INFORME DE LABORATORIO LABORATORIO ANÁLISIS BOMBA CENTRIFUGA.
UNIVERSIDAD NACIONAL DE COLOMBIA. FACULTAD ACULTAD DE INGENIERÍ INGEN IERÍA. A. DEPARTAMENTO DE INGENIERÍA CIVIL Y AGRÍCOLA HIDRÁULICA BÁSICA BOGOTÁ D.C. 2015
OBJETIVOS. •
Obtee! "#$ %&!'#$ %#!#%te!($t)%#$* C#!+# ,e "# b-b# '$ %#&,#"/ E%)e%)# '$ %#&,#"/ -te%)# #" !e- '$ %#&,#"/ NPSH '$ %#&,#"/ %&#,- "# b-b# %et!)&+# +)!# # "# 'e"-%),#, ,e 1000 !. P#!# e$t# )$# 'e"-%),#, ,e +)!- ,e)! "# 'e"-%),#, e$e%(%# 3 %"#$)%#! "# b-b#.
•
•
Me,) Me,)# #te te "# #") #")%# %#%) %)4 4 ,e "#$ "#$ "e3e "e3e$$ ,e $)) $))") ")t& t&, , -bte -btee e!! "#$ "#$ %&!' %&!'#$ #$ %#!#%te!($t)%#$ %&#,- "# b-b# +)!# # 115 !. S-b!e$ ,)%6#$ +!7%#$ %-"-%#! "-$ ,#t-$ e8e!)et#"e$ -bte),-$ #!# e$t# )$# 'e"-%),#,. A#")9#! $) "# )$t#"#%)4 $&!e - - ,e %#')t#%)4 #!# "#$ %-,)%)-e$ ,e -e!#%)4 ,e" -,e"-.
DESCRIPCIÓN DEL EQUIPO.
E$te E$te "#b-!# "#b-!#t-! t-!))- $e !e#") !e#")9# 9# $-b!e $-b!e &# &# e$t#%) e$t#%)4 4 ,e b-beb-be- )$t#" )$t#"#,# #,# e e" "#b-!#t-!)- ,e 6),!7&")%# ,e "# U)'e!$),#, N#%)-#". E" -t#:e %-$t# ,e & t#;&e ,e #b#$te%))et- ,e" %&#" &# b-b# %et!)&+# e8t!#e e" #+&# 6#%)# & t#;&e t#;&e ,e ,e$%#!+#. ,e$%#!+#. E" t#;&e t#;&e ,e ,e$%#!+# t)ee t)ee & 'e!te,e!'e!te,e!- ,e #!e, #!e, ,e"+#,# 3 -!# t!)#+&"#! %- & 7+&"- ,e 0
PROCEDIMIENTO.
P#!# %#&,#"e$ ,ete!)#,-$ 3 &# 'e"-%),#, %-$t#te ,e" )&"$-! ,e 1000 !/ $e !e+)$t!# "-$ $)+&)ete$ ,#t-$* 1. P!e$)4 P!e$)4 e "# $&%%)4 $&%%)4 >P$? 3 !e$)4 !e$)4 e "# ,e$%#! ,e$%#!+# +# >P,? ,e "# b-b# b-b#.. E$t#$ !e$)-e$ e$t7 ,#,#$ e %et(et!-$ ,e e!%&!)- >% H+?. 2. M#+)t&, M#+)t&, ,e "# &e!9# &e!9# ;&e $e e:e!%e e:e!%e $-b!e $-b!e e" e:e ,e !-t#%)4/ !-t#%)4/ e @)"-+!#- @)"-+!#- &e!9# >@+?. . N)'e" N)'e" ,e" #+&# #+&# e e" 'e!te,e! 'e!te,e!- H' e %et(e %et(et!-$ t!-$ >%?. >%?. E$te E$te )$ )$- !-% !-%e, e,) ))e )et t- $e !e) !e)te te e!e!- #6-! #6-!# # #!# #!# %#&, %#&,#" #"e$ e$ 3 &# &# 'e"-%),#, ,e" )&"$-! ,e 1150 !. CÁLCULOS Y RESULTADOS
E e" "#b-!#t-!)- $e -bt&')e!- "-$ $)+&)ete$ !e$&"t#,-$* !e$&"t#,-$*
T#b"# 1. D#t-$ -bte),-$ e e" "#b-!#t-!) H 0=13 cm
E" %#&,#" $e ,ete!)# %- "# e%&#%)4 ,e" 'e!te,e!-/ e8&e$t# e e" 2,45 "#b-!#t-!)-/ 3 ,e$%!)t# -! "# e%&#%)4 Q=0,0165 ∗ H >E%&#%)4 1? %- H e %et(et!-$ 3 e ")t!-$ -! $e+&,-. D-,e* H = H V − H 0 >E%&#%)4 2? 1?. Se e%-t!4 e" H #!# %#,# %#&,#"* M&e$t!# ,e %7"%&"- #!# e" %#&,#" 1. H = H V − H 0 H =13,5 cm −13 cm
H =0,5 cm
2?. Se !ee"#94 e "# E%&#%)4 1 3 $e 6#""4 e" %#&,#" #!# %#,# H* M&e$t!# ,e %7"%&"- #!# e" %#&,#" 1. 2,45 Q=0,0165 ∗ H 2,45
Q=0,0165 ∗( 0,5)
LPS
Q=0,0030 LPS 3
Se e8!e$# e
m s
m Q=0,0000030 s
3
E "# $)+&)ete t#b"# $e &e$t!# "-$ !e$&"t#,-$ #!# "-$ &e'e %#&,#"e$.
T#b"# 2. C#&,#"e$ e"e#,-$ e e" "#b-!#t-!)-. De "# T#b"# 1 %-'e!t)-$ "#$ !e$)-e$ e %et(et!-$ ,e e!%&!)- # et!-$ ,e %-"&# ,e #+&#. Tee-$ ;&e* H m Hg =
P ɣ Hg
Se ,e$e:# "# !e$)4* P= H m Hg∗ɣ Hg C-- $#be-$ ;&e "# !e$)4 e$ )+&#" e "# %-"&# ,e #+&#* H magua =
P ɣ agua
Se !ee"#9# P e =$t# e%&#%)4* H m Hg∗ɣ Hg H magua = ɣ agua
kg
C-- "# ,e$),#, ,e" e!%&!)- e$ 15/0
3
m
#!# e" %#&,#" 1 e e"
)e94et!- T >&e$t!# ,e %7"%&"- #!# , e e" %#&,#" 1?*
( 0,88 m )∗(133210,38 N 3 ) H magua =
m
(9810
N 3
m
)
H magua =11,95 m
C-- e" #4et!- ,e ,e$%#!+# $e e%&et!# 2% -! ,eb#:- ,e" &t,-,e $e e%&et!# %-e%t#,- # "# t&be!(#/ $e ,ebe !e$t#! e$t-$ 2% # "# !e$)4 "e(,# -! e" #4et!- #!# e%-t!#! "# !e$)4 e e" &t- ,. Et-%e$* Pd =11,95 m−0,28 m
Pd =11,67 m
E "# $)+&)ete t#b"# $e !e"#%)-# t-,-$ "-$ !e$&"t#,-$ ,e "-$ #4et!-$ e et!-$ ,e #+&# #!# "-$ ,)e!ete$ %#&,#"e$.
T#b"# . P!e$)-e$ e et!-$ ,e %-"&# ,e #+&#. P#!# 6#""#! "# %#be9# ,e "# b-b# $e #")%# "# e%&#%)4 ,e ee!+(# et!e P$ 3 P, te)e,- e %&et# ;&e e$t7 $e#!#,-$ -! &# #"t&!# ,e 0%. Ee!+(# et!e $ 3 ,/ te)e,- %-- )'e" ,e !ee!e%)# "# #"t&!# ,e P$. 2
P ps V ps Z ps + + γ 2g
2
P V + H B =Z pd + pd + pd γ 2g
+ he ps y pd
C-- e" )'e" ,e !ee!e%)# $e e%&et!# e $/ e" ,)7et!- ,e "# t&be!(# ,e $&%%)4 3 ,e ,e$%#!+# $- )+&#"e$ 3 "#$ "-+)t&,e$ ,e "#$ t&be!(#$ $- e;&e#$ "#$ =!,),#$ ,e ee!+(# - $e t)ee e %&et#/ "# e%&#%)4 ;&e,# ,e "# $)+&)ete #e!#* P ps γ
+ H B =Z pd +
P pd γ
Y ,e$e:#,- "# %#be9# ,e "# b-b#* H B =Z pd +
P pd P ps γ
−
γ
M&e$t!# ,e %7"%&"- #!# e" %#&,#" 1 H B =0,6 m+ 11,67 m−0,95 m
H B =11,32 m
E "# $)+&)ete t#b"# $e !e"#%)-# e" %#&,#" 3 "# %#be9# ,e "# b-b#.
T#b"# 5. C#be9# 3 %#&,#" ,e "# b-b#.
G!#%# 1. '$ HB. L&e+- $e ,ete!)4 "# -te%)# #" !e- ,e "# b-b# #!# %#,# %#&,#" # #!t)! ,e "# $)+&)ete -!&"#* P ( kW )=
F ( kg )∗ N ( rpm) 2000
P#!# e" %#&,#" 1/ $e -bt&')e!- "-$ $)+&)ete$ !e$&"t#,-$* P ( kW )=
2,9 kg∗1000 rpm 2000
P=1,45 kW
A %-t)&#%)4 $e &e$t!# "-$ !e$&"t#,-$ -bte),-$*
T#b"# .P-te%)# #" !e- ,e "# b-b#.
G!#%- 2. '$ P. A #!t)! ,e "# -te%)# #" !e- e%-t!#,# $e ,ete!)4 "# e%)e%)# # #!t)! ,e "# $)+&)ete e%&#%)4* Pf =
γ ∗Q∗ H η
De ,-,e*
η=
γ ∗Q∗ H ∗100 pf
P#!# e" %#&,#" 1 $e e%-t!#!- "-$ $)+&)ete$ !e$&"t#,-$*
( 9,81 kN )∗( 0,000003 m 3 )∗(11,32 m) η=
s
1,45
∗100
η= 0,023
A %-t)&#%)4 $e &e$t!# "-$ !e$&"t#,-$ -bte),-$*
T#b"# .E%)e%)# ,e "# b-b#.
G!#%- . '$ e%)e%)#. P#!# %#"%&"#! e" NPSH ,)$-)b"e/ $e #")%# "# $)+&)ete e%&#%)4* NPSHd = Habsbs − Hv
>E%&#%)4 1?
P!)e!- $e %#"%&"# e" H#b$ e "# b!),# ,e $&%%)4/ #!# e$t- $e #")%# "# e%&#%)4 ,e ee!+(# et!e P$ 3 "# b!),# ,e $&%%)4*
2
P ps V ps + Z ps + γ 2g
2
Pbs V bs = Z + + bs γ 2 g
+
he ps y pd >E%&#%)4 2?
D-,e* 2
Pbs V bs Habsbs= Z bs+ + γ 2 g
&e,#,- "# e%&#%)4 2 ,e "# $)+&)ete #e!#*
2
P ps V ps Z ps + + = Habsbs + he ps y pd >E%&#%)4 ? γ 2g
C-- P$ e$t7 e e" )$- )'e" ;&e e" "#- ,e b-be-/ $J0 3 %-- "# "-+)t&, ,e t&be!(# ##")9#,# e$ e;&e# - $e t)ee e %&et# "#$ =!,),#$ ,e ee!+(#/ et-%e$ ,e$e:#,- H#b$* 2
P Ps V Ps
Habsbs=
γ
+
2g
Y !ee"#9#,- e "# e%&#%)4 1* 2
P Ps V Ps NPSHd = + −h v >E%&#%)4 ? γ 2g
P#!# 6#""#! "# %#be9# ,e 'e"-%),#,/ !)e!- $e e%&et!# e" 7!e# ,e "# $e%%)4 %-- $)+&e* π 2 A = ∗ 4
A = 2
A = 0,008107 m
L&e+- $e 6#""# "# 'e"-%),#,* V =Q / A
P#!# e" %#&,#" 1
π 4
∗( 4 pu!g )2
3
V =
m 0,0000030 s
2
0,008107 m
V =0,00037 m / s
L&e+- $e 6#""# "# %#be9# ,e 'e"-%),#,* 2
V H = 2g
P#!# e" %#&,#" 1 m ( 0,00037 ) s H = m 2∗9,81
s
2
2
−5
H =1,89 " 10 m
Se t-# "# !e$)4 ,e '#-! ,e" #+&# #!# 20
NPSHd =
γ
+
2
2g
− Hv −5
NPSHd =0,95 m + 1,89 " 10 m− 0,24 m NPSHd =0,71 m
A %-t)&#%)4 $e &e$t!# "-$ !e$&"t#,-$ #!# t-,-$ "-$ %#&,#"e$ e8e!)et#"e$*
T#b"# . NPSH ,)$-)b"e.
G!#%- . '$ NPSHD. P#!# 6#""#! "# 'e"-%),#, e$e%(%# $e t-# e" &t- ,e 78)# e%)e%)#/ e &e$t!- %#$-
T#b"# . P&t- ,e 78)# e%)e%)#. L# 'e"-%),#, e$e%(%# $e %#"%&"# # #!t)! ,e "# $)+&)ete e8!e$)4* 1
Ns=
Q 2∗ N H
3 4
P-! "- t#t-* 1
Ns=
( 0,037 m 3 / s )2∗1000 rpm ( 6,57 m )
3 4
Ns= 46,61
P#!# 6#""#! "# %&!'# ,e "# b-b# # 1150 ! $e 6#%e '#!)#$ %&!'#$ ,e )$-e%)e%)# $-b!e &t-$ ,e "# %&!'# %#!#%te!($t)%# # 1000!/ #!# e$t- $e e$%-+)e!- %#&,#"e$ #"e#t-!)-$ 3 $e ,ete!)4 "# %#be9# !e$et#,# #!# %#,# %#&,#". E$t- $e 6)9- # #!t)! ,e "# e%&#%)4 ,e !e+!e$)4 6#""#,# e E8%e" ,e "# %&!'# # 100!. L# e%&#%)4 e$ "# $)+&)ete* 2
H =270,3 ∗Q −151,21∗Q + 11,526
P#!# & %#&,#" ,e 0/001 K$/ $e -bt&')e!- "-$ $)+&)ete$ !e$&"t#,-$* 3 2
3
m m H =270,3 ∗( 0,001 ) −151,21∗(0,001 )+ 11,526 s s H =11,38 m
A %-t)&#%)4 $e &e$t!# "-$ !e$&"t#,-$ #!# "-$ %#&,#"e$ e"e+),-$.
T#b"# 10. P&t-$ #!# 6#""#! %&!'#$ ,e )$-e%)e%)#. A #!t)! ,e e$t-$ ,#t-$ $e 6#""4 "# e%&#%)4 #!# %#,# %&!'# ,e e%)e%)#/ e%-t!#,- e" '#"-! ,e C ,e "# $)+&)ete #e!#* H =# Q
# =
H Q
2
2
P#!# e" !)e! %#&,#" e"e+),-* # =
11,38 m 3 2
m ( 0,001 ) s
# =11375060,3
P-! "- t#t- "# e%&#%)4 ,e "# %&!'# ,e )$-e%)e%)# ;&e,# ,e "# -!#* H =11375060,3∗Q
2
A %-t)&#%)4 $e &e$t!# "#$ %-$t#te$ #!# %#,# %#&,#" e"e+),-.
T#b"# 11. C-$t#te$ ,e "#$ %&!'#$ ,e )$-e%)e%)#. A #!t)! ,e "# e%&#%)4 ,e )$-e%)e%)# 6#""#,# #te!)-!ete/ $e !ee"#9#!- "-$ %#&,#"e$ 3 6#""#-$ "# %#be9# e %#,# &t-. P#!# e" %#&,#" ,e 0/001 K$* H =11375060,3∗Q
2
3 2
m H =11375060,3∗( 0,001 ) s H =11,38 m
A %-t)&#%)4 $e &e$t!# "-$ !e$&"t#,-$ #!# "#$ %&!'#$ ,e )$-e%)e%)#.
T#b"# 12. P&t-$ ,e "#$ %&!'#$ ,e )$-e%)e%)#.
G!#%- 5. C&!'#$ ,e )$-e%)e%)#. A #!t)! ,e "#$ %&!'#$ ,e )$-e%)e%)#/ $e #")%# "#$ "e3e$ ,e $))")t&, et!e e" &t- %--%),- $-b!e "# %&!'# %#!#%te!($t)%# # 1000 ! 3 e" &t- ;&e ;&e!e-$ 6#""#! e "# %&!'# ,e 1150 !/ #!# e$t- $e &$# e" #!7et!- ,e %#!+# 3 e" #!7et!- ,e %#&,#" %-- $)+&e. Q1000 Q1150 π 1= = 3 3 N 1000∗ 1000 N 1150∗ 1150 H 1000 H 1150 π 2= = 2 2 2 2 N 1000 ∗ 1000 N 1150 ∗ 1150 P1000 P1150 π 3= = 3 5 3 5 N 1000 ∗ 1000 N 1150 ∗ 1150
C-- e" ,)7et!- e!#e%e %-$t#te/ "#$ e%&#%)-e$ ;&e,# ,e "# $)+&)ete #e!#* Q1000
=
Q 1150
N 1000 N 1150
H 1000
H 1150
N 1000
N 1150
= 2
2
P1000
P1150
N 1000
N 1150
= 3
3
De$e:#,- e" %#&,#"/ "# %#!+# 3 "# -te%)# #" !e- # 1150 !* Q1000∗ N 1150
Q1150=
N 1000
H 1150=
H 1000∗ N 1150
2
2
N 1000
3
P1150=
P1000∗ N 1150 3
N 1000
P#!# e" %#&,#" 0/001 K$*
(
) 3
m 0,001 ∗1150 rpm s Q1150= 1000 rpm 3
m Q1150=0,0012 s
H 1150=
H 1000∗ N 1150
2
2
N 1000
(11,38 m)∗(1150 rpm )2 H 1150= (1000 )2 H 1150=15,04 m
3
P1150=
1,45 kW ∗( 1150 rpm )
(1000 rpm )3
P1150=2,21 kW
A %-t)&#%)4 $e &e$t!# "-$ !e$&"t#,-$ #!# %#,# %#&,#" e"e+),-.
T#b"# 1. C#&,#"/ %#!+# 3 -te%)# #" !e- # 1150 !.
G!#%- . C&!'# %#!#%te!($t)%# 1150 ! 3 ,#t-$ e8e!)et#"e$.
L# -te%)# e8e!)et#" $e 6#""# %- "# )$# e%&#%)4 ;&e #!# "# b-b# ,e 1000 !.
P ( kW )=
F ( kg )∗ N ( rpm) 2000
P#!# e" %#&,#" 1/ $e -bt&')e!- "-$ $)+&)ete$ !e$&"t#,-$* P ( kW )=
7,8 kg∗1000 rpm 2000
P= 4,49 kW
A %-t)&#%)4 $e &e$t!# "-$ !e$&"t#,-$ -bte),-$*
T#b"# 1. P-te%)# #" !e- e8e!)et#" # 1150 !.
G!#%- . P-te%)# #" !e- 1150 ! 3 ,#t-$ e8e!)et#"e$.
ANÁLISIS DE RESULTADOS
A #!t)! ,e" '#"-! ,e "# 'e"-%),#, e$e%(%#/ -,e-$ -b$e!'#! ;&e $e e%&et!# e e" !#+- ,e / 3 -! "- %&#" -,e-$ ,e%)! ;&e "# b-b# ,e" "#b-!#t-!)- e$ &# b-b# t)- !#,)#" ;&e +ee!# %#be9#$ ,e ee!+(# b#:#$ #!# %#&,#"e$ !e"#t)'#ete #"t-$. A" -b$e!'#! "-$ ,#t-$ 6#""#,-$ -! e,)- ,e "#$ "e3e$ ,e $))")t&, #!# 1150 ! 3 "-$ ,#t-$ t-#,-$ ,)!e%t#ete e "# !7%t)%#/ -,e-$ -t#! ;&e $e #%e!%# b#$t#te/ e$e%)#"ete "# %#be9# 3 e" %#&,#"/ "-$ %&#"e$ $e e%&et!# e+#,-$ # "# %&!'# 6#""#,# -! $))")t&,. E$t- -$ ),)%# ;&e "#$ "e3e$ ,e $))")t&, $e #!-8)# b#$t#te # "#$ %-,)%)-e$ ,e -e!#%)4 !e#"e$ ,e "#$ b-b#$ 3 $- &# -!# ee%t)'# ,e ##")9#! ,)e!ete$ b-b#$ $) tee! & e!!-! %-$),e!#b"e e e" ,)$e-. L# %#')t#%)4 e e" $)$te# $e &e,e %-#!#,- "# !e$)4 #b$-"&t# e "# b!),# ,e $&%%)4 3 "# !e$)4 ,e '#-!. A #!t)! ,e "-$ %7"%&"-$ ,e NSHPD -,e-$ -b$e!'#! ;&e "# !e$)4 e "# b!),# e$ #3-! ;&e "# !e$)4 ,e '#-! ,e #+&# 3 '# ,e$%e,)e,- # e,),# ;&e $e #&et# e" %#&,#"/ e$t- ;&)e!e ,e%)! ;&e #!# %#&,#"e$ &3 b#:-$/ "# %#be9# ,e !e$)4 6#%e ;&e e" "(;&),e)e%e # e'#-!#!$e 3 # %#b)#! ,e e$t#,-/ -! e$t# !#94 e" $)$te# !e$et# %#')t#%)4 %&#,- $e #e:# %#&,#"e$ b#:-$ &,)e,- !e$et#! ,#-$ e e" $)$te# # "#!+- "#9-. CONCLUSIONES. •
•
E" #7")$)$ ,e $))")t&, #!# "#$ b-b#$ e$ %-"et#ete '#"),- 3# ;&e "-$ ,#t-$ e8e!)et#"e$ $e #!-8)# b#$t#te # "-$ ,#t-$ te4!)%-$ 6#""#,-$ # #!t)! ,e "-$ #!7et!-$ #,)e$)-#"e$. E$te #7")$)$ e$ &# -!# !7%t)%# #!# ##")9#! ,)e!ete$ %-,)%)-e$ ,e &%)-#)et,e &# b-b# 3 ,e e$t# #e!# -,e! t-#! &# ,e%)$)4 %- "# $e+&!),#, ,e ;&e - $e e$t7 %-et)e,- & e!!-! %-$),e!#b"e 3 ;&e "#$ %-,)%)-e$ e$t&,)#,#$ te4!)%#ete $e #!-8)#!# b#$t#te # "#$ %-,)%)-e$ !e#"e$ ,e -e!#%)4. A #!t)! ,e "#$ %&!'#$ ,e -te%)# #" !e- $e &e,e -b$e!'#! %-- & #&et- e;&e- e e" +)!- ,e" )&"$-! &e,e %#&$#! +!#,e$ )%!eet-$ e e" %-$&- ,e -te%)#/ e &e$t!- %#$- #!# e" #&et- ,e 150 !/ $e ,&")%- e" %-$&- ,e -te%)# "- %&#" ,ebe $e! te),- e %&et# # "# 6-!# ,e $e"e%%)-#! & -e!#! e" e;&)- #!# "-+!#! & e;&)")b!)- et!e e" %-$t- 3 $& &t)"),#,.
•
•
L-$ $)$te#$ ,e b-be- $e ,)$e# #!# & !#+- ,e %#&,#"e$ ,ete!)#,- !-%&!#,- ;&e $)e!e t!#b#:e e e" &t- ),e#" #!# e" %&#" &e ,)$e#,-/ -! e$t# !#94 $e ,ebe tee! e %&et# ;&e #" $#")!$e ,e e$t-$ !#+-$ - #" !e$et#!$e %-,)%)-e$ e8t!e#$ ,et!- ,e" $)$te#/ "# !e$)4 &e,e ""e+#! # $e! 7$ #"t# ;&e "# !e$)4 ,e '#-! e e" $)t)- 3 !e$et#! %#')t#%)4/ "- %&#" &e,e +ee!#! ,#-$ ,et!- ,e "# b-b#/ "-$ #%%e$-!)-$ - e "# t&be!(# )$#. E &e$t!- %#$- $e -b$e!'# %-- %- %#&,#"e$ &3 b#:-$/ "# !e$)4 e "# b!),# ,e $&%%)4 e$ #3-! ;&e "# !e$)4 ,e '#-! ,e #+&# -! "- %&#" -,e-$ %-%"&)! ;&e e %)e!t#$ %-,)%)-e$ ,e %#&,#"e$ &3 b#:-$/ e" $)$te# !e$et# %#')t#%)4. P#!# -,e! 6#%e! &# $e"e%%)4 ,e & $)$te# ,e b-be- #,e%&#,- 3 -! "- t#t- & ,)$e- e%)ete/ $)e!e $e ,ebe tee! !e$ete ;&e e "#$ b-b#$ # e,),# ;&e #&et# e" %#&,#"/ "# %#be9# ,e ee!+(# e "# b-b# ,)$)&3e %-- $e &,- %-!-b#! e e" "#b-!#t-!)- 3 &e,e ""e'#! # #"&%)-#)et-$ e e" $)$te#.
BIBLIOGRAFIA. P!e$)4 ,e '#-! ,e" #+&# # ,)e!ete$ tee!#t&!#$. Re%&e!#,- ,e
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