Laboratorio de Operaciones Unitarias

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 &ao) # #%!*# +,! ,!* *#,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 60120 120.2 .2 !7 8?. 8?.90; 90; = 1
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2.1 El &o$%,ol (# la &al!(a( 8CC7 # "$ +,o&#o *" (!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(oa*#$%# la &o$(!&!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 8CAITULO2 ELDER7

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2.2< La 3'/,!&a (o$(# %,a/aa 3a/,!&a #$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 +,o&#o #%' 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!*#$%# #$ "$a oa (# &'l&"lo lo (a%o (# la #,!# +,"#/a  &al&"l# la *#(!a (# la *"#%,a   la (#!a&!-$ #%'$(a, (# la *"#%,a 8S =7) (# +,#3#,#$&!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 8CAITULO2 ELDER7

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[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 $o 3"# "5&!#$%#  (#/!(#%#$#,# #l +,o&#o #$ alg4$ *o*#$%o (# la (o #*a$a #$ la &"al# #%"o a"#$%# +a,a (a, *a$%#$!*!#$%o al !%#*a. &"'$(o "/!## !(o ,ao$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&"lo7 (#+") (#%#,*!$# Q *#(!a$%# "$a &al&"la(o,a  #=+,## " ,#+"#%a #$ $o%a&!-$ &!#$%5&a  (#&!*al) a#g",'$(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 8CAITULO2 ELDER7

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[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.

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cristales =200 D−10 D 2 ( D en mm ) min


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[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 #$ %,*!$o (# D 8+"lga(a7. V#,!5"# la 3o,*"la &o$ #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 8CAITULO2 ELDER7

'g!$a 19


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 !$;7 #$ %,*!$o (# %87 /7 La 3"$&!-$ #=+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(oa 8o/#,# #l ,#"l%a(o (#l !$&!o a.7


'g!$a 1:


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 /.


'g!$a 1


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  $o aalo,# (#   Y. 8la ol"&!-$ (# !$&!o a. # (a &o*o ##*+lo.7 a7 U$a g,'5&a (# l$Y   #$ &oo,(#$a(a ,#&%a$g"la,# +aa +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$a g,'5&a loga,%*!&a (#   = +aa +o, 81)27  82)17 (7 U$a g,'5&a #*!loga,%*!&a (# =8## loga,%*!&o7  @=) +aa +o, 81.<)?<.27  82.<):<9.<7 #7 U$a g,'5&a loga,%*!&a (# 2@=  8=>27 +aa +o, 81.<) ?<.27  82.<) :<9.<7.


'g!$a 2<


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 &ao 8la ol"&!-$ (#l !$&!o 8a7 # (a &o*o ##*+lo7 −b

a7

y

2

=a e x

Sol"&!-$ &o$%,"a "$a g,'5&a #*!loga,!%*!&a (# &o$%,a

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o

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g,a5&a

ln ( y

2

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y =m x −n

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+ 1 = 1 a √ x b ln ( y −3 )

(7

( y + 1)2 =[ a ( x −3 )3 ]

−1


'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&!-$

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S# 


al!*#$%a$ a!,# #&o a 'g!$a 22

[LABORATORIO DE OPERACIONES UNITARIAS] #lo&!(a(# (# "o X &o$o&!(a  # *#&la$ +a,a 3o,*a, "$a &o,,!#$%# (# ga &o$ &o$%#$!(o (# ag"a &o$o&!(o. S# a$o%a la l#&%",a (# !g,-*#%,o. L"#go) # *o(!5&a la #lo&!(a( (# "o) a #a (#l ag"a o (#l a!,#) +a,a +,o("&!, "$a &o,,!#$%# &o$ (!3#,#$%# &o$%#$!(o (# ag"a  # a$o%a la $"#a l#&%",a)  a "&#!a*#$%#. S# o/%!#$#$ lo !g"!#$%# (a%o

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'g!$a 2;


2.;; La %#*+#,a%",a (# "$a "$!(a( (# +,o&#o # &o$%,ola a&!#$(o +aa, ag"a a #lo&!(a( &o$%,ola(a a %,a (# "$a &a"#%a (# #$3,!a*!#$%o "# #$"#l# a (!&a "$!(a(.

La ,#la&!-$ #=a&%a #$%,# la %#*+#,a%",a "$!%a,!a T8JC7  la #lo&!(a( (# "o (#l ag"a (# #$3,!a*!#$%o

∅

( ) # *" L s

&o*+l#a)  # (##a (#,!a, "$a 3o,*"la #*+,!&a !*+l# +a,a a+,o=!*a, #%a ,#la&!-$ #$ "$ ,a$go l!*!%a(o (# #lo&!(a(# (# "o  %#*+#,a%",a. S# %o*a$ (a%o (# T &o$%,a ∅

g,'5&a (# T &o$%,a #*!loga,!%*!&a $ =a ∅ + b y $ =a e

b∅

(a$

∅

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#$ &oo,(#$a(a ,#&%a$g"la,# 

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&o*o +o!/l# 3"$&!o$# #*+,!&a7) +#,o la

g,'5&a loga,%*!&a %!#$# la !g"!#$%# a+a,!#$&!a

Al %,aa, la l$#a "# +aa +o, lo (a%o # o/#,a "# a%,a!#a lo +"$%o 8

∅1

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a7 C"'l # la ,#la&!-$ #*+,!&a #$%,#

∅


y $ 

'g!$a 2?

[LABORATORIO DE OPERACIONES UNITARIAS] /7 E*+l#a$(o la #&"a&!-$ (#,!a(a) &al&"l# la #lo&!(a(# (# "o (#l ag"a (# #$3,!a*!#$%o $#&#a,!a +a,a *a$%#$#, la %#*+#,a%",a (# la "$!(a( (# +,o&#o a :0JC) 190JC  2
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g C % ( ) L ) #$ 3"$&!-$ (#l %!#*+o 8*!$7)

(#(# #l !$!&!o (# la ,#a&&!-$


'g!$a 20


El *#&a$!*o (# ,#a&&!-$ +,o+"#%o +,#(!&# "#

C %

 % (#/#$

#%a, ,#la&!o$a(a +o, la #=+,#!-$ ln

C % −C %e C %D− C %e

=−kt

Do$(# P # la &o$%a$%# (# #lo&!(a( (# ,#a&&!-$. a7 a+oa$ lo (a%o #%a +,#(!&&!-$ E$ &ao a5,*a%!o) (#%#,*!$# #l alo, (# P8#*+l## "$a g,'5&a #*!loga,!%*!&a +a,a ,#ol#, #%# +,o/l#*a7 /7 S! #l ol"*#$ (#l %a$"# # ;<.0 galo$#  B $o #=!%# #$ #l %a$"# &"a$(o %<) Q" &a$%!(a( (# B8g7 &o$%#$(,' (!&o %a$"# %,a$&",,!(a (o o,a


'g!$a 26


2.;0 E l *o*#$%o &"l*!$a$%# (# la +#l&"la [la /#,#$#$a "# #$g"llo a N"#a F#,#\ # +,o("&# &"a$(o #l o#$  (#%a&a(o &!#$%5&o a$"$&!a "# (#&"/,!- la #&"a&!-$ +a,a (#%#,*!$a, #l ol"*#$ (# la /#,#$#$a V ( f t )=3.53 x 10 exp ( 2 t ) −2

3

2

Do$(# % # #l %!#*+o #$ o,a (#(# #l *o*#$%o #$ "# #l a*+!,o !$#&%o #$ la /#,#$#$a "$a ol"&!-$ +,#+a,a(a &o$ la a$g,# (# la #,*oa !g!#$!%a (#$%al. a7 C"'l# o$ la "$!(a(# (# ;.0; = 1<>2  2 /7 El &!#$%5&o o/%"o la 3o,*"la *!(!#$(o V &o$%,a %  (#%#,*!$a(o lo &o#5&!#$%# +o, ,#g,#!-$ l!$#al C"'l a,!a/l# g,a5&o &o$%,a &"al o%,a  #$ " %!+o (# &oo,(#$a(a" a/,a o/%#$!(o &o*o la +#$(!#$%#  la !$%#,#&&!-$ #$ #%a g,a5&a &7 El (!%,!/"!(o, #",o+#o (# la +#l&"la !$!%# #$ "# la 3-,*"la +a,a #l ol"*#$ # (# #$ * ; #$ 3"$&!-$ (# %87. (#,!# la 3o,*"la.

2.;6 La ,#la&!-$ #$%,# la +,#!-$   #l ol"*#$ V (# a!,# #$ "$ &!l!$(,o (",a$%# #l a&#$o (# "$ +!%-$ #$ "$a &o*+,#o,a (# a!,# +"#(# #=+,#a,# &o*o !g"# k

PV =C

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'g!$a 29


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2.;9 Al *o(#la, #l #3#&%o (# "$a !*+",#a o/,# #l &,#&!*!#$%o (# "$ &,!%al) # (#,!- la !g"!#$%# #&"a&!-$ & −& L

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2.;: S# &,## "# la l#&%",a (# "$ !$%,"*#$%o (# +,o&#o) Z8ol%7) # ,#la&!o$a &o$ la #lo&!(a( (# "o (# la &o,,!#$%# (# +,o&#o

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[LABORATORIO DE OPERACIONES UNITARIAS] S# o/%"!#,o$ (a%o (#l +,o&#o #$ (o &o$"$%o (# &o,,!(a. E$ "$a # *a$%"o

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Laboratorio de Operaciones Unitarias

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