INDICE I. II. INTRODUCCIÓN................................................................................... OBJETIVOS...................................................................................... .... 4 5 III. JUSTIFICACIÓN.................................................................................. 6 IV. ALCANCES..................................................................................... ... 7 V. REVISIÓN DE L A LITERATURA........................................................... .11 VI. METODOLOGIA Y PROCEDIMIENTO.................................................17 VII. CÁLCULOS...................................................................................... 18 VIII. CONCLUSIONES.............................................................................47 I!. APLICACIONES................................................................................ 51 !. BIBLIOGRAF"A..................................................................................5# !I. LIN$OGRAF"A................................................................................. 5# XII. ANEXOS........................................................................................53
3
I.
INTRODUCCIÓN
E% &' '%(')*+, *-'/0% (+/+ ', '%&*+-' &' *-2'-*'/+ ', '%&* &' , &' ,*&% +,/'&'&/ &' ,+'% &' /*-+9 '/+%9 +:;<*,'%9 '&**)*%9 )=*:'-'+%9 (*,+/'% &' ('-'%9 '/+% %:+/*-+%9 +<*-'%9 +,+%9 '). )>+ *-'/(/'+)*;- ('&' =+)'/%' &'%&' ,+ ;(*)+ &' ,% '?'/-%. L% ,% &'-:*-+&% S@'% +:*0- ): ,% (/2/'%*<% %- +',,% ' )//' (+/ R' 5 > '% :> () ):'- ,+ (/)*)+ *-&%/*+, %*- ':+/2 *'-' '?)'()*-'% *:(/+-'% ): ,+ ,/*)+)*;- '- '%(+)*% :> (''%9 ', , + /+<0% &' :'&*% (/%%9 ', ):(/+:* '- &' ,% 2,;,% /% '- ', //'-' %+-2-'9 ', , +,/'&'&/ &' (''+% 2*+%9 '). L% ,% :% /')'-' % %- +',,% ' *'-' - R' 5 > (+/+ % '%&* ('&' &*<*&*/%' '- ,+% %*2*'-'% /'% )+'2/+%. I.
F, %:'/2*& '- ,*&%9 '- )> :* '%- (/ '':(, ,% ,+'% &' ,+% /*-+% > :+%9 %:+/*-%9 +<*-'% &' ++ <',)*&+&9 +:;<*,'%9 '&**)*%9 ').
II.
F, &' ,*&% )- -+ %('/*)*' ,*/' ): '- ,% +/)%9 - (*,+/ &' ('-'.
III.
F, &' 2+%'% )- )'/(% <*++-& + 2/+- <',)*&+&9 '% &')*/ )- <',)*&+&'% :+>/'% + 1 :%9 ): %- ,% +<*-'%9 ,% (/>')*,'%9 )=''%9 ').
L% F,% %*2-**)+* <+:'-' :% *:(/+-'% %- ,% ,% <*%)%% '- ,+ ' ,% '')% &' ,+ <*%)%*&+& - %' ('&' &'%(/')*+/ ('/ '- +%' + ,+ '?('/*'-)*+ %' =+ '-)-/+& ' ,% ,% - <*%)%% ' ('&'- :&',+/%' %- ,% &' ,+ ),+%' &' ,% '?'/-%9 '- /+% (+,+/+% ,% ,% +,/'&'&/ &' )'/(% %;,*&% ): )//' '- , % ,+'% &' -+ /*-+9 - ('/*, &' +,+ &' +<*;-. D' '?*%*/ '')% <*%)%% &' '%' *( &' ,%9 '%% '%- )-*-+&% '- -+ (''+ )+(+ &',2+&+ ,,+:+&+ )+(+H,*:*' ' %' '-)'-/+ -*&+ + ,+ /-'/+ &', %;,*&.
4
II. OBJETIVOS A.OBJETI VO GENER AL
E, '*< -&+:'-+, &' ,+ '?('/*'-)*+ '% ,+ <*%+,*+)*;- &' ,% )+:(% &' ,+% ,-'+% &' )//*'-' ' %' /:+ )+-& - ,*& + ++ <',)*&+& (+%+ + /+<0% &' )'/(% %;,*&% *-:'/%% (/ '':(, ('/,'% =*&/&*-:*) %9 )/),%9 /')-2,%9 -2,%9 '). P+/+ '% '% (/')*% ),/'+/ ,+% ,-'+% &' )//*'-' :'&*+-' +, &*%,<'/%' VIOLETA DEGENCIANA ,'-+:'-' (/(/)*-+- - :'&* %%'-*& &' %'/<+)*;-.
B.OBJETIVOS ESPEC"FICOS O'*<+)*;- &' , % '')% &*-:*)% &' ,%
K*&% '- :<*:*'- %/' ,% )'/(% %+,*&% *-:'/%%. S* %- )-)*&% )+/+)'/%*)+% &', ,*&9 ', :&', &' ('/, %),9 %% )'*)*'-'% &' +//+%/' > &' %%('-%*;- ('&'&''/:*-+/%' ,+% '/+% &' +//+%/' > &' %%'-+)*;-. C:(+/+/ ,% <+,/'% '?('/*:'-+,'% )- ,+
/'+,*&+&. A(,*)+/ ,% )-)*:*'-% ';/*)% +(/'-&*&% '),+%' (+/+ ,+ %,)*;- &' - (/,':+ /'+,.
III. JUSTIFICACIÓN L+ (/)*)+ &' )+(+ ,*:*' -% ('/:*' %'/<+/ -+ ):(+/+)*;- *:(/+-' (/ '':(, (+/+ /'+,*+/ ', &*%' &' ,% (*,+/'% &' -+ ('-' ,+ (/'%*;- &'' '%+/ :> *'- &*%/**&+ > +&':% &'':% %+'/ );: %' &*%/*>' A, '?*%*/ <',)*&+& &' K9 > :)=+% <')'% '%' K '% ', /'%(-%+,' &' ,+ '/%*;- &' ,% (*,+/'% &' ,% ('-'%9 '% (/ ',, ' %' '%)2'- ('/,'% )/<% )- ', - &' &*%:*-*/ '%' ''). P+/+ +%'2/+/ ,+ '%+*,*&+& &' ,% ('-'% %' =+)' (/'+% )- %;,*&% %':'+-'% ' -% ('&+- /*-&+/ *-/:+)*;- > %+)+/ )-),%*-'% (+/+ /'+,*+/ - (/' '%&*.
IV. ALCANCES L% :+'/*+,'% ' %' %+/- '- '%+ (/)*)+ &' ,+/+/* %- •
M'%+ &' )+(+ ,*:*' E, '*( '% )-)'*& (+/+ 2'-'/+/ K% (,+-% *&*:'-%*-+,'% '- /02*:'- ,+:*-+/ &' +('-+% 3 ::. &' '%('%/. P%'' -+ :+ &' ,+ '-'/2+ &' ,+ '-' &' %:*-*%/ &' +2+ :'&*+-' 2/+<*,,+9 (+%+-& ,'2 + -+ ):+/+ &' /'(% + /+<0% &' -+ %'/*' &' /*)*% &' &-&' %+,' -+,:'-' (/ /'%+:*'-% + ,+ :'%+ &' %'/<+)*;- )-%*%'-' '- - <*&/* (,+- &' 11 ::. D' '%('%/ )+&/*),+&. ESPECIFICACIONES:
T*'-' *-)/(/+& -+ )+-*&+& +&')+&+ &' 2/+<*,,+9 ' +)+- ): &*%*(+&/'%9 ,/ > -*/:*+& &' K. E% '*(+& )- -+ <,<,+ '%0/*)+ &' 38 (+/+ ', %:*-*%/ &' +2+ &' ,+ '-' '?'/-+ > &% <,<,+% '%0/*)+% &' 1# (+/+ ', &'%+2'. E% '*(+& )- -+ ):+/+ &' %+,*&+ (+/+ /')2'/ ', +2+ ' %+,' &' ,+ :'%+ (+/+ % '<+)+)*;-. DIMENSIONES: Mesa: o o o o o o
o o o o
•
A,/+ 113 ::. A-)= &', +,'/ 5# ::. A-)= &', '*( 54::. L+/2 &', +,'/ 811 ::. L+/2 &', '*( 4::. E%('%/ &' ,+% (,+-)=+% 11 ::. Soporte: A,/+ 8 ::. A-)= 57 ::. L+/2 1 ::. E%('%/ &' ,+% (,+-)=+% 11 ::
R'2,+ 2/+&+&+
E% - *-%/:'- &' :'&*)*;- )- /:+ &' (,+)=+ &',2+&+ > /')+-2,+/ ' *-),>' -+ '%)+,+ 2/+&+&+ &*<*&*&+ '- -*&+&'% &' ,-2*&9 (/ '':(, )'-:'/% (,2+&+% F*2.NQ#.R'2,+ 2/+&+&+
•
V*,'+ &' 2'-)*+-+ E, ,*& ):-:'-' )-)*& ): <*,'+ &' 2'-)*+-+ '% -+ (/'(+/+)*;- &' ),// &' (+/+/%+-*,*-+ ='?+:'*, +2+ '- &' %,)*;-. E% ', ):),/+-' %+& '- ',> (/)'% ,+/+/* &' (/*:+/* ,+ (/'+ &' *-)*;- &' G/+:. E% - +-*%0(*) ;(*)9 /'(','-' > )*)+/*+-' /'):'-&+& '- '%)/*+)*-'%9 ,)'/+% > ='/*&+% &' ,+ (*',9 )+%/+)*-'%9 )/+)*-'% &' :,*29 &'%),'% &' <*-% > (/)*-% > ): +-*%0(*) (%('/+/*. U*, (+/+ ,+ )/+)*;- &' ,'%*-'% )+%+&+% '- ,+ )+ > ,% (*'% (/ ,+% '-'/:'&+&'% <'%*),+/'%.
F*2.NQ3.V*,'+ &' 2'-)*+-+
•
A2+ S%+-)*+ ,*&+ %*- ,/9 ),/ -* %+/ ' %' '-)'-/+ '-+/+,'+ '- '%+& :'-% (/ /:+-& /%9,+ ,+2% > :+/'%9 )(+:% ,+% /'% )+/+% (+/'% &',
(,+-'+ T*'//+ > /:+ (+/' &' ,% %'/'% <*<% '% )-%**&+ (/ =*&/;2'- > ?2'- H2 O .
F*2.NQ4.+,&'%
•
F/+-',+
F*2.NQ5.F/+-',+
•
J'2 &' %;,*&% S,*&% &' &*'/'-' /:+9 *&*:'-%*-+,'% > /*&*:'-%*-+,'%. F+/*)+&% &' <*&/*% ' <+/+- %% '%('%/'% > :'&*&+%. 8 '- +,.
F*2.NQ7.J'2 &' %;,*&%
V. REVISIÓN DE LA LITERATURA 1CAP A L"MIT E *. DEFINICIÓN
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
F*2.NQ8.Detalle del campo de presiones que recorre una vela” (APLICACIONES EN BARCOS
F*2.NQ.!radiente de velocidades en la capa l"mite #idrodin$mica”(DIA!RA%A
**. IMPORTANCIA
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
iii. CLASES +. P+/+ K% '?'/-% Ríos, quebradas E- ,% /% '?*%' K /,'-. E, K /,'- %' )+/+)'/*+ (/' ', K*& )-*-+:'-' %' :'),+9 &' /:+ )+;*)+9 ): )-%')'-)*+ &' ,+ /(/+ &' - K /&'-+& &' <;/*)'%9 ' +')+- -+% '&*/'))*;- &', :<*:*'-. E, K &', +2+ '- ,% /% ', :<*:*'- &', +*/' )'/)+ &' ,+ %('/)*' &' ,+ *'//+ %- '':(,% (*)% &' K% /,'-%. Canales C+-& ', +2+ '-/+ + -
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
1 ', K ' '-/+ +, )+-+, '% ,+:*-+/ > &' &*%/*)*;- -*/:' &' <',)*&+&'% # -*-2-+ /'%/*))*;- '?*%' + ,+ '-/+&+ ' (&*'/+ )+%+/ &*%/* +/( &' ,+ %('/)*' &', +2+ > &' ,+ &*%/*)*;- &' <',)*&+& 3 ,+ (/-&*&+& &', K '% 2/+-&'9 +% ' ,+ (/-&*&+& &', K %' ('&' )-%*&'/+/ )-%+-' )+-& ', K '-/+ +, )+-+,
Fig.N°10.”Desarrollo de la capa lii!e en un canal abier!o con una condici"n ideal de en!rada”
Fig.N°11.”Capa lii!e en el rio”
. P+/+ K% *-'/-% #uberías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
+-,*%*%. Fig.N°12.”Capa lii!e en %u&os e'!ernos”
VI. METODOLOGIA Y PROCEDIMIENTO a) N*<',+/ ,+ :'%+ &' +-+,2+% &' S@'%. b) C-')+/ + - *-'//(/ ,+ :+ &' +2+ 9 0%+
+,)+-+/ - -*<', +(/?*:+& &' 3::. c) E%('/+/ - *':( (/&'-' =+%+ ' ', K %'
'%+*,*)'. d) E%(+/)*/ ,+ V*,'+ &' G'-)*+-+ %/' ,+ %('/)*' &',
K )'/)+ &', *-2/'% &' +2+. e) C,)+/ ,% &*<'/%% ('/,'%9 %'/<+/ ' *&'-*)+/ ,+
)+(+ ,:*' > ,+ '%',+ ' %' /:+/- '- ,% /&'% &' )+&+ ('/,.
FOTO
VII. CÁLCULOS *. V+/*+,'% &' *-'/+))*;-
v = velocidad τ xy = esfuerzoal corte
ρ= densidad
μ= viscocidad dinamica
**. +,,+-& )+&+ <+/*+,'% SOLIDO NQ1
Capa !"ite a"i#ar: ♣
C,), &', 2/%/ &' ,+ )+(+ ,:*' X
D+% ? #.1 ): .#1:9 < 1.163Z1[W6 14\C9 U .667 :%'2 δ = 4.65∗2.1∗
√
−6 1.163 10
∗ ∗
0.0667 0.021
δ =0.28145 cm
♣
C,), &', '%'/ )/+-' ]
D+% ? #.1 ): .#1 :9 116.1Z1[W5 14\C9 ^ .# @2:39 U .667 :%'2.
√
τ =0.322∗
−5
116.1∗10
3
∗999.2∗0.0667
0.021 2
τ =0.0412 N / m ♣
C,), &', )')*'-' &' +//+%/'
D+% U .667 :%'29 , #.1 ): .#1 :9 < 1.163Z1[W6 14\C. CD=
1.328
√
U ∗l v 1.328
CD=
√
0.0667 0.021 −6 1.163 10
∗ ∗
C D =0.0383 ♣
C,), &', +//+%/'
D+% CD .3839 ^ .# @2:3 14_C9 U .667 :%'29 , #.1 ): .#1 :. Arrastre =
∗
∗
2
0.0383 999.2 0.0667 2
∗0.021= 0.001785
C+(+ ,:*' /,'-+ ♣
C,), &', 2/%/ &' ,+ )+(+ ,:*' X
D+% < 1.163Z1[W69 U .667 :%'29 ? 7. ):.
(
δ = 0.37∗
−6 1.163 10
∗
0.0667
)∗ 1 5
7.9
4 /5
δ = 0.21609 cm ♣
C,), &', '%'/ )/+-' ]
D+% ^ .# @2:3 14\C9 U .667 :%'29 < 1.163Z1[W6 14\C9 ? 7. ): .7 :. 2
τ =0.029∗ 999.2∗0.0667 ∗(
−6 1.163 10
1 /5
∗ ) 0.0667∗0.079
τ =0.023915 N / m 2 ♣
C,), &', )')*'-' &' +//+%/'
D+% U .667 :%'29 , 7. ): .7 :9 < 1.163Z1[W6 14\C. C D =0.072∗(
C D =0.01337
∗ ∗
0.0667 0.079 −6 1.163 10
− 1/ 5
)
♣
C,), &', +//+%/'
D+% ^ .# @2:3 14\C9 U .667 :%'29 , 7. ): .7 :9 < 1.163Z1[W6 14\C. Arrastre =0.036∗999.2∗0.0667
♣
(
2
∗0.079∗
)
1
∗10− = 0.00235 N: 0.0667∗0.079 1.163
6
5
C,), &' ,+ R'%*%'-)*+ &' F/:+
L+ ')+)*;- '&+ &'-*&+ ): C D∗( π ∗r + 2∗r ∗L )∗ ρ∗U FD= 2
2
2
Datos: CD = 0.0383, r = 2.45 cm = 0.0245 m, L = 7.2 cm = 0.072 m, p = 999,2 kg/m3 (14ºC), = 0.0!!7 m/s"g.
FD=
∗( π∗0.0245 + 2∗0.0245∗0.072 )∗999.2∗0.0667
0.0383
F D =0.000461 N
a) S$ido %:
2
2
2
Capa !"ite a"i#ar: ♣
C,), &', 2/%/ &' ,+ )+(+ ,:*' X
D+% 3.1# ): .31# :9 < 1.163Z1[W6 14\C9 U .667 ?:%'2 δ = 4.65∗3.12∗
√
−6 1.163 10
∗ ∗
0.0667 0.0312
δ = 0.343 cm ♣
C,), &', '%'/ )/+-' ]
D+% ? 3.1# ): .31# :9 116.1Z1[W5 14\C9 ^ .# @2:39 U .667 :%'2.
√
τ =0.322∗
−5
116.1∗10
3
∗999.2∗0.0667
0.0312
2
τ =0.0338 N / m ♣
C,), &', )')*'-' &' +//+%/'
D+% U .667 :%'29 , 3.1# ): .31# :9 < 1.163Z1[W6 14\C.
CD=
1.328
√
U ∗l v
CD=
1.328
√
∗ ∗
0.0667 0.0312 −6 1.163 10
C D =0.0314 ♣
C,), &', +//+%/'
D+% CD .3149 ^ .# @2:3 14_C9 U .667 :%'29 , 3.1# ): .31# :. Arrastre =
2
∗999.2∗0.0667 ∗0.0312=0.0021755 / N m
0.0314
2
Capa !"ite t&rb&e#ta: ♣
C,), &', 2/%/ &' ,+ )+(+ ,:*' X
D+% < 1.163Z1[W69 U .667 :%'29 ? 7.# ):.
(
δ = 0.37∗
−6 1.163 10
∗
0.0667
)∗ 1 5
7.2
4/ 5
δ = 0.2006 cm
♣
C,), &', '%'/ )/+-' ]
D+% ^ .# @2:3 14\C9 U .667 :%'29 < 1.163Z1[W6 14\C9 ? 7.# ): .7# :. 2
τ =0.029∗ 999.2∗0.0667 ∗(
−6 1.163 10
1 /5
∗ ) 0.0667∗0.072
τ =0.02436 N / m 2 ♣
C,), &', )')*'-' &' +//+%/'
D+% U .667 :%'29 , 7.# ): .7# :9 < 1.163Z1[W6 14\C. C D =0.072∗(
∗ ∗
0.0667 0.072 −6 1.163 10
−1 / 5
)
C D =0.01362
♣
C,), &', +//+%/'
D+% ^ .# @2:3 14\C9 U .667 :%'29 , 7.# ): .7# :9 < 1.163Z1[W6 14\C. Arrastre =0.036∗999.2∗0.0667
♣
2
(
∗0.072∗
−6 1.163 10
)
1
∗ =0.002178 N / m 0.0667∗0.072
C,), &' ,+ R'%*%'-)*+ &' F/:+
L+ ')+)*;- '&+ &'-*&+ ):
5
(
C D∗ FD=
π ∗r 2
)
2
+ r ∗h ∗ ρ∗U
2
2
Datos: CD = 0.0314, r = 2.75 cm = 0.0275 m, # = 5.89 cm = 0.0589 m, p = 999,2 kg/m3 (14ºC), = 0.0!!7 m/s"g.
(
)
2
∗0.0275 ∗ π + 0.0275∗0.0589 ∗999.2∗0.0667
0.0314
FD=
2
2
2
F D =0.00019595 N
b) S$ido ':
Capa !"ite a"i#ar: ♣
C,), &', 2/%/ &' ,+ )+(+ ,:*' X
D+% ? 3.3 ): .33 :9 < 1.163Z1[W6 14\C9 U .667 :%'2
√
δ = 4.65∗3.3∗ δ = 0.353 cm
−6 1.163 10
∗ ∗
0.0667 0.033
♣
C,), &', '%'/ )/+-' ]
D+% ? 3.3 ): .33 :9 116.1Z1[W5 14\C9 ^ .# @2:39 U .667 :%'2.
√
τ =0.322∗
−5
116.1∗10
0.033
τ =0.03286 N / m ♣
3
∗999.2∗0.0667
2
C,), &', )')*'-' &' +//+%/'
D+% U .667 :%'29 , 3.3 ): .33 :9 < 1.163Z1[W6 14\C. CD=
CD=
1.328
√
U ∗l v 1.328
√
∗ ∗
0.0667 0.033 −6 1.163 10
0.03053
CD=
♣
C,), &', +//+%/'
D+% CD .3539 ^ .# @2:3 14_C9 U .667 :%'29 , 3.3 ): .33 :.
Arrastre =
∗
2
∗
0.03053 999.2 0.0667 2
∗0.033 =0.002237 N / m
Capa !"ite t&rb&e#ta: ♣
C,), &', 2/%/ &' ,+ )+(+ ,:*' X
D+% < 1.163Z1[W69 U .667 :%'29 ? 6.4 ):.
(
δ = 0.37∗
−6 1.163 10
∗
0.0667
)∗ 1 5
6.49
4 /5
δ = 0.18464 cm ♣
C,), &', '%'/ )/+-' ]
D+% ^ .# @2:3 14\C9 U .667 :%'29 < 1.163Z1[W6 14\C9 ? 6.4 ): .64 :. 2
τ =0.029∗ 999.2∗0.0667 ∗(
−6 1.163 10
1 /5
∗ ) 0.0667∗0.0649
τ =0.02487 N / m 2
♣
C,), &', )')*'-' &' +//+%/'
D+% U .667 :%'29 , 6.4 ): .64 :9 < 1.163Z1[W6 14\C. C D =0.072∗(
=0.0139
C D
∗ ∗
0.0667 0.0649 −6 1.163 10
− 1/ 5
)
♣
C,), &', +//+%/'
D+% ^ .# @2:3 14\C9 U .667 :%'29 , 6.4 ): .64 :9 < 1.163Z1[W6 14\C.
(
2
Arrastre =0.036∗999.2∗0.0667 ∗0.0649∗
♣
)
1
∗10− = 0.002004 N / m 0.0667∗0.0649 1.163
6
5
C,), &' ,+ R'%*%'-)*+ &' F/:+
L+ ')+)*;- '&+ &'-*&+ ): C D∗( π ∗r )∗ ρ ∗U 2
FD=
2
2
Datos: C D = 0.03053, r = 3.15 cm = 0.0315 m, p = 999,2 kg/m 0.0!!7 m/s"g.
FD=
∗( π∗0.0315 )∗999.2∗0.0667 2
0.03053
2
F D =0.0002115 N
c) S$ido (:
Capa !"ite a"i#ar:
2
3
(14ºC), =
♣
C,), &', 2/%/ &' ,+ )+(+ ,:*' X
D+% ? 3.1 ): .31 :9 < 1.163Z1[W6 14\C9 U .667 :%'2 δ = 4.65∗3.12∗
√
−6 1.163 10
∗ ∗
0.0667 0.031
δ = 0.34196 cm ♣
C,), &', '%'/ )/+-' ]
D+% ? 3.1 ): .31 :9 116.1Z1[W5 14\C9 ^ .# 3
@2: 9 U .667 :%'2.
√
τ =0.322∗
−5
116.1∗10
3
∗999.2∗0.0667
0.031
2
τ =0.0339 N / m
♣
C,), &', )')*'-' &' +//+%/'
D+% U .667 :%'29 , 3.1 ): .31 :9 < 1.163Z1[W6 14\C. CD=
1.328
√
U ∗l v
CD=
1.328
√
∗ ∗
0.0667 0.031 −6 1.163 10
C D =0.0315 ♣
C,), &', +//+%/'
D+% CD .3159 ^ .# @2:3 14_C9 U .667 :%'29 , 3.1 ): .31 :. Arrastre =
∗
2
∗
0.0315 999.2 0.0667 2
∗0.031= 0.002168 N / m
Capa !"ite t&rb&e#ta: ♣
C,), &', 2/%/ &' ,+ )+(+ ,:*' X
D+% < 1.163Z1[W69 U .667 :%'29 ? 6.3 ):.
(
δ = 0.37∗
−6 1.163 10
∗
0.0667
)∗ 1 5
6.3
4 /5
δ = 0.1803 cm ♣
C,), &', '%'/ )/+-' ]
D+% ^ .# @2:3 14\C9 U .667 :%'29 < 1.163Z1[W6 14\C9 ? 6.3 ): .63 :. 0.029 999.2 0.0667
τ=
∗
∗
−6 1.163 10
1 /5
∗ 0.0667 ∗( ∗0.063 )
2
τ =0.025023 N / m 2 ♣
C,), &', )')*'-' &' +//+%/'
D+% U .667 :%'29 , 6.3 ): .63 :9 < 1.163Z1[W6 14\C. C D =0.072∗(
∗ ∗
0.0667 0.063 −6 1.163 10
− 1/ 5
)
C D =0.01399 ♣
C,), &', +//+%/'
D+% ^ .# @2:3 14\C9 U .667 :%'29 , 6.3 ): .63 :9 < 1.163Z1[W6 14\C. Arrastre =0.036∗999.2∗0.0667
♣
2
(
∗0.063∗
)
1
∗10− = 0.001957 N / m 0.0667∗0.063 1.163
6
5
C,), &' ,+ R'%*%'-)*+ &' F/:+
L+ ')+)*;- '&+ &'-*&+ ):
( ∗ )∗ ∗
C D∗ FD=
6l
a
2
ρ U
2
2
Datos: CD = 0.0315, $ = 3.2 cm = 0.032 m, a = 2.77 cm = 0.0277 m, p = 999,2 kg/m3 (14ºC), = 0.0!!7 m/s"g.
(∗
∗
0.0315
FD=
6
∗
0.032 0.0277 2
)∗
∗
999.2 0.0667
2
2
F D =0.0001862 N
d) S$ido :
Capa !"ite a"i#ar:
W
C,), &', 2/%/ &' ,+ )+(+ ,:*' X
D+% ? #.8 ): .#8 :9 < 1.163Z1[W6 14\C9 U .667 :%'2
√
δ = 4.65∗2.8∗
∗ ∗
6 1.163 10−
0.0667 0.028
δ = 0.3249 cm ♣
C,), &', '%'/ )/+-' ]
D+% ? #.8 ): .#8 :9 116.1Z1[W5 14\C9 ^ .# @2:39 U .667 :%'2.
√
τ =0.322∗
−5
116.1∗10
3
∗999.2∗0.0667
0.028
2
τ =0.03568 N / m ♣
C,), &', )')*'-' &' +//+%/'
D+% U .667 :%'29 , #.8 ): .#8 :9 < 1.163Z1[W6 14\C. CD=
CD=
1.328
√
√
U ∗l v
1.328 0.0667 0.028 −6 1.163 10
∗ ∗
C D =0.03315
♣
C,), &', +//+%/'
D+% CD .33159 ^ .# @2:3 14_C9 U .667 :%'29 , #.8 ): .#8 :. Arrastre =
∗
∗
2
0.03315 999.2 0.0667 2
∗0.028 =0.002061 N / m
Capa !"ite t&rb&e#ta:
♣
C,), &', 2/%/ &' ,+ )+(+ ,:*' X
D+% < 1.163Z1[W69 U .667 :%'29 ? 7.4 ):. 1
−6 1.163 10
∗
δ = 0.37∗
(
0.0667
4 /5
5
)
∗7.4
δ = 0.2051 cm ♣
C,), &', '%'/ )/+-' ]
D+% ^ .# @2:3 14\C9 U .667 :%'29 < 1.163Z1[W6 14\C9 ? 7.4 ): .74 :. 2
τ =0.029∗ 999.2∗0.0667 ∗(
1.163
∗10− ) / 0.0667∗0.074 6
1 5
τ =0.02423 N / m 2
♣
C,), &', )')*'-' &' +//+%/'
D+% U .667 :%'29 , 7.4 ): .74 :9 < 1.163Z1[W6 14\C. C D =0.072∗(
∗ ∗
0.0667 0.074 −6 1.163 10
C D =0.01355 ♣
C,), &', +//+%/'
− 1/ 5
)
D+% ^ .# @2:3 14\C9 U .667 :%'29 , 7.4 ): .74 :9 < 1.163Z1[W6 14\C.
(
2
Arrastre =0.036∗999.2∗0.0667 ∗0.074∗
♣
−6 1.163 10
)
1
∗ =0.002226 N / m 0.0667∗0.074 5
C,), &' ,+ R'%*%'-)*+ &' F/:+
L+ ')+)*;- '&+ &'-*&+ ): FD=
C D∗( ∗h )∗ ρ∗U
2
2
Datos: CD = 0.0315, # = 5 cm = 0.05 m, % = 10.2 cm = 0.102 m, p = 999,2 kg/m 3 (14ºC), = 0.0!!7 m/s"g.
FD=
(
)
2
0.0315∗ 0.05∗0.102 ∗999.2∗0.0667 2
F D =0.000357 N
e) S$ido *:
Capa !"ite a"i#ar: ♣
C,), &', 2/%/ &' ,+ )+(+ ,:*' X
D+% ? 1. ): .1 :9 < 1.163Z1[W6 14\C9 U .667 :%'2
√
δ = 4.65∗1.9∗
−6 1.163 10
∗ ∗
0.0667 0.019
δ = 0.2677 cm ♣
C,), &', '%'/ )/+-' ]
D+% ? 1. ): .1 :9 116.1Z1[W5 14\C9 ^ .# @2:39 U .667 :%'2.
√
τ =0.322∗
−5
116.1∗10
3
∗999.2∗0.0667
0.019
τ =0.04331 N / m 2
♣
C,), &', )')*'-' &' +//+%/'
D+% U .667 :%'29 , 1. ): .1 :9 < 1.163Z1[W6 14\C. CD=
CD=
1.328
√
U ∗l v 1.328
√
∗ ∗
0.0667 0.019 −6 1.163 10
C D =0.04024 ♣
C,), &', +//+%/'
D+% CD .4#49 ^ .# @2:3 14_C9 U .667 :%'29 , 1. ): .1 :. Arrastre =
∗999.2∗0.0667
0.04024
2
∗0.019=0.001698 N / m
2
Capa !"ite t&rb&e#ta: ♣
C,), &', 2/%/ &' ,+ )+(+ ,:*' X
D+% < 1.163Z1[W69 U .667 :%'29 ? 3.5 ):.
(
δ = 0.37∗
−6 1.163 10
∗
0.0667
)∗ 1 5
3.05
4 /5
δ = 0.1009 cm ♣
C,), &', '%'/ )/+-' ]
D+% ^ .# @2:3 14\C9 U .667 :%'29 < 1.163Z1[W6 14\C9 ? 3.5 ): .35 :. 2
τ =0.029∗ 999.2∗0.0667 ∗(
−6 1.163 10
1 /5
∗ ) 0.0667∗0.0305
τ =0.0289 N / m 2 ♣
C,), &', )')*'-' &' +//+%/'
D+% U .667 :%'29 , 3.5 ): .35 :9 < 1.163Z1[W6 14\C.
C D =0.072∗(
∗ ∗
0.0667 0.0305 −6 1.163 10
− 1/ 5
)
C D =0.0162 ♣
C,), &', +//+%/'
D+% ^ .# @2:3 14\C9 U .667 :%'29 , 3.5 ): .35 :9 < 1.163Z1[W6 14\C.
(
2
Arrastre =0.036∗999.2∗0.0667 ∗0.0305∗
♣
)
1
∗10− = 0.0012 N / m 0.0667∗0.0305 6
1.163
5
C,), &' ,+ R'%*%'-)*+ &' F/:+
L+ ')+)*;- '&+ &'-*&+ ): FD=
C D∗( ∗h )∗ ρ∗U
2
2
Datos: CD = 0.04024, # = 4.7 cm = 0.047 m, % = 4.95 cm = 0.0495 m, p = 999,2 kg/m3 (14ºC), = 0.0!!7 m/s"g.
FD=
(
)
2
0.04024∗ 0.047∗0.0495 ∗999.2∗ 0.0667
F D =0.0002081 N
+) S$ido ,:
2
Capa !"ite a"i#ar: ♣
C,), &', 2/%/ &' ,+ )+(+ ,:*' X
D+% ? #.3 ): .#3 :9 < 1.163Z1[W6 14\C9 U .667 :%'2
√
δ = 4.65∗2.8∗
−6 1.163 10
∗ ∗
0.0667 0.023
δ = 0.2945 cm ♣
C,), &', '%'/ )/+-' ]
D+% ? #.3 ): .#3 :9 116.1Z1[W5 14\C9 ^ .# @2:39 U .667 :%'2.
√
τ =0.322∗
−5
116.1∗10
0.023
τ =0.03936 N / m ♣
3
∗999.2∗0.0667
C,), &', )')*'-' &' +//+%/'
2
D+% U .667 :%'29 , #.3 ): .#3 :9 < 1.163Z1[W6 14\C. CD=
CD=
1.328
√
U ∗l v 1.328
√
∗ ∗
0.0667 0.023 −6 1.163 10
C D =0.036574
♣
C,), &', +//+%/'
D+% CD .365749 ^ .# @2: 3 14_C9 U .667 :%'29 , #.3 ): .#3 :. Arrastre =
∗999.2∗0.0667
0.036574
2
∗ 0.023=0.00186783 N / m
2
Capa !"ite t&rb&e#ta: ♣
C,), &', 2/%/ &' ,+ )+(+ ,:*' X
D+% < 1.163Z1[W69 U .667 :%'29 ? 5.# ):. 1
−6 1.163 10
∗
δ = 0.37∗
(
0.0667
4/ 5
5
)
∗5.2
δ = 0.15465 cm ♣
C,), &', '%'/ )/+-' ]
D+% ^ .# @2:3 14\C9 U .667 :%'29 < 1.163Z1[W6 14\C9 ? 5.# ): .5# :. 2
τ =0.029∗ 999.2∗0.0667 ∗(
−6 1.163 10
1 /5
∗ ) 0.0667∗0.052
τ =0.026 N / m 2
♣
C,), &', )')*'-' &' +//+%/'
D+% U .667 :%'29 , 5.# ): .5# :9 < 1.163Z1[W6 14\C. C D =0.072∗(
∗ ∗
0.0667 0.052 −6 1.163 10
−1 / 5
)
C D =0.01454 ♣
C,), &', +//+%/'
D+% ^ .# @2:3 14\C9 U .667 :%'29 , 5.# ): .5# :9 < 1.163Z1[W6 14\C. 2
(
Arrastre =0.036∗999.2∗0.0667 ∗0.052∗
♣
−6 1.163 10
)
1
∗ =0.0016785 N / m 0.0667∗0.052
C,), &' ,+ R'%*%'-)*+ &' F/:+
5
L+ ')+)*;- '&+ &'-*&+ ): C ∗( ∗h )∗ ρ∗U D
FD=
2
2
Datos: CD = 0.03!574, # = 4.5 cm = 0.045 m, % = 7.8 cm = 0.078 m, p = 999,2 kg/m3 (14ºC), = 0.0!!7 m/s"g.
FD=
∗( 0.045∗0.078 )∗999.2∗0.0667
2
0.036574
2
F D =0.0002853 N
-) S$ido :
Capa !"ite a"i#ar: ♣
C,), &', 2/%/ &' ,+ )+(+ ,:*' X
D+% ? 1.# ): .1# :9 < 1.163Z1[W6 14\C9 U .667 :%'2
√
δ = 4.65∗2.8∗
−6 1.163 10
∗ ∗
0.0667 0.012
δ = 0.2128 cm ♣
C,), &', '%'/ )/+-' ]
D+% ? 1.# ): .1# :9 116.1Z1[W5 14\C9 ^ .# 3
@2: 9 U .667 :%'2.
√
τ =0.322∗
−5
116.1∗10
0.012
τ =0.054497 N / m
♣
3
∗999.2∗0.0667
2
C,), &', )')*'-' &' +//+%/'
D+% U .667 :%'29 , 1.# ): .1# :9 < 1.163Z1[W6 14\C. CD=
1.328
√
U ∗l v 1.328
CD=
√
0.0667 0.012 −6 1.163 10
∗ ∗
C D =0.0506 ♣
C,), &', +//+%/'
D+% CD .365749 ^ .# @2: 3 14_C9 U .667 :%'29 , 1.# ): .1# :.
Arrastre =
∗
2
∗
0.0506 999.2 0.0667 2
∗0.012 = 0.001349 N / m
Capa !"ite t&rb&e#ta: ♣
C,), &', 2/%/ &' ,+ )+(+ ,:*' X
D+% < 1.163Z1[W69 U .667 :%'29 ? 3.4 ):.
(
δ = 0.37∗
−6 1.163 10
∗
0.0667
)∗ 1 5
3.4
4 /5
δ = 0.1101 cm ♣
C,), &', '%'/ )/+-' ]
D+% ^ .# @2:3 14\C9 U .667 :%'29 < 1.163Z1[W6 14\C9 ? 3.4 ): .34 :. 2
τ =0.029∗ 999.2∗0.0667 ∗(
∗10− / ) 0.0667∗0.034 1.163
6
1 5
τ =0.0283 N / m 2 ♣
C,), &', )')*'-' &' +//+%/'
D+% U .667 :%'29 , 3.4 ): .34 :9 < 1.163Z1[W6 14\C. C D =0.072∗(
C =0.015826 D
∗ ∗
0.0667 0.034 −6 1.163 10
− 1/ 5
)
♣
C,), &', +//+%/'
D+% ^ .# @2:3 14\C9 U .667 :%'29 , 3.4 ): .34 :9 < 1.163Z1[W6 14\C. Arrastre =0.036∗999.2∗0.0667
♣
2
(
∗0.034∗
−6 1.163 10
)
1
∗ = 0.001195 N / m 0.0667∗0.034 5
C,), &' ,+ R'%*%'-)*+ &' F/:+
L+ ')+)*;- '&+ &'-*&+ ): C D∗( l )∗ ρ∗U 2
FD=
2
2
Datos: CD = 0.050!, $ = 4.! cm = 0.04! m, p = 999,2 kg/m 3 (14ºC), = 0.0!!7 m/s"g.
FD=
∗( 0.046 )∗999.2∗0.0667
0.0506
2
2
2
F D =0.00023798 N
VIII.
CONCLUSIONES /) S$ido /:
C+(+ ,:*' ,+:*-+/ W W W W
A-)= X .#8145 ):. E%'/ C/+-' ] .41# N:#. C')*'-' &' +//+%/' C D .383. A//+%/' A//+%/' .1785 N:.
C+(+ ,:*' /,'- W W W W
A-)= X .#16 ):. E%'/ C/+-' ] .#315 N:#. C')*'-' &' +//+%/' C D .1337. A//+%/' A//+%/' .#35 N:.
R'%*%'-)*+ &' F/:+ FR .461 N. E)+)*;- %'2- % 2':'/+ FD=
C D∗( π ∗r
2
+ 2∗r ∗L )∗ ρ∗U
2
2
%) S$ido %:
C+(+ ,:*' ,+:*-+/ W W W W
A-)= X .343 ):. E%'/ C/+-' ] .338 N:#. C')*'-' &' +//+%/' C D .314 A//+%/' A//+%/' .#1755 N:.
C+(+ ,:*' /,'- W W W W
A-)= X .#6 ):. E%'/ C/+-' ] .#436 N:#. C')*'-' &' +//+%/' C D .136#. A//+%/' A//+%/' .#178 N:.
R'%*%'-)*+ &' F/:+ FR .155 N.
E)+)*;- %'2- % 2':'/+
(∗
C D∗ FD=
π r
)
2
2
+ r ∗h ∗ ρ∗U
2
2
') S$ido ':
C+(+ ,:*' ,+:*-+/ W W W W
A-)= X .353 ):. E%'/ C/+-' ] .3#86 N:#. C')*'-' &' +//+%/' C D .353. A//+%/' A//+%/' .##37 N:.
C+(+ ,:*' /,'- W W W W
A-)= X .18464 ):. E%'/ C/+-' ] .#487 N:#. C')*'-' &' +//+%/' C D .13. A//+%/' A//+%/' .#4 N:.
R'%*%'-)*+ &' F/:+ FR .#15 N. E)+)*;- %'2- % 2':'/+ C D∗( π ∗r )∗ ρ ∗U 2
FD=
2
2
() S$ido (:
C+(+ ,:*' ,+:*-+/ W W W W
A-)= X .3416 ):. E%'/ C/+-' ] .33 N:#. C')*'-' &' +//+%/' C D .315. A//+%/' A//+%/' .#168 N:.
C+(+ ,:*' /,'- W W W
A-)= X .183 ):. E%'/ C/+-' ] .#5#3 N:#. C')*'-' &' +//+%/' C D .13.
W A//+%/' A//+%/' .157 N:. R'%*%'-)*+ &' F/:+ FR .186# N.
E)+)*;- %'2- % 2':'/+
FD=
6l
∗a ∗ρ∗U
( )
C D∗
2
2
2
) S$ido :
C+(+ ,:*' ,+:*-+/ W W W W
A-)= X .3#4 ):. E%'/ C/+-' ] .3568 N:#. C')*'-' &' +//+%/' C D .3315. A//+%/' A//+%/' .#61 N:.
C+(+ ,:*' /,'- W W W W
A-)= X .#51 ):. E%'/ C/+-' ] .#4#3 N:#. C')*'-' &' +//+%/' C D .1355. A//+%/' A//+%/' .###6 N:.
R'%*%'-)*+ &' F/:+ FR .357 N. E)+)*;- %'2- % 2':'/+ FD=
C D∗( ∗h )∗ ρ∗U
2
2
*) S$ido *:
C+(+ ,:*' ,+:*-+/ W W W W
A-)= X .#677 :. E%'/ C/+-' ] .4331 N:#. C')*'-' &' +//+%/' C D .4#4. A//+%/' A//+%/' .168 N:.
C+(+ ,:*' /,'- W W W W
A-)= X .1 ):. E%'/ C/+-' ] .#8 N:#. C')*'-' &' +//+%/' C D .16#. A//+%/' A//+%/' .1# N:.
R'%*%'-)*+ &' F/:+ FR .#81 N.
E)+)*;- %'2- % 2':'/+ FD=
C D∗( ∗h )∗ ρ∗U
2
2
,) S$ido ,:
C+(+ ,:*' ,+:*-+/ W W W W
A-)= X .#45 ):. E%'/ C/+-' ] .336 N:#. C')*'-' &' +//+%/' C D .36574. A//+%/' A//+%/' .186783 N:.
C+(+ ,:*' /,'- W W W
A-)= X .15465 ):. E%'/ C/+-' ] .#6 N:#. C')*'-' &' +//+%/' C D .1454.
W A//+%/' A//+%/' .16785 N:. R'%*%'-)*+ &' F/:+ FR .#853 N. E)+)*;- %'2- % 2':'/+ FD=
C D∗( ∗h )∗ ρ∗U
2
2
) S$ido :
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XII.
ANEXOS CONJUNTO DE SOLIDOS EN EXPERIMENTO
