3 -+ (&32&-' , 5+ 25+' “O” '&+*&+/ &+

-5&+', 5&? 2( 0, 9&)&'(, /& 0, /*3'(*5-*.+ /& 2(&3*+&3? “F1” &3',( ,20*-,/, , “0”

“F” , “07” ,),3 /3 /&0 25+' )3 -&(-,+ , 0, 352&(4*-*& /&0 405*/%

1

Q

! QM K Q Q 7+(

% % %

M F e F F = → + = +

∑ E-% 1

E3 /&-*(? 0,3 /3 45&(6,3 5& +3 5&/,+ ,20*-,/,3 , 0,3 /*3',+-*,3 -+-*/,3? 9&+&(,+ &0

)*3) ))&+' 5& 5+, 45&(6, '',0 “F 2” ,20*-,/, , 5+, /*3',+-*, /,/, C&+'( /&

P(&3*+&3? “C 2”K%

F$%. 4

6



D&32&,+/ /& 0, &-5,-*.+ ,+'&(*( '&+&)3 5&:

1

1

Q$

% ( (e

( (

−=

+

E-%

T&+*&+/ &+ -5&+', 5& 0, 2(&3*.+ */(3''*-, +3 /*-& 5&:

Q Q ( * . ρ =

E-% 7

Q5& ,20*-,+/ &+ +5&3'( -,3:

1

Q Q-3 QM K

Q Q-3 QM K

+*

+*

% ( * /

% ( * /

ρ α

ρ α

= −

= −

E-% 8

E+'(,+/ &+ 0, &-5,-*.+ ,+'&(*(:

1Q +*

% e

/=

E-% "

C+ &3', &-5,-*.+ /&/5-*(&)3 0, /*3',+-*, /&0 -&+'( /& 2(&3*+&3 ,0 25+' /& 9*(

25+' /& ,20*-,-*.+ /& 0, 45&(6, &5*,0&+'&K%

+( +* L L e= +

E-% $

7



F$%.

2.2 D&'&()$*+$-* & /+ 5&(+ (&5/'+*'&.

L, 2(&3*.+ &&(-*/, 2( 5+ 405*/ 3(& 5+, 352&(4*-*& 35)&(9*/, /&2&+/& /& 0, /&+3*/,/

/&0 405*/ /& 0, /*3',+-*, /&0 3.0*/ , 0, 352&(4*-*& /&0 405*/ “”

Q Q+* +* P * . ρ =

E-%

E3', 2(&3*.+ ,(*,( -+ 0, 2(45+/*/,/ /*3',+-*, /&0 3.0*/ , 0, 352&(4*-*& /&0 405*/

“”K? ,5)&+',+/ , )&/*/, 5& &0 &0&)&+' 3& 35)&(9& , )3 2(45+/*/,/% L,

&-5,-*.+ ,+'&(*( ',)*H+ 3& 25&/& &3-(**( -):

Q Q-3 Q+* +* P * . ρ α =

E-%

L, 45&(6, (&350',+'& &3 &0 (&350',/ /& 0, 2(&3*.+ 3(& &0 -&+'( /& 0, 9(,&/,/ /& 0,

352&(4*-*& /& '(,, )50'*20*-,/ 2( &0 (&, /& 0, 352&(4*-*& 35)&(9*/,%

8



Q P +* , F P A=

E-% <

2.3 D&'&()$*+$-* & (&$0*&.

E+ 0, 4*95(, $ &)3 5& 0, /*3'(*5-*.+ /& 2(&3*+&3 2( 0,3 352&(4*-*&3 -5(,3 +

2(/5-&+ +*+9+ ))&+' -+ (&32&-' ,0 && /& 9*(? 2( &3',( &+ 0, /*(&--*.+ (,/*,0 ,

&3'& 1 r r P / P

K% L, /*3'(*5-*.+ /& 2(&3*+&3 &+ 0, -,(, 4(+',0 -,(, -+ 0, &3-,0,

9(,/5,/,K &3 *95,0 /& 3&+'*/ 25&3' , 0, /& 0, -,(, 23'&(*( -,(, 25&3', , 0, /& 0,

&3-,0, 9(,/5,/,K% P( '/ &3' 0, +*-, 352&(4*-*& 5& 2(-, 5+ ))&+' -+

(&32&-' ,0 25+' /& 9*( “O” &3 0, 352&(4*-*& 25&3', P 2K%

F$%. 6

9



2.4 S5&($$& /+*+ +($+/)&*'& 5)&(%$+.

F*95(, S52&(4*-*& 20,+, 2,(-*,0)&+'& 35)&(9*/,

F*95(, ;<!°

10



F*95(, < =><!°

2.4.1 D&'&()$*+( &/ &*'(0 & (&$0*& + 89:; +($+/)&*'& 5)&(%$0.

C5,+/ '&+&)3 &0 40',/( 2,(-*,0)&+'& 35)&(9*/ ,3+/+3 &+ 0, &-5,-*.+ "

'&+*&+/ &+ -5&+', 5& &+ &3', 3*'5,-*.+ “0;” & “-9;”? '&+&)3 5&:

1QM PK $

. .e e

.= → =

E-5,-*.+ 1!

P,(, 0 -5,0 &0 -&+'( /& 2(&3*+&3 3& &+-+'(,( , 5+, /*3',+-*,:

7

+( (

. L L= −

E-5,-*.+ 11

S*&+/ L2 &0 (,/* &J'&(+ /& 9*( /*3',+-*, /&0 25+' /& 9*( ,0 )3 35)&(9*/? &3

/&-*( 0, )J*), 2(&3*.+ 2? L2;, / 0& (&3',)3 7 2(5& '&+/(&)3 5+,

/*3'(*5-*.+ /& 2(&3*+&3 '(*,+950,(? + '(,2&6*/,0 2( &3',( 2,(-*,0)&+'& 35)&(9*/K%

11



2.4.2 D&'&()$*+( /+ 5&(+ (&5/'+*'& + 89:; +($+/)&*'& 5)&(%$0.

L, 2(&3*.+ &&(-*/, 3(& 0, 352&(4*-*& 20,+, /&0 &' ;!K &3:

Q Q

+*

. P * ρ =

E-% 1

Y &0 (&, 35)&(9*/, 3&(:

Q , A . 0=

E-% 17

C+ 0 5& 0, 45&(6, &5*,0&+'& 5&/,(:

Q Q Q

+(

. F * 0 ρ =

E-% 18

2.4.3 D&'&()$*+( &/ &*'(0 & (&$0*& + <=9:;C, +($+/)&*'& 5)&(%$0.

C5,+/ '&+&)3 &0 40',/( 2,(-*,0)&+'& 35)&(9*/ ,3+/+3 &+ 0,3 &-5,-*+&3

,+'&(*(&3 '&+*&+/ &+ -5&+', 5& &+ &3', 3*'5,-*.+ “0;-3” “-9;-3”?

'&+&)3 5&:

L, 2(&3*.+ &&(-*/, 3(& 0, 352&(4*-*& 20,+, /&0 &'? 0, -,0-50,)3 -+ 0, 3*95*&+'&

&J2(&3*.+:

-3 QQ Q

+*

% ( *

α ρ =

E-% 1"

Y &0 (&, 35)&(9*/, 3&(:

12



Q , A % 0=

E-% 1$

C+ 0 5& 0, 45&(6, &5*,0&+'& 3&(:

-3 Q

Q Q Q

+(

% F * 0

α ρ =

E-% 1

2. S5&($$& /+*+ '0'+/)&*'& 5)&(%$+.

F$%.

1: S52&(4*-*& 20,+,

'',0)&+'& 35)&(9*/,

13



F*95(, 11 ;<!°

F$%. 12 =><!°

2..1 D&'&()$*+( &/ &*'(0 & (&$0*& + 89:;C '0'+/)&*'& 5)&(%$0.

C5,+/ '&+&)3 &0 40',/( '',0)&+'& 35)&(9*/? “0;/” “-9;/”? 3& '*&+&:

1QM K

d e

d .

=

−

E-% 1

P( 0 ',+' +3 &+-+'(,)3 5& &0 -&+'( /& 2(&3*+&3 3& &+-+'(,( , 5+, /*3',+-*,:

1QM K 1QM K

+( +* +(

d d d L L L !

d d . .

= + → = + +

− −

E-% 1<

2..2 D&'&()$*+( /+ 5&(+ (&5/'+*'& + 89:; '0'+/)&*'& 5)&(%$0.

14



L, 2(&3*.+ &&(-*/, 3(& 0, 352&(4*-*& 20,+, /&0 &'? 0, -,0-50,)3 ,3+/+3 & 2,(,

;!% R&-(/&)3 5& “0;/” “-9;/”

Q QMB K+*

d ( * ρ = −

E-% !

Y &0 (&, 35)&(9*/, 3&(:

Q , A d 0=

E-% 1

P( 0 5& 0, 45&(6, &5*,0&+'& 3&(:

Q Q M KQ Q

(

d F * . d 0 ρ = −

E-%

2..3 D&'&()$*+( &/ &*'(0 & (&$0*& <=9:; '0'+/)&*'& 5)&(%$0.

C5,+/ '&+&)3 &0 40',/( '',0)&+'& 35)&(9*/ ,3+/+3 &+ 0,3 &-5,-*+&3

,+'&(*(&3 '&+*&+/ &+ -5&+', 5& &+ &3', 3*'5,-*.+ “0;/” “-9;-3/”? '&+&)3:

1QM K-3

d e

. d

α

=

−

E-% 7

P( 0 ',+' &0 -&+'( /& 2(&3*+&3 3& &+-+'(,( , 5+, /*3',+-*, /&:

1QM K

-3

+( +* +(

d d L L e L !

. d

α

= + → = + +

−

E- 8

2..4 D&'&()$*+( /+ 5&(+ (&5/'+*'& <=9:; '0'+/)&*'& 5)&(%$0.

15



Q-3Q QMB K

+*

d ( *

α ρ = −

E-% "

Q , A d 0=

E-% $

Q-3Q QM K Q Q

(

d F * . d 0

α ρ = −

E-%

3. OBJETIVO

• D&'&()*+,( 0, 23*-*.+ /&0 -&+'( /& 2(&3*+&3 3(& 5+, 352&(4*-*& 20,+,?

2&(2&+/*-50,( , 0, 352&(4*-*& /&0 405*/? 2,(-*,0)&+'& 35)&(9*/, &+ 5+ 05*/ &+

(&23%• A+,0*6,( 03 &4&-'3 5& 5+ 405*/ *+-)2(&+3*0& &+ (&23 &&(-& 3(& 5+,

352&(4*-*& 35)&(9*/, &+ 5+ 05*/%• D&'&()*+,( &J2&(*)&+',0)&+'& 0, 0+&, /& ,--*.+ 0, ),9+*'5/ /& 0, 45&(6,

(&350',+'& &&(-*/, /&*/ , 0, 2(&3*.+ /&0 405*/%

4. MATERIAL O EQUIPO A UTILIZAR

B,+- /& 2(5&,3 FME! ),(-, EDIBON

. PROCEDIMIENTO A DESARROLLAR

1% N*&0,( &0 /&2.3*' ,-'5,+/ -+&+*&+'&)&+'& 3(& 03 2*&3 /& 353'&+',-*.+?

5& 3+ (&950,0&3? )*&+'(,3 3& 3&(, &0 +*&0 /& 5(5,%

16



F$%. 13 B5(5, /& +*&0

% M&/*( '),( +', /& 0,3 -',3 /&3*9+,/,3 2( ,? L? / &3',3 0'*),3

-((&32+/*&+'&3 , 0, 352&(4*-*& 20,+, 3*'5,/, ,0 &J'(&) /&0 -5,/(,+'&% N

0*/& &3'& 2,3 2,(, 5+, ),( &J,-'*'5/ /& 0,3 )&/*/,3%

F$%. 14 B,+- /& 2(5&,3 FME!

7% C+ &0 /&2.3*' &)20,6,/ 3(& &0 B,+- G(52 @*/(50*-? -0-,( &0 (,6

,3-50,+'& 3(& &0 ,2% C09,( &0 20,'*00 ,0 &J'(&) /&0 (,6%

17



F$%. 1 A2 /& 0, ,0,+6,

F$%. 16 G,+- /& '2&

8% C&((,( 0, &32*', /&0 /&3,9& /&0 4+/ /&0 /&2.3*'% D&320,6,( &0 -+'(,2&3 /&0

(,6 ,3-50,+'& ,3', -+3&95*( 5& 0, 352&(4*-*& 20,+, , &3'5/*,( 3&,

2&(2&+/*-50,( , 0, ,3& /&0 /&2.3*' ,3& 5& +*&0,)3 2(&*,)&+'&K% C+ &3'&

2,3 -+3&95*)3 -)&+6,( 0,3 )&/*/,3 /&3/& 5+, 23*-*.+ '',0 /& &5*0*(*?

,3 '/3 03 -,)*3 3& 2(/5-*(+ 2( )&/* /& 5+, /*4&(&+-*, &+ &0 05)&+

/& ,95, 2( 5+, /*4&(&+-*, &+ 0,3 ),3,3 5& -0-,)3 &+ &0 20,'*00% E3'&

25+' &3 /& &J'(&), *)2(',+-*, 2,(, 5+, 5&+, '), /& )&/*/,3 &0 &5*2

'*&+& ,(*,3 )5&3-,3 &+ &0 “9,+- '2&”? 0, -&+'(,0 */&+'*4*-, &3'& 25+' /&

&5*0*(*K%

"% I+'(/5-*( ,95, &+ &0 /&2.3*' ,3', 5& 0, 352&(4*-*& 0*(& /& H3', (&350'&

'+*%&*'& +/ >0(& )? $*&($0( &/ 5+(+*'& ,3', 53' &0 25+' *+4&(*( /&0&0&)&+' 40',/(K% E0 ,53'& 4*+ /& /*- +*&0 3& 25&/& 09(,( 3(&2,3,+/

18



0*9&(,)&+'& &0 00&+,/ 2(&'&+/*/ ? 23'&(*()&+'&? /&3,95,+/ 0&+',)&+'& ,

'(,H3 /& 0, &32*',% P,(, /&3,95,( &3 23*0& 5& '&+9,3 5& *+-0*+,( 0&&)&+'&

&0 /&2.3*' ,-*, &0 0,/ /& 0, &32*',% S* '*&+&3 5& ,-&(0 ,3&9(,'& /&325H3

5& &0 &5*2 2&(),+&6-, -((&-',)&+'& +*&0,/

$% C0-,( 5+ 2&3 -,0*(,/ 3(& &0 20,'*00 /& ,0,+6, ,W,/*(? 0&+',)&+'&? ,95,

,3', 5& 0, 352&(4*-*& 20,+, , &3'5/*,( 3&, 2&(2&+/*-50,( , 0, ,3& /&0 /&2.3*'%

P,(, &0 ,53'& /& &3', 23*-*.+ +3 ,0&)3 /& 0, ,5/, /& 0, ),(-, 0,+-, 5&

3& &+-5&+'(, &+ &0 '2& /&0 (,6 9,+-'2&K? 53' ,0 0,/ /&0 20,'*00%

A+',( &0 +*&0 /& ,95,? *+/*-,/ &+ &0 -5,/(,+'&? &0 ,0( /&0 2&3 3*'5,/

3(& &0 20,'*00% N',: -)2(,( 3* 0,3 2&3,3 &3'+ ),(-,/,3 &+ 9( 9(4 ; NK%

L,3 -05)+,3 3)(&,/,3 &+ 0, ',0, -((&32+/&+ , 03 /,'3 '&+*/3

&J2&(*)&+',0)&+'&? &3'3 3+ 03 5& -5)20*)&+',(&)3 &+ &3', 2,('& /& 0,

2(-'*-,%

F$%. 17 P&3,3

% R&2&'*( 0, 2&(,-*.+ ,+'&(*( ,(*,3 &-&3? ,5)&+',+/ &+ -,/, 5+, /& &00,3? 2(9(&3*,)&+'&? &0 2&3 &+ &0 20,'*00 ,3', 5&? &3',+/ +*&0,/ &0 (,6

,3-50,+'&? &0 +*&0 /& 0, 352&(4*-*& 0*(& /&0 ,95, &+(,3& -+ 0, ,(*3', 352&(*( /&

0, 352&(4*-*& 20,+, (&-',+950,( 5& 2(&3&+', &0 &J'(&) /&0 -5,/(,+'& ,3',

-5(*( '',0)&+'& 0, 352&(4*-*& 20,+,K%

% A 2,('*( /& &3& 25+'? &+ (/&+ *+&(3 , -) 3& 45&(+ -0-,+/ 3(& &0

20,'*00? 3& ,+ (&'*(,+/ 03 *+-(&)&+'3 /& 2&3 /,/3 &+ -,/, 2&(,-*.+? 3&

19



+*&0, &0 (,6 /&325H3 /& -,/, (&'*(,/,K 5'*0*6,+/ 0, &32*', /& /&3,9& 3&

,+ ,+',+/ 03 2&33 &+ &0 20,'*00 03 +*&0&3 /& ,95, K%

20



P(?'$+ 1@ D&'&()*+,( &0 -&+'( /& 2(&3*+&3 -+ +950 X;<! ? 2,(-*,0)&+'&ᵒ

35)&(9*/

L0&+,/ /&2.3*' V,-*,/ /&2.3*' P()&/*3 C0-503

P&33 A0'5(,3 P&33 A0'5(,3F) 9K ) )K L-2 )K F-2 NK

F 9(K ))K F9(K ))K

1! 1 1! 17

! 8 ! 7

7! 7$ 7! 7

$! 8 $! 8$

! $! ! $1

11! 11! "

1"" 8 1"" 7

1! < 1! <8

T+>/+ 1 L0&+,/ /& 0, ',0, -+ /,'3 &J2&(*)&+',0&3

P,(, = / *+)&(3*.+ 2,(-*,0K

C.1. M&/*( 0,3 -',3 ,? ? / L:

,; 1!! ))

; ! ))

/; 1!! ))

L; " ))

21



C.2. P()&/*,( 03 ,0(&3 '&+*/3 -)20&)&+',( &+ 0, T,0, 1[ 0,3 -05)+,3 F)

)%

L0&+,/ /&2.3*' V,-*,/ /&2.3*' P()&/*3 C0-503

P&33 A0'5(,3 P&33 A0'5(,3F) 9K ) )K L-2 )K F-2 NK

F 9(K ))K F9(K ))K

1! 1 1! 17 !?1!< !?!1

! 8 ! 7 !?1!7 !?!"

7! 7$ 7! 7 !?1!! !?!7$

$! 8 $! 8$ !?1! !?!8$

! $! ! $1 !?!<7 !?!$!

11! 11! " !?!<8 !?!8

1"" 8 1"" 7 !?1!< !?!

1! < 1! <8 !?1!! !?!<8

T+>/+ 2 L0&+,/ /& 0, ',0, -+ 2()&/*3 &J2&(*)&+',0&3

A+,0*6,( 0,3 /&3*,-*+&3 '&+*/,3? -+ (&32&-' , 03 ,0(&3 /& (*9&+%

C.3. C,0-50,( 03 ,0(&3 /& L-2? '&+*&+/ &+ -5&+', 5&:

7

+( (

. L L= −

S*&+/ L2 &0 (,/* &J'&(+ /& 9*( L2 ; , /K%

Lp2=0.1+0.1

Lp2=0.2m

22



P(?'$+ 2@ R&,0*6,( &+ -0-50 /& 0, 45&(6, (&350',+'& F-2 -+ 5+ +950 /& <!° 2(

)&/* /& 0, 4.()50,

Fcp= ρ∗g∗h

2 -+ 03 /,'3 2(&*,)&+'& '&+*/3%

L0&+,/ /&2.3*' V,-*,/ /&2.3*' P()&/*3 C0-503

P&33 A0'5(,3 P&33 A0'5(,3F) 9K ) )K L-2 )K F-2 NK

F 9(K ))K F9(K ))K

1! 1 1! 17 !?1!< !?!1 !?1<7 !?!"$

! 8 ! 7 !?1!7 !?!" !?1<!1 !?1$!7! 7$ 7! 7 !?1!! !?!7$ !?1" !?88

$! 8 $! 8$ !?1! !?!8$ !?17 !?887

! $! ! $1 !?!<7 !?!$! !?1 1?77

11! 11! " !?!<8 !?!8 !?17" 1?!

1"" 8 1"" 7 !?1!< !?! !?1!1 ?78<

1! < 1! <8 !?1!! !?!<8 !?1$! ?<181T+>/+ 3 L0&+,/ /& 0, ',0, -+ -0-503

C.4. EJ20*-,( 0, 2,('*-50,(*6,-*.+ ,+'&(*( 2,('*&+/ /& 0, &-5,-*.+ E-% "K E-% $K%

1Q +*

% e

/=

E-% "K

+( +* L L e= +

E-% $K

T&+*&+/ &+ -5&+', 0,3 &-5,-*+&3 2(&*,)&+'& '&+*/,3? 2(-&/&)3 , -(&,( 5+,

(&0,-*.+ &+'(& 0,3 )*3),3? '&+*&+/ &+ -5&+', 5& 2,(, Y-9? 3& -(&,( 2( 5+, (&0,-*.+

&+'(& 0, ,0'5(,? 0, -5,0 3& -+3*/&(, 5& Y-9;? '&+*&+/ 5+, 0+9*'5/ L;? 3& 2(-&/& ,

'&+&( 5+, 2,('*-50,(*/,/ 43*-, 7 2(5& '&+/(&)3 5+, /*3'(*5-*.+ /& 2(&3*+&3

'(*,+950,(? + '(,2&6*/,0 2( &3',( 2,(-*,0)&+'& 35)&(9*/K%

23



C.. A+,0*6,( -)&+',( 03 /,'3 '&+*/3? -)&+',( 23*0&3 /*3-(&2,+-*,3 -+ 03

/,'3 &32&(,/3%

• E+ 0, 2(*)&(, 2(,-'*-, 2/&)3 ,+,0*6,( 0, (&0,-*.+ 5& &J*3'& &+'(& 0, ),3,

,20*-,/,? &+ &3'& -,3 , , 3&( 0, 45&(6, -+ 0, 5& ,)3 , '(,,,( 0, ,0'5(,

-+ 0, -5,0 3& /&3,((00,/, 0, 40',*0*/,/ /& 5+ 3*3'&), 2,(-*,0)&+'& 35)&(9*/%• S& -)2(5&, &0 ),(9&+ /& &((( &J*3'&+'&? 2( /*4&(&+'&3 3*'5,-*+&3? /& 03

-5,0&3 &0 2()&/* /& 0,3 )*3),3? +3 ,-&(-, , 5+, (&,0*/,/ /& /,'3? &J*3'&+'&3

&+'(& 03 (&350',/3 , -,0-50,( 0, &J2&(*)&+',-*.+ /,/,%• T&+*&+/ &+ -5&+', 0, 0*)*', 2&(/*/, /& 405*/ 5& &J*3'& &+ 0, 2(&3&+'& 2(-'*-,?

3& /&'&()*+, 5& 03 /,'3 '&+*/3? &3'+ 0*9,/3 , 03 )&/*3 &J'&(+3

-+/*-*+&3 , 0,3 -5,0&3 3& 2(/5 0, 2(-'*-,%

P(?'$+ 3@ D&'&()*+,( &0 -&+'( /& 2(&3*+&3 -+ +950 X=><! ? 2,(-*,0)&+'&ᵒ

35)&(9*/

L0&+,/ /&2.3*' V,-*,/ /&2.3*' P()&/*3 C0-503

P&33 A0'5(,3 P&33 A0'5(,3

F) 9K ) )K L-2 )K F-2 NK α1>90F 9(K ))K F9(K ))K

! $ 20 28 5,5

7! 8! 30 415,5

8! 8$ 40 455,5

"! "1 50 505,5

$! "" 60 615,5

! "< 70 605,5

! $8 80 67 5,5

<! $$ 90 675,5

T+>/+ 4 L0&+,/ /& 0, ',0, -+ /,'3 &J2&(*)&+',0&3 2,(, 5+ +950 = <!°

24





C.2. P()&/*,( 03 ,0(&3 '&+*/3 -)20&)&+',( &+ 0, T,0, 8 "[ 0,3 -05)+,3

F) )%

L0&+,/ /&2.3*' V,-*,/ /&2.3*' P()&/*3 C0-503P&33 A0'5(,3 P&33 A0'5(,3

F) 9K ) )K L-2 )K F-2 NK α1<90F 9(K ))K F9(K ))K! $ 20 28 !?!! !?! 5,5

7! 8! 30 41 !?!7! !?!81 5,5

8! 8$ 40 45 !?!8! !?!8$ 5,5

"! "1 50 50 !?!"! !?!"1 5,5

$! "" 60 61 !?!$! !?!"< 5,5

! "< 70 60 !?!! !?!$1 5,5

! $8 80 67 !?!! !?!$" 5,5

<! $$ 90 67 !?!<! !?!$$ 5,5

T+>/+ 6 L0&+,/ /& 0, ',0, -+ 2()&/*3 &J2&(*)&+',0&3 2,(, 5+ +950 = <!°

L0&+,/ /&2.3*' V,-*,/ /&2.3*' P()&/*3 C0-503P&33 A0'5(,3 P&33 A0'5(,3


1" 18 15 15 !?!1" !?!1" 185,5" " 25 24 !?!" !?!" 185,57" 78 35 35 !?!7" !?!7" 185,58" 8! 45 41 !?!8" !?!81 185,5"" 8$ 55 45 !?!"" !?!8$ 185,5$" " 65 51 !?!$" !?!" 185,5" "" 75 56 !?!" !?!"$ 185,5" $1 85 62 !?!" !?!$ 185,5

T+>/+ 7 L0&+,/ /& 0, ',0, -+ 2()&/*3 &J2&(*)&+',0&3 2,(, 5+ +950 > <!°

C.3. C,0-50,( 03 ,0(&3 /& L-2? '&+*&+/ &+ -5&+', 5&:

7

+( (

. L L= −

S*&+/ L2 &0 (,/* &J'&(+ /& 9*( L2 ; , /K%

Lp2=0.1+0.1

Lp2=0.2m

26



P(?'$+ 4@ R&,0*6,( &+ -0-50 /& 0, 45&(6, (&350',+'& F-2 -+ 5+ +950 => <!° 2(

)&/* /& 0, 4.()50, Fcp= ρ∗g∗h

2 -+ 03 /,'3 2(&*,)&+'& '&+*/3%

L0&+,/ /&2.3*' V,-*,/ /&2.3*' P()&/*3 C0-503P&33 A0'5(,3 P&33 A0'5(,3


! $ 20 28 !?!! !?! !?1<! !?8"$ 5,5

7! 8! 30 41 !?!7! !?!81 !?18" !?""$ 5,5

8! 8$ 40 45 !?!8! !?!8$ !?1 !?$<" 5,5

"! "1 50 50 !?!"! !?!"1 !?111 !?"<

5,5

$! "" 60 61 !?!$! !?!" !?1$ 1?1778 5,5

! "< 70 60 !?!! !?!$! !?11 1?1< 5,5

! $8 80 67 !?!! !?!$$ !?1$1 1?88"" 5,5

<! $$ 90 67 !?!<! !?!$ !?1" 1?8<!1 5,5

T+>/+ ! L0&+,/ /& 0, ',0, -+ -0-503 2,(, 5+ +950 = <!°

27



L0&+,/ /&2.3*' V,-*,/ /&2.3*' P()&/*3 C0-503P&33 A0'5(,3 P&33 A0'5(,3

F) 9K ) )K L-2 )K F-2 NK α2<90F 9(K ))K F9(K ))K

1" 18 15 15 !?!1" !?!1" !?1<71 !?!! 185,5" " 25 24 !?!" !?!" !?1< !?!7 185,57" 78 35 35 !?!7" !?!7" !?1$" !?8!11 185,58" 8! 45 41 !?!8" !?!81 !?18" !?"" 185,5"" 8$ 55 45 !?!"" !?!8$ !?1 !?$<" 185,5$" " 65 51 !?!$" !?!" !?1! !?<7$ 185,5" "" 75 56 !?!" !?!"$ !?1<" 1?!7 185,5" $1 85 62 !?!" !?!$ !?1" 1?87 185,5

T+>/+ 9 L0&+,/ /& 0, ',0, -+ -0-503 2,(, 5+ +950 > <!°

C.4. EJ20*-,( 0, 2,('*-50,(*6,-*.+ ,+'&(*( 2,('*&+/ /& 0, &-5,-*.+ E-% "K E-% $K%

1Q +*

% e

/=

E-% "K

+( +* L L e= +

E-% $K

T&+*&+/ &+ -5&+', 0,3 &-5,-*+&3 2(&*,)&+'& '&+*/,3? 2(-&/&)3 , -(&,( 5+,

(&0,-*.+ &+'(& 0,3 )*3),3? '&+*&+/ &+ -5&+', 5& 2,(, Y-9? 3& -(&,( 2( 5+, (&0,-*.+

&+'(& 0, ,0'5(,? 0, -5,0 3& -+3*/&(, 5& Y-9;? '&+*&+/ 5+, 0+9*'5/ L;? 3& 2(-&/& ,

'&+&( 5+, 2,('*-50,(*/,/ 43*-, 7 2(5& '&+/(&)3 5+, /*3'(*5-*.+ /& 2(&3*+&3

'(*,+950,(? + '(,2&6*/,0 2( &3',( 2,(-*,0)&+'& 35)&(9*/K%

C.. A+,0*6,( -)&+',( 03 /,'3 '&+*/3? -)&+',( 23*0&3 /*3-(&2,+-*,3 -+ 03

/,'3 &32&(,/3%

• E+ 0, '&(-&(, 2(-'*-, 2/&)3 ,+,0*6,( 0, (&0,-*.+ 5& &J*3'& &+'(& 0, ),3,

,20*-,/,? &+ &3'& -,3 , , 3&( 0, 45&(6, -+ 0, 5& ,)3 , '(,,,( 0, ,0'5(,

-+ 0, -5,0 3& /&3,((00,/, 0, 40',*0*/,/ /& 5+ 3*3'&), 2,(-*,0)&+'& 35)&(9*/%• S& -)2(5&, &0 ),(9&+ /& &((( &J*3'&+'&? 2( /*4&(&+'&3 3*'5,-*+&3? /& 03

-5,0&3 &0 2()&/* /& 0,3 )*3),3? +3 ,-&(-, , 5+, (&,0*/,/ /& /,'3? &J*3'&+'&3

&+'(& 03 (&350',/3 , -,0-50,( 0, &J2&(*)&+',-*.+ /,/,%• T&+*&+/ &+ -5&+', 0, 0*)*', 2&(/*/, /& 405*/ 5& &J*3'& &+ 0, 2(&3&+'& 2(-'*-,?

3& /&'&()*+, 5& 03 /,'3 '&+*/3? &3'+ 0*9,/3 , 03 )&/*3 &J'&(+3

-+/*-*+&3 , 0,3 -5,0&3 3& 2(/5 0, 2(-'*-,%

28



• C+3&(,( /*- +950? &+ &0 -5,0? 0, ,0'5(, , 3&( )&/*/, , , ,(*,(

-+3*/&(,0&)&+'&? , 5& ,0 3&( 5+ +950 /*4&(&+'&? 3& 2(2(-*+, 5+,

/*3-(&2,+-*, &+'(& ,),3 2(-'*-,3? '),+/ &+ -5&+', 5& ,0 ,5)&+',( &0 2&3?

0, ,0'5(, 2,(, 5& &J*3', /*- +950? /&&( &3',( *)20*-,/ -+ 5+ ,5)&+' /&

405*/%

P(?'$+ @ D&'&()*+,( &0 -&+'( /& 2(&3*+&3 -+ +950 X;<! ? '',0)&+'& 35)&(9*/ᵒ

L0&+,/ /&2.3*' V,-*,/ /&2.3*' P()&/*3 C0-503

P&33 A0'5(,3 P&33 A0'5(,3F) 9K ) )K L-2 )K F-2 NK

F 9(K ))K F9(K ))K8" 117 8" 11

"" 11" "" 118

$" 11 $" 11<

" 11 " 1!

" 18 " 1"

<" 1 <" 17!" 17! 7!" 1<

71" 177 71" 17

T+>/+ 1: L0&+,/ /& 0, ',0, -+ /,'3 &J2&(*)&+',0&3? '',0)&+'& 35)&(9*/

29



P,(, = / *+)&(3*.+ 2,(-*,0K

C.1. M&/*( 0,3 -',3 ,? ? / L:

,; 1!! ))

; ! ))

/; 1!! ))

L; " ))

C.2. P()&/*,( 03 ,0(&3 '&+*/3 -)20&)&+',( &+ 0, T,0, 1![ 0,3 -05)+,3 F)

)%

L0&+,/ /&2.3*' V,-*,/ /&2.3*' P()&/*3 C0-503

P&33 A0'5(,3 P&33 A0'5(,3F) 9K ) )K L-2 )K F-2 NK

F 9(K ))K F9(K ))K

8" 117 8" 11 !?8" !?117

"" 11" "" 118 !?"" !?11"

$" 11 $" 11< !?$" !?11<

" 11 " 1! !?" !?11

" 18 " 1" !?" !?1"

<" 1 <" 1 !?<" !?1

7!" 17! 7!" 1< !?7!" !?17!

71" 177 71" 17 !?71" !?177

T+>/+ 11 L0&+,/ /& 0, ',0, -+ 2()&/*3 &J2&(*)&+',0&3? '',0)&+'& 35)&(9*/

30



C.3. C,0-50,( 03 ,0(&3 /& L-2? '&+*&+/ &+ -5&+', 5&:

7

+( (

. L L= −

S*&+/ L2 &0 (,/* &J'&(+ /& 9*( L2 ; , /K% Lp2=0.1+0.1

Lp2=0.2m

P(?'$+ 6@ R&,0*6,( &+ -0-50 /& 0, 45&(6, (&350',+'& F-2 -+ 5+ +950 /& <!°? &+ 5+

3*3'&), '',0)&+'& 35)&(9*/? 2( )&/* /& 0, 4.()50,

Fcp= ρ∗g∗h

2

-+ 03 /,'3

2(&*,)&+'& '&+*/3%

L0&+,/ /&2.3*' V,-*,/ /&2.3*' P()&/*3 C0-503

P&33 A0'5(,3 P&33 A0'5(,3F) 9K ) )K L-2 )K F-2 NK

F 9(K ))K F9(K ))K

8" 117 8" 11 !?8" !?117 !?1"<" 8?81"

"" 11" "" 118 !?"" !?11" !?1"$7 8?"71

$" 11 $" 11< !?$" !?11< !?1"$ 8?<$

" 11 " 1! !?" !?11 !?1"! "?!"$

" 18 " 1" !?" !?1" !?1"" "?7<1$

<" 1 <" 1 !?<" !?1 !?1"8 "?$"!"

7!" 17! 7!" 1< !?7!" !?17! !?1"8 "?$"

71" 177 71" 17 !?71" !?177 !?1"7" $?!<"

T+>/+ 12 L0&+,/ /& 0, ',0, -+ -0-503? '',0)&+'& 35)&(9*/

31



C.4. EJ20*-,( 0, 2,('*-50,(*6,-*.+ ,+'&(*( 2,('*&+/ /& 0, &-5,-*.+ E-% "K E-% $K%

1Q +*

% e

/=

E-% "K

+( +* L L e= +

E-% $K

T&+*&+/ &+ -5&+', 0,3 &-5,-*+&3 2(&*,)&+'& '&+*/,3? 2(-&/&)3 , -(&,( 5+,

(&0,-*.+ &+'(& 0,3 )*3),3? '&+*&+/ &+ -5&+', 5& 2,(, Y-9? 3& -(&,( 2( 5+, (&0,-*.+

&+'(& 0, ,0'5(,? 0, -5,0 3& -+3*/&(, 5& Y-9;? '&+*&+/ 5+, 0+9*'5/ L;? 3& 2(-&/& ,

'&+&( 5+, 2,('*-50,(*/,/ 43*-, 7 2(5& '&+/(&)3 5+, /*3'(*5-*.+ /& 2(&3*+&3

'(*,+950,(? + '(,2&6*/,0 2( &3',( 2,(-*,0)&+'& 35)&(9*/K%

C.. A+,0*6,( -)&+',( 03 /,'3 '&+*/3? -)&+',( 23*0&3 /*3-(&2,+-*,3 -+ 03

/,'3 &32&(,/3%

• E+ 0, 5*+', 2(-'*-, 2/&)3 ,+,0*6,( 0, (&0,-*.+ 5& &J*3'& &+'(& 0, ),3,

,20*-,/,? &+ &3'& -,3 , , 3&( 0, 45&(6, -+ 0, 5& ,)3 , '(,,,( 0, ,0'5(,

-+ 0, -5,0 3& /&3,((00,/, 0, 40',*0*/,/ /& 5+ 3*3'&), 2,(-*,0)&+'& 35)&(9*/%• S& -)2(5&, &0 ),(9&+ /& &((( &J*3'&+'&? 2( /*4&(&+'&3 3*'5,-*+&3? /& 03

-5,0&3 &0 2()&/* /& 0,3 )*3),3? +3 ,-&(-, , 5+, (&,0*/,/ /& /,'3? &J*3'&+'&3

&+'(& 03 (&350',/3 , -,0-50,( 0, &J2&(*)&+',-*.+ /,/,%• T&+*&+/ &+ -5&+', 0, 0*)*', 2&(/*/, /& 405*/ 5& &J*3'& &+ 0, 2(&3&+'& 2(-'*-,?

3& /&'&()*+, 5& 03 /,'3 '&+*/3? &3'+ 0*9,/3 , 03 )&/*3 &J'&(+3

-+/*-*+&3 , 0,3 -5,0&3 3& 2(/5 0, 2(-'*-,%• A0 (&0,-*+,( 0 , )&+-*+,/? &+'(& 03 2&33 0, 2(45+/*/,/ , 0, -5,0 3&

),+'*&+& &0 -5&(2? '),)3 &+ -5&+', 0, ,0', ,(*,-*.+ 2,(, L-2 F-2 -+ 0,3

',0,3 2(&*,)&+'& '&+*/,3? ,0 ,5)&+',( 35 ,0'5(,? &0 -&+'( /& 2(&3*+&3

/*3)*+5*(? /& ',0 ),+&(, 5& 0, 45&(6, (&350',+'& ,5)&+',(? -,3* *+&(3,)&+'&%

32



PRCTICA 7@ D&'&()*+,( &+'( /& 2(&3*+&3 -+ +950 X=><! ? '',0)&+'&ᵒ

35)&(9*/

L0&+,/ /&2.3*' V,-*,/ /&2.3*' P()&/*3 C0-503P&33 A0'5(,3 P&33 A0'5(,3

F) 9K ) )K L-2 )K F-2 NK α1<90F 9(K ))K F9(K ))K$! 11! $! 111 "?"" 118 " 113 "?"<! 11< <! 117 "?"7!" 1 7!" 121 "?"7! 17! 7! 128 "?"77" 178 77" 132 "?"7"! 17$ 7"! 134 "?"7$" 18! 7$" 138 "?"7! 18" 7! 144 "?"

7<" 1"! 7<" 151 "?"T+>/+ 13 L0&+,/ /& 0, ',0, -+ /,'3 &J2&(*)&+',0&3 2,(, 5+ +950 = <!°

L0&+,/ /&2.3*' V,-*,/ /&2.3*' P()&/*3 C0-503P&33 A0'5(,3 P&33 A0'5(,3

F) 9K ) )K L-2 )K F-2 NK α2>90F 9(K ))K F9(K ))K8" 11" 8" 114 1",5

"" 11 "" 1161",5

$" 1! $" 1211",5

" 17 " 122 1",5

" 1$ " 1271",5

<" 17! <" 1291",5

7!" 17 7!" 1311",5

71" 17" 71" 1341",5

T+>/+ 14 L0&+,/ /& 0, ',0, -+ /,'3 &J2&(*)&+',0&3 2,(, 5+ +950 > <!°

P,(, = / *+)&(3*.+ 2,(-*,0K

C.1. M&/*( 0,3 -',3 ,? ? / L:

,; 1!! ))

; ! ))

/; 1!! ))

L; " ))

33



C.2. P()&/*,( 03 ,0(&3 '&+*/3 -)20&)&+',( &+ 0, T,0, 17 18[ 0,3

-05)+,3 F) )%

L0&+,/ /&2.3*' V,-*,/ /&2.3*' P()&/*3 C0-503P&33 A0'5(,3 P&33 A0'5(,3

F) 9K ) )K L-2 )K F-2 NK α1<90F 9(K ))K F9(K ))K$! 11! $! 111 !?$! !?11! "?"" 118 " 113 !?" !?111 "?"<! 11< <! 117 !?<! !?11 "?"7!" 1 7!" 121 !?7!" !?17 "?"7! 17! 7! 128 !?7! !?1 "?"77" 178 77" 132 !?77" !?177 "?"7"! 17$ 7"! 134 !?7"! !?17" "?"

7$" 18! 7$" 138 !?7$" !?17 "?"

T+>/+ 1 L0&+,/ /& 0, ',0, -+ 2()&/*3 &J2&(*)&+',0&3 2,(, 5+ +950 = <!°?

'',0)&+'& 35)&(9*/

L0&+,/ /&2.3*' V,-*,/ /&2.3*' P()&/*3 C0-503P&33 A0'5(,3 P&33 A0'5(,3 F) 9K ) )K L-2 )K F-2 NK α2>90

F 9(K ))K F9(K ))K8" 11" 8" 114 !?8" !?11" 1"?""" 11 "" 116 !?"" !?11 1"?"$" 1! $" 121 !?$" !?11 1"?"" 17 " 122 !?" !?17 1"?"" 1$ " 127 !?" !?1 1"?"

<" 17! <" 129 !?<" !?17! 1"?"7!" 17 7!" 131 !?7!" !?17 1"?"71" 17" 71" 134 !?71" !?17" 1"?"

T+>/+ 16 L0&+,/ /& 0, ',0, -+ 2()&/*3 &J2&(*)&+',0&3 2,(, 5+ +950 > <!°?

'',0)&+'& 35)&(9*/

A+,0*6,( 0,3 /&3*,-*+&3 '&+*/,3? -+ (&32&-' , 03 ,0(&3 /& (*9&+%

C.3. C,0-50,( 03 ,0(&3 /& L-2? '&+*&+/ &+ -5&+', 5&:

34



7

+( (

. L L= −

S*&+/ L2 &0 (,/* &J'&(+ /& 9*( L2 ; , /K%

Lp2=0.1+0.1

Lp2=0.2m

P(?'$+ !@ R&,0*6,( &+ -0-50 /& 0, 45&(6, (&350',+'& F-2 -+ 5+ +950 => <!° 2(

)&/* /& 0, 4.()50, Fcp= ρ∗g∗h

2 -+ 03 /,'3 2(&*,)&+'& '&+*/3%

L0&+,/ /&2.3*' V,-*,/ /&2.3*' P()&/*3 C0-503

P&33 A0'5(,3 P&33 A0'5(,3 F) 9K ) )K L-2 )K F-2 NK α1<90F 9(K ))K F9(K ))K$! 11! $! 111 !?$! !?111 !?1$1 8?118 "?"" 118 " 113 !?" !?118 !?1$! 8?78!" "?"<! 11< <! 117 !?<! !?11 !?1" 8?$<1" "?"7!" 1 7!" 121 !?7!" !?1 !?1"" 8?<7< "?"7! 17! 7! 128 !?7! !?1< !?1""1 "?$!1 "?"77" 178 77" 132 !?77" !?177 !?1"7 "?<$!1 "?"7"! 17$ 7"! 134 !?7"! !?17" !?1"71 $?18! "?"7$" 18! 7$" 138 !?7$" !?17< !?1"1 $?"1!1 "?"

T+>/+ 17 L0&+,/ /& 0, ',0, -+ -0-503 2,(, 5+ +950 = <!°

L0&+,/ /&2.3*' V,-*,/ /&2.3*' P()&/*3 C0-503P&33 A0'5(,3 P&33 A0'5(,3 F) 9K ) )K L-2 )K F-2 NK α2>90F 9(K ))K F9(K ))K8" 11" 8" 114 !?8" !?11" !?1"< 8?818 1"?""" 11 "" 116 !?"" !?11 !?1"<1 8?"71 1"?"$" 1! $" 121 !?$" !?11 !?1" 8?<" 1"?"" 17 " 122 !?" !?17 !?1"1 "?!"$7 1"?"

" 1$ " 127 !?" !?1 !?1"" "?7<1 1"?"<" 17! <" 129 !?<" !?17! !?1"8 "?$"!$ 1"?"

35



7!" 17 7!" 131 !?7!" !?17 !?1"81 "?$" 1"?"71" 17" 71" 134 !?71" !?17" !?1"71 $?!<"8 1"?"

T+>/+ 1! L0&+,/ /& 0, ',0, -+ -0-503 2,(, 5+ +950 > <!°

36



C.4. EJ20*-,( 0, 2,('*-50,(*6,-*.+ ,+'&(*( 2,('*&+/ /& 0, &-5,-*.+ E-% "K E-% $K%

1Q +*

% e

/=

E-% "K

+( +* L L e= +

E-% $K

T&+*&+/ &+ -5&+', 0,3 &-5,-*+&3 2(&*,)&+'& '&+*/,3? 2(-&/&)3 , -(&,( 5+,

(&0,-*.+ &+'(& 0,3 )*3),3? '&+*&+/ &+ -5&+', 5& 2,(, Y-9? 3& -(&,( 2( 5+, (&0,-*.+

&+'(& 0, ,0'5(,? 0, -5,0 3& -+3*/&(, 5& Y-9;? '&+*&+/ 5+, 0+9*'5/ L;? 3& 2(-&/& ,

'&+&( 5+, 2,('*-50,(*/,/ 43*-, 7 2(5& '&+/(&)3 5+, /*3'(*5-*.+ /& 2(&3*+&3

'(*,+950,(? + '(,2&6*/,0 2( &3',( 2,(-*,0)&+'& 35)&(9*/K%

C.. A+,0*6,( -)&+',( 03 /,'3 '&+*/3? -)&+',( 23*0&3 /*3-(&2,+-*,3 -+ 03

/,'3 &32&(,/3%

• E+ 0, '&(-&(, 2(-'*-, 2/&)3 ,+,0*6,( 0, (&0,-*.+ 5& &J*3'& &+'(& 0, ),3,

,20*-,/,? &+ &3'& -,3 , , 3&( 0, 45&(6, -+ 0, 5& ,)3 , '(,,,( 0, ,0'5(,

-+ 0, -5,0 3& /&3,((00,/, 0, 40',*0*/,/ /& 5+ 3*3'&), 2,(-*,0)&+'& 35)&(9*/%• S& -)2(5&, &0 ),(9&+ /& &((( &J*3'&+'&? 2( /*4&(&+'&3 3*'5,-*+&3? /& 03

-5,0&3 &0 2()&/* /& 0,3 )*3),3? +3 ,-&(-, , 5+, (&,0*/,/ /& /,'3? &J*3'&+'&3&+'(& 03 (&350',/3 , -,0-50,( 0, &J2&(*)&+',-*.+ /,/,%

• T&+*&+/ &+ -5&+', 0, 0*)*', 2&(/*/, /& 405*/ 5& &J*3'& &+ 0, 2(&3&+'& 2(-'*-,?

3& /&'&()*+, 5& 03 /,'3 '&+*/3? &3'+ 0*9,/3 , 03 )&/*3 &J'&(+3

-+/*-*+&3 , 0,3 -5,0&3 3& 2(/5 0, 2(-'*-,%• C+3&(,( /*- +950? ,0 &3',( '',0)&+'& 35)&(9*/? 0, ,0'5(, , 3&( )&/*/, ,

, ,(*,( -+3*/&(,0&)&+'&? , 5& ,0 3&( 5+ +950 /*4&(&+'&? 3& 3&(, -)

35 ,0'5(, ,5)&+', -+3*/&(,0&)&+'&? '),+/ &+ -5&+', 5& ,0 ,5)&+',( &0

2&3? 0, ,0'5(, 2,(, 5& &J*3', /*- +950? /&&( &3',( *)20*-,/ -+ 5+

,5)&+' /& 405*/%

37



6. DISCUSIÓN, OBSERVACIONES E INTERPRETACIÓN DE

RESULTADOS

N',)3 0, ,(*,-*.+ 5& &J*3'& ,0 -)2,(,( 0,3 ',0,3? &+ (&0,-*.+ , 0,3 5& 3& '),(+&+ -5&+', 30 03 <!° 0,3 5& '*&+&+ 5+ +950 /*4&(&+'& , &3'&? 0, 2(2(-*+,0*/,/

2,(, ,)3 -,33? 3& (&0,-*+, -+ 0, 45&(6, (&350',+'& /& 03 )*3)3% A0 '&()*+,( /&

(&,0*6,( 0,3 2(&3&+'&3 2(-'*-,3? 0, (&0,-*.+ &+'(& &3',3? &3' /,/, -+ ,0', -0,(*/,/ , 5&

,0 '),( &+ -5&+', 4,-'(&3 -)5+&3 -) 0, '&)2&(,'5(,? 405*/ )&/*3 &+ 03 -5,0&3

3& (&,0*6,(+? 3& (&0,-*+,+ 2(2(-*+,0)&+'&? -+ 5+, ,(*,-*.+ &J2&(*)&+',0 2(

3*'5,-*+&3 /& -+3*/&(,-*.+? -) 3+ &0 +950 , '),( &+ -5&+', 03 2&33

*)20*-,/3 &+ 03 )*3)3%

7. CONCLUSIONES RECOMENDACIONES

7.1 C0*/5$0*&@

• S& , /&'&()*+,/? 2( )&/* /& 0, &J2&(*)&+',-*.+? 0, 23*-*.+ /&0 -&+'( /&

2(&3*+&3 3(& 5+, 352&(4*-*& 20,+,? 2&(2&+/*-50,( , 0, 352&(4*-*& /&0 405*/? 2,(-*,0 '',0)&+'& 35)&(9*/, &+ 5+ 05*/ 5& 3& &+-5&+'(& &+ (&23%

• A20*-,+/ 03 -+-*)*&+'3 2(&*,)&+'& '&+*/3 &+ -0,3&? 3& 25&/& -+-05*(

5& 0, (&0,-*.+ &+'(& 0, 2(-'*-, 0, '&(, 3& 25&/& /&)3'(,(? (&,0*6,+/ 03

-0-503 -+/*-*+&3 (&0,-*+,/,3 &+'(& 3? /& 0,3 -5,0&3 &J*3'&+ )(9&+&3 /&

&(((? 03 -5,0&3 3& 25&/&+ -+'(0,( 2,(, 5& 3&,+ )+*)3 23*0&3%

• S& -+-05& 5& -5,+/ 0, 45&(6, /& 40',*0*/,/ &3 ),( , 0, /&0 2&3 /& 5+

-5&(2 5& 3& &+-5&+'(& 2,(-*,0)&+'& 35)&(9*/ &+ 5+ 05*/? &3'& 40',(

53-,+/ 35 25+' /& &5*0*(*? )*&+'(,3 5& 3* 3& &+-5&+'(, '',0)&+'&

35)&(9*/ 0, 45&(6, /& 40',*0*/,/ 3&( )&+( 2&( /& '/,3 ),+&(,3 3& 53-,(

5+ +*&0 /& &5*0*(* , )&+3 5& 3& '&+9, 5+, 45&(6, /& 40',*0*/,/ +&9,'*,

/,+/ -) (&350',/ 5+ &5*0*(* 2,(-*,0%

7.2 R&0)&*+$0*&@

38



• M,+'&+&( 5+ ),(9&+ /& &((( )+*)? , 5& /& &3' /&2&+/& 0, &J,-'*'5/ /& 0,

2(-'*-, , (&,0*6,(3&%• U3,( /*4&(&+'&3 405*/3 2,(, 5+, )&( -)2(&+3*.+ /& 03 4&+.)&+3 5& 3&

2(&3&+',+ &+ 0, 2(-'*-, ,3 /*4&(&+-*,( 03 (&350',/3 -+ /*-3 405*/3%• U'*0*6,( &5*2 &3'*)&+', ,/&-5,/,? 0, -5,0 ,5/,( , (&,0*6,( 0, 2(-'*-, /&

)&( ),+&(, &*',(, ,--*/&+'&3%

!. BIBLIO"RAFÍA

• C&+9&0? Y% A%? \ C*),0,? ]% M% !1!K% Me+&#+! de %u#d),- Fu&d!e&'),

!(%#+!+#)&e, I "1$7K% MHJ*-: M-G(,^@*00%

• M''? R% L% !!$K% Me+&#+! de F%u#d), I "7 M<1)K% MHJ*-: PEARSON%

39



ANE#OS

B,+- /& 2(5&,3 FME! EDIBON N*&0,-*.+ &3',*0*6,-*.+ /&0 ,+- /& 2(5&,3

A20*-,-*.+ /&0 F05*/ &+ &0 B,+- /& 2(5&,3 S52&(4*-*& 20,+, 2,(-*,0 '',0)&+'& 35)&(9*/,

Tabla 19 Fotografías captadas durante a rea!"ac!#n de a

pr$ct!ca.

Date post:	18-Feb-2018
Category:	Documents
Upload:	jorge-manobanda
View:	214 times
Download:	0 times

SUPERFICIES-SUMERGIDAS.docx

Documents