TALLER TALLER INFORME DE MECANICA DE FLUIDOS FLUIDOS
EVELYN EVELYN DARIANA ARDILA SANABRIA;201420004
UNIVERSIDAD PEDAGOGICA Y TECNOLOGICA DE COLOMBIA FACULTAD DE INGENIERIA ESCUELA DE INGENIERIA ING ENIERIA AMBIENTAL AMBIENTAL TUNJA 2016 TALLER TALLER INFORME DE MECANICA DE FLUIDOS FLUIDOS
. Prese!"#$ %$r EVELYN EVELYN DARIANA ARDILA SANABRIA;201420004
Prese!"#$ "& ING. ANDRES JULIAN DIA' MORENO
Fe()" #e e!re*"&10+12+16
UNIVERSIDAD PEDAGOGICA Y TECNOLOGICA DE COLOMBIA FACULTAD DE INGENIERIA ESCUELA DE INGENIERIA ING ENIERIA AMBIENTAL AMBIENTAL TUNJA 2016 C$!e,#$ 2. INTRODUCCIÓN
5
3. OBJETIVOS
6
4. MARCO TEÓRICO
7
5. TALLER
13
6. ANÁLISIS Y DISCUSIÓN
24
1. GLO GLOSARI SARIO O CAUDAL& es -" ("!,#"# #e /,#$ /e (,r(/-" " !r"s #e /" se((,3 #e#/(!$ !/5er"7 ("8er"7 $-e$#/(!$7 r$7 (""-7...9 %$r /,#"# #e !,e:%$.
N$r:"-:e!e se ,#e!,(" ($ e- /<$ $-/:!r,($ $ $-/:!r,($ $ $-/:e /e %"s" %$r / =re" #"#" e -" /,#"# #e !,e:%$. Me$s >re(/e!e:e!e7 se ,#e!,(" ($ e- /<$ :=s,($ $ :"s" /e %"s" %$r / =re" #"#" e -" /,#"# #e !,e:%$. FLUJO MASICO& C"!,#"# #e :"!er,"- e?%res"#$ e /,#"#es #e $-/:e7 /e "!r",es" /" se((,3 !r"sers"- #e =re" e / #/(!$ %$r /,#"# #e !,e:%$ e
2. INTR INTRODUC ODUCCI@N CI@N E -" #,=:,(" #e /,#$s se %/e#e /s"r s,s!e:"s e #$#e -" %$s,(,3 -" >$r:" %/e#e (":5,"r " :e#,#" /e !r"s(/rre e- !,e:%$ e / %r$(es$. E -" ,#" re"- se /!,-," :"$r:e!e $-:ees /e s$ <$s e ,#e>$r:"5-es e #$#e -" :"s" %/e#e e!r"r s"-,r #e s/s >r$!er"s
-$ (/"- se ($$(e ($:$ $-/:e #e ($!r$- es :/()$ :=s ($e,e!e %"r" %"r" !r"5 !r"5"< "<"r "r.. P$r -$ !"! !"!$7 $7 res/es/-!" !" :/ :/ !,!,- %$#e %$#err re-"( e-"(,$ ,$" "rr -"s -"s "r,"(,$es #e- s,s!e:" ($ -$s (":5,$s e -$s $-:ees #e ($!r$-. Es,*/,e!e ,>$r:e ($!,ee /" 5ree ,!r$#/((,3 "- -e(!$r "(er(" #e!e:" e #$#e se :/es!r" "-*/"s >3r:/-"s %r$(e#,:,e!$s7 "//e e- e>$/e %r,(,%"- #e- ,>$r:e es -" res$-/(,3 #e "-*/$s e
. OBJ OBJETI ETIVO VOS S • • •
Res$-er "-*/$s e
4. MAR MARCO CO TE@RICO TE@RICO TEOREMA DE TRANSPORTE TRANSPORTE DE REYNOLDS1 P"r" #e#/(,r e- !e$re:" #e :"er" :=s se(,--" se )"r= /s$ #e- Te$re:" Te$re:" #e Le,5,!7 e -" ers,3 /,#,:es,$"- #e es!e !e$re:" se %er:,!e #er," #er,"rr /" ,!e*r" ,!e*r"-- (/$s (/$s -:,! -:,!es es #e ,!e*r" ,!e*r"(,3 (,3 s$ >/(,$ >/(,$es es /e 1 CENGEL7 Y//s CIMBALA7J)$. MECANICA DE FLUIDOS FUNDAMENTOS Y APLICACIONES. APLICACIONES. E5$$s "("#:,($s.
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POTENCIA IDRAULICA2 Es :/ )"5,!/"- e e- !r"s%$r!e #e /,#$s /!,-,"r e-e:e!$s :e(=,($s /e "%$r!" eer*" %res,3 "- :,s:$ %"r" >"$re(er $ ,(-/s$ %$s,5,-,!"r s/ :$,:,e!$ !r"s%$r!e. Es!$s e-e:e!$s re(,5e e$:5re #e 5$:5"s ),#r=/-,("s. U$ #e -$s %"r=:e!r$s :=s ,:%$r!"!es #e es!$s :e(",s:$s es -$ /e --":"re:$s %$!e(," ),#r=/-,(". L" %$!e(," P9 #e /" 5$:5" ),#r=/-,(" es -" re-"(,3 e!re -" eer*" #e /<$ %r$%$r(,$"#" %$r -" 5$:5" e- !,e:%$ /e -" :,s:" )" es!"#$ e >/(,$":,e!$ %"r" ($:/,("r #,()" eer*". ee r*". N$r:"-:e!e es!" :"*,!/# se s/e-e e?%res"r ($:$ e- %r$#/(!$ #e -" %res,3 #e- /,#$ %$r s/ ("/#"-&
E !$#"s -"s ,s!"-"(,$es s,e:%re se %r$#/(e %r#,#"s7 %$r -$ /e s,e:%re -" %$!e(," #e -" 5$:5" ),#r=/-,(" #e5e ser :"$r /e -" %$!e(," !e3r,(" %re,s!". Se #ee "s e- re#,:,e!$7 ($:$ e- ($(,e!e e!re -" %$!e(," !,e(es"r," -" %$!e(," ($s/:,#" %$r -" 5$:5". Es!e "-$r s,e:%re ser= :e$r /e -" /,#"#. 2 )!!%&++e
#/("!,".("!e#/.es+44K0016+"/-"+"r(),$s+re%$s,!$r,$+4K0+41+)!:-+ 2%$!e(,"),#r/-,(".)!:-
A es!" %$!e(," ($s/:,#" )"5r= /e s/:"r -" %r#,#" #e %$!e(," ("-(/-"#" e e- "%"!"#$ "!er,$r7 %$r -$ !"!$&
L"s e?%res,$es /e )e:$s $5!e,#$ s$ =-,#"s %"r" ($#/((,$es re(!,-e"s $ ($ / *r" "r($ #e (/r"!/r". C/"#$ e -"s !/5er"s )" ($#$s7 r"($res7 $ (/"-/,er $!r$ !,%$ #e $5s!=(/-$7 e- >"5r,("!e %r$%$r(,$" /"s !"5-"s e -"s /e se ,#,(" /" -$*,!/# e/,"-e!e " e:%-e"r e ("s$ #e (=-(/-$7 es!" -$*,!/# ser" -" e/,"-e!e " /" !/5er" re(!,-e" /e %r$#/
. TALLE ALLER R 19P$r / ($#/(!$ /e ",re; e s/ se((,3 A e- #,=:e!r$ es #e 100 ::7 -" !e:%er"!/r" 1C7 -" %res,3 *+(:2 -" e-$(,#"# 2 :+s. E -" se((,3 B e- #,=:e!r$ es #e 200 ::7 -" !e:%er"!/r" C -" %res,3 17 *+(:2. Se %,#e&
"9 Ve-$(,#"# e-$(,#"# e -" se((,3 se((,3 B. Se !,ee /e; Q ₁=Q ₂ Q= v . A
V ₁ A 1=V ₂ A ₂
Des%e<"#$ $5!ee:$s V ₁ A 1 A ₂
=V ₂
E- =re" #e -" se((,3 A 19 1=¿ 100 mm ∅¿
1m
1=¿ 100 mm mm∙∙
1000 mm
=0.1 m
∅¿
A 1= π ∙
A 1= π ∙
∅
2
4
0.1 m
2
4
A 1=0.00785 m
2
E- =re" #e -" se((,3 B 29& ₂
=¿ 200 mm ∅¿
₂
=¿ 200 mm∙
1m 1000 mm ∅¿
A = π ∙
∅
₂
A ₂= π ∙
2
4
0.2 m
2
4
A ₂= 0.0314 m
2
Ree:%-""#$ e
=0.2 m
V ₁ A 1 A ₂
=V ₂
O5!ee:$s 25 m / s∗0.00785 m ² 0.0314 m ²
=V ₂
2
V =6.25 m / s
59 C"/# C"/#""- e e %es$ %es$.. Q=V ∗ A
Q ₁ =Q ₂ Q=6.25 m / s∗ 0.0314 m ² 3
Q=0.1963 m / s
C"/#"- e %es$ ,*/"- " 3
Qp=0.1963
m ∗3600 s s ∗1 Kg 1h 1000 m ³
Qp=0.701 Kg / h
D"!$& C$s!"!e /,ers"- #e- ",re 2K714 :.N+* Q.
2. L" 5,>/r("(,3 :$s!r"#" e -" */r" (,r(/-" "*/" " 20 C r 1000 *+:9. E- /<$ e %es$ e!r"!e9 e -" se((,3 1 es #e 00 N+s7 -" e-$(,#"# e -" se((,3 es #e :+s.
C"-(/-"r& "9 Ve-$(,#"# e-$(,#"# e -" se((,3 se((,3 1.
E- /<$ :=s,($ se )"--" " %"r!,r #e -" s,*/,e!e e(/"(,3& ρ ∙V = ρ∙ ρ ∙ A ∙ v = ṁ
Te,e#$ Te,e#$ e (/e!" /e& •
•
•
•
•
ρ= densidad
V = flujo volumetrico volumetrico A = area area de lasección lasección v =veloci velocidad dad de la secció sección n ṁ= flujomasico
A %"r!,r #e -$s #"!$s s/:,,s!r"#$s !ee:$s e- /<$ :=s,($ #e -" se((,3 /$ 197 -" #es,#"# #e- /,#$ "*/"9 " %"r!,r #e- #,=:e!r$ se %/e#e ("-(/-"r ("-(/-"r e- =re"; !e,e#$ !e,e#$ ($ es!$ %$s,5-e #es%e<"r -" e-$(,#"# %"r" -" se((,3 /$ 19. ṁ
v= ρ ∙ A
C"-(/-$ #e- =re" %"r" -" se((,3 /$ 19& 1=¿ 450 mm ∅¿
A 1= π ∙
∅
2
4
1=¿ 450 mm∙
1m 1000 mm ∅¿
A 1= π ∙
0.45 m 4
2
= 0.45 m
A 1=0.15904312 m
2
E- /<$ :=s,($ se ($,er!e " /,#"#es #e *+s& ṁ =5300
N 1 kg ∙ s 9.8 N
ṁ =540.816
kg s
Ree:%-""#$ 540.816
v 1=
ṁ
ρ ∙ A
= 1000
kg 3
m
kg s
∙ 0.1590 4312 m2
v 1=3.400 m / s
59 F-/<$ :=s,($ s"-,e!e e -" se((,3 .
3= ¿ 200 mm mm∙∙
1m 1000 mm
∅¿
3= ¿ 0.2 m ∅¿
A 3= π ∙
A 3= π ∙
∅
3
4
0.2 m
2
4
0.0314 2 m A 3= 0.0314
2
A)$r" !ee:$s; A 3= 0.0314 m
v 3=
2
5m
s
Ree:%-""#$ e ṁ = ρ ∙ A ∙ v
ṁ 3=1000
kg m
2
∙ 0.03142 m ∙ 5
3
m s
ṁ 3=157.1 kg / s
C. Ve-$(,#"# e-$(,#"# e -" se((,3 se((,3 2.
P"r" #e!er:,"r es!" e-$(,#"# e(es,!":$s e- #"!$ #e- /<$ :=s,($ #e -" se((,3 #$s 297 /e se $5!,ee " %"r!,r #e ṁ 1=ṁ2+ ṁ3
Des%e<"#$& ṁ 2=ṁ1−ṁ3
Ree:%-""#$ ṁ 2=540.816 kg / s −157.1 kg / s
ṁ 2=383.716 kg / s
re" se((,3 #$s 29 2=¿ 300 mm mm∙∙ ∅¿
∅2=0.3 m
1m 1000 mm
A 2= π ∙
A 2= π ∙
∅
3
4
0.3 m
2
4
A 2=0.071 m
2
Ree:%-""#$ e v 2=
ṁ
ρ ∙ A
383.716
v 2= 1000
kg 3
m
kg s
∙ 0.071 m 2
v 2=5.404 m / s
. E- ()$rr$ #e "*/" /e s"-e %$r /" !$5er" es #e 10 :: #e #,=:e!r$ ()$(" ($!r" /" s/%er(,e se:,es>r,(". "--e -" >/er" /e )" /e re"-,"r %"r" /e -" s/%er(,e se:,es>r,(" $ s/>r" #es%-"":,e!$ "-*/$. A%-/e-$ %"r" e- ("s$ #e /e e- ("/#"- $-/:!r,($ e!r"!e se" #e 07001 :+s. C$:e!e -"s ),%3!es,s re"-,"#"s.
IPOTESIS& L" >/er" ($!r"r,$ $ >/er" /e se #e5e er,(" $ se #es%-"(e #e5e !eer -" :,s:" :"*,!/#7 %er$ e se!,#$ ($!r"r,$.
Te,e#$ Te,e#$ e (/e!" /e ∑ ! =
d ( m∗ v ) + ( v∗ ρ∗V ∗dA ) salida −( v∗ ρ∗V ∗ dA ) entrada dt
d ( m∗v ) =0 dt
D$#e v =Volumen ρ= "ensidad V = velocidad dA = #eccio #eccion n de area area
A*r/%"#$ !r:,$s se:e<"!es7 "- s/%$er /e -" e-$(,#"# #e e!r"#" #e s"-,#" s$ ,*/"-es7 $5!ee:$s ! =2∗ v∗ ρ∗Q
V ∗dA =Q
Y" Y" /e
E!$(es ree:%-""#$ "-$res !ee:$s /e ! =25.46 N
P$r !"!$7 ($:$ -" >/er" %"r" /e -" s/%er(,e se:,es>r,(" #e5e es!"r e se!,#$ ($!r"r,$ $5!ee:$s ! =−25.46 N
4. U 5$!e re/,ere 20 N #e e:%/
"9 C/=!$s C/=!$s :+s #e "*/" "*/" #e5e #e ser !$:"#$s !$:"#$s e?%/-s"# e?%/-s"#$s $s %$r / !/5$ #e 00 :: %"r" :"!eer ese :$,:,e!$ Pr,:er$ %"s":$s !$#$s -$s #"!$s " / :,s:$ s,s!e:" #e /,#"#es =20 kN =20 kN ∗1000=20000 N V =25 km / h
V =25
Km ∗1000 m h ∗1 h 1 Km 3600 s
V =6.94 m / s
P"r" #e!er:,"r e- ("/#"- %"s":$s e- #,=:e!r$ " =re"
∅¿ 500
mm
2
A = π ∙
∅¿ 500
∅
4
mm∙
A = π ∙
1m 1000 mm
0.5 m
=0.5 m
2
4
=0.196 m ²
C$ es!$ se %/e#e #e!er:,"r e- ("/#"Q=V ∗ A
Q =6.94 m / s∗0.196 m ²
3
Q=1.36 m / s
59 C/= C/=-- es e- re# re#,: ,:,e ,e! !$ $ !$!" !$!"-- #e#e- s,s! s,s!e: e:" " #e 5$:5 5$:5e$ e$ !,e !,ee e / re#,:,e!$ #e- 60 Te,e#$ Te,e#$ e (/e!" /e -" %$!e(," es ,*/"- " %res,3 %$r ("/#"-7 se %r$(e#e " )"--"r -" %res,3. $=Q∗ p p=
p=
A 20000 N 0.196 m ²
p=102040.81 N / m ²
3
$=1.36 m / s∗102040.81 N / m ² $=138923.89 Nm/ s
L" %$!e(," !,- es ,*/"- " $=138923.89
Nm ∗0.6 s
$=83354.34 Nm / s
N$!"& %"r" -" s$-/(,3 #e es!e %/!$ -$s es!/#,"!es #e5er= ,es!,*"r s$5re& %$!e(," !$!"-7 %$!e(," %er#,#" %$!e(," !,-.
6. AN ANLISIS LISIS Y DISCUSI@N DISCUSI@N E -" ,*e,er" ":5,e!"- -" :e(=,(" #e /,#$s se )" /e-!$ ese(,"%/es es!= ("#" e se ,$-/(r" :=s e -" ("-,#"# #e- "*/"7 -" e(/"(,3 #e ("!,#"# #e :$,:,e!$ se %/e#e "%-,("r e& E- se*/, se*/,:, :,e e!$ !$ #e --e --e"# "#$ $ "(, "(,"# "#$ $ #e !" !"/e /ess e %-" %-"!" !"ss #e !r"!":,e!$. E e- se*/ se*/,:, ,:,e! e!$ $ #e -" ("-, ("-,#"# #"# #e#e- "*/"7 "*/"7 %/es %/es s,e:% s,e:%re re /e /e e?,s!" e?,s!" /" #,>ere(," #e ($(e!r"(,3 #e #$s $ :=s s/s!"(,"s e /" :e(-" #e /,#$s s/(e#er= / !r"s%$r!e. E -$s -$s (""-es (""-es "5,e "5,er!$ r!$s7 s7 !":5, !":5, e !/5e !/5er" r"ss "-("! "-("!"r, "r,--" --"ss e -$s -$s /e se ,#e!,/e ,#e!,/e e- /<$ /e se :/ee e es" s/%er(,e s/%er(,e !$:"r :e#,#"s #e ($!r$- %"r" e,!"r /e es!$s se #e>$r:e. E -" ),#r ),#r$:e! $:e!r r"7 "7 %"r" %"r" e- #,se #,se8$ 8$ /s$ /s$ #e ,s! ,s!r/ r/:e :e! !$s $s %"r" %"r" -" :e#, e#,(,3 #e ("/#"-7 "-7 !e:% e:%er"!/ "!/r"7 ,e- !r"s%$ s%$r!e #e se#,:e!$s. E *eer"- -" e(/"(,3 #e ("!,#"# #e :$,:,e!$ e -" ,*e,er" ":5,e!"- se %/e#e "%-,("r %r,(,%"-:e!e e e- (":%$ #e -"s %-"!"s #e5,#$ " /e e e--"s se !r"5"<" ($ "*/"7 "#e:=s #e se#,:e!$s #e:= #e:=ss es!" es!" e(/" e(/"(, (,3 3 %er:, %er:,!e !e --e" --e"rr / ($! ($!r$ r$-- es!r es!r,( ,(!$ !$ #e -$s -$s %r$(es$s /e se es! --e"#$ " ("5$.
