UNIVERSIDAD NACIONAL DE INGENIERÍA FACULTAD DE INGENIERÍA CIVIL
LABORATORIO N°2
CINE CI NEMA MAT TIC ICA: A: VIS VISUA UALI LIZA ZACI CI N DE FLU FLUJO JOS S
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[1]
CINEMATICA VISUALIZACIÓN DE FLUJOS MECANICA DE FLUIDOS I HH223-G INTEGRANTES o o o
UIS!E TINTA TINTA" "A# M$%&'( E)$*+, SILVA SILV A MACHUCA MACHUCA## C/$*0$& C/$*0$&, , E)/ TA!IA VA VASUEZ# SUEZ# J$4 J+5&,
INSTRUCTOR o
I,78 R+7/ H$)&(7+
FECHA DE LA E9!ERIENCIA o
L,* 1; ) &4+ )( 21;
21.2 2F 21.22F 21..G 21. .G 2131.6E 2131 .6E
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[2]
RESUMEN_________________________________________________________________3 INTRODUCCIÓN____________________________________________________________3 OBJETIVOS________________________________________________________________3 TITULO 1 Teoría____________________ Teoría____________________________________ _________________________________ _________________________4 ________4 TITULO 2 Descripci! " Ma#eria$es_________________ Ma#eria$es___________________________________ ____________________________% __________% TITULO 3 &roce'i(ie!#o 'e $as E)perie!cias___________________________________11 TITULO 4 C*es#io!ario_____________________________ C*es#io!ario______________________________________________________12 _________________________12 TITULO + CONCLUSIONES__________________________________________________21 Bi,$io-ra.ía______________________ Bi,$io-ra.ía______________________________________ ______________________________ __________________________22 ____________22
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[3]
RESUMEN E( &/+* ) &,/& ?$*&( (+* 0$<+* ) @(%+* =*$+* @(%+ (&$,&/# @(%+ @,0 *$)/+# @(%+ 0/=(,0+# @(%+ *0&$+,&/$+# 08 , (+* )$@/,0* $<+* ) (&=+/&0+/$+8 L& , (& *& ) @(%+ (&$,&/# , ( &( * / , (& *& ) S0+*# , ( &( * / , (& ?& ) R4,+()*# ( &( ,+* </$0 +=*/?&/ (+* @(%+* 0/=(,0+*# @(%+* ) 0/&,*$$, 4 @(%+ (&$,&/# ( &$,&/# +, &4)& ) (& @(+/*',&# )<,)$,)+ )( &)&( *$,$*0/&)+8
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[.]
INTRODUCCIÓN E( *0)$+ ) (+* @(%+* * ) <&/0$(&/ $<+/0&,$& <&/& (+* $,7,$/+*# )=$)+ & , &)&)+ &,($*$* ) ((+# </$0 ( )$*+ ) *0/0/&* * &), &( <&*+ )( @(%+ 4 (& )<+*$$, ) *)$,0+*8 !&/& <+)/ /&($>&/ , &,($*$* ) *0+* @(%+* * 0$, +,*$)/&/ @(%+* +, ,K/+* ) R4,+()* &(0+* &4+/* & 1# (+* &(* * &)&, * & (+* &, </$0$/, (& )*/$<$, ) (+* @(%+* , )$*0$,0&* +,)$$+,*8
OBJETIVOS EXPERIENCIA I MESA DE FLUJO LAMINAR •
•
O=*/?&/ 4 )*/$=$/ ( +<+/0&$,0+ </$,0&( ) , @(%+ </&,,0 & 0/&?* ) (& 0/&40+/$& *$7 ( +(+/&,0 F(+/*',& O=*/?&/ 4 )*/$=$/ (& *</<+*$$, ) , @(%+ </&,,0 +, , @(%+ @,0 + , @(%+ *$)/+# +=*/?&,)+ (& 0/&40+/$& )( +(+/&,08
EXPERIENCIA II MESA DE ANALOGÍAS DE STOKES •
O=*/?&/ 4 )*/$=$/ (+* @(%+* *
EXPERIENCIA III CUBA DE REYNOLDS •
C(&*$@$&/ ( @(%+ *7K, ( ,K/+ ) R4,+()* 4 /(&$+,&/(&* +, (& +=*/?&$, ) (& </$,$&8
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[]
TITULO 1 T+/'& T+/'& DESCRIPCIÓN DEL MOVIMIENTO DE LOS FLUIDOS E, , @(%+ )&)+# (& )0/$,&$ )0/$,&$, , </$,0&( </$,0&( + 0/$& 0/$& ) (&* &/ (+*
Método de!"#$t#%o e&'e"#()o A#0 <#4#>#0 )( @(%+# 4 ,+ (+* &=$+* ) , ) &=$+ ) (& ?(+$)&) ∂ V / ∂ x # ∂ V / ∂ y 4 ∂ V / ∂ z & )$)& (&* <&/0'(&* <&*&, <+/ ( <,0+# 4 <+)+* )0/$,&/ *$ (& ?(+$)&) *0 &=$&,)+ +, ( 0$<+ * * <,0+ , <&/0$(&/# *0+ * ∂ V / ∂ t # , *0& +,)$$, ) &,($*$*# , (&*
-
Método de!"#$t#%o '(*"()*#()o M4 & * )$ * , F(%+ E*0&=( + E*0&$+,&/$+8 E, *0 &*+ 0+)&* (&* &,0$)&)* ) @(%+ , , <,0+ )&)+ *+, $,)<,)$,0* )( 0$<+# * )$/: ∂ V ∂p ∂ ρ =0 = 0 =0 ∂ t ∂x ∂x
LINEAS DE TRAYECTORIA U,& 0/&40+/$& + *,)& * ( &$,+ *7$)+ <+/ ,& <&/0'(& ) @($)+ , +?$$,0+8 !&/& 5&/ ?$*$=( ,& 0/&40+/$&# * <+)/'& $),0$@$&/ ,& <&/0'(& ) @($)+ , , $,*0&,0 )&)+# <+/ %<(+# *&,)+ 0$,0&# 4 0+&/ ,0+,* ,0+,* ,& @+0+7/&@'& @+0+7/&@'& ) (&/7& <+*$$, <+*$$, ) , +?$$,0+ *=*$7$,0 *=*$7$,088 L& (',& 0/&>&)& &*' <+/ (& <&/0'(& * ,& 0/&40+/$&8
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[;]
LINEAS DE TRAZA S ),+$,& (',& ) 0/&>& &( (7&/ 7+0/$+ ) (&* <&/0'(&* , $,*0&,0* **$?+* <&*&/+, <+/ , <,0+ )&)+8 S &/0/ * 0&=$, @,)&,0&(,0 </$,0&( 4 , (& & )=+*
Re$"ee)t(!#-) e$(!#(' ./0 ,1 de &) !(2$o de %e'o!#d(de , de ('*&)( '+)e( de 3'&4o 4&)to !o) %("#(
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[6]
L+)e( de !o""#e)te
E, , @(%+ </&,,0# (& ?(+$)&) , &)& <,0+ , ( &<+ ) @(%+ </&,/ +,*0&,0 +, ( 0$<+ 4# +,*,0,0# (&* (',&* ) +//$,0 ,+ ?&/'&, ) , $,*0&,0 & +0/+8 E*0+ $<($& ,& <&/0'(& (+&($>&)& *+=/ ,& (',& ) +//$,0 )&)& </&,/ *+=/ (& $*& (',& ) +//$,08 A)*# <&/0'(&* +,*0$?&* <&*&,)+ <+/ , <,0+ @$%+ , ( *<&$+ *0&/, *+=/ (& $*& (',& ) +//$,0 4 </&,/, *+=/ *0& (',& *=*,0,08 A*'# A*'# , , @(%+ </&,,0# (&* 0/&40+/$&*# (&* (',&* ) $*$, 4 (&* (',&* ) +//$,0 *+, (',&* $),0$&* , ( &<+ /@(%+8 L& @+/& ) (&* (',&* ) +//$,0 <) ?&/$&/ ) , $,*0&,0 & +0/+ *$ ( @(%+ * ,+ </&,,08 E, *0 &*+# (&* 0/&40+/$&*# (&* (',&* ) $*$, 4 (&* (',&* ) +//$,0 ,+ +$,$),8
TUBO DE CORRIENTE U, 0=+ ) @(%+ + ) +//$,0 *0 @+/&)+ <+/ , 5&> ) (',&* ) @(%+8 C++ (&* (',&* ) @(%+ *+, 0&,7,0* &( ?0+/ ?(+$)&) , &)& <,0+# (&* (',&* ) @(%+ ,+ &0/&?$*&, (&* <&/)* )( 0=+ ) @(%+8 E*0+ * &*' <+/ (&* <&/)* *0, & * ?> @+/&)&* <+/ (',&* ) @(%+ 4 *$ (&* &0/&?*&/&, )+* (',&* ) @(%+ * +/0&/'&,# *0&,)+ (& ?(+$)&) $,)0/$,&)& , ( <,0+ ) +/08 !+/ 0&,0+# & <*&/ ) *0&/ ($$0&)+ <+/ (& *</@$$ @$0$$& ,?(? ( 5&> ) (',&* ) @(%+# *0 * +<+/0& & 0+)+* (+* @0+* ++ ,& *</@$$ $</&=(
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[] -
-
-
-
-
F'&4o &)+0 7#0 t"#d#2e)#o)(' t"#d#2e)#o)(' E( @(%+ * (&*$@$& ++ ,$# =$ 4 0/$)$,*$+,&( )<,)$,)+ )( ,K/+ ) ++/),&)&* *<&$&(* //$)&* <&/& )*/$=$/ ( &<+ ) ?(+$)&)8 E( &<+ ) ?(+$)&) <) */ ,& @,$, ) 0/* ++/),&)&* *<&$&(* 4 )( 0$<+8 D$5+ &<+ ) @(%+ * ),+$,& 0/$)$,*$+,&( 0&=$, * ,+ </&,,0 + 0/&,*$0+/$+ 4& (& ?(+$)&) , &($/ <,0+ )( &<+ ) @(%+ )<,) ) (&* 0/* ++/),&)&* *<&$&(* //$)&* <&/& (+&($>&/ ( <,0+ , ( *<&$+8 N+ 0+)+* (+* &<+* ) @(%+ *+, 0/$)$,*$+,&(*8 !+/ %<(+# ( @(%+ </&,,0 & 0/&?* ) ,& 0=/'& /0& ) *$, 0/&,*?/*&( ,$@+/8 F'&4o %#!oo , )o %#!oo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[] E*0 E*0 * , $,*0 $,*0/ / ,0 ,0+ + </ </$0$0 *$ *$(& (&// @, @,, ,+* +* 4 )$@ )$@/ /,0 ,0* * +,) +,)$ $$+, $+,* * , +)( +)(+* +* =$)$,*$+,&(* , <& *&(&# +@/ ,& /+,& ) &/7& ) &7& +, ,& ?(+$)&) (+ *@$$,0,0 =&%&# <&/& (&* @/>&* ) $,/$& *&, )*+,& ) &/7&8 L& 0$,0& *0 +,0,$)& , , /$<$,0 0/&,*<&/,0 <&/& ( +,0/+( ) * +,0,$)+8
Me( de 3'&4o '(2#)("
V9'%&'( de' 3'&4o 3&e)te
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[1] S *&/& ++ *$,$*0/+ ) &7& ,& @,0 )+*0$&8
DESCRIPCIÓN •
•
•
•
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
MATERIALES •
•
•
•
•
•
C+,*0/$)+ ',07/&,0 , <($7(*# &($)&) /$*0&( /+ ) 13 ) *<*+/ ,$)+ +, <7&,0+ 4 0+/,$((+* (+* 5&, 5 &, /*$*0,0 & (+* $<&0+* 4 +, 7&/,$$+,* 7 &/,$$+,* ) =/+,* /+&)+*8 T$, $,+/<+/&)+ ,& &,0$)&) &&)+/ ) @(%+8 E*0 $<&)+ +, ,& ?(?(& *@/$& ) 3P <&/& ( *$,$*0/+ ) &7& ) (& @,0 0/,& 4 )+* ?(?(&* *@/$&* ) 12P <&/& ( )*&7Q8 E*0 $<&)+ +, ,& &/& ) *&($)& <&/& /+7/ ( &7& *&( ) (& *& <&/& * ?&&$,8 L& *& 0$, 16 ) &(0/&# .. ) &,5+ 4 11 ) (&/7+ ( *<*+/ ) (&* <(&,5&* * ) 13 4
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[11]
Pe"3#'e
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[12]
L& =& 0$, (&* *$7$,0* )$,*$+,*:
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[13]
TITULO 3 !/+)$$,0+ ) (&* E</$,$&* EXPERIENCIA I MESA DE FLUJO LAMINAR 18 S *$,$*0/ *$,$*0/& & &7&# &=/$,)+ &=/$,)+ (& ?(?(& ?(?(&## ( &( @(4 @(4 , )$+ ) ) (&* <(&&* <(&&* ) ?$)/$+ ?$)/$+ )=$)+ &( )*,$?( 5&4 ,0/ ( &($,0&)+/ ) &/7& 4 ( ?/0)/+8 28 S &=/, (& (& ?(?(& ?(?(& ) (& @(+/*', @(+/*',&# &# ( &( *$7 *$7 ,& 0/&40 0/&40+/$& +/$& /0& /0& 0/$& 0/$&88 38 S &=/ (& </$((& </$((& N° 1 <&/& <&/& &0 &0 ++ @,0# @,0# 4 * * +=*/?& +=*/?& (& *</<+*$ *</<+*$$, $, ) , @(%+ @(%+ </&,,0 4 , @(%+ @,08 .8 S &=/ (& </$((& </$((& N° 1 <&/& <&/& &0 &0 ++ *$)/ *$)/+# +# 4 * +=*/?& +=*/?& (& *</<+*$ *</<+*$$, $, ) , @(%+ @(%+ </&,,0 4 , @(%+ *$)/+8 8 S &=/ (& </$((& </$((& N° 1 4 N° ; ++ ++ @,0 @,0 4 *$)/+ *$)/+ /*<0$? /*<0$?&,0 &,0 <&/& +=*/?&/ +=*/?&/ (& @+/&$, )( +?&(+ ) R&,$,8
EXPERIENCIA II MESA DE ANALOGÍAS DE STOKES 18A,0* ) +,>&/ +, (& ?$*&($>&$, ) (& </$,$& * /&($>& , /+,+$$,0+ ) $<+8 28S ,$?(& ( $<+ ) 0&( &,/& &(( , )*,$?( ,0/ ( &($,0&)+/ 4 ( ?/0)/+8 38S +(+& (+* 7/,(+* ) </&,7&,&0+ ) <+0&*$+ &( +$,>+ ) (& <(&& ) ?$)/$+# <&/& <+)/ ?$*&($>&/ (&* (',&* ) +//$,0*# 4 * &=/ ( *$,$*0/+ ) &7&8 & 7&8 .8S ,0& +, , +,%,0+ ) </@$(* (+* &(* * $/, +(+&,)+ , (& <(&& ) ?$)/$+# $,0//<$,)+ ( @(%+ ,$@+/# 4 * &/ 4 /&($>&/ (&* )*/$<$+,* ) */$<$+,* +//*<+,)$,0*8 8S
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[1.]
E( <&*+ &,0/$+/ * /<$0$ <&/& ( @(%+ 0/&,*$$+,&(# 4 <&/& ( ( 0/=(,0+ * 0+ )$)&*8
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[1]
TITULO . C*0$+,&/$+ CUESTIONARIO N<= MESA LAMINAR =6 De3#)( De3#)( 'o !o)!e$to !o)!e$to te-"#!o te-"#!o , e' $"o!ed#2#e) $"o!ed#2#e)to to ( e*&#" $("( o7te)e" o7te)e" 'o 'o #*&#e)te #*&#e)te 3'&4o0 3'&4o0 (de29 de *"(3#!("'o (1 F'&4 F'&4o o &)#3 &)#3o" o"2e 2e E*0 0$<+ ) @(%+ * &/&0/$>& <+/ &($/ &7,$0) * &,&($# </&, $,?&/$&,0 , 0+)&* (&* *$+,* )( &,&(8
O7te)!#-)> C++ ( @(%+ * ,$@+/ ,0+,* V 0# *&0$*@& (&* +,)$$+,* ) $//+0&$+,&($)&) 4 ++ ( @(%+ * ,$)$/$+,&( , ( % +=0,+*: ∂Φ ∂Φ =V , = 0 ∂x ∂y
D+,): ψ = funcion funcionde decorr corrien iente te Φ =funcion potencial
∂ ψ ∂ψ ∂ ψ =V , = 0 ∂y ∂x
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[1;]
F'&4o &)#3o"2e #)!'#)(do
71 F'&4o F'&4o F&e)te F&e)te ? S&2# S&2#de" de"o o E* , @(%+ * <&,) + * +,0/& ) , <,0+ & 0+)&* (&* )$/$+,* ) @+/& /&)$&( <+/ ,) (
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[16]
L+)e( de !o""#e)te L#)e( e@&#$ote)!#('e
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[1] 2 ay
−1
θ− m ( θ1 −θ2 )=¿ u0 y − m tan
2
x + y
2
−a
2
u0 r sin ¿
CUESTIONARIO N > MESA MES A DE ANALOGÍAS ANALOGÍAS DE STOKES 28 C+, /*<0+ & (& M*& ) A,&(+7'&* ) S0+*# )*/$=& *$ * <+*$=( /&($>&/ (+* *$ 7$,0* </$,0+* 4 )0&(( (
(1 V#&('#5 V#&('#5(!#-) (!#-) , !&()t#3# !&()t#3#!(!#!(!#-) ) de F'&4o F'&4o Pe"2() Pe"2()e)te6 e)te6 L& +=*/?&$, ) (& </$,$& *$, *&/ (+* </@$(* 4 *$, ?&/$&/ ( &)&( )( *$,$*0/+ *0/& , @(%+ </&,,0# 4& (&* +,)$$+,* ) ?(+$)&) ,+ ?&/'&, +, ( 0$<+ 4# *$ (+ 5&,# (&* ?&/$&$+,* *+, 0&, <&* +, /*<0+ & (+* ?&(+/* )$+*8 71 V#&('#5 V#&('#5(!#-) (!#-) , !o2$o"t(2# !o2$o"t(2#e)to e)to de '( '+)e( '+)e( de !o""#e)te !o""#e)te ('"ededo" ('"ededo" de $e"3#'e $e"3#'e o !&e"$o
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[1]
CUESTIONARIO N< > MESA MES A LAMINAR LAMINAR Y MESA DE ANALOGIAS DE STOKES =6 E $o#7'e $o#7'e ($"e!#(" ($"e!#(" e' !o)o!#2#e !o)o!#2#e)to )to de '( '+)e( '+)e( de 3'&4o &)#3o"2 &)#3o"2e e ('"ededo" ('"ededo" de &) !&e"$o !&e"$o ;#d"od#)92#!o $o" 2ed#o de '( 2e( '(2#)(" R$t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[2]
L+)e( de !o""#e)te #2$e"2e(7'e
6 E $o#7'e $o#7'e o7e"%(" o7e"%(" 'o 3'&4o 3'&4o 79#!o 79#!o e) '(7o"(to"# '(7o"(to"#o o E'(7o"e E'(7o"e &) !&(d"o !&(d"o !o) 'o 3'&4o 3'&4o
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[21] , 7,/&(8 E*0& /7$, )( @(%+ /$= ( ,+=/ ) .$*/o 'e #ra!sici! , 4 , ((& ( @(%+ &=$& ) (&$,&/ & 0/=(,0+8
6 N2e"o de Re,)o'd !"+t#!o0 Re,)o'd !"#t#!o &$e"#o" , Re,)o'd !"#t#!o #)3e"#o" !&/& &<($&$+,*
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[22]
0$*/o La(i!ar S +=*/? * @+/&=& ,& (',& ) +(+/&,0 +(+/&,0 )(7&)& 4 =$, )@$,$)&8 " * +=0?+ ,K/+ ) R4,+()* ,+/* 238
T#e2$o
A*&(
.2L1 $.2L1 D .221
.!St1
Re
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[23]
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[2.]
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[2]
TITULO CONCLUSIONES =6 MESA MESA DE FLU FLUJO JO LAMI LAMINA NAR> R> -
L&* L&* &
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