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AÑODELADIVERSIFIC

ACIÓN

PRODUCTIVA

YDELFOR

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UNIVERSIDAD NACIONAL DE CAJAMARCA“ESCUELA ACADÉMICO PROFESIONAL DE INGENIERÍA DE MINAS”

I INTRODUCCION

Los sifons no!"#$s son %s#&os '#!# (!#ns'o!(#! #)%# '!o*nin( &

+#n#$s 'o! &,#-o & +#!!(!#s . */#s & (!n &,#-o & !/os . 0%,!#s1(+2 P#!# 0% %n# s(!%+(%!# & s( (i'o $$)% # s% f%n+ion#"in(o (in 0%3#,! %n# &if!n+i# & '!sions n(! $# n(!# 4P!si5n #("osf6!i+#7 . n$ in(!io! &$ +on&%+(o 4P!si5n +!o o '!58i"# # +!o72 Los s(%&ios+on5"i+os . $#s +onsi&!#+ions (o'o)!9fi+#s1 )o$5)i+#s 3i&!o$5)i+#s1&(!"in# $# f#+(i,i$i& & %s#! %no % o(!o (i'o & s(!%+(%!#2

Los sifons '%&n s! (#n &i"in%(os +o"o 'o"os i"#)in#! 3#s(#*!&!#s o,!#s in)ni!i$s1 si"'! 0% n $ +#so &$ #)%# $# #$(%!# n(!$# f%n( . $# '#!( "9s $*# &$ sif5n no s%'! $os &i: "(!os1 'o!0% $#'!si5n #("osf6!i+# no '%& "#n(n! $ 'so & %n# +o$%"n# & #)%# #

s# #$(%!#2

E$ '!sn( s(%&io (in 'o! o,-(o '!o'o!+ion#! #$ in)ni!o %n "6(o&o &+9$+%$o (5!i+o;8'!i"n(#$ '#!# &i"nsion#! %n sif5n si"'$1 &s(in#&o #*#+i#! %n !+i'in( & fo!"# +%#$0%i!# n %n (i"'o &(!"in#&o2

Es( (i'o & sifons s %(i$i:#n '#!# #++ion#! +o"'%!(#s #%(o"9(i+#s &&s+!is'#+i5n n ,o+#(o"#s & #$(# "on(#

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III ALCANCES

L# '!9+(i+# !#$i:# 'os )!#n i"'o!(#n+i#1 &,i&o # 0% nos si!*

+o"o ,#s '#!# $ #n9$isis +o"o %n# s(!%+(%!# 0% '!"i( '#s#! $

#)%# 'o! %n o,s(9+%$o2

A&"9s '#!# 0% noso(!os 'o"os n(n&! . 8'$i+#! $os

'!o+&i"in(os . !s%$(#&os & $os '#!9"(!os & &is

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Es(!%+(%!# 3i&!9%$i+# 0% '!"i( +on&%+i! %n $/0%i&o &s& %n ni*$ & +o(#(o'o)!9fi+# #$(# 3#s(# %n '%n(o "9s ,#-o= '!o #(!#*s#n&o '%n(os "9s #$(os0% $os &$ ni*$ & n(!#

Un sif5n s %n &is'osi(i*o 3i&!9%$i+o 0% s %(i$i:# '#!# (!#s*#s#! %n $/0%i&o

& %n !+i'in( # o(!o2 Consis( si"'$"n( n %n (%,o n fo!"# & Uin*!(i n $# 0% %n# & $#s !#"#s s "9s $#!)# 0% $# o(!#2 %!"os(!#s*#s#! #)%# n(! &os &'5si(os 4*#sos71 %no "9s #$(o 0% $ o(!o1 3#s(#0% s i)%#$n $os ni*$s & #)%#2 E$ '!o,$"# 0% s nos '!sn(# s 0%n+si(#"os 0% $ #)%# #s+in

En $# Fi)%!# #n(!io! s o,s!*# %n# (%,!/# 0% %n &os s(#n0%s. 0% 'o! #$)%n# !#:5n1 0%'o&!/# s! & (i'o (o'o)!9fi+o1

(in %n(!#"o #$(o0%0%so,! $# $/n#&

)!#&in(2 A s( sis("#3i&!9%$i+o s $ &no"in# sif5n2 H s $# +#!)#22L# $/n# & )!#&in( s(9 !'!sn(# #'!o8i"#"n( 'o! $# $/n# !+(#0% %n $#s s%'!fi+is $i,!s & $os s(#n0%s 4n !#$i& $# $/n# &)!#&in( no s !+(#1 '%s $# (%,!/# no $o s72 To&o $ (!#"o & $# (%,!/#0% s(9 so,! $# $/n# & )!#&in( (in '!si5n n)#(i*#2 En $os '%n(os &in(!s++i5n n(! $# $/n# & )!#&in( . $# (%,!/# $# '!si5n s +!o2

D, (n!s '!sn( 0% 3#,$#"os & '!sions !$#(i*#s2 Po! $o (#n(o“'!si5n +!o” si)nifi+# “'!si5n #("osf6!i+#” . “'!si5n n)#(i*#” si)nifi+#“'!si5n "no! 0% $# #("osf6!i+#”2

b. Concepto e !ifón no"#$%.

E$ sif5n no!"#$1 $$#"#&o si"'$"n( sif5n 'o! $# "#.o!/# & $os #%(o!s+on&%+ $ #)%# '#s#n&o so,! $ o,s(9+%$o 4+o"o s "%s(!# n $# fi)%!#7 .s% f%n+ion#"in(o s &, # $# '!si5n #("osf6!i+# 0% #+(@# n $# s%'!fi+i&$ #)%# # $# n(!#= '#!# ini+i#! s% f%n+ion#"in(o s n+s#!io '!o&%+i! $

*#+/o n $ in(!io! &$ +on&%+(o1 n(on+s $# &if!n+i# & '!si5n n(! $#

FUER>AS SO?RE SUPERFICIES SUMERGIDAS

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n(!# 4P!si5n #("osf6!i+#7 . n $ in(!io! &$ +on&%+(o 4P!si5n +!o o'!58i"# # +!o7 3#+ 0% $ #)%# f$%.# n sn(i&o #s+n&n( #$ $$)#! # $#+!s(# A1 $ #)%# +# 'o! )!#*& 3#+i# $# !#"# &!+3# &-#n&o %n *#+/o n$# +!s(# $o 0% 3#+ 0% $ f$%-o s# +on(in%o "in(!#s no s in(!o&%:+# #i! n$ +on&%+(o1 'o! s(# !#:5n $# n(!# #$ sif5n &, s(#! si"'! #3o)#

Un -"'$o "%. +o"@n & s( (i'o & sifons s $ "'$#&o 'o! $os#)!i+%$(o!s '#!# #'$i+#! $ #)%# # $os s%!+os # (!#*6s &$ ,o!&o &$ +#n#$2

+2 C&LCULO 'IDR&ULICO DE UN SIFÓN.

P#!# 0% +%"'$# s% f%n+i5n $ &is

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An#$i:#!"os n $#s 'osi+ions . 1 '#!# $o +%#$ #'$i+#"os $# +%#+i5n & $#n!)/# s'+/fi+#B

P1γ +V

1

2

2g +Z 1= P2

γ +V 2

2

2 g +Z 2+htotales

∆ h= P1

γ +

V 12

2g +Z

1−(

P2

γ +

V 22

2g +Z

2)

S $o '%& &fini! (#",i6n +o"o %n# s(!%+(%!# 3i&!9%$i+# 0% '!"i(

+on&%+i! %n $/0%i&o &s& %n ni*$ & +o(# (o'o)!9fi+# #$(# 3#s(# %n '%n(o "9s,#-o= '!o #(!#*s#n&o '%n(os "9s #$(os 0% $os &$ ni*$ & n(!#

P#s#n&o $ '$#no !f!n+i#$ 'o! $ 8(!"o & s#$i & $# (%,!/# . #'$i+#n&o$# +%#+i5n & $# n!)/# n(! $# f%n( . $# s++i5n & s#$i &$ +on&%+(o2

∑→

+++=++21

2

2

22

2

2

1

11

1

22 pérdidas

g

V Z

P

g

V Z

P α

δ α

δ

Con&i+ions & f!on(!#B


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021 === at P P P

4P!sions "#no"6(!i+#s7

=1

Z Cons(#n( 4f$%-o '!"#nn(7

02 = Z

4E$ '$#no & !f!n+i# '#s# 'o! $ +n(!oi& &$8(!"o & &s+#!)#7

01 =V

4F$%-o '!"#nn(7

V V =2

4V$o+i& n +%#$0%i! s++i5n &$ +on&%+(o7

1=α

4F$%-o (%!,%$n(o7S%s(i(%.n&o $#s +on&i+ions & f!on(!# n $# +%#+i5n & $# n!)/# .(nin&o n +%n(# #&"9s 0% $ (6!"ino & '6!&is in+$%. $#s '6!&is 'o! f!i++i5n . $#s sin)%$#!s1 s $$)# # $# si)%in( 8'!si5n2

++=∆ K f

D

L

gD

Q H 1

8

42

2

π

=∆ H Dsni*$ n(! $# f%n( . $ 8(!"o & s#$i

=QC#%$ & &is

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A'$i+#n&o $# +%#+i5n & $# n!)/# n(! $# f%n( . $#

s++i5n +!/(i+# “c

” & '!sions n)#(i*#s2

∑→

+++=++c

cc pérdidas

g

V Z

P

g

V Z

P

1

22

1

1

1

22

α

δ

α

δ

En $# f%n( s (in $#s "is"#s +on&i+ions & f!on(!#1 s5$o 0% #3o!#+onsi&!#"os '!sions #,so$%(#s '#!# +o"'#(i,i$i:#! +on $# '!si5n & *#'o! &$ $/0%i&o 0% (in *#$o! #,so$%(o2

R"'$#:#n&o s(#s +on&i+ions n $# +%#+i5n & $# n!)/# . &s'-#n&o $#

'!si5n +!/(i+# &$ '%n(oc

2

++−−

=

´´

18

42

2

K f D

L

gD

Qh

P P c

atm

abs

c

π δ δ

c P

P!si5n #,so$%(# n $# s++i5n +!/(i+# +

P#(" P!si5n ,#!o"6(!i+#

ch

Dsni*$ n(! $# f%n( . $# s++i5n +!/(i+# +

Q C#%$ &$ &isAS SO?RE SUPERFICIES SUMERGIDAS

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Los #++so!ios i"'!s+in&i,$s n $ sif5n no!"#$ sonB %n# 'i+3in+3#1+ons(i(%i 'o! %n# +o$#&!# . %n# *9$*%$# +3+ o & 'i= %n (#'5n & +,#&on $# '#!( "9s #$(#1 %n# *9$*%$# & #i! . %n# *9$*%$# & +o"'%!(# o &'%!)#2

VI MATERIALES:

V&LVULA (IC'ANC'A

LLAVE DE (ASO

CONDUCTOS DE TUBER)A RESERVORIO


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VII (ROCEDIMIENTO:

P#!# $ ini+io & $# '!9+(i+#1 s '!o+&i5 #$ $$n#&o #$ (#n0% & #)%# +on

%n# "#n)%!# +on+(# # %n +#

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L%)o s '!o+&i5 # $# $i"'i:# &$ $%)#! & (!#,#-o . # $# ins(#$#+i5n &

$os #++so!ios +o"'$"n(#!ios1 .# 0% $# o,!# 3i&!9%$i+# s(#,# n&(!io!o2


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Ds'%6s s '!o+&i5 # $# (o"# & "&is & $os #++so!ios 0% s

(in &%!#n( $ #fo!o & $# '!9+(i+#2


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S)%i"n( '!o+&i"os #$ +9$+%$o &$ +#%$ 0% +i!+%$# # (!#*6s &

$# (%,!/# # (!#,#-#!1 s(o s !#$i:5 +on "&is !'(i(i*#s +on %n#

"%s(!# & (!#,#-o 0% +on(#,# & %n ,#$& & +#'#+i& #'!o8i"#


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& $i(!os1 (o"#n&o (os &$ (i"'o 0% s &"o!# n $$n#! &i+3o*o$%"n1 s 3i+i!on H !'(i+ions2

Fin#$"n( n %n '!o+&i"in(o & )#,in( s '!o+&i5 #$ &s#!!o$$o &

+9$+%$os . &is

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E$ +#%$ $o o,(n"os +on ns#.os !'(i(i*os '#!# 3#$$#! %n (i"'o '!o"&io2

Toma N°Tiempo(Seg)

Volumen(Lts)

1 23.76 20

2 23.64 203 23.56 20

4 23.81 20

5 23.11 20

6 23.75 20

Promedio 23.!" 2!

Caudal=Volumen

Tiempo =

20

23.605=0.8473 Lit /Seg

Diseño Hidráulico.

Datos de diseño obtenidos en el campo:

Longitud de diseño (L) = 13.14 m

Diámetro de la tubería (D) = 1 pulg = 0.024 m

!"elera"i#n gra$itatoria (g) = %.&1 m's2

Dieren"ia de alturas ( 1 * 2 ) = 3.40 m

Perdidas locales:

+odo %0, (1) =0.%

+odo 4 , (1) =0.4

-ál$ula de aire (1) =4

-ál$ula globo (1) =0.2

-ál$ula "e/ (1) = 2.

raslape (1) =0.04

or "ondi"iones te#ri"as sabemos ue

P1

γ +

V 12

2g +Z

1=

P2

γ +

V 22

2 g +Z

2+∑ H f +∑ H l

Condiciones de frontera:

P1= P2= Pat =0( Presiones manometricas)


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V 1=0( Flujo permanente)

P1

γ +

V 12

2g+Z

1=

P2

γ +

V 22

2 g+Z

2+∑ H f +∑ H l

Z 1−Z

2=

V 22

2 g +∑ H f +∑ H l

Z 1−Z

2=

V 22

2 g+ f

L

D

V 2

2g+k

V 2

2g

∆ H =V

2

2g+ f

L

D

V 2

2 g+k

V 2

2 g

∆ H =V

2

2g (1+ f L D +k )

∆ H = 8

2

! 2

g D4 (1+ f L D +k )

Asumiendo un f = !"# tenemos:

3.4= 8

2

! 2

"9.81"0.02544

(1+0.02

13.14

0.0254

+2.5+0.9+0.45+0.04+4+0.2

)=0.000939m3/S

=0.939 Lts

S

Comprobamos el valor de f

Sabemos que:

#= 4$ " ! " D

2

#= 4∗0.000939

1.142"10−6

" ! "0.02542

#= 4∗0.000939

1.142"10−6

" ! "0.02542

R = 2*106


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%

D=

0.0015

2.54=0.0006

Entrando al da!rama de "ood# $on%

D $ # tenemos un f =¿ 0%01&'

3.4= 8

2

! 2

"9.81"0.02544 (1+0.0195 13.140.0254+2.5+0.9+0.45+0.04+4+0.2)

=¿ 0%000&4' m()S

=¿ 0.945 Lts/S


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I0 CONCLUSIÓNES * RECOMENDACIONES

Lo)!#"os !#$i:#! . o,s!*#! $ f%n+ion#"in(o & %n sif5n no!"#$2 Lo)!#"os +#$+%$#! $#s '6!&is & $o+#$s n (o $# +on&%++i5n &$

sif5n no!"#$2 R#$i:#! $# '!9+(i+# +on %n# "#.o! +#n(i& & *o$%"n & #)%#1

'#!# 0% #s/ 'o"os #'!+i#! & %n# "-o! "#n!# $f%n+ion#"in(o &$ sif5n no!"#$2

R#$i:#! $# '!9+(i+# +on (%,!/#s & #+!o1 '#!# 0% #s/ & s(#

"#n!# n%s(!o &is

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