INTEGRANTES: • • •
GARCIA RODRIGUEZ EMMA SABINO SABIN O GRAUS KATHER KATHERYNE YNE VASQUEZ BAYONA MARQUINHO
PROFESOR: •
ING.
WALTER
MORENO
[LABORATORIO DE OPERACIONES UNITARIAS] UNITARIAS] 2.16 Haga lo lo ! !g"!#$%# &' &'l&"lo. E$ E$ &a &a(a &a &ao) # #%!*# +,! ,!* *#,o la ol"&!-$ !$ "a, &al&"la(o,a ,a)) !g"! "!# #$(o #l +,o +, o(!* (!*!#$ !#$%o %o "# # (# (#&,! &,!/# /# #$ la #& #&&!&!-$ $ 0/. ) (# (#+" +" #3#&%4 #3# &%4# # #l &'l &'l&"l &"lo o +, +,#% #%a$( a$(o o a%# a%#$&! $&!-$ -$ a la !g !g"!# "!#$%# $%# &!3 &!3,a ,a !g$!5&a%!a. !7 82.978:.6;27 !!77 8;. !! ;.6 6<< = 1< 1<>? 7 @ ?0 !!!77 2.; !!! 2.;60 60120 120.2 .2 !7 8?. 8?.90; 90; = 1 7 8 = 1< 27
2.19 Al ,#ol#, "$ +,o/l#*a) # o/%"o la !g"!#$%# #=+,#!-$ 4
5.386 x 10
¿ (0.6700 )( 264.980 )( 6 )¿ R =¿
El 3a&%o, 6 # "$ #$%#,o +",o. E%!*# #l
alo, (# R !$ "a, "$a &al&"la(o,a !g"!#$(o #l +,o(!*!#$%o "# # (#&,!/# #$ la #&&!-$ 0/.D#+" &al&"l# E=+,#a$(o " ,#+"#%a #$ $o%a&!-$ &!#$%5&a (#&!*al) a#g",'$(o# (# "# %#$ga #l $4*#,o &o,,#&%o (# &!3,a !g$!5&a%!a
EFERCICIOS DE I UNIDAD 8CAITULO2 ELDER7
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[LABORATORIO DE OPERACIONES UNITARIAS]
2.1: a,a +,o/a, (o %#,*o+a,# 8(!+o!%!o +a,a *#(!, la %#*+#,a%",a7 # !$#,%a,o$ " o$(a #$ ag"a !,!#$(o) # ,#g!%,a,o$ la l#&%",a) # ,#%!,a,o$ #&a,o$ la o$(a) l"#go # ,#+!%!- #l +,oo. Lo ,#"l%a(o (# 0 *#(!&!o$# 3"#,o$ lo !g"!#$%# T8JC7%#,*o+a, A T8JC7%#,*o+a, B
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a7 Cal&"l# +o, &a(a &o$"$%o (# l#&%",a (# %#*+#,a%",a) la *#(!a) #l ,a$go la (#!a&!-$ #%'$(a, (# la *"#%,a. /7 Q" l#&%",a (#l %#,*o+a, +,##$%a$ *ao, g,a(o (# (!+#,!-$ &"'l %#,*o+a, # *' #=a&%o
2.1 El &o$%,ol (# la &al!(a( 8CC7 # "$ +,oo *" (!3&!l #$ la !$("%,!a (# 3a/,!&a&!-$ (# %!$%# &"al"!#, a,!a&!-$ l## #$ la &o$(!&!o$# (# ,#a&&!-$ +,o(" &a*/!o $o%o,!o #$ #l &olo, (#l +,o("&%o ) &o*o lo &l!#$%# ,#"!#,#$ al%a ,#+,o("&!/!l!(a( (# &olo, (# "$ lo%# al !g"!#$%#) a%a #l *' l!g#,o &a*/!o (# %o$al!(a( +"#(# o&a!o$a, "# # ,#&a #l +,o("&%o. S"+o$ga "# lo (!#,o alo,# (# 3,#&"#$&!a # !$%#$!(a( (#l &olo, "# &o*+,#$(#$ #l a$'l!! (# #%# # &o*/!$a$) +a,a (#%#,*!$a(o %!$%# a*a,!llo) #$ "$ olo alo, $"*,!&o lla*a(o C. (",a$%# "$ +#,!o(o (# +,"#/a #$ #l &"al # &o$%,ola$ &"!(a(oa*#$%# la &o$(!&!o$# (#l ,#a&%o,) #%# # l!*+!a a 3o$(o #$%,# lo%# "!o 8lo &"al $o # "$ +,o(!*!#$%o ""al7) #l a$'l!! (#l +,o("&%o (# 12 lo%# &o,,!(o #$ (a "!o (a la !g"!#$%# l#&%",a (# &olo, EFERCICIOS DE I UNIDAD 8CAITULO2 ELDER7
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[LABORATORIO DE OPERACIONES UNITARIAS]
LOT E C
1
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a7 La #+#&!5&a&!-$ (# CC +a,a la +,o("&&!-$ (# ,"%!$a # "# "$ lo%# "# # al## *' (# (o (#!a&!o$# #%'$(a, (# la *#(!a (#l +#,!o(o (# +,"#/a) (#/# #, ,#&aa(o ,#+,oa(o. D#%#,*!$# lo alo,# *$!*o *'=!*o a+%a/l# +a,a C. /7 U$ #=+#,%o #$ #%a(%!&a "# %,a/aa #$ &o$%,ol (# &al!(a( "$ !$g#$!#,o (# +,o("&&!-$ (!&"%#$ ,a$P (##a a"*#$%a, la #+#&!5&a&!-$ (# CC a %,# (#!a&!o$# #%'$(a, Foa$$# (##a ,#("&!,la a "$a. Vol#, a +,oa, lo lo%# %o*a %!#*+o) &a,o *" +o&o +o+"la, #$%,# lo !$g#$!#,o "# %!#$#$ "# a,lo. "!$ # *' +,o/a/l# "# #a #l #=+#,%o #$ #%a(%!&a "!#$ #l !$g#$!#,o E=+l!"# " ,#+"#%a. &7 S"+o$ga "# #$ la +,!*#,a #*a$a (# o+#,a&!-$ # +,o("$ *" +o&o lo%# !$a+%a/l#) +#,o (#+" " $4*#,o &o*!#$a a a"*#$%a, #$ 3o,*a &o$%a$%#. ,o+o$ga &!$&o &a"a +o!/l# # !$(!"# &o*o (#%#,*!$a &"'l (# #lla # la ,#+o$a/l# (# la &a(a #$ la &al!(a(.
EFERCICIOS DE I UNIDAD 8CAITULO2 ELDER7
'g!$a 11
[LABORATORIO DE OPERACIONES UNITARIAS]
2.2< La 3'/,!&a (o$(# %,a/aa 3a/,!&a #$ol%",a (# +l'%!&o +a,a al*a$a, al!*#$%o. La ,#!%#$&!a al (#ga,,# (# la #$ol%",a) "# # +,##$%a &o*o ) (#/# &o$%,ola,# +a,a "# #%a +"#(a (#+,#$(#,# (#l ,ollo !$ #3"#,o) +#o "#) al *!*o %!#*+o) #a (!3&!l ,o*+#,la &o$ #l "o $o,*al. E$ "$a #,!# (# &o,,!(a (# +,"#/a) # 3a/,!&a$ 10 ,ollo (# #$ol%",a #$ &o$(!&!o$# &o$%,ola(a &o$ g,a$ &"!(a(o # *!(# la ,#!%#$&!a al (#ga,,# (# &a(a ,ollo. Lo ,#"l%a(o # #*+l#a$ &o*o /a# (# "$a especifcación de control de calidad. S! #l alo, +a,a "$ ,ollo "# # +,o(" (#+" # al#a *' (# (o (#!a&!o$# #%'$(a, (#l +,o*#(!o &o,,#+o$(!#$%# al +#,!o(o (# +,"#/a) # (#&la,a "# #l +,oo #%' 3"#,a (# #+#&!5&a&!-$ # "+#$(# la +,o("&&!-$ +a,a (a, *a$%#$!*!#$%o a la ,"%!$a. Lo (a%o o/%#$!(o #$ "$a #,!# (# +,"#/a o$ lo !g"!#$%# ROLL 1 O 1; ?
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a7 Al!*#$%# #$ "$a oa (# &'l&"lo lo (a%o (# la #,!# +,"#/a &al&"l# la *#(!a (# la *"#%,a la (#!a&!-$ #%'$(a, (# la *"#%,a 8S =7) (# +,#3#,#$&!a #*+l#a$(o 3"$&!o$# (#l +,og,a*a +a,a #3#&%"a, lo &'l&"lo. /7 Se obtienen los siguientes valores de resistencia al desgarre para los rollos producidos en 14 corridas consecutivas de producción subsecuentes a la serie de prueba: 128, 131, 133, 135, 137, 133, 137, 136, 137, 13. !n la "o#a de c$lculo %de pre&erencia e'pleando la capacidad de grafcar de la 'is'a(, elabore una gr$fca de control ) contra el nu'ero de corrida, indicando con EFERCICIOS DE I UNIDAD 8CAITULO2 ELDER7
'g!$a 12
[LABORATORIO DE OPERACIONES UNITARIAS] l*neas "ori+ontales los valores correspondientes a ), )2S= 2S = (#l +#,!o(o (# +,"#/a) # !$(!"# "# +"$%o &o,,#+o$(#$ a la 1? &o,,!(a (# +,o("&&!-$. " *#(!&!o$# o&a!o$a,o$ "# # "+#$(!#,a la +,o("&&!-$ &7 T,a la 4l%!*a &o,,!(a (# +,o("&&!-$) #l !$g#$!#,o #$ #3# (# +la$%a ,#g,#a (# " a&a&!o$#) #=a*!$a #l ,#g!%,o (!a,!o (# la +la$%a &o*#$%a "# # #!(#$%# "# #l *a$%#$!*!#$%o (# ,"%!$a $o 3"# "5&!#$%# (#/!(#%#$#,# #l +,oo #$ alg4$ *o*#$%o (# la (o #*a$a #$ la &"al# #%"o a"#$%# +a,a (a, *a$%#$!*!#$%o al !%#*a. &"'$(o "/!## !(o ,ao$a/l# a, #%o +o, "
2.21 S# ,#+o,%a "# la a,!a/l# Q %!#$# #l alo, (# 2.;6< = 1<>? Kg.*2@ a7 E&,!/# "$a #&"a&!-$ (!*#$!o$al +a,a Q) #l alo, (# la a,!a/l# #"!al#$%# #=+,#a(a #$ "$!(a(# a*#,!&a$a (# !$g#$!#,a) #*+l#a$(o a lo #g"$(o &o*o "$!(a( (# %!#*+o. /7 E%!*# Q !$ "a, &al&"la(o,a) *#(!a$%# #l +,o(!*!#$%o ,'+!(o "# # *#$&!o$a #$ la #&&!-$ 0/. 8*"#%,# " &'l&"lo7 (#+") (#%#,*!$# Q *#(!a$%# "$a &al&"la(o,a #=+,## " ,#+"#%a #$ $o%a&!-$ &!#$%5&a (#&!*al) a#g",'$(o# (# "# %#$ga #l $"*#,o &o,,#&%o (# &!3,a !g$!5&a%!a.
2.22 El $4*#,o (# ,a$(%l) N %) # "$ g,"+o a(!*#$!o$al !*+o,%a$%# #$ lo &'l&"lo (# %,a$3#,#$&!a (# &alo, # (#5$# &o*o C+@P (o$(# C+ # la &a+a&!(a( &alo,5&a (#l "!(o P EFERCICIOS DE I UNIDAD 8CAITULO2 ELDER7
'g!$a 1;
[LABORATORIO DE OPERACIONES UNITARIAS] # la &o$("&%!!(a( %,*!&a. a,a "$ "!(o (a(o) C+ <.0:; F@8gJC7) K<.2:6W@8*JC7) 1;6 l/*@83%.7. #%!*# #l alo, (# N% !$ #*+l#a, &al&"la(o,a.
2.2; El $4*#,o (# R#$ol( # "$ g,"+o a(!*#$!o$al "# # (#5$# &o*o !g"# +a,a "$ l"!(o "# "# +o, "$a %"/#,a.
ℜ= Duρ / μ Do$(# D # #l (!'*#%,o (# la %"/#,a) " # la #lo&!(a( (#l "!(o) ρ # " (#$!(a( μ " !&o!(a(. C"a$(o #l alo, (#l $4*#,o (# R#$ol( # *#$o, (#) a+,o=!*a(a*#$%#) 21<<) #l "o # la*!$a,) # (#&!, #l l"!(o # *"## #$ l$#a (# "o "a#. a,a $4*#,o (# R#$ol( *ao,# (# 21<<) #l "o la*!$a, # %",/"l#$%o) &a,a&%#,!a(o +o, &o$!(#,a/l# ag!%a&!-$. La *#%!l #%!l %o$a 8MEK7 l!"!(a "# a %,a (# "$a %"/#,a &o$ (!'*#%,o !$%#,$o (# 2.<69 +"lga(a a #lo&!(a( +,o*#(!o (# <.?: 3%@. ! la %#*+#,a%",a (#l "!(o # 2
EFERCICIOS DE I UNIDAD 8CAITULO2 ELDER7
'g!$a 1?
[LABORATORIO DE OPERACIONES UNITARIAS]
2.2? La !g"!#$%# #&"a&!-$ #*+,!&a &o,,#la&!o$a lo alo,# (# la a,!a/l# (# "$ !%#*a "# &o$%!#$# +a,%&"la -l!(a #$ "+#$!-$ #$ "$ ga "# "# μ ρD
¿ ¿
k g d p y =2.00 + 0.600 ¿ D
A*/o) 8 ( μ / ρD )
d pμρ μ
) o$ g,"+o a(!*#$!o$al#
k g
#
"$ &o#5&!#$%# "# #=+,#a la #lo&!(a( a la &"al "$a #+#&!# (a(a # %,a$5#,# (#l ga a la +a,%&"la -l!(a lo &o#5&!#$%# 2.<< <.6<< o$ &o$%a$%# a(!*#$!o$al# "# # o/%!#$#$ a"%a$(o (a%o #=+#,!*#$%al# "# a/a,&a$ "$ a*+l!o ,a$go (# alo,# (# la a,!a/l# (# la #&"a&!-$. E k g
$#a,!o &o$o, #l alo, (#
+a,a
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*#(!a$%# la &o,,#la&!-$ (a(a. Lo alo,# (# la a,!a/l#
o$ lo !g"!#$%# d p=5.00 mm y =0.100 adimensional
D <.1<< &*2@ −5
μ=1.00 x 10 N . −3
ρ=1.00 x 10
s m
2
g / cm
3
u=10. < *@
a7 C"'l # alo, #%!*a(o (#
k g ?
EFERCICIOS DE I UNIDAD 8CAITULO2 ELDER7
'g!$a 10
[LABORATORIO DE OPERACIONES UNITARIAS] /7 o, " +o(,a (!3#,!, (# *a$#,a !g$!5&a%!a #l alo, #,(a(#,o (#
k g
(#l ,#a&%o, &o$ ,#+#&%o al alo,
&al&"la(o #$ #l !$!&!o 8a7
2.20 U$ &,!%al !$!&!a(o, (# (!'*#%,o D 8**7 # &olo&a #$ "$a ol"&!-$ (# al (!"#l%a # o/#,a la $"&l#a&!-$ (# $"#o &,!%al# 83o,*a&!-$7 a #lo&!(a( &o$%a$%# , 8&,!%al#@*!$7. Lo #=+#,!*#$%o &o$ &,!%al# !$!&!a(o,# (# (!3#,#$%# %a*ao !$(!&a$ "# la #lo&!(a( (# $"&l#a&!-$ a,!a) #g4$ #l (!'*#%,o (# #%o) &o*o !g"# r
(
)
cristales =200 D−10 D 2 ( D en mm ) min
EFERCICIOS DE I UNIDAD 8CAITULO2 ELDER7
'g!$a 16
[LABORATORIO DE OPERACIONES UNITARIAS] a7 &"'l# o$ la "$!(a(# (# la &o$%a$%# 2<< 1< 8"+o$ga "# a #&"a&!-$ (a(a # 'l!(a ) +o, %a$%o) (!*#$!o$al*#$%# o*og$#a7. /7 Cal&"l# la #lo&!(a( (# $"&l#a&!-$ #$ &,!%al#@#g "# &o,,#+o$(# al (!'*#%,o (#l &,!%al (# <.<0< +"lg. &7 D#,!# "$a 3-,*"la +a,a , 8&,!%al#@#g7 #$ %,*!$o (# D 8+"lga(a7. V#,!5"# la 3o,*"la &o$ #l ,#"l%a(o (#l !$&!o /
2.26 La (#$!(a( (# "$ "!(o # o/%!#$# *#(!a$%# la !g"!#$%# #&"a&!-$ #*+,!&a ρ=70.5 exp ( 8.27 x 10
−7 P
)
ρ= densidad ( lbm )/ ft 3 ¿
P= presion ( −7 P
a7 C"'l# o$ la "$!(a(# (# 9<.0 :.29 x 10
lbf
¿2
)
/7 Cal&"l# la (#$!(a( #$ g@&*; +a,a "$a +,#!-$ (# .<< =1<6 N@*2 &7 D#,!# "$a 3-,*"la +a,a
ρ 8g@&*;7 #$ 3"$&!-$ (#
8N@*27. &o*+,"#/# " ,#"l%a(o #*+l#a$(o la ol"&!-$ (#l !$&!o /. EFERCICIOS DE I UNIDAD 8CAITULO2 ELDER7
'g!$a 19
[LABORATORIO DE OPERACIONES UNITARIAS]
2.29 El ol"*#$ (# "$ &"l%!o *!&,o/!a$o a"*#$%a #g4$ la 3o,*"la V ( cm 3 ) =e
t
t =tiempo ( seg. )
a7 Cal&"l# la #=+,#!-$ +a,a V8 !$;7 #$ %,*!$o (# %87 /7 La 3"$&!-$ #=+o$#$&!al " a,g"*#$%o (#/#$ #, a(!*#$!o$al#. E$ a+a,!#$&!a) la 3"$&!-$ (a(a &o$%,a(! a*/a ,#gla ) !$ #*/a,go) # 'l!(o. E=+l!"# #%a +a,a(oa 8o/#,# #l ,#"l%a(o (#l !$&!o a.7
EFERCICIOS DE I UNIDAD 8CAITULO2 ELDER7
'g!$a 1:
[LABORATORIO DE OPERACIONES UNITARIAS]
2.2: C!#,%a &o$$%,a&!-$ C8*ol@L7 a,!a &o$ #l %!#*+o8*!$7 #g4$ la #&"a&!-$ C =3.00exp (−2.00 t )
a7 C"'l# o$ la "$!(a(# (# ;.<< 2.<< /7 S"+o$ga "# la &o$$%,a&!-$ # *!(# #$ %< %1 *!$. E*+l## la !$%#,+ola&!-$ o #=%,a+ola&!-$ l!$#al (# (o +"$%o +a,a &al&"la, C 8%<.6 *!$7 % 8C <.1< *ol@L7 a +a,%!, (# lo alo,# *#(!(o &o*+a,# #%o ,#"l%a(o &o$ lo alo,# #,(a(#,o (# #%a &a$%!(a(# &7 D!/"# "$a &",a (# C &o$%,a %) #al# #$ la g,'5&a lo +"$%o "# (#%#,*!$o #$ #l !$&!o /.
EFERCICIOS DE I UNIDAD 8CAITULO2 ELDER7
'g!$a 1
[LABORATORIO DE OPERACIONES UNITARIAS]
2.;< Co$%,"a la g,'5&a "# # (#&,!/#$ a &o$%!$"a&!-$ &al&"l# la #&"a&!o$# +a,a Y8=7 a +a,%!, (# la !$3o,*a&!-$ "# +,o+o,&!o$a*o. To(a la g,'5&a o$ l$#a ,#&%a. O/#,# "# la &oo,(#$a(a (a(a # ,#5#,#$ a la a/&!a la o,(#$a $o aalo,# (# Y. 8la ol"&!-$ (# !$&!o a. # (a &o*o ##*+lo.7 a7 U$a g,'5&a (# l$Y #$ &oo,(#$a(a ,#&%a$g"la,# +aa +o, 81.<)<.6;7 82.<) <.<7 # (#&!,) #$ #l +,!*#, +"$%o 1.< L$Y <.6; bx
Ln =bx + lna! y = a e
b=
( ln y 2−ln y 1 ) x 2− x 1
=
0−0.693 =−0.693 2.0−1.0
lna = ln y 1−b x 1=0.693 + 0.693∗1.0 =1.386 !a =e
1.386
=4
"
−0.693 x
y = 4.00 e
/7 U$a g,'5&a #*!loga,!%*!&a 8## loga,%*!&o7 &o$%,a = a%,a!#a +o, 81)27 82)17. &7 U$a g,'5&a loga,%*!&a (# = +aa +o, 81)27 82)17 (7 U$a g,'5&a #*!loga,%*!&a (# =8## loga,%*!&o7 @=) +aa +o, 81.<)?<.27 82.<):<9.<7 #7 U$a g,'5&a loga,%*!&a (# 2@= 8=>27 +aa +o, 81.<) ?<.27 82.<) :<9.<7.
EFERCICIOS DE I UNIDAD 8CAITULO2 ELDER7
'g!$a 2<
[LABORATORIO DE OPERACIONES UNITARIAS]
2.;1 D!ga "# g,a5&a,a +a,a o/%#$#, "$a ,#&%a ! %"!#,a "# &o,,#la&!o$a, (a%o #=+#,!*#$%al# (# 8=)7 *#(!a$%# la !g"!#$%# #&"a&!o$#) # !$(!"# &"al# #,a$ la +#$(!#$%# la !$%#,a&&!o$# #$ %,*!$o (# lo +a,'*#%,o (# la ,#la&!o$#. S! # +"(!#,a$ a+l!&a, #$ 3o,*a &o$#$!#$%# (o %!+o (!%!$%a (# g,'5&a) !$(!"# "# g,a5&a,a #$ &a(a &ao 8la ol"&!-$ (#l !$&!o 8a7 # (a &o*o ##*+lo7 −b
a7
y
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Sol"&!-$ &o$%,"a "$a g,'5&a #*!loga,!%*!&a (# &o$%,a
1@=
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3
/7
y =m x −n
&7
+ 1 = 1 a √ x b ln ( y −3 )
(7
( y + 1)2 =[ a ( x −3 )3 ]
−1
EFERCICIOS DE I UNIDAD 8CAITULO2 ELDER7
'g!$a 21
[LABORATORIO DE OPERACIONES UNITARIAS] #7
y =exp ( a √ x + b )
37
[ a ( x + y ) +b] xy =10
g7
[ ]
2
y=
b ax + x
2
−1
2.;2 U$ !g,-*#%,o) #l &"al *!(# la "*#(a( #$ "$a &o,,!#$%# (# ga) # a a &al!/,a, &o$ #l a+a,a%o "# # *"#%,a a &o$%!$"a&!-$
a+o,
S#
EFERCICIOS DE I UNIDAD 8CAITULO2 ELDER7
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EFERCICIOS DE I UNIDAD 8CAITULO2 ELDER7
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EFERCICIOS DE I UNIDAD 8CAITULO2 ELDER7
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EFERCICIOS DE I UNIDAD 8CAITULO2 ELDER7
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EFERCICIOS DE I UNIDAD 8CAITULO2 ELDER7
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[LABORATORIO DE OPERACIONES UNITARIAS]
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EFERCICIOS DE I UNIDAD 8CAITULO2 ELDER7
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EFERCICIOS DE I UNIDAD 8CAITULO2 ELDER7
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[LABORATORIO DE OPERACIONES UNITARIAS]
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EFERCICIOS DE I UNIDAD 8CAITULO2 ELDER7
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EFERCICIOS DE I UNIDAD 8CAITULO2 ELDER7
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[LABORATORIO DE OPERACIONES UNITARIAS]
EFERCICIOS DE I UNIDAD 8CAITULO2 ELDER7
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