apuntes mecanica de fluidos i prof lautaro
TRANSCRIPT
-
LAUTARO LAUTARO LAUTARO LAUTARO DE LA FUENTE R.DE LA FUENTE R.DE LA FUENTE R.DE LA FUENTE R.
APUNTESAPUNTESAPUNTESAPUNTES MECANICA DE LOS FLUIDOS IMECANICA DE LOS FLUIDOS IMECANICA DE LOS FLUIDOS IMECANICA DE LOS FLUIDOS I
Para las carreras de Ingeniera en Maquinaria y Para las carreras de Ingeniera en Maquinaria y Para las carreras de Ingeniera en Maquinaria y Para las carreras de Ingeniera en Maquinaria y Vehculos automotrices y Mantenimiento Industrial.Vehculos automotrices y Mantenimiento Industrial.Vehculos automotrices y Mantenimiento Industrial.Vehculos automotrices y Mantenimiento Industrial.
INACAP MAIP EDICIN N1
-Marzo 2011-
-
! !" #
$%"% $&"!" '
%""!" (
)""" '
*$" +
,, -
" -
!$."& /
0"*"%!""$1"
*$" '
#
#
! #'
".&$ #2
%"""&$ (+
*$" +'
3 4,56 +2
$"%71*8" +2
"%$"%1 29
"""%!1 2#
%" %71 -
5*1!8 -
-
/
,:;"1"$""""%1"?@$"1."""> " $> %$ = $ .& 1 1 @$ %">$%)$%>"%!">?1 "$%""
8=" %"$ $? % > $" !$ % " " =%" % > " *8" 8="
-
/:6 $& " !" " 18> = " $%$ " !" %" C."&D> $ $?$CB&$D :
$> %$""" ! C8=$""$7""&"">""%& "!0 1 $%$ !> " % ." $ . = " "" !0 > !$&"
-
'
!
$!"> " % !&$ %="
$!"> " % !&$ %="
"!! "!!
$%"* $%"*
""%!*C?D % % = "
# :6" !" %" $?$> % ?"" %" "> .1
-
#
( 6
!$%""1"%%";
"/ ""%8! ?"%8!' ," "%!# "?$7( 3""+ " 3%
( C)
""*""$1=H%" $"""$
"
#"$?%"%% $?$=7"%
=
-
(
;N""%8!PN"3N3$(/6
$ $" "$
"$7
"$1"
"$1"
$
O1!$
$
*
%""%8!%=7$T"%8!T"1!%$"
NN
;N"""N""%8!"" N"1N999QO1R$SCD N""%8!1N-29QR$SCD(' ,: % *"? = !" " !" = " $0 "
$%$"!$$*"" "%! "!0="=%$=*1"%8?% " !" **)">1"*=?" "%!"$
-
+
" "%! " * ? !0 " "%!
-
2
(( 3?"""%%"?"!""&1""=%!! !$"" "$"!0"!" ?"" %" "" !V " !" *)?""! " %"* 7$" "1 H%$ "$" " %" 1" C1 K D> !"!)!0%"*%"%"%%%?CD%&CD%>?"$%%"%"%8*>"%*"?"1H%" ;
-
-
!"*1H%" >"11!
%%C) , ="8"%%!>1;
N ;N0"*%$ ?
N%%3N3=%%$ ?N%$ ?.N"%"%8!
$" $"$""1H%" >"=;
N CD
! !0CD"$"
C), 1;
NC*D
$%0$" C*D CD> " *& "1H%" ;
N N! "#"$
*"$I!"%?""!?"">1V
!N %&'&(
-
$ =H" " C
1?"#"$D>="$?""&$*"H%$$".$"=% !" $%$!1K#>!%";!N9!NW! )"W
C!N9D ! > " ?"" " *="%!
!$ ?CR $ $" 1$ 1
%";
NW"W
K#1$1
" ?"" " *="%!"!0CXD%
!$ ?CR
-
((/ 35,
$ $" "$
"$7
"$1"
"$1"
* +,
"$/
C"D
U1!"
$/
"
$/
COD
*"
/
(( 3,,3C)
%& % "%! ?"" " !"> "% " "
*"> " 0
$ I?"" $&J> = "
?"" &$ *" ! CY) $ %*"?""1H%" ;
=
"?""$@$"*"$?""8$C3!1K (D> $ $% = $ " ?$ "0 > ?7"!*C1K+D>$%"0C'9
-
/
K+$%"?""8$ "" %"$> "1@ " " " %"
-
8=""$ " = " . 0 %" ?% "%" %$%C1*
99[%" *D%" ?%""""-./0/N-/9QO1R$S\&"?$"QO1S]
N1 3N/99N9>/$
"%)$"$N3N-/92314H9>/$N2'O1/ % "1%"PN'#99>\$"?@$ "> " "%"
"%8!"^N-29QR$S]
^N5
"%)?$3N6 N789
:;7 4 N'>+2$
N'+29>2"
=="$% ">1?"%8!N9>+#\$""+#A9992314N+#92314
^9NH?-3#-N9>+#H-29 #
-
'
; =
""%*$N`HN8$N#$N99#$>"N`H9>9#$N9>#+$
PN*@ N9>9/QS>1 = = AB?$")9>9/-Q$S
NUNE
N'*N'99999R$/
!N/'#*N/'#99999R$/
$%0""! $;
UNE89
B8
=>DA:EABF14 H9>9$N(>H92 ?"" &$ = ")
-
#
N%1N9>/#%N2%1N9>(+%"%*$NHHHNHH9>/#%H9>(+%N9>#/(%/.N9>99%1N9>999/#%N/9*3N9>'R"$%0""! $";
!NGG N IJ
9K/A9LK/M8K/NON9>9/'IGPQR+/Q$S17$!) />( Q$S $*" " 1 9 Q$S $ ?""8==
"%"">"""%9>-Q$S%$?1(9Q%$S
NNN
"%)?"""=;!NGG "%*$"=;.N/>($a/$N9($N9>99($N/H`H/$H9$N//(>2$/N9//(/$/
%NH>1N-SS NA:1#
?"3NbHN(9S/T1UHVS-"7S/T H71ULW H9>/$N9+#'1W $$%0"" ;
!NGG N CA9O N9/(2
-
(
(-5
/#9Q$$S&$* " %"> ? !$ Q$R"S * &$
1$ $%"""%9>-Q$S%$?1(9Q%$S("#)*048*."5
/
+%=G11/+QKS>"Q$$S8%" 1"#>29H9EQO1R$/S$/(H9E/QR$SD("#)6-*6
-
+
1.9 $ ? ?$ Q$dS 1 /9 QKS $ %" /9Q*"SC"UN//9H9+QR$/SD("#)60*62*
38.9/9%""1""H%$"$$ "?$7 1> " %" ' Q*S ?$ 9>9 Q$dS> 9/-Q$dS("#)=;40992*
-.5/ !1 $" $%" .0 ? %" $% 1 $%$> " %" " $%" % ) 1eG $%"!0N(/'>/QU1!S%" ((QS8%" *$*19>Q$S9/#Q$S&$
-
2
,,
/:/: 1> " !" ) !0" $"
$"!0"%" !$%" >$!0$"$*1> $1
-
-
K2""%""*">$"!7>$$7="* "%!">%& %" $"!7> ?8 " " " *> "$"$ " ! " "$ 1"=%"1
I"*$%" $"!7"*!8" " $ & =""$&"$"
-
/9
//:5,C*"D " %" $ $ *" " $ %" *"4""$"1H%" ;
*"N$g$
/:
$ $" "$
"$7
"$1"
"$1"
N
*,
$/
C"D
O1!$/
$/
*/
Q"SNQSNQ H%" = I ! ! " % !0HC"$%$D>%" 1""$1" !"! H% % %" !$$%
-
/
K-"& " % %" " %% % " = " % *"? !1K9
K9"
-
//
*"?!1K9>"=;
N771""""=V
77N
"!0"$%%" &/>"&;
NAC7DNACbbcD/
" "$ % ?7" !> $*" %"" H%$"%0$> 1" "?@$""%0"%$*"%"""1">"=;
3N3/HN/H/
>%" /"&;
NHC7DNHCbcbD/
%"*)"0"%$*"%""";
PNHP/N/H/""$">"$%=PNP/>*=.$*7"&$"$>1;
N/
7MP70 NMP0
F;%!1K9>"N#$/
-
/
D \L7!0/""$&?7"%" /QU1!S>"!0%
%" "N#999QU1!S]"""/"$%H%" ;
NAC7DN#999H7.1
9.1 N9999
*D " N$>\"&
%" /Q$$S]
$%" />"0 ;
NHC7DN$A 9.1
7.1N9>#$N#$$
D \L7%""$&?7"%" />"N9>/"]%"$H%" ;
/NMP0 N7
23dMA
91W N/#923d1W H 7CLef>O N>/-B
//:,B,,5//B,,."&$"$%$"!"%" %$ =? %" " "$ = H" !0" "> " @!0""%!$!"?$!%"%*="=*!%"* " " * @ " !0" *" %" C%D> = " =*!0*$"C1D>1;
%g1N9CD
-
/'
;K$!!%"
0*$">"%"%$!%">";1NPN]g G$N]g GZG3N]g GZGCH0DCD0"$"!0"1)AC3!1KD>"=;
HNHC
-
/#
&1$%")"0;
-
/(
*D o kKk$jZG vN9D o kKkp oZG xN9
*"?"""""=%" !%">"?81)hC3!1KD>"%!!
8=>1;
kKkpu oZG x>%"kKkpN"K"p
" "K"p NoZG xy % No]lz> 1 1 "
>=;C0DNE1Z0j$ *>"$ "&%!"$%"*"C8="D%"
-
/+
>"*&V
CDNC/Dg1ZC0/E0DCD "> H%" = %" = % !CD> " C hD " !> " 1 %" %
$$"%C/D>$"%" 1%$!C0/E0D="$*"%"%&%" %!%">"$)$""%!!>"1).>1V
.NC0/E0D
$%0h >=!$; tz u tj]}C/D;C0DN" %!%"9N" %"%"%!8=N"!1N 1?.N""%!*%%" "&>=%$$? %" =%!%">"$$7*" ///F,=!1K>"
1"hN/$~]^ _` \L7i.$"01*%0 $>="""=]
;
tz u tj]}% "%"
-
/2
1>"%" "%"""%"%"O1!R$
/N/-'99R$/
} u 3p3 N:8
7:L
:;
< 1a< 14a N'>--$//,,: %& % $ ? %" $&= ""$.&> " $% "$ % $ %" >
$ $ $ $"$"!1K'
K'%" "$;
-
/-
t u G }C" $$7D"%""%8!="" * ? H$ *" N 9 "$1 % = $V * = %" $"!7"!0=@$$"%!*$>""%*.".>=%"?%" $"!7
K#5 $$////:,,5 $ $ * IJ C1 K (D> " * ? %&""%!$IJ>%$
8=C!$$7D$ = " $0 " ""H$""*8!$$%=!!
8= $
-
9
K+ $,*
"1"C1K+D"%"*8%".!
-
E5Ni.CjB1ajD///':,,5"%$ $"*=" "?"8%* $ " $" !1 K- %" $"!7%?$ $>*"!H"%%" $ $*?0">"=1)""%"*"$ "%"$"$%%$*)" "*" $ $ " $* 1
-
/
/9 $1/,"%"
/h5/h5$""* %""8="%" % !0 "CD *) ? ." "> % " ! "& "$$1!0")$"8 1"""* %"""*"%!&CD>!0"=?;
-
t u "" > "%) l> " ; ltl> 1 " 1$">*$" CD * u tl CD CD>1&"%"?""8"!0"!"CD>$"$ >">=" ""%*"%!"%"//h5 " " "%!" %"> " 0& " % " %" "%!"%";
D %!"%".0"*D %!"%"?"D %!%""
//Bh,*="!0"!""*"%!.0$"$ >"?& CD $&"$ "%!".0> "!0"!"CD"1""* %"""&!$>$"%!1K/
1; * u tl > "? % ""%!%>"*$";
* Ntd G ;!N" "*"%!.0N.0K/0"*"%!
%.0
-
'
"*%$"=!0"=)!C8=D"*"%!.0"1%%" =@"*
>%"&
8VtdN G "$ !0"%"%!%.0>"&;
* N G G ;B9N"?=%!.0
N""%8!8=N.0$ " " $ 8 * !0">"&="%%C=!"&$"$"=?" "&"!0"!""*"C1K/'D =?%%""!$";
D % % " "% @ % "%!"$1%>$$"!0""*""%=)=%"%.%"
*D "% @ ""$ ! *> % )$% CH>
-
#
F "= * !1> /Q$S "
8= "?N>>."Q$S>%"""$"">;
D !0"CD>=8=
)"*"%!*D * !0"C D
;* N G G
D $&"%!.0";NV8G NV8G Q$S>""1"?N>>"!>"*;
[#"N[#"-3#-N>H999314N99314
1V* N G G u$H99314N99U1
*D $"&"!>"&"">NbN1 N$///3,"%!?*%!C8=D>$%" ?8"%!C1K/#D> "* %"""&!$>8 !0"IJ%"&%"1? ="$&$%""
-
(
K/#"* %"""*"%!%?
!1 K/# %" "* "%!? ? ?$&H$ " % ! " "%! $$" &"$1 C"D *%!>VN1?
}N""%!*1?&"$1}.KN""%!*%""N!{N.&"$1%!1K/#$*7>"%*"?="*"* %"" " !$> " !0" !" " %%" & *%!>%"?& %"%!"%""$1">%$ !0"%"%!%?>"*&; * u tl CD
"?1>""&;
* NtGWN G } G W H%" ">"=$ !0""1
%%" 1?CD%&"$1C"D !$ &1 " "%!" %" .0"> " "%!"%"?">$*78 8""*&%>
-
+
$$!0">" 1$$1% !0"!""*"> " "" " * % 1 1" ' Q$S )%1*D * 8 !0"$
;
* u tl NtGWN G } G W
}.Ku QOg}
D "$1N*H.N'$H/$N2$/
-
2
D""%!*1?$%;
}N81 N/$D !0")%1;
* N G } G WN-29314H/$H2$/N#(-(9N(9(>9U1!?D* 8 !0";$"%!"$1$"&1>$$"*;
M uI47 N1M8417 N9>(+$'
}.Ku QOg}N 7LC11M;1g/$N/>(+$FK/ $ !1 "1 " * 1
-
-
* u tl NtGWN G } G W }.Ku QOg}
1CD;D $%N*H.N/$H/$N'$/
D ""%!*1?$%;
}Ng u'$g1 N#$D !0")%1;
* N G } G WN-29314H#$H'$/N-(/99N/99/9>'U1!1C*D?D * 8 !0";
$"%!"$1$"&1>$$"*;
M uI47 N1M417 N>$'
}.Ku QOg}N 7ABB191M81g#$N#>9+$1 CD; $ !0 "* % CD> " " 0 1$%*$%>="$"!1"1?D 1$%*$%;
-
'9
?D 0"$$$"C "%%C9D>=
%$%*">"1.>"*;
N9*H,o*SH*
;*NC}.KE}Dg NC#>9+$a#$Dg1 N>9+$
1;*KNI N7:L
"*$&CD>*%!C0D>!0!CD*%" ."&"; l*Ntl."8>t u z>"Vl*Nzl=""!0"!"CD"%""8
-
'
K/("* ) z u > 1 0 $%0 C*D>*$"; * u l CD
CD %" " 1 % * !0 "CD "%!" %" "> " $*1 . H%" % "%! "$1> = % $" > ! $!1 0! &$" CD>$"; * u l CD
! &; Nu7 l
;u l CD
-
'/
" = ! " $%"* %1$8"%V N C!D
1$%0 C!D CD>*$"V * uzCD
CD> "%$& $? $ !0 "CD! %!C0D*"?" CD;
D !0 " = ) ! %" "* "%! %> $1 =? %" "%!>$%%&$"$
/D "1!=!0"@&CDD ?!0"CD"%&1 CkD
"%!> % " 1 &> $ $"$$ %!0">"$%1=
" "%!" ?"> $% & "%!"$1=.$"$%""C%D %$ &1 " "%!" ?"> 8 !0 "> "& * % C%D H" =* $$1%!0"
-
'
; N""" "%""%!"$1."&"%!$%$
WN"$1FK % !1 "1 %" $% #Q$S
-
''
D " " % "%! * % > 1?$%CMD;*"?!1>"%1$8; N G yN N B1 BN($D !0")%1"*$%;* u G G N-29314H$H9>+-$/N//'->+N/+/'+U1!?D* 8 !0";1C*D$"%!"$1$"!>$$"*;
M uVbL8 NVM71L8 N'-Hv$'1V8 "*&1)M;
u Q(OgN8:7M71LAC:1 g($N(>9$
FK/;$%!1"1>"*"1H$!I5J
-
'#
D !0"=)1"*$%*D * 8 !0"$
D 0" *
$)"%%"$%
;* u tl NtGWN G G Wu Q(Og 1CD;
D "$1N.HN'$H$N/`;"%*$>%! """&"$1D " " % "%! * % > 1?$%CMD;
*"?!1>"VN81 N/$>/#U1!1C5D;?D$"%!"$1$"&1>$$"*;
M uI47 NB1M84147 N($'1V8 "*&1)$
-
'(
1CD;01$%*$%;
N9,H#$aHN9 " ? N >/# % \& " %" $$7 "8 $"'>$*]("#)3*+8*.15
/
-
'+
/ "$%$"5"&"9/9QO1R$/S>"$ $"$"""\L7?&A$ $>"$ $"G%" />QO1R$/S]("#)0-*./
/' =!1"%"0N/>+QUSSC$D" 8=" $"*" $ $> IJQ$$S 8='("#)-./
+, $ $ ! * IJ !1> = !$$7"?N92>""%"
-
'2
/( 9K>$"$"!1#Q%S >/#;
D 0"
*D * 8
%"!%("#) >;48*- ?1;,0;
-
'-
D !0")%1"*"%!
*D * 88 !0"$
$)"%%"$%
("#)*660,./@*064,./
/2 % "!1"
"?N92>2#" $";
D !0 " "*
$%I5JU1!*D * !0 " $>
%%I5JD 0 ) % %" P9
U1!$)"%%"$%
("#)>;--,0.=/@;./
$A@B*;88,40.=/
-
#9
,
"""$?$"!"%)$%"">18>5
"%%""$">""!)""%>"8""$?$!)""??%"%0""" ""
" !"> * = $?" %" " !$ $ * " % &"" . !$ > $&" "" >"$$& 0 $%" %" "
& +
H%" =?CgD%!>"! %" Cg D $ % *"?" !1 K/#> = %" "$!
-
#
=$"%8"!"!$="$$%?"%" %8"$%?%" CgD
CgD;CH?>WDK/#$%?" 1!)!
/F,, ) " %$ C3 !1 K /(D "% @ $% ?" = ? % % "% ?8 "% $%*.=!)"$%=%8!" $? ? > $" @ %8 $ % $ ""?"1$%!)%>=
"%8"=%"%%*"? !&"$%$"$?
K/()"%$ " !) "> ? " %8" % " %" >1; gNgCg
-
#/
F!)!$"%C3!1K/+D@$%=?"" 0 *"? > "* "% ?%?$%>">"%!1!)!$""
K/+)!$
'
, " $& " " .* < $ 8 11$7"%""""?"%8$$%!)$* $& !" " ! % $" @ % "%! $?$!!$8=
81??""%"C!1K/2D!)""%%! ?"?N0
1V"!$*7$V
-
#'
u m
;LN"
N3"$N" !)#,
$ $" "$
"$7
"$1"
"$1"
,B+
$
"
$
"
$
"
"
#/F!$$"!=?"" !)>%$%1"VLN0 *&V
` u m
-
##
%$ $ ? !) $&" % !)?$7#//F
$ $" "$
"$7
"$1"
"$1"
+
O1
"
,
"
1
"
1
"
(F$!)""$$%$ 1"?$7 ! % $ 1" $&" "" %" "" 8 *8 = "% ! ,$*7 "
$"$">$"!)!) $"H" ?"" $&"
-
#(
K9,*3K!(/F35"%?*%&""*"!$%"*.*>$"
?"$"H81
K/&$(F,:" " "> = *) % %"> $ $" 1&" $%"" ="%%1?7"$ 8=$>""G"
-
#+
*%" %"1"="!$"G7C3!1"K"*"%"? 18 ="*""%"!$">?$C3D % "%! CD> " ?$"%= " % %"" $" ! ! $*7 $ ""$$ %" ! = % ?$ ? "$%
K#3$
-
#2
/,,,M $ "% "V "1"0 N9C%"? $"D>"!C*8D>!)$&"%CD>"&1!)$&"%C/DC1K(D>"$%""$"=;
-
#-
` N` ! V ` u G >1V 7G 7NG >LN?H>$"V 7 G 7 G 7 u G G "!ZN>"*&V 7 G 7 u G C D
;?N?"$N" !)
& " > " NV8 > $%0
>$"=V
7 G 7N G C ! "&"D&"" ""%>="&" !)% "$ !) $> ? "$< " &"$?"$$&/:5%% 5
> $*7 $ 5
,$5
>"*$%$!$?7"18 H%"% 5
" * C+2D 18 = %" ! %$ " 1 "
5
C+99E+2/D> $7 H%"" "*$" $&!",$*7""$$&"%">!"!8
-
(9
"$>18!=%">""$%";
,Nggh
,N18%"$!)N18!)>"18=!*%" =%"N187>"18*?=%"!hN18%1?>"18*=!%"/::5 5
>*"?$" !1K+>?$" "$*"17"=% !"G0>""%01*8!1>""G" %" " . "%0 ? i ?$%i"../
-
(
M? 18%>"&V
0N$]}o$]}7N7$} o }7D
">"$? 187$"%>"V
,N7$ o 7Dg7$} o }7DCD%"!)!0"*"%" "*% !">"*"NH " " !0 "VPNHNHH1*)CPD"&VPNPaP/NHH E/H/H/>%3NHN/H/> ="?$$$">"V
PN,1>$%0""CD"*& 5
c j Tcjz7N j Tjz
-
(/
;N" !N3!zNN""%8!!1N 1?/N"" %$ $ %" > ? !> =%"$*8>$%"18>%"" " 7$" " " 1> "@$ 17"?>%" 17".18=%"$!>"H%"7$"18CB,D>=%$"H%"$;
B,NgT
3gz
"""18 5
>"$%$@$$%"$!>%)$%Q$SC$$1D
-
(
//:5,5FF; 5
$ = % "$" *"* 18 "$!"!"% $%=%" 18 % % $&=> = " $ 18 $&= .& @ CB$.D " $ 5
%*))>"%H%"$V c j Tcjz7B$.N j Tjz;CgD$&=1C5$*DCED$&=$C,*D
;K25
*))"!1K2>CBD%"18=H"$&=18.&$=CB$.D"1!"18B/
-
('
0"$%0">*$"V
NMM0 >"3NHyNM0 ">%.&=&H%"$V
BN G 1G
;N""%8!!1N18$&=.&LN=%"?7"$&=/#,,FCD "%$&=1*"*$&=.&")>="$&=1C5$*D""!$18.&C3!1K-D$&=$C5$*D>"!$ 18".&$&
K-$&.&5$*
-
(#
%$"%H%"$;
N13M " H%$ %7"" $&= C3$7"> .&" " =H"18*=%"*$*"V
l,5*N0&0H99
;l,5*N$!*$*.N.&N$)/+,,4,M,,4,*$*.&0*$*1%% %"""">"$"%$7"$!$7>"%$ % 7"$"%7C3!1K'9D
K'9
-
((
7 "$" % 7> " $ $ ""1"H%""; t+R[/.0NmCDt+R[/.0Nm C$!&"Dt+R[/.0Nmmm C!&"D
;N3)8" Z3SN"QS N%C9>+#a9>2D$!$7>=" %=$7"$"")"H%"$"1H%" ;
l7N00H99
;N$)$77N7
BF::5,5FFFK"=1!1>"1?7"*8%1&$> . 1 C5D ? "= %$ ">;
D 31%C5D$R"
*D ?7" *8 R$
D 3 %" %Q*SCD
-
(+
7 G 7N G C Dc j Tcjz7N j TjzC 5
"*))"D1CD%$" 5
"%"M5V
BNB5 j TjzN j Tjz 1>"%CDN9>3N9(Q$R"S1 C5D; % C5D> " % $ "1H%" V
L5N35H5&$"%1N9>9/#'$>">
5NV8 NV8 vAv`N#Hv8`
1?7"*8"&V uAN->($R"H#Hv8`N9>9/`BR"H7
014 H LW71UN/99Z,+N`Y1CD;% 5
"%"
-
(2
j TjzN j Tjz
1>"%C5D5N9>35N->($R" ( $R" > " 5
=&V jv`N$
t NHC#9aDN-29R$H'-$N'29(-9QR$/YH 7I-S7
-
(-
7 G 7N G C Dc j Tcjz7N j TjzC 5
"*))"D
%$" 5
"%"M/V
BNB/c j Tcjz7N j Tjz1>"%CDN9>3N9"=V
/NECHh/DNEC>H-29R$H$DNE99R$/NE>/*/F::5,5FFFK!1$"" *$*8!1"$1>$%%H1"%0 29 Q$S%!
-
+9
7 G 7N G C Dc j Tcjz7 1N j TjzC 5
*))"DBNjHB$.HL
1CD;%$" 5
"%"M/V
BjB$.NB/c j Tcjz7jB$.N j Tjz
1>"%CDN9>3N9(Hv14W N/#+>(PN/>#/UP1CD;$*$*.&";
l,5*N0&0H99
1>%$>"&V
-
+
N0&N7A92L9 N->/(UP
1CD;$$7";
lN00H99
1>%"$%7>"&V
N0& N7:AL2;8 N//>-UP
FK/ !1 $" .7> =""1"1e="*)"="?"1$*" " $*"#9m
D 7 "$"E 7 UP> " $ 1 " -9m;
7 G 7N G C Dc j Tcjz7 1N j TjzC 5
*))"DBNjHB$.HL
-
+/
;1CD;%$" 5
"%"M/V
BoB$.NB/c j Tcjz7oB$.N j Tjz
1>"%CDN9>3N9+-$/ NN914 WAC:1 N>+1W "%)B$.*$"V
B$.N/+$ETN/+$EBA7C
1 WM:A;1 W N/(>#$1C*D;%.&*"*%*>"*$H%" V
BNHB$.HLN-29R$H/(>#$H/>#14W N9/'/>#PN9/>'9UP$*"V
l,*N00&H99
">%"$")>"&V
N#SIU- HBN9>#H9/>'9UPN##>/UP
-
+
1CD;"=$17>"V
lN00 H99
>%"$"7>"&V
)N/U/S-"S H)N9>-H##>/UPN-(>9UP
5 %" = !1 )" *=
C&$ 9 1D> % % ? . +# %R" C&$ 9>+#%1D>!"129K>%="""&>22Q"1R%S
("#);,0.#"/
/"%" "((>/U$
%" C5D
("#);9806.=/
-
+'
"=="$"!1>>1="%
*=
-
+#
("#);802*
39.
95"/
(!1$"$!)>%!"%"""$*8"*"">
-
+2
':5,5FF " % 5
> ""$ *$* " "> " %H%"V
BB$.NB/giBE/c j Tcjz7B$.N j TjzgiBE/
'/,4,,56
%18*8CiBE/D>""$"
" %7" 18 = " H%$ 1 "$ ! % %.&%%!>"&1;
D ""*$*";B$BNBgiBE/
*D ""*";B$BNBEiBE/;BN? C5$*DBN8C,*DiBE/N18%718"H%"$!">"VQ$SN$"$1
-
+-
Q%SN"$"1'/:3,C.!D %7 1 % ! ?"" 1 C$"D> " ! $ %718%""=*8G8%%"!"%%718>! $%">"%71$!)"$ *8 71$!)>""%7""&$">$*"71$"*>"%7""&$"">"$""1"%"18$"!);
D 71$$*D 71$" D 71$*
'/471$$>!"$?%"&$"" $* $?$ C3 !1 K 'D " " * "!"%"!0"?"""!
K')$'//4,:"%71$"0%"$"%"&$">%%"1"0"*C1K'/D
-
29
K'/)," '/4,5,71$*"0%$?$"&
" %8" !> H" $* $">="$*>"!7$"@$%$$%71$!)*8
-
2
/99 !) " $ 71$%"$*>%"8"""%!"*8>
$&""071$0"
K''H%$"%$"
-
2/
*"? " $ %%$ 1 "%"""$*"H$"1CD>"!$ %718
K'#"%! ?""
F*8*/9$"11?3N/>#$R""!! ^N999/>$%%1! ?""*8$%0"" %7%! ?""V
.NdGGTG3Gb NA
M1MA91
WM:A;1 W M7:1 u9>(+Q$S'/+,:!! "%&$>=" "8""!>
-
"%71$!)>!$%""1""V
D 71$$;^*D 71$ * *8 0;
C 5""D
D )**81";
D 71$,"
;^N! N@$ $ % % 71$> @$
" % *!
"%71$!)>!! ^D>"%$$%""1""V
u L8* *8 0; ^ u L8cN C3& ."
)**81";7dN>'a9>2(l bC
71$," ;7dNE9>2(l bBAC j A97dC
!
N@$ $ % % 71$> @$
$ ? !
-
2'
'/-:BhaPC.D"%7"%! ?""$*7%""$ B0="H%"%; u cAA;GcAGbAQ1.-1 S;LN"%Q$R"SN&$*8Q$S
N!1"B0
-
2#
;3N3 !UN"$"%71"!11N 1?C->2$R"/D"?"U%"""!1>"$"*!1K'2
K'2,*?"U%"" L N 3 H " $ ? "$ 1*8>"1H%" ;
3N8GVGb
;LNQ$R"SN&$*8Q$R"S
-
2(
3N3"$Q$R"S1V"LN(>(QR"SN999((Q$R"S"=;
3N8GVGbN8GA
LL1
4 WVGC9 N>'-Q$R"S
$%0 ? * $ ! $ %7 18 % !1
-
2+
'BFK; !1 $" ""$ $ 1" >
-
22
$ "&$" " *8" "% '14
S
L**N2>'14S N#>9'H9E1
4W
$ " ?" "% "%*"&$">$"1H%" V
-WKu 8VN8M9A874>4O VM71 W N2>9H9E/$N2>9$p1"
"/W. u 8VN8M9A874>4O VM1 W N#>+9H9E/$N#>(($/p1"
1C*D18.&*$*>% 5
"%"3N9#$
-
2-
"%7""""$"&V
iBE/N }[ j }d"%7""% "&V
8"% ;
iB"%N^ 7A971G71 WG3G;A7G71 gABA9AG71 W3 N^>#-g#>H9E/$"%!"%*$>!! "^N9>9/#>"
iB"%N9>9/#H>#9$g#>H9E/$N99-$
8"1;
iB"N^ A971G1 WG3G9ALLG71 gA9AG1 W3 N^>#-g#>H9E/$"%!"%*$>!! "^N9>9/#>"
iB"N9>9/#H/>(/$g#>#H9E/$N92+$
1%7CiBE/D"&V
iBE/N9>9-$g9>2+$N9>-($".&%%%*$*";
B$.N92>/$giBE/N92>/$g9>-($N9->-$1CD;
0V.Nj./HB$.HLN-29 -$H#>9'H9E14W .N#-2>(/PN#>'9UP!*$*"(9m>%$$7*$*>"*H%" V
N0& N
9A82AL N-UP
-
-9
''5'*$*"$1*%%0%!%+>'#1$
%1 &$> " ! ""$ = "$" !1 " %7 9>#%"""$"VD%.&"$%*$*1B*D $ *$* " % $"B("#)$;*089.CY@($;897
'/ *$* = " $" !1 " " > 2# $"=%" C5D"/+#CUD %718 ""$ " />/# ?" 187!)>%.&%%*$*!UP("#)$;*096.=BY
' !1"$"*$*=H2'9CR$DN9>2# $* $$ "*&."%$%""$%"$D%718""$"'C$D>%.&*$*UP*D %7 "% " >' $>%" *$*U("#)$;*089.=BY@;3880-.=Y
-
-
''""%!"%*$*$*"*$ ?"*=*"$" 1"'9"1">%" " #9C$$ B1D ?8
-
-/
55
$ $D $&
&05! &""
" ?" .E/99+
* & " "%
" EB
B"%$
.$"?1B &"" WB
E/99
3 &"" WB
E/99