UNIVERSIDAD NACIONAL DEL CENTRO DEL PERÚ FACULT FACULTAD AD DE INGENIERÍA INGENIERÍ A QUÍMICA CARRERA PROFESIONAL DE INGENIERÍA QUÍMICA AMBIENTA AMBIENTAL
CATEDRA: ANÁLISIS Y SIMULACIÓN SIMULACIÓN DE PROCESOS
TEMA: DISEÑO Y SIMULACIÓN DE VACIADO DE TANQUES
PRESENTADO A: Dr. GUEVARA YANQUI, Pas!a"
Presentado por: C#AVE$ PAUCAR, %&s'
#UANCAYO( PERÚ )*+
Í-/' +.
........................................................... ........................................ ........................................... ....................... 2 RESUMEN.......................................
).
OB%ETIVOS....................................................................................................3
).+.
OB%ETIVO GE GENERAL...................................................................................3
).). ).).
OB% OB%ETIV ETIVOS OS ESPE ESPEC CÍFIC ÍFICOS OS...........................................................................3
0.
INTRODUCCIÓN .............................................................................................3
1.
MARCO TE TEORICO...................................... .......................................................... ........................................ ................................. ............. 4
1.+.
TANQUES...................................................................................................4
1.).
FLUIDO...................................... .......................................................... ....................................... ............................................. .......................... 5
1.0.
FLU%O........................................................................................................6
1.1. 1.1.
MODE MODELO LO MA MATEMÁ TEMÁTI TICO CO DEL DEL TANQ NQUE UE..........................................................8
2. PARTE E3PE E3PERI RIME MENT NTA AL................................................................................13 2.+. 2.+.
MAT MATERIA ERIALE LES S Y REAC REACTI TIVO VOS S.......................................................................13
2.). 2.).
PROC PROCED EDIM IMIE IENT NTO O E3PE E3PERI RIME MENT NTA AL.............................................................13
. CALC CALCUL ULOS OS Y RESU RESUL LTADO DOS S..........................................................................13 .+.
Da4&s........................................................................................................13
.). .).
Da4&s a4&s '5 '56'r/ 6'r/7' 7'-4 -4a" a"'s 's..................................................................................14
.0.
C8"!"&s9...................................................................................................14
:. DISC DISCUS USIÓ IÓN N DE RES RESUL ULT TADO DOS S.......................................................................17 ;.
CONCLUSIONES..........................................................................................17
<.
RECOMENDACION ONE ES...................................................................................17
+ *.
BIBLIOGRAFÍA..........................................................................................18
++.
ANE3OS...................................................................................................19
1. RESUMEN Para '" 6r's'-4' "a=&ra4&r/&, s' '76'>? 6&r /s'@ar '" '!/6& 4a-!' /"-r/& r'4&, "!'& />& "as &rr/as. E" 7?!"& 4/'-' !- /s'@& 6ara s'r !4/"/>a& '- '" "a=&ra4&r/&, s!s /7'-s/&-'s s&-9 a"4!ra '" H"!/& a!a 6ara "a 6r!'=as '56'r/7'-4a"'s 's ' *.+ 7 &2
!- /87'4r& ' *.+ 7. E" /87'4r& '" &r/H//& ' 'sara 's ' *.**2 7. A &-4/-!a/?s' 'a"!? "&s a"&r's ' "&s a4&s &=4'-/&s s' ""'? a a-8"/s/s 6ara 'r s/ !76"a- & -& &- "&s 6ar87'4r&s 's4a="'/&s, s/'-& "&s r's!"4a&s "&s s/!/'-4's9 T/'76& 4&4a" ' a/a& r'a" <*.20 '" &'H//'-4' ' 'sara
c =0.5970 .
2. OBJETIVOS 2.1.
OBJETIVO GENERA •
D'4'r7/-ar '" 4/'76& ' a/a& ' !- 4a-!' /"-r/& a 4raJs ' !- &r/H//& '- "a 6ar4' /-H'r/&r =as'.
2.2.
OBJETIVOS ESPEC!"ICOS •
D'4'r7/-ar "&s &'H//'-4's ' 'sara. .
•
C&76arar "&s r's!"4a&s 4'?r/&s K 6r84/&s.
#. INTRODUCCI$N E" a/a& ' 4a-!'s &- 'sara "a4'ra" & '- '" H&-& a s/& 's4!/a& a76"/a7'-4' s' a- 6!="/a& 7&'"&s !' r'6r's'-4a- "a /-H"!'-/a ' ar/a/&-'s '- '" /87'4r& H&r7a '" &r/H//& '- '" H"!& &"!7J4r/&. Es r'a"/>a& '- "as "a=&r's /ar/as ' !-a /-!s4r/a, H8=r/as, '76r'sas 7/-'ras, '4., ' a -!'s4r& /-4'rJs ' '4'r7/-ar '" 4/'76& ' a/a& ' !- 4a-!'. La H&r7a ' "&s 4a-!'s 6!''- ar/ar, '-4r' '""&s 4'-'7&s9 /"/-r&s, !=&s, 6/ra7/a"'s, ?-/&s, 4ra6'>&/a"'s, '4. E- '" 6r's'-4' /-H&r7' s' 's4!/ar8 '" 4/'76& ' a/a& ' !- 4a-!' /"-r/& r'4&, 6ara r'a"/>ar "as 6r!'=as 4&7ar "&s a4&s, '" 4a-!' 's4ar8 '- s! H&r7a 'r4/a". Para 6&'r '4'r7/-ar '" 4/'76& ' a/a& s' !4/"/>ar8 /H'r'-4's 6r/-/6/&s &7& s&-9 =a"a-' ' 7asa, =a"a-' ' 7&/7/'-4& =a"a-' ' '-'ra. P&r 7'/& ' "a a6"/a/?- ' "&s 6r/-/6/&s ' &-s'ra/?- ' 7asa 7&7'-4!7 s' H&r7!"ar8 !- 7&'"& 7a4'784/& !' 'sr/=' '" a/a& ' !- 4a-!' a" !' -& s' "' r'6&-' a!a, 6ara s'r a"/a& '56'r/7'-4a"7'-4'.
3
%. MARCO TEORICO %.1.
TAN&UES La 7a&r 6ar4' ' "&s "!/&s 7a-'a&s '- "as /-!s4r/as ' 6r&'s&s s' a"7a'-a a ra-'" '- 4a-!'s !' &6'ra- '- '" '-4&r-& ' "a 6r's/?- a47&sHJr/a. La -''s/a ' s4& '- "as 6"a-4as 6!'' 6r's'-4ars' 4a-4& '- '" a6r&/s/&-a7/'-4&. C&7& '- '" 's6a& ' 6r&!4&s '"a=&ra&s, s'a- 's4&s /-4'r7'/&s & H/-a"'s '" 6r&'s&. La a6a/a 4&4a" ' a"7a'-a' &7& "a /-//!a" ' aa 4a-!' '6'-'r8 s'- '" as& a-a"/>a& '9 • •
• •
%.1.1.
E" =a"a-' '-4r' '" H"!& 6r&!/& '7a-a& 6&r '" &-s!7/&r La r's'ra H/aa &7& r4/a, '56r'saa '- as ' 7ara & &"!7'7-/7& L&s 7'/&s, a6a/a &s4&s ' 4ra-s6&r4' "&s4/a E" 's6a/& /s6&-/="' '- 6"a-4a.
VACIADO DE TAN&UES E- "as /-!s4r/as '5/s4' "a -''s/a ' a/ar s!s 4a-!'s s'a &- H/-'s ' "/76/'>a 4'76&rar/a & s/76"'7'-4' 6ara 'H'4!ar a"- 4ra=a& ' 7a-4'-/7/'-4& '- "&s 7/s7&s, & !76"/'-& s/76"'7'-4' s! 4ar'a. E- &4ras s/4!a/&-'s, s' 6r'/sa 4rasasar 6r&!4& ' !- '!/6& a &4r& a6r&'a-& "as /H'r'-/as ' -/'"'s '-4r' '""&s !a"!/'ra s'a s! /s6&s//?-, 's4& 's, 'sara 6&r ra'a 's' !- -/'" s!6'r/&r a &4r& /-H'r/&r & =/'- '-4r' 4a-!'s !=/a&s &r/>&-4a"7'-4'. S' =!sa 6!'s '"/7/-ar a4//a's !' '-'r'- &s4&s -& ar'!'- a"&r a & "&s 6r&!4&s '"a=&ra&s E" a/a& ' 4a-!'s r'/6/'-4's 's !- 6r&'s& 'rJ/7'- -& 's4a/&-ar/& a& !' 4'-'7&s !-a sa"/a ' 7asa '" s/s4'7a a !-a '"&/a ar/a="' !' '6'-'r8 '" -/'" ' "!/& '- '" 7/s7&.
%.1.2.
TIPOS DE TAN&UES L&s 4a-!'s ' a"7a'-a' 6!''- "as/H/ars' s'- /s4/-4&s r/4'r/&s s! s'"'/?- '6'-'r8 '" a-8"/s/s "&=a" ' "a /-s4a"a/?- ' s! /76a4& s&=r' "&s 6r&'s&s as&/a&s. As '-&-4ra7&s "&s s/!/'-4's /s'@&s9
Tan'(es )(adrados o re)tan*(+ares: S' '76"'a- 6ara a"7a'-ar 6r&!4&s -& ar's/&s a!a, 7/'"'s, ara='s, '4. s&- ' =aa a6a/a V)* 7 0. S&- &-s4r!/&s '-'ra"7'-4' ' a'r& a" ar=&-& &6'ra- a 6r's/?- a47&sHJr/a 4
Tan'(es ),+-ndr,)os or,/onta+es: S' '76"'a- 6ara a"7a'-ar 6r&!4&s ' /H'r'-4' -a4!ra"'>a !7/a 8/&s, 8"a"/s, &7=!s4/="'s, "!=r/a-4's, '4.. S&- ' 7'/a-a a6a/a ' a"7a'-a' V+2* 7 0. Es4&s 4a-!'s a s! '> 6!''s'r9 aJr'&s a=&'r&!- s4&ra' & s!=4'rr8-'&s !-'rr&!- s4&ra' 6!''- 4'-'r s!s '54r'7&s 6"a-&s & a=&'a&s.
Tan'(es ),+-ndr,)os 0ert,)a+es: S' '76"'a- 6ara a"7a'-ar 6r&!4&s ' /H'r'-4' -a4!ra"'>a !7/a 8/&s, 8"a"/s, /r&ar=!r&s, 'H"!'-4's /-!s4r/a"'s, '4. s&- ' raa6a/a ' a"7a'-a' V+* a )*.*** 7 0. Es4&s a s! '> 6!''s'r "as/H/a&s s'- "&s /s4/-4&s as6'4&s9
T,po de )oert(ra: a=/'r4&s & 4'a&s T,po de te)o: H/& & H"&4a-4'. T'&s H"&4a-4's a 6&-4?- & a 7'7=ra-a T,po de ondo: 6"a-& & ?-/&. C&- r'"a/?- a "a s'"'/?- ' "&s 4a-!'s /"-r/&s, &64ar 6&r !-a ! &4ra H&r7a '6'-'r8 '" &"!7'- r'!'r/&, '" 's6a/& /s6&-/="', "as /-'rs/&-'s '5//as, '4. !' ar8- !' '- a"!-as s/4!a/&-'s !- 4/6& '4'r7/-a& s'a 78s /-/a& !' &4r& !' a=r8 !' '4'r7/-ar 'aa as& '- 6ar4/!"ar.
%.2.
"UIDO L&s H"!/&s, &7& 4&&s "&s 7a4'r/a"'s, 4/'-'- 6r&6/'a's Hs/as !' 6'r7/4'ara4'r/>ar !a-4/H/ar s! &76&r4a7/'-4& as &7& /s4/-!/r"&s ' &4r&s. A"!-as ' 's4as 6r&6/'a's s&- '5"!s/as ' "&s H"!/&s &4ras s&- 46/as ' 4&as "as s!s4a-/as. Pr&6/'a's &7& "a /s&s/a, 4'-s/?- s!6'rH//a" 6r's/?- ' a6&r s&"& s' 6!''- 'H/-/r '- "&s "!/&s as's. S/- '7=ar& "a 7asa 's6'H/a, '" 6's& 's6'H/& "a '-s/a s&- a4r/=!4&s ' !a"!/'r 7a4'r/a.
%.2.1.
PROPIEDADES DE OS "UIDOS. •
V,s)os,dad: 's !-a 6r&6/'a ' "&s H"!/&s !' s' r'H/'ra '" ra& ' Hr//?- /-4'r-a s' as&/a &- "a r's/s4'-/a !' 6r's'-4a- &s a6as aa'-4's 7&/J-&s' '-4r& '" H"!/&. D'=/& a 's4a 6r&6/'a 6ar4' ' "a '-'ra /-J4/a '" H"!/& s' &-/'r4' '- '-'ra /-4'r-a.
•
Dens,dad: 's "a r'"a/?- '-4r' "a 7asa '" &"!7'- !' &!6a, 's '/r "a 7asa ' !-/a ' &"!7'-.
•
Vo+(3en espe)-,)o: 's '" &"!7'- !' &!6a !- H"!/& 6&r !-/a ' 6's&. 5
•
Peso espe)-,)o: &rr's6&-' a "a H!'r>a &- !' "a 4/'rra a4ra' a !-a !-/a ' &"!7'-.
•
Gra0edad espe)-,)a: /-/a "a '-s/a ' !- H"!/& r's6'4& a "a '-s/a '" a!a a 4'76'ra4!ra 's48-ar. Es4a 6r&6/'a 's /7'-s/&-a".
%.2.2.
TIPOS DE "UIDOS •
"+(,do ne4ton,ano: U- H"!/& -'4&-/a-& 's !- H"!/& !a /s&s/a 6!'' &-s/'rars' &-s4a-4' '- '" 4/'76&. La !ra !' 7!'s4ra "a r'"a/?'-4r' '" 'sH!'r>& & />a""a &-4ra s! 4asa ' 'H&r7a/?- 's "/-'a" 6asa 6&r '" &r/'-. E" 7'&r ''76"& ' 's4' 4/6& ' H"!/&s 's '" a!a '&-4ra6&s//?- a" 6'a7'-4&, "a 7/'" & "&s '"'s !' s&- ''76"&s ' H"!/& -& -'4&-/a-&. U- =!'- -7'r& ' H"!/&s &7!-'s s' &76&r4a- &7& H"!/&s -'4&-/a-&s =a& &-//&-'s -&r7a"'s ' 6r's/?- 4'76'ra4!ra9 '" a/r', '" a!a, "a as&"/-a, '" /-& a"!-&s a'/4's 7/-'ra"'s.
•
"+(,do no ne4ton,ano: Es a!J" !a /s&s/a ara &- "a 4'76'ra4!ra 6r's/?-, 6'r& -& &- "a ar/a/?- ' "a '"&/a. Es4&s H"!/&s s' 6!''ara4'r/>ar 7'&r 7'/a-4' &4ras 6r&6/'a's !' 4/'-'- !' 'r &- "a r'"a/?- '-4r' '" 'sH!'r>& "&s 4'-s&r's ' 'sH!'r>&s =a& /H'r'-4's &-//&-'s ' H"!&, 4a"'s &7& &-//&-'s ' 'sH!'r>& &r4a-4' &s/"a4&r/&.
Es /76&r4a-4' "as/H/ar "&s H"!/&s -& -'4&-/a-&s '- /-'6'-/'-4's '" 4/'76& & '6'-/'-4's '" 4/'76&. A"!-&s ''76"&s ' H"!/&s /-'6'-/'-4's '" 4/'76& s&-9 '" 6"as7a sa-!-'&, 6&"/'4/"'-& H!-/&, "84'5, a"7/=ar's, a's/&s, 7a"a>as 4/-4as. L&s H"!/&s !' '6'-'- '" 4/'76& s&- /H/"'s ' a-a"/>ar 6&r!' s! /s&s/a a6ar'-4' ar/a &- '" 4/'76&. E'76"&s ' '""&s s&- 6'4r?"'&s r!&s a 4'76'ra4!ras =aas, 4/-4a 6ara /76r's&ras, -"&-, /'r4as '"a4/-as, 7'>"as ' ar/-a ar/as s&"!/&-' ' 6&"7'r&.
%.#.
"UJO Es 4&& 's6"a>a7/'-4& ' !- H"!/& !' s' &-!' 6&r !-a 4!='ra, a-a", '4.
"+(5o +a3,nar: S' ara4'r/>a 6&r!' '" 7&/7/'-4& ' "as 6ar4!"as '" H"!/& s' 6r&!' s/!/'-& 4ra'4&r/as =as4a-4' r'!"ar's, s'6araas 6'r H'4a7'-4' 'H/-/as a-& "a /76r's/?- ' !' s' 4ra4ara ' "87/-as & a6as 78s & 7'-&s 6ara"'"as '-4r' s, "as !a"'s s' 's"/>a- s!a'7'-4' !-as s&=r' &4ras, s/- !' '5/s4a 6
7'>"a 7ar&s?6/a & /-4'ra7=/& 4ra-s'rsa" '-4r' '""as. •
La "' ' N'4&- ' "a /s&s/a 's "a !' r/' '" H"!& "a7/-ar9
•
E" -7'r& ' R'-&"s 6ara 's4' 4/6& ' H"!& 's 7'-&r a )+**
"+(5o t(r(+ento: Es4' 4/6& ' H"!& 's '" !' 78s s' 6r's'-4a '- "a 6r84/a ' /-'-/'ra. E- 's4' 4/6& ' H"!& "as 6ar4!"as '" H"!/& s' 7!''- '- 4ra'4&r/as 'rr84/as, 's '/r, '- 4ra'4&r/as 7! /rr'!"ar's s/- s'!/r !- &r'- 's4a="'/&, &as/&-a-& "a 4ra-sH'r'-/a ' a-4/a ' 7&/7/'-4& ' !-a 6&r/?- ' H"!/& a &4ra, ' 7&& s/7/"ar a "a 4ra-sH'r'-/a ' a-4/a ' 7&/7/'-4& 7&"'!"ar 6'r& a !-a 'sa"a 7a&r. •
La '!a/?- 6ara '" H"!& 4!r=!"'-4& s' 6!'' 'sr/=/r ' !-a H&r7a a-8"&a a "a "' ' N'4&- ' "a /s&s/a.
•
E" -7'r& ' R'-&"s 6ara 's4' 4/6& ' H"!& 's 7a&r a 0***
"+(5o de trans,),6n: Es4' 4/6& ' H"!& 's48 '-4r' '" H"!& "a7/-ar '" 4!r=!"'-4& '" -7'r& ' R'-&"s s' '-!'-4ra '-4r' )+** 0***
"+(5o )o3pres,+e: Es a!'" '- "&s !a"'s "&s a7=/&s ' '-s/a ' !- 6!-4& a &4r& -& s&- 's6r'/a="'s.
"+(5o per3anente: L"a7a& 4a7=/J- H"!& 's4a/&-ar/&. Es4' 4/6& ' H"!& s' ara4'r/>a 6&r!' "as &-//&-'s ' '"&/a ' 's!rr/7/'-4& '- !a"!/'r 6!-4& -& a7=/a- &- '" 4/'76&, & s'a !' 6'r7a-''- &-s4a-4's &- '" 4/'76& & =/'-, s/ "as ar/a/&-'s '- '""as s&- 4a- 6'!'@as &- r's6'4& a "&s a"&r's 7'/&s. As 7/s7& '- !a"!/'r 6!-4& ' !- H"!& 6'r7a-'-4', -& '5/s4'- a7=/&s '- "a '-s/a, 6r's/?- & 4'76'ra4!ra &- '" 4/'76&, 's '/r9 ∂ρ ∂ T ∂P = 0 ; = 0 ; = 0 ∂ t ∂t ∂ t
Da& a" 7&/7/'-4& 'rr84/& ' "as 6ar4!"as ' !- H"!/&, s/'76r' '5/s4'- 6'!'@as H"!4!a/&-'s '- "as 6r&6/'a's ' !- H"!/& '- !- 6!-4&, !a-& s' 4/'-' H"!& 4!r=!"'-4&. Para 4'-'r '- !'-4a 's4as H"!4!a/&-'s s' '=' '-'ra"/>ar "a 'H/-//?' H"!& 6'r7a-'-4' s'- '" 6ar87'4r& ' /-4'rJs, as9 N t =
1
t
t
∫ Ndt 0
E" H"!& 6'r7a-'-4' 's 78s s/76"' ' a-a"/>ar !' J" -& 6'r7a-'-4', 6&r "a 7
&76"'/a !' "' a//&-a '" 4/'76& &7& ar/a="' /-'6'-/'-4'.
%.%.
MODEO MATEM7TICO DE TAN&UE
Figura N° 1: diagrama de un tanque
A6"/a-& '" 6r/-/6/& ' &-s'ra/?- ' 7asa m´ 1−m´ 2=
dm (1 ) dt
D&-'9 m´ 1 H"!& 78s/& '" "!/& !' '-4ra '- '" 4a-!' m´ 2 H"!& 78s/& '" "!/& !' sa"' '" 4a-!'
m 7asa '" "!/& a!7!"aa '- '" 4a-!' t 4/'76&
Sa='7&s !' m´ 1=0 , a !' -& '-4ra "!/& s' &=4/'-'9 m=h × A 1 × ρ ( 2)
m´ 2=q × ρ (3 )
D&-'9 A 1 8r'a 4ra-s'rsa" '" H"!& h a"4!ra '" "!/& '- '" 4a-!'
8
q H"!& &"!7J4r/& ρ '-s/a '" H"!/&
S!s4/4!'-& "a '!a/?- ) 0 '- +, s' &=4/'-'9
−q × ρ =
d (h × A 1× ρ) dt
( 4)
S' &-&' !' A 1 y ρ s&- &-s4a-4's, s' &=4/'-' "a s/!/'-4' '!a/?-9
−q A1
dh dt
= ( 5 )
S' &-&' !' q =v 2 × A2 , s!s4/4!/7&s '- "a '!a/?- 2 &=4'-'7&s9
−v × 2
A 2 A 1
=
dh (6 ) dt
A 2 8r'a 4ra-s'rsa" '" &r/H//&
A6"/a-& !- =a"a-' ' '-'ra 7'8-/a '-4r' '- 6!-4& + ).
Nota: 6ara '" =a"a-' ' '-'ra 7'8-/a s' &-s/'ra '" -7'r& ' R'-&"s R', 6ara 6&'r '4'r7/-ar '" Ha4&r ' Hr//?- ' Dar f D a s/ '" R')+** s' !sa "a '!a/?- #a'-(P&/s'!/""'9 2
2
2
punto 2 f D . v . L g P 1 v 1 g P2 v 2 z 1 + + = z 2 + + + (a) g c ρ1 2 g c gc ρ2 2 g c punto 1 2. gc . D
∑
= s/ '" R'0*** s' !sa "a '!a/?- ' C&"'=r&&9 1
f D
=
−2 2.3056
ln
(
)
ε 2.51 + (b ) 3.7 . D ℜ √ f D
D&-'9 ε =rugosdad d!" mat!ra"
D'=/& a !' '" R')+** s' !sa "a '!a/?- a, 's4& s' 's6'/H/ara &- 7a&r '5a4/4! '- "&s 8"!"&s
9
2
2
2
punto 2 f D . v . L g P 1 v 1 g P2 v 2 z 1 + + = z 2 + + + (7) g c ρ1 2 g c gc ρ2 2 g c punto 1 2. gc . D
∑
D'sarr&""a-& '" "4/7& 4Jr7/-& ' "a '!a/?- : punto 2
∑
punto 1
2
2
2
f D . v . L f D . v 1 . L f D . v 2 . L = + ( 8) 2. gc . D 2. g c . D1 2. gc . D 2
S!s4/4!'-& "a '!a/?- ; '- "a '!a/?- : a/'-& "as s!6&s//&-'s 6'r4/-'-4's 6ara s/76"/H/ar"a9 La 6r's/?- 's /!a" '- a7=&s 6!-4&s9 P1= P2
La '-s/a 's /!a" '- a7=&s 6!-4&s, a !' 's '" 7/s7& H"!/&9 ρ1= ρ2
La a"4!ra ' r'H'r'-/a '- '" 6!-4& ) 's -!"a9 z 2=0
E- '" 6!-4& + -& '5/s4' '"&/a9 v 1= 0
C&- 4&as "as s!6&s//&-'s 6'r4/-'-4's, s' ""'a a9 2
2
g v 2 f D . v 2 . L z 1 = + (9 ) g c 2 g c 2. gc . D 2 gc
S/76"/H/a-& z 1 . g =
v2
2
2
2
f . v . L + D 2 (10 ) 2. D 2
Or'-a-& "a '!a/?- +* z 1 . g =
v2
2
2
[
1
+
]
f D . L D2
( 11)
D's6'a-& "a '"&/a v 2 9 v 2=
√
2. z 1 . g
f D . L 1+ D2
( 12 )
S' sa=' !'9 10
z 1=h + L
P&r "& 4a-4&9 v 2=
√
2.
( h + L ) . g
1
+
f D . L
(13 )
D2
S!s4/4!'-& "a '!a/?- +0 '- "a '!a/?- , s' &=4/'-'9 dh − A2 = dt A 1
√
2.
( h + L ) . g
f D . L 1+ D2
(14 )
D'=/& a !' '- '" 7?!"& -& a 4!='ra ' 'sara9 L=0
S' &=4/'-'9 dh − A2 = √ 2. g .h ( 15) dt A 1
Or'-a-& "a '!a/?- +2, &=4'-'7&s9 dh − A 2 = √ 2. g dt ( 16 ) √ h A1
I-4'ra-& "a '!a/?- + h
∫ #
t dh − A2 = √ 2. g dt √ h A 1 0
∫
D&-'9 # 9 A"4!ra 785/7a '" H"!/& h 9 A"4!ra '" H"!/& '- !- '4'r7/-a& 4/'76& m g= 9.81 s
2
9 Gra'a
O=4'-'7&s 2
( √ # −√ h )=
A 2 A1
√ 2. g t ( 17 )
D's6'a-& t 9
11
t =
2
( √ # − √ h )
(18 )
A 2 √ 2. g A 1
D's6'a-& h 9
(
A 2
h = √ # −
A 1
)
2
√ 2. g t 2
(19 )
Las '!a/&-'s +; +< s&- 6ara as&s /'a"'s, !a-& '" &'H//'-4' ' 'sara 's +. E-4&-'s "a 'ra'ra '!a/?- '='ra s'r9 t =
2
( √ # − √ h )
A c 2 √ 2. g A1
(
c
h = √ # −
A2 A1
(18 )
)
2
√ 2. g t 2
(19 )
D&-'9 c 9 C&'H//'-4' ' 'sara
8AANDO E COE"ICIENTE DE DESCARGA: Cas&s /'a"'s9 La &-s4a-4' C '6'-' ' "a H&r7a '" &r/H//&9
Or,,),o R'4a-!"ar Tr/a-!"ar C/r!"ar
Constante 9) *.; *,2 C *,:2. *,
Cas&s r'a"'s9
"$RMUA DE ATSC8U Para R' ra-'s s' s!/'r' '" !s& ' "a H?r7!"a ' A"4s!" !' 's 6ar4/!"ar7'-4' a'!aa 6ara R'+*1, 6'r& !' 4a7=/J- r's!"4a !-a a6r&5/7a/?- a'!aa 6ara R' 7'-&r's. 12
c =0.59 +
ℜ=
5.5
√ ℜ
( 20 )
v ×d × ρ $
D&-'9 v '"&/a a !-a '4'r7/-aa a"4!ra d /87'4r& '" &r/H//& $ /s&s/a
R''76"a>a-& "a '!a/?- )) '- "a '!a/?- +; +< r's6'4/a7'-4', &-' s' &=4/'-'9 t =
2
( √ # − √ h )
A c 2 √ 2. g A1
(
h = √ # −
c
A2 A1
(21 )
)
2
√ 2. g t 2
(22 )
;. PARTE E
MATERIAES = REACTIVOS + Ta-!' /"-r/&. + Cr&-&7'4r&. 13
A!a.
;.2.
PROCEDIMIENTO E
>. CACUOS = RESUTADOS >.1.
Datos
Tabla 1: datos estratégicos para el cálculo
Par87'4r& D/87'4r& '" 4a-!' D
D/87'4r& '" &r/H//& A"4!ra '" "/!/&
V/s&s/a $
D'-s/a ρ
M'/a
U-/a
0.10
cm
0.005
cm
0.10
cm
1.1294 × 10
−2
g cm.s g
0.9988
3
cm
Gra'a
m
9.81
s
>.2.
2
Datos e?per,3enta+es
Tabla 2: datos obtenidos en las corridas
A+t(ra 9)3 *.+ *.*; *.* *.*1 *.*) *
1@ )orr,da 9s * <.; +<.;) 01.1< 1;.;; <+.:+
2@ )orr,da 9s * <.2; +<.10 01.++ 1<.*0 <*.)0
#@ )orr,da 9s * +*.*) )*.+) 00.2) 2*.)1 ;<.2 14
Reno+ds 9Re +<0.:* 220<.;+ 1:<:.) 0<+:.)1 ):<.<+ *
Pro3ed,o 9s * <.: +<.:< 01.*1 1<.0; <*.20
>.#.
C+)(+os: a. 8a++ando A1 9rea de+ espe5o de+ a*(a: A 1=
%D
2
4
2
A 1=
% ( 0.1 ) 4
2
A 1=0.007854 m
. 8a++ando A2 9rea de+ or,,),o: A 2=
A 2=
%d
2
4
% ( 0.0005 )
2
4
−5
A 2=1.9635 × 10 m
2
). Ca+)(+o de +a 0e+o),dad te6r,)a: v 2= √ 2 gh v 2= √ 2 ( 9.81 ) ( 0.1 )
v 2=1.40071
m s
d. Ca+)(+o de+ )a(da+ te6r,)o &T = A 0 . v 2 &T =1.9635 × 10 √ 2 ( 9.81 ) ( 0.1 ) −5
15
−5 m
&T =2.75029 × 10
3
s
e. 8a++ando e+ )oe,),ente de des)ar*a
ℜ=
√ 2 ( 981 ) ( 0.1 ) × 0.5 × 0.9988 1.1294 × 10
−2
ℜ= 6193.70 c =0.59 +
c =0.59 +
5.5
√ ℜ 5.5
√ 6193.70
c =0.5970
. 8a++ando e+ t,e3po de des)ar*a te6r,)o t =
2
( √ # − √ h )
c
A2 A1
√ 2. g
C!a-& * #*.+ 2
t = 0.5970 ×
( √ 0.1 )
0.007854
−5 √ 2 × 9.81
1.9635 × 10
t =95.6697 s
16
*. Datos te6r,)os oten,dos
*.+
*
T/'76& s E56'r/7'-4a " *
*.*;
+*.+**+
<.:
*.01*+
*.*
)+.210
+<.:<
+.::10
*.*1
02.+)<
01.*1
+.+))<
*.*) *
2).;;1< <2.<:
1<.0; <*.20
0.2*1< 2.+0<:
A"4!ra 7
T'?r/&
D/H'r'-/a 4'&. K '56. *.****
comparacion de datos 120 100 80 tiempo (s)
60 40 20 0
0
0.02
0.04
0.06
0.08
altura (h)
da tos teoricos
da tos experime ntales
. DISCUSI$N DE RESUTADOS
17
0.1
0.12
•
E" 4/'76& ' a/a& '" 4a-!' s' a"!"? ' 7a-'ra r'a" <*.20 s 4'?r/a <2.<: s. E5/s4/'-& !-a /H'r'-/a ' 2.+0<:s, '-4r' "&s r's!"4a&s 4'?r/&s '56'r/7'-4a"'s, 's4& s' '=' a !' '- '" 4'?r/& s' 4ra=aa &- !&'H//'-4' ' 'sara as/ /'a" c =0.5970 , a !' '" &'H//'-4' '
•
'sara 6ara &r/H//&s /r!"ar's 's ' *. La '!a/?- A"4s!" 's 6ara R' ra-'s, 's 6ar4/!"ar7'-4' a'!aa 6ara R'+*1, 6'r& !' 4a7=/J- r's!"4a !-a a6r&5/7a/?- a'!aa 6ara R' 7'-&r's
. CONCUSIONES E" 4/'76& ' a/a& '" 4a-!' 4'?r/& 's <2.<: s'!-&s '" r'a" 's ' <*.20 s'!-&s &- !-a /H'r'-/a ' 2.+0<: s'!-&s E" &'H//'-4' ' 'sara r'a" 's /!a" c =0.5970 Hr'-4' a" a"&r 4'?r/& ' *. 4'?r/&. La '"&/a ' 'sara 4'?r/a, 's 7a&r a "a '"&/a ' 'sara r'a" '=/& a !-a &-s4a-4' ' 'sara !' 6'r7/4' !' Hr//&-' '" a!a 6&r '" &r/H//&.
. RECOMENDACIONES E" '!/6& '=' 's4ar '- !- "!ar H/& &"&a& a'!aa7'-4' ' 7a-'ra !' -& a/4' !ra-4' "a &rr/a '" '56'r/7'-4&. E" 4a-!' '=' 4'-'r !-a 'sa"a ' 7'/a ' "as a"4!ras '" H"!/&.. S' '=' 4'-'r 7!& !/a& a" 7&7'-4& ' "as &rr/as 6ara r'/s4rar "&s a4&s ' 4/'76&s a"4!ras.
18
1F.BIBIOGRA"!A Himmelblau, D. . !1976". “Análisis y Simulación de procesos”. #spa$a% &e'erte (.). Hunter *. +illiam, . H. !2004". “Estadística para investigadores,Introducción al diseño de experimentos análisis de datos y construcción de modelos. #spa$a% &e'erte (.). -e'ers, -. d. !2006". !ecanica de "luidos para Ingenieros #uimicos. exico% /ontiental.
19
11. ANE
0?>h5(c A_95A_- >(9g'& disp(['_______________________________________'& disp(['_______________________________________'& i*-. A-*(pi;D<95:. disp(['_______________________________________'& disp(['area del espe@o de agua'& disp([A-& disp(['_______________________________________'& A9*(pi;d<95:. disp(['_______________________________________'& disp(['area del orificio'& disp([A9& disp(['_______________________________________'& 2e*(sqrt(9;g;-++;0;-++;d;-++;p5u. disp(['_______________________________________'& disp(['numero de reynolds'& disp([2e& c*+/3(+//5sqrt(2e. disp(['_______________________________________'& disp(['coeficiente de descarga'& disp([c& disp(['_______________________________________'&
fprintf('n altura(h tiempo(! Bn' fprintf('i :7f :7f Bn',i?-,+,+ for h*+++90 t*(9;(sqrt(0?sqrt(h5(c;(A95A-;sqrt(9;g. fprintf('i ::f ::f Bn',i,h,t i*i-. end end
EJECUCI$N DE PROGRAMA )/)D D# )-#( siendo los datos iniciales inresa el diametro del tanue0.1 inrese el diametro del ori:cio0.005 inresa la altura del ;uido0.1 inresa la ra'edad9.81 inrese la temperatura del ;uido16 inrese la 'iscosidad a la temperatura deteminada0.011294 inrese la densidad a la temperatura determinada0.9988 (#-D <) #/)/- H)<<)D) t2!=H>=?"@!c )2@)1 =!2.""" area del espeAo de aua
0.0079 area del ori:cio 1.9635e>05 numero de reBnolds 6.1937eC03 coe:ciente de descara 0.5970 n
altura!?"
tiempo!"
0
0.000000
0.000000
1
0.0000
95.6697
2
0.0200
52.8849
3
0.0400
35.1629
4
0.0600
5 6
0.0800 0.1000
21.5643 10.1001 0.0000
