"!
#$&%')(+*-,-.0/1(
2436587:9<;>=@?A7CB+DE3FG=HFG9I7;KJGLM3NOL&9P;>=HQSRT9UFG9V;>=@?A7CB =WFG3S7TBYX9PD 9<NOJ[ZHFG9
\ ]_^1`ba \4cd]e^[`Yf gh]_^1`i
j L&kl;nmpoCNO=W9P;qr3;6qr3;ts7C=@?[Fu7 vwJ[3 \ c ]_^1` L&3NODx7T?[3QS7 9 DE3;8DE9ys{z
FG3|;>33;8L&3N>7CN}v~J[3|LA7TN>TDU3€qrNO9l;3;6qr=@D‚7TFG9P;JG;7)?[FG9Tƒ„;K3 \ ]_^1` q7TD†…MzD
m07TN8=H3Dˆ‡ 243‚q7T=H;‰LA7CN>TDU3€qrNO9P;UŠ‹9ŒNO3D X9P?G;>=HFG3Nr7TFG9P;IX9lDU9m07CNO=Žom03=H;
7TBW3S7qrklNO=‘7);sAvwJA7C=@;;K3N8=Ž7TD 7T;’;KJA7);XS7TNr7TX€qr3NOZ@;Oq>=WXS7);{3;Oq7Sq>ZH;6qr=HXS7);“
Ž”
•(1–"—G')˜d™w—1.0/[( *›šˆœž%t˜‹Ÿ —u*›([')š~† ¡¢(u$£Œšw˜d%t(u
j L&9lB‘7TN8=@¤)7TQSRC9¥K¦§©¨)ªK«¬z|FG3­[?[=HFu7:X9PDE9
® a ¯±°e³M² ´Mµ ³ i
œ š~Ÿ - –d( Ž” "!1
¨€§¨
ª "§ ¨
¨
"! #%$ ¬9P?G;>=HFG3NO3
&
\ ]_^1`ba
'
]_^[` f gh]_^1`*)ž^‚a
(
)i)iSi/.0)
+)*,-)
;>3?[FG9‰vwJ[3 ( ]_^[` z7:3?wq>N>7CFu7‰FG9<;>=@;Oq>3D‚7<3 ' z 921w7T?%3[9y‡±2hJGL&9l?[FG9
vwJ[3‰9nNOJ[ZHFG9n?ART9ˆ7)Š‹3€q>3x7‚3?0q>Nr7TFu7 ( ]_^1` s+JGD‚7UŠ‹9ŒN6D‚7‚FG3V;>3V3;6qr=@D‚7TN
9 1~7)%? 3[9 ' 7nLA7CN q>=WN†FG9P;:Fu7TFG9l;FG3I3?0qrN>7CFu73U;7TZWFu7FG9ˆ;K=H;6qr3Dx7z
4
XS7TBWXJ[BŽ7CN
\ ]_^1` i
.
( ]_^[`
687:9
j LM9ŒBŽ7CNO=@¤)7CQSRT9FG3;Oq>3V3;Oq>=HDx7CFG9lNžL&9~FG3:;>3N{FG3€q>3NODU=H?A7TFu77ILA7TN qr=HN
Fu7†FG3­[?[=WQSRT9UX9PDE9V;>3|;K31ŒJ[3 ;
² a
'
a ¯±° ' ² ´uµ
<
a
5
+
+
.
=
'
.
a
a
'
687:9
5
687:9
5
+
+
.
5
=
¯±°>'
687:9
´ µ
±
¯
°
h
g
_
]
1
^
`
f ( ]e^[` ?
gh]_^1` i
( ]_^1`
(
]e^[`Yf gh]_^1` ´ µ
( ]_^[`
?
'
'
@
42 36587 \ ]_^1` a _] ^ µ +` ³ f gh]_^[` s vwJ[3 Œ1 3N>7 JGD X9P?l5 JG?0q>9 FG3
3vwJA7CQ~3;’FG9Vq>=HL&9 a ³ f ys 3
³² a )
;>3?[FG9 7 ¨ €§ ! ªrª ª3 zbJGD‚7 Dx7Sq>N8=@¤ XJl5 9P;-3BW3DU3?0qr9P;
FG3L&3?[FG3D GF 9P; N831ŒNO3;K;>9lNO3;‡?0q€RT9Gs4qr3D:ƒ„;>3
® a ±¯ °
´Aµ
a ¯±°
U] ³
a ¯±° ]
µ
a ¯±°
µ
³
)
f 1 ` ´uµ ³ )
` ³M´ f ¯±°
´ )
p´d³ f ¯±°
´ )
7TN>7<vwJ[37:L&9lB‘7TNO=H¤)7TQSRC9E;K36587:?~J[B‘7n¥©® a «}7T;;K3 ŒJ[=@?0qr3;X9l?G;K=WFG3N>7ƒ
Q~3;’L[NO3X=H; 7TD ;>3N±;7qr=@;8Š‹3= q€7);
1
;
¡¢(A$-˜"*›š0')—u.p/1( "!1 j D‚7q>N8=@¤ FG3€mw3|;K3N¬q7CB vwJ[3 a ‡
¢¡ (A$-˜"*›š0')—u.p/1( Ž” ;{3BH3DE3?0qr9P;žFG3 ?ART9x3;OqRC9‚X9ŒNONO3B‘7TX=W9P?A7tƒ
FG9P;X9PD 9†mw3€q>9ŒN’FG3|3N8NO9 š sGBW9 1Œ9 ¯±°
´ a ±¯ °
´ ¯±° ´ ‡
¡¢(A$-˜"*›š0')—u.p/1( 3NON89FG3€m03 q>3N DEzFG=Ž7¤t3NO9Gs0=@;Oq>9zŒs ¯±° ´ a ‡
¡¢(A$-˜"*›š0')—u.p/1( ›|š z 9lN qr9 p1 9P?A7TB BH=H?%3A7); GF 3 slBH9 1p9 ±¯ °
´ a ‡
•(1–"—G')˜d™w—1.0/[( *›( œ{%t˜"Ÿ —1*›(1'
3 ;6qr=@D‚7TFG9lNFG3 DEZ@?[=HDU9l;vwJA7CFGN>7TFG9l;z JGD 3;Oq>=@D‚7TFG9ŒNBW=@?[3S7TNFG9’q>=HLM9
³ ² a sG;K3?[FG9‰vwJ[3
a i
9
j X9l?[FG=HQSRT9xDx7C=@;{N83BH3€m07)?0qr3†LA7TNr7U9x3;Oq>=@D‚7TFG9ŒNFG3DUZH?[=@DE9P;{vwJA7ƒ
FGN>7CFG9P; z7
‡4‡
œ š~Ÿ - –d( "!1
¨€§¨
ª "§ ¨
;7)?[FG9x7†FG3­[?[=WQSRT9UFG3|L&9lBŽ7CNO=H¤)7TQSRT9
® a ±¯ °e³ ² G´Mµ ³
a ¯±°
´Aµ
a ¯±°
] ³
a ¯±° ] µ
a ¯±°
µ
)
³
)
f 1 ` ´uµ ³ )
` ³M´ f ¯±°
´ )
p´d³ f ¯±°
´ )
;>3?[FG9v~J[3 a ° ´ 9 3 zxJGD‚7D‚7qrNO=H¤nFG3IL&3;>9P;
X9P?G;Oq7T?0q>3;‡ j ;YDU3;KDx7T;YX9l?G;K=WFG3N>7CQ~3;
4‡ 7
‡ s)D‚7); X9PD a s
FG3€m03D ;>3NI;7qr=@;8Š‹3= q€7);LA7TNr7 1w7CN>7)?wq>=HNnvwJ[39 m03€qr9lN‚FG3 LA7TNr)DE3€q>N89P;
@
3;Oq>=@D‚7TFG9l;ts ³ ² sy;K365K7?ART9‰L&9lB‘7TNO=H¤)7TFG9G‡
!"#$%&'%(
243 9 3;6qr=@D‚7TFG9ŒN*)*+ Š‹9ŒN‚JG;7TFG9Gs{9 mw3€q>9ŒNnFG3 N83;KZWFyJ[9P;;>3N>o4s-, a
µ ² a µ ˆ³/² .10 ‡32 9 1p9ys
a µ ˆ
³ ² .10
a ³ f µ ³/² .10
a †] ³ µ ³/² .40 `Yf i
,
;NO3;>ZHFyJ[9l;’;RT9U9lN q>9 Œ9P?A7C=@;|7C9P; NO3 pNO3;K;K9ŒNO3;s1L&9lN q€7)?0qr9
1
, a
1
5
a :] ³ µ ³ ²
3
.10
a †] /³ ² .40µ
¯±° ´ a ±¯ ° :] ³ ² .10
a ¯±°@] ³ ² .10
FG39P?[FG3žmw3D vwJ[3
®
.40
`Yf )
³`
µ ³ `´
µ ³ `´)
a ° ´ 9 ±¯ ° ´ i
[? 3X3;K; oCNO=H9 v~J[3b9±m03€q>9ŒN›FG3b3NON89;K365K7 9ŒN qr9 Œ1 9l?A7TB [3 =HLM3NO;8JGL&3N6Š‹ZHX=W3
1Œ3Nr7TFu7:L&3BH9P; N831ŒNO3;K;>9lNO3;
‚a 5i
6
œ š~Ÿ - –d( Ž” ¨€§¨
§ ¨
§ ¨
# #
2436587 \ ]_^[` a _] ^ µ +` ³ f gh]e^[` ‡ 2hJGL&9P?[FG9)ƒ„;>3|vwJ[39U3NONO9‰;>36587
gh]_^1` a
^f 
f
]_^1`*)
;>3?[FG9xvwJ[3 Y]e^[` zJGDx7<mp7CNO=‘o€mw3B 7CBH3S7qrklN8=Ž7x?ART97)J q>9hX9lNON83BŽ7CX=H9P?A7CFu7
¥"NOJ[ZHFG9…[Nr7)?[X90«ž3 3 ;RT9X9l?G;6q€7)?0qr3;t‡ 9lN q7T?0q>9Gs gh]e^[` ?ART9 q>3D
DEzFG=Ž7?hJ[BŽ7h‡ m07TBW9lN’Fu7;7TZHFu7:DE3FG=HFG9V?[9‰=@?G;Oq7T?0q>3 ^ z
_] ^ µ +` ³ f
\ ]_^[` a ^f
f
]_^1`i
2hJGL&9P?%3A7vwJ[3 JGD FG9P;N831ŒN83;8;>9lN83; ;>36587 \ ]_^ µ +t` ‡ 9lNX9PDULA7TN>7CQSRT9
X9PD 9<XS7T;K9x7)?wq>3NO=W9lNs qr3D:ƒ„;>3
\ ]_^ µ + ` a _] ^ µ ,P` ³ f gh]_^ µ + `*)
D‚7); A3 oJGD‚7†NO3B‘7TQSRC9‰XB‘7TN>7<3?0qrNO3 gh]_^1` 3 gh]_^ µ + ` vwJ[3z
@
gh]_^ µ + ` a }° ^ µ + ´ f f Y]_^ µ
a ^f f ]_^1`+f ]_^
a gh]_^1`Yf Y]_^ µ +` µ `
+
µ +` µ µ
µ Y]_^1`i
]_^1`
NO3 ŒN83;8;>9lN \+]_^ µ t` 3;Oqo{X9lN8NO3B‘7TX=H9l?A7TFG9X9PD gh]_^1` s ¯±° ´ a ‡
1
+
œ š~Ÿ - –d( § #M¨P§ ª ¨P§ ª
§©¨
# #
8000
7500
7000
6500
6000
5500
5000
4500
4000
3500
0
10
20
30
t (min)
40
50
60
3
vazão (g/min)
2.95
2.9
2.85
2.8
2.75
0
10
20
30
40
t (min)
50
60
70
80
pN>o)­1X9 ;8JGL&3NO=W9lN:z‚JGDx7;>zNO=H3 FG3x;7q>J[N>7TQSRC9 FG3
9y= ?[=H9<FG=H;8;>9lB m =HFG9V?[9†; 7T? lJ[3 FG3JGD ~JGD‚7)?[9y‡ j
3;>XS7TBŽ7mw3N qr=HXS7TB¬3;Oqo 3D JG?[=HFu7CFG3;U7TNO…[= q>NroTN8=Ž7);‡ ŒNroS­1X9E=@?yŠ"3NO=H9ŒN}z|JGD‚7;>zNO=W3FG3žm07)¤)RT9UFG37TN±?~JGD‚7
L[BŽ7T?0q7VL[=WBH9Tqr9EFG3 19Cq7CQSRT9E3D X9ŒB@JG?A7h‡
1
1
%1
3
1
@
$%&'%(! $%
2436587†JGD DE9~FG3BH9 j
]_^ µ ` a ° \ ]_^ µ ` i)iSi>\+]_^ µ ` ]_^ µ ` i)iSi ]_^ µ
³ a )i iSi i)iSi i
+
+
9
<
(
9
+
8(
`´
<
j L[BW=HXS7T?[FG9)ƒ„;>3 9 DU9hFG3BH9 7TX=@D‚7 7T9 BH9l?%1Œ9 FG9P;IFu7CFG9P;s 1p3N>7tƒ„;>3 7
3vwJA7CQSRT9nDx7Sq>N8=HX=Ž7CB a ³ f ‡ j X9P?[FG=WQSRT9nLA7TNr7‚vwJ[3:9 3;Oq>=HDx7ƒ
FG9lN )*+ ;K36587I?ART9 L&9lB‘7TNO=H¤)7TFG9z:vwJ[3:9l;|N831ŒN83;8;>9lN83; 3 ?ARC9‚;>36587)D
X9lN8NO3B‘7TX=H9l?A7TFG9l;t‡
6 X9P?0mw3?[=H3?0qr3 3;KXN83€m03N’9VDE9~FG3BH9<?A7Š"9lN6D‚7
]!p` \ ]_^1`ba " ]#p` ( ]_^1`+f gh]e^[`*)
;>3?[FG9{vwJ[3 gh]_^1` a ]!p` Y]_^1` 3 ]_^[` z …[Nr7)?[X9G‡ j DU3?[9l;vwJ[3 ]!p` a
DU9~FG3BW9P; j 3NON89P;
+ s gh]e^[` ?ARC9V;>3N>o†NOJ[ZHFG9<…[N>7)?[X9G‡ 9lN q7T?0q>9Gs[3D
FG3NO3 1ŒN83;8;RT9 …[N>7T?[X9P;ž?ART9xN83;8J[B q7)D 3D L&9lB‘7TNO=H¤)7TQSRC9 FG9x3;Oq>=HDx7CFG9lN
)*+:sT7T9LA7);K;>9 vwJ[3 7 7CFG=HQSRT9{FG3 N6J[ZWFG9…[N>7T?[X9 3D DE9~FG3BW9P;FG3 3NONO9?A7
;7TZHFu7 ¥"N6J[ZWFG9FG3VDE3FG=HQSRC90«7CXS7TNON83€q73D L&9ŒBŽ7TN8=@¤)7CQSRT9ˆFG93;Oq>=HDx7CFG9lN
FG
3 )*+:‡
œ š~Ÿ - –d( ›
¨€§¨
*
/ ª
M¨ ªt¨ ¨
* #
DE9~FG3BH9 j ;>=@D†J[BŽ7CFG9VŠ‹9Œ=
\+]e^[`ba
)\ ]_^ µ t+ ` µ )
)\+]e^ µ l, `+f + )
)
(
]_^ µ + `+f
]_^1`*)
;>3?[FG9:vwJ[3 ( ]_^1` 3 ]_^[` ;RT9:;>=@?A7C=@;7CBH3S7qrklN8=H9P; X 9lD GF =@;Oq>NO=H…GJ[=HQSRC9V?[9lN ƒ
D‚7TB©s&DEzFG=Ž7‰?~J[B‘7I3¢m07TN8=ŽT?[X=Ž7); a + 3 a ) ‡ DE9~FG3BW9‚FG3
3NON89<?A7†; 7CZHFu7:JG; 7CFG9VŠ"9l=
U]_^1` a + )‰]e^ µ + ` µ )‰]e^ µ P, ` f \ ]_^1` a ‰]e^[`Yf Y]e^[`*)
)
(
]_^ µ + `
;>3?[FG9 ( ]e^[` 3 Y]e^[` FG3­[?[=HFG9l; Fu7IDE3;KDx7EŠ‹9lNODx7‚vwJ[3<LA7TNr7x9nDE9~FG3ƒ
BH9 j ‡ …G;>3N m07TN v~J[3I7 ;>=@D†J[B‘7TQSRT9 FG9DU9hFG3BH9FG3U3NONO9ˆ?A7‚; 7CZHFu7
X9lN8NO3;KL&9P?[FG37†;K=HDJ[B‘7TN7Š‹JG?[QSRT9<FG3žqrN>7T?G;OŠ‹3N ?[X=Ž7
]!p` a
]#p`ba #] p`
"
+
µ
+ )
)
9
9
f )
)
3 yX= q7TFu7{L&3B‘73?wq>N>7CFu7 ( _] ^1` s1Œ3Nr7)?[FG97T;8;>=@D U
]_^1` 3±LM9l;6qr3NO=W9lN6DE3?0qr3
7TXN83;KX3?wq7TN9‰N6J[ZHFG9 ]_^[` s L&9P?0qr9I7†L&9P?0qr9y‡
10
(d)
(a)
10
5
0
1,3
1,35
1,4
1,45
1,5
0
1,3
1,55
1,35
1,4
1,45
1,5
(e)
5
5
0
−0,75 −0,7 −0,65 −0,6 −0,55 −0,5
0
−0,75 −0,7 −0,65 −0,6 −0,55 −0,5
10
10
5
0
0,45
1,55
10
(f)
(b)
10
(c)
5
5
0
0,45
=H;6qr9 1ŒNr7)D‚7);±FG3LA7CN>TDU3€qrNO9P;¬3;Oq>0,5=HDx7CFG9P; JG; 0,557T?[FG9)ƒ„;>3
93;Oq>=HDx7CFG9lN )*+:‡ ; 1ŒN>o)­1X9P;}¥_7Œ«s[¥‹…A« 3{¥©XS« ;>3 N83Š‹3ƒ
NO3D 7T9DE9~FG3BH9FG3 3NON89¢?A7; 7CZHFu7 3 9P; 1ŒNroS­1X9l;|¥"Fu«s
¥"3S«3n¥dŠ>«;K3:N83Š‹3NO3D 7T9‚DU9hFG3BH9 j ‡ ;{m07TBH9ŒNO3;
NO3S7C=@;’FG9P;±LA7CN>TDU3€qrNO9P;}; RC9 ;’¥_7l« 3V¥©Fu« 9 a + )
¥‹…A«
3U¥"3S
« a µ ) 3U¥©XS«¬3‰¥‹Š>« a ) ¥"…[=Ž7T; {«€‡ @
0,5
0,55
8
œ š~Ÿ - –d( ¨€§¨
\ ]_^ µ `
§ ¨ ¨
! ªrª ª
2436587V9VDE9~FG3BW9 j
\ ]_^1`ba } \ ]_^ µ + `+f
X9PD
gh]_^1` a Ygh]e^ µ t+ `+f
;>3?[FG9<vwJ[3
] A`ba )
\ ]_^1`ba } \ ]_^ µ t+ ` f
3
]_^ µ + `+f gh]_^[`
< (
]_^1`*)
a ‡ -3DVƒ„;K33?wqRT9
< (
]_^ µ + `+f
\ ]_^ µ + `ba ± \ ]_^ µ P, ` f
gh]_^ µ + ` f Y ]e^[`
]_^ µ P, `Yf gh]_^ µ t+ `i
< (
7T¤t3?[FG9)ƒ„;>3|;8JG…G;Oq>= qKJ[=WQ~3;ts19l… q>zDVƒ„;K3
\ ]_^[` a
° ±\ _] ^ µ ,P`+f < ( ]_^ µ P, `+f gh]_^ µ +t` ´ f
f gh]_^ µ +` f Y]_^1`i
< (
]_^ µ + `
243|?ARC9 [3 9lJ m03;K;K3N831ŒNO3;K;>9lNO3;FG9:q>=HLM9 \ ]_^ µ ` s4q>3N ƒ„;K3ƒ =‘7
\ ]_^[` a
a
< (
< (
3;K;K3XS7T;K9GsG9U3;Oq>=@D‚7TFG9ŒN
]e^ µ +`Yf gh]_^ µ + `+f
e] ^ µ +Y` f gh]_^1`i
)*+
]_^1`
3;Oq>=@D‚7TN8=Ž7 {< ;K3D L&9lB‘7TNO=H¤)7TQSRC9y‡
@
j LM9ŒBŽ7CNO=@¤)7CQSRT9 L&9~FG3x;K3N m =@;Oq7 X9lDU99NO3;KJ[B q7CFG9 FG9 3;Oq>=HDx7CFG9lN
3;Oq7TN„Š‹9lN8QS7)?[FG9 , a ¥‹L[NO9lL[NO=W3Fu7TFG3EFG3‰9ŒN qr9 1Œ9l?A7TBW=HFu7TFG3 3?0q>N83
NO3 1pNO3;K;K9ŒNO3;‚3ˆNO3;>ZHFyJ[9P;«s±;>3?[FG9 vwJ[3 a ‡ D 9PJ qrN>7);‚LA7TBŽ7ƒ
m Nr7);s 7ELM9ŒBŽ7CNO=@¤)7CQSRT9 ;8J[N 1Œ3:3D Š‹JG?[QSRT9‚FG9‚X9P? 1= qr9‚vwJ[3†3 y=H;6qr3:3?0q>N83
7L[NO9PL[N8=H3Fu7CFG3{FG93;6qr=@D‚7TFG9lN FG3DEZ@?[=HDU9l; v~JA7TFGN>7CFG9P;s , a s~3ž7
L[NO9lL[NO=W3Fu7TFG3 FG9‰3NONO9UFG3NO3 1pNO3;K; RC9ys a ‡
! 9lBŽ7CNO=H¤)7TQSRT9:FG9¢3;6qr=@D‚7TFG9lN )*+ v~JA7)?[FG9¢93NON89 ?ART9
z†9lN q>9 1p9P?A7CB 7C9P;|NO3 1ŒN83;8;>9lN83;t‡ 3;8;>3†XS7);>9x9P;žLA7TN>ƒ
DE3€q>NO9l;:X9lNON83€q>9l;:; RC9 ° 9 ´ s-3I9 3;6qr=@D‚7TFG9ŒN )*+
FG3€q>3NODU=H?A7 ° ² " 9 ² " ´ ‡
"' $% &
' " &' 9l?G;K=WFG3NO3
(
'
*) 6
)
-, _] ^1` a ( c ]_^1`+f ]_^1`*)
\ ]_^1` a \ c _] ^1` f g ]_^1`i
6
(& ( +
6
6
6
"! 6 ! 6
$
# %
T7 ?0q>9†9;K=H?A7TBMFG33?0qrN>7TFu7¢vwJA7T?0q>9†9FG3; 7CZHFu7¢3;OqRT9
X9P?wq7)DE=@?A7CFG9P; L&9lN ¦ ª ¨ ‡
7qr3Dx7Sq>=WXS7)DE3?0q>3Œs q>3DVƒ„;K3
]!p` \ c ]e^[` a "]!0` c ]_^1`
U
U]!0` ° \ ]_^[` µ g ]_^1` ´ a "!] 0` ° _] ^1` µ ]_^1` ´
U!] p` \+]_^1` a "!] 0` ]_^1` f °
U]!0` ]!0` ]_^1` µ " ]!p` ]_^1` ´
(
(
(
)
;>3?[FG9nv~J[3 ]_^1` 3 ]_^1` ;RT9NOJ[ZHFG9P;¢…[N>7)?[X9l;?ART9X9lN8NO3B‘7TX=H9l?A7TFG9l;
3?0qrNO3;>=©‡ ±; LA7CN>)DE3€q>N89P;FG9<DU9~FG3BW9V;>3N>RC9‰3;Oq>=HDx7CFG9P;JG; 7T?[FG9)ƒ„;>3
U]!0` \+]e^[`ba " ]!p` ]_^[`Yf gh]_^1`
(
*)
3N8NO9?A7x3vwJA7TQSRC9FG3VNO3 pNO3;K; RC9?ART9z:…[N>7T?[X9ys L&9Œ=@;7)L&3;7TN|FG3
…[Nr7)?[X9l;ts47);K;8JGDE3ƒ„;K3’vwJ[3’9P; ­1B q>N89P; U]!p` ]!p` a ]_^1` 3 ]_^1` ;>3NO3D
3 "]!0` a ‡
D‚7 9PJ qrN>7nŠ‹9lNODx7nFG3U3?0qr3?[FG3N7 L&9lBŽ7CNO=H¤)7TQSRT9 ?[3;Oq>3UXS7);>9z‰9l…4ƒ
;>3N m07TN’vwJ[3žq7T?0q>9U9U3NONO9UFG3|NO3 pNO3;K; RC9
1
+
+
1
gh]_^1` a U]!p` ]!p` ]_^[` µ " ]#p` _] ^1`
vwJA7T?0q>9 7 L[NOklL[NO=‘73?0qrN>7CFu7FG3L&3?[FG3D GF 3 ]_^1` ‡ 9ŒN q7T?0q>9 ( _] ^1` 3
gh]_^1` 3;OqRT9UX9lN8NO3B‘7TX=H9l?A7TFG9l;tsu9lJ;K365874s _] ^1` a ‡
' 6 +
(
( 6
*)
6
6
"! 6 6
# $ %
! 6 ;>=@?A7TB FG3I3?0qrN>7CFu73;OqoX9P?wq7)DE=@?A7CFG9LM9ŒN ¨ ¨ €‡ 7TB p9lN8= qKDE9ysu3?wq>NO3€q€7)?0qr9ys1JG;7:9‰;>=@?A7TB
=HFG3S7CB c ]_^1` ‡ ;K=H?A7TB¬FG3I;7TZWFu7 3;6q€oX9l?0q7TDU=H?A7TFG9
L&9lN § ‡ 3;6q€7†;>= q>JA7TQSRC9ysu9<3;Oq>=HDx7ƒ
FG9lN )*+ ;>k|?ART9 ;>3N>o{L&9lB‘7TN8=@¤)7TFG9 ;K3 !] p` a !] 0`
3 "!] p` a ‡
1
(
9
+
)
7qr3Dx7Sq>=WXS7)DE3?0q>3Œs q>3DVƒ„;K3
]!0` \4cd]_^1` a "]!p` e] ^[`
U
U]!0` ° \+]e^[` µ g ]_^1` ´ a "!] p` c ]e^[`f ]_^1` U!] p` \ ]_^1` a "!] p` c ]_[^ `f U]#p` ]#p` ]_^1`f " ]!p` ]_^1`i
(
(
(
9lN q7)?wq>9ys093;6qr=@D‚7TFG9ŒN )*+ ;>k ;>3N>o}L&9lB‘7TN8=@¤)7TFG9ž;>3 U]#p` ]#p` ]_^1`
?ART9 Š‹9lN›…[Nr7)?[X9GsCJGD‚7¬m03¤ vwJ[3 c ]_^1` ?ART9FG3L&3?[FG3 FG3 ]_^1` ‡ J¢;>36587hs
9N6J[ZHFG9†FG3ž7SqKJA7TFG9ŒN}7)LA7CNO3X3 ?[93NON89Fu7 3vwJA7CQSRT9†FG3NO3 pNO3;K; RC9ys4D‚7);
?ART9‰?[9V;>=@?A7CB FG33?wq>N>7CFu7†J qr=HBW=@¤)7TFG9UL&3BH9‰3;6qr=@D‚7TFG9ŒN‡
(
1
j
¡¢(y—['S˜u$-£p˜‹— *›šˆœ{%t˜‹Ÿ —1*-(['Sš~
¨ €§ #§ ¨
¨ ¨ §
-
´a
° 7TNr7žJGD m03€qr9lN
3z
s~7
)
¨ § #§©¨ q>3D FG=HDU3?G;RT9
¯±° ´ ` ´i
´ z|;>=@DEz€q>NO=WXS7:3|;>3DE=HFG3­[?[=HFu7†L&9P;>= q>= m07h‡ 7)D†…&zDs
´a
¨
!
"§
#"
¨ €§
¨
)
¨
° ´ i
§ FG3|JGD 3;KXS7CBŽ7TN
%$'& ° 37
¨ €§
´ a ¯ ] µ ±¯ ° ´ `€] µ
a ¯±° ´Aµ ±¯ ° ´ ¯±° ° ¨
ª r¨ ¨nz
a ¯ " ] µ ¯±° ´ ` ° ° / !
"§
&*&,+ ° z
´ a ¯±°( ´ )
#"
´a ¯
§ FG3 JGD m03€q>9ŒN
i
z
1&'!"
&' "
40
35
número de ocorrências
30
25
20
15
10
5
0
−4
−3
−2
−1
0
valores de teta
1
2
3
4
H= ;6qr9 1ŒNr7)D‚7 FG3 m07TBW9lN83;3;Oq>=HDx7CFG9P; FG3 JGD LA7TN>ƒ
DE3€q>NO9 X9lD m07TBH9ŒN 4s h‡ )3;KDU9 vwJ[3 9 3;6qr=@D‚7TFG9lN
J q>=WBH=H¤)7TFG9?ARC9nŠ‹9P;K;>3<L&9lB‘7TN8=@¤)7TFG9 ¥"X9P?yŠ"9lN6DE3x7x­ 1lJ4ƒ
N>7Œ«s[L&3NOX3…&3ƒ„;>3žvwJ[3žm07CBH9lN83; NO3BŽ7Sq>= mp7TDU3?wq>37)Š 7);Oq7ƒ
FG9P; FG3 4s q D L[N89P…A7T…[=HBH=WFu7TFG3:7TB q€7<FG3 9hX9lNON83N‡
T7 FG99n;K=H;6qr3Dx7 \ ]_^1`|a ]_^ µ +t` ³ f gh]_^1` sY9 mw3€q>9ŒNFG3VLA7TNr)DE3ƒ
q>N89P;:L&9~FG3E;>3N†9P… q>=WFG9LM9ŒN¢JGD 3;Oq>=@D‚7TFG9ŒN†FG9qr=@L&9 ³ ² a ‡ 243I9
3;Oq>=@D‚7TFG9ŒN Š"9lN}?ART9‰LM9ŒBŽ7CNO=@¤)7CFG9ysM7:;8JA7†Dx7Sq>NO=H¤¢FG3|X9m07CNO=ŽT?[X=Ž7<;>3N>o
)
„° ³M² ´ a ¯
a ¯
a ¯
a ¯
S] ³ ² µ
©]
U]
µ¢³ ] ³
a ¯ ]
µ¢³ ] 7);X9PDE9 a ¯±°„³M² ´ `€]S³² µ ¯±°e³M² ´ ` µ ³ `€]
µ ³ ` µ ³ µ ³ f ³›³ ³ f 1`€] ³ f 1` µ U] ³ f 1` ³ f 1` f ³-³ ³ f 1`€] ³ f 1` µ ] ³ f 1` ³ ³ f 1` f ³›³ i
° ³M² ´ a ¯ ] ³ f [`] ³ f 1` µ ] ³ f [` ³ µ³ ] ³ f 1` f ›³ ³ i
=@?A7TBHDU3?wq>3 X 3[31~7tƒ„;>37
° ³M² ´ a ¯ i
œ š~Ÿ - –d( ›"!1 ¨ § #§©¨
ª "§ ¨
ª
"§
³² a {JA7CBz<7Ump7CNO=‘)?[X=Ž7xFG3†JGD 3;Oq>=HDx7CFG9lN FG9Eqr=@L&9 ³ ² a ?[9‚XS7T;K9
3D v~J[39<3NON89‰FG3N831ŒN83;8;RT9EzN6J[ZWFG9<…[Nr7)?[X9w“
243 š zNOJ[ZHFG9I…[Nr7)?[X9ys&3BH3L&9~FG3;K3N 3 L[N83;8;>9xFu7‰;>31lJ[=H?0q>3Š‹9ŒN6D‚7-;
° ´ a ¯±° ´ a ‡ 9lN q€7)?0qr9ysM7mp7CNO=‘)?[X=Ž7Vz
+
e° ³M² ´ a ¯ )
;>3?[FG9 vwJ[3 z¬7¬m07TNO=‘)?[X=‘7FG9N6J[ZWFG9y‡ 7TN>7}9 3 ;Oq>=HDx7CFG9lN-FG3 DEZ@?[=@DE9P;
vwJA7CFGN>7TFG9l;ts ;7)…&3ƒ„;>3vwJ[3 a ° ´ 9 3Œs LM9ŒN q€7)?0qr9ys7 [B q>=HDx7
3vwJA7CQSRT9Vq>9lNO?A7tƒ„;>3
° ³²
.10
´ a ¯ ‹ ] ` 9
i
@
D‚7 9P…G;>3N m07TQSRC9’=HD‰L&9ŒN q7T?0q>3¬7 ;>3N Š‹3= q€7±z vwJ[3Œs)vwJA7T?[FG9}9±m03€qr9lN FG3
3NON89P; š z±…[N>7T?[X9ys 7m07TNO=‘)?[X=‘7 FG9 3;Oq>=@D‚7TFG9ŒNbFG3}DUZH?[=@DE9P; vwJA7CFGN>7CFG9P;
z 7nDE3?[9lNFG3‰q>9~FG9l;:9P;:3;6qr=@D‚7TFG9ŒNO3;:FG9qr=@L&9 ³ ² a vwJ[3E;>36587)D
#: ¨ €§ ¨ ª‡ J;K365874s °e³ ² .10 ´
°e³M² ´ ‡
œ£p˜~$£Œ˜"— *›š œž%t˜‹Ÿ —u*›([')š~
j  § #§ ¨
-
ª "§ ¨
¯›a
zFG3­[?[=HFu7:X9PDE9
9
° ³M² ´
;>3?[FG9 ¯ 7 3­1X= ?[X=Ž7 FG9 3;Oq>=@D‚7TFG9ŒN FG3 ³ 3 9 sV7 ?[9lNODx7 FG3
& Nr7)DEzN ƒ 7T9G‡ D
3;6qr=@D‚7TFG9ŒN?ART9EL&9lB‘7TNO=H¤)7TFG9 ³ ² a n] )
` z ¨P§ ª
9PJ q>N89 3;6qr=@D‚7TFG9ŒN ³ ² a ] )
` ;>3 °e³M² ´
§ # FG9 vwJ[3IJGD
° ³M² ´ ‡ D 3;Oq>=@D‚7TFG9ŒNbz § # ;K3};8JA7 m07CNO=ŽT?[X=Ž77q>=H?%1Œ3{7{?[9lNODx7
FG3 & Nr7)DEzN ƒ 7T9G‡
)
j
7
#
'
3 ;Oq>=HDx7CFG9lN’FG3 ³ z
¨ K¨ #" ¨ FG3 JGD
¨ €§ § # ¨ § ª $ ys zFG3­[?[=WFu7†X9PDE9
&'
9
sy9P?[FG3
'&
= ³
³
a ¯ ³ ³ " !$# ]d\ % ` ? ³ " !$# ]d\ % ` ?
=
]d\ % ³ ` &
a µ ¯ ( ³ "! # ³ )
?
=
;>3?[FG9 # ]d\)% ³ ` 7 Š‹JG?[QSRT9†FG3{FG3?G;>=HFu7CFG3FG3L[N89P…A7)…[=WBH=WFu7TFG3 Fu7);¬DE3FG= ƒ
Q~3; \ Fu7TFG9<9:m03€qr9lNFG3 LA7TN>TDU3€qrNO9l; ³ ‡
6 LM9l;8;>Z mw3B+L[N89m07CN’v~J[3žLA7CN>7V3;6qr=@D‚7TFG9ŒNO3; ?ART9<L&9lBŽ7CNO=H¤)7TFG9P;
e° ³ ² ]‹\G` ´+*
9
i
s
œ š~Ÿ - –d( "!1 § #§©¨
ª "§ ¨
# ¨ §¨
3 ;K365K7tƒ„;>3 3;Oq>=HDx7CNV9LA7TN>TDU3€qrNO9 Fu7ŠdJG?[QSRC9 FG3‚FG3?G;>=HFu7TFG3nFG3
L[NO9l…A7)…[=WBH=HFu7CFG3 # ]d\ % ` a ] + `Y° µ \
´ ){\ * s&7†LA7CN qr=HNFG3 .
DE3FG=HQ~3;=H?[FG3LM3?[FG3?wq>3;FG3 \ ‡ N8=@DE3=HN>7TDU3?wq>3Œsu;>3N>o‰FG3€qr3N6DE=@?A7TFu7
7V?[9lNODx7VDEZ@?[=@D‚7VFG3 & Nr7)DEzN ƒ 7T9xFG3 JGD 3;Oq>=HDx7CFG9lN’?ART9EL&9ŒBŽ7TN8=@¤)7ƒ
FG9vwJA7CBHvwJ[3NFG9LA7TN>TDU3€qrNO9 ‡ D ;>3 1lJG?[FG9BH%J 1w7CNs-;K3NronFG3€q>3NODU= ƒ
?A7TFu7 7xm07TN8=Ž)?[X=‘7FG9ˆ3;6qr=@D‚7TFG9lN3D vwJ[3;OqRC9ys ² a "!$#&% (' *) ,+-/.0,+21 34!6587 ) 9 #:! !' 1 8; 7=< ">$7 !?7 + %@! 5 A + !B%DC +E2F !678G
H I <8J4>$7K5 8) 1 5L!$5 5 NM+ 7PO"!BO 1 # 1 5L!$5 3,7PPQR<8('S!/5L!B)T% 5 1 J,U )
VW M ! + !DNX Y=ZB[B[4[\Z] C
gih W
^VW
%(bcdX bfe [
%(bc X
# ^V_Y,SZ4[B[4[`ZVa #
b
j
H )k) ;P< 1 0' ) (' 1 5L!65 ) M 7l5 % !B;m7 + !n) ,+ 5 ' ,+ % 1 "!65L!6)po
h
h qsrdt u vwbc X qsr b
VWxzwb
xy
h
{ qsrdt
u
w
v
c
b
X
@
w
z
/
b
|
VW
zwb~}
{b
h  { } qsrdt
VW
zwb€4[
{ b } u vwbc X @zwb~}
<8O8)2' 1 'x< 1 587 E ) ' % E ) h g
h  VWxzwb€ j
X @
zwb~}
xy
h
 W
X @zwb } |
Z
b €
%N!B) 3,7=%D7
VW
yX b ('S>67 W
yX b G('S>67
h
 b
X @zwb } |
b €
X @zwb } [
7=;w7 e X b } zp C !n7 + %N!n% 1 %N!5 A + !B%DC +E2F !67 M ! + ! ) ' % M # 78G 7 + 'S!B('7 b b } zp G F ) 'S!/!6;m7 + ! 5 ' ,+ % 1 "! + !
. ! +1 3 1 ! 587 )2' 1 %N!6587 + o
h
! b KX b bc } h 
X " } b W
| b }$#
}
X b~} z [
7 + 'S!B('7 L7 ) ' 1 %N!6587 + 5 )2' % M # 7 C 3 1 (' G
%
+
!
"$#&%'
%'()+*
",#&%'
%'(-)
.0/!21436587:9;<7>=?@3
S 3:99DBT5U7>=?K3WV
XYH
A@3
BDCFEG;IHJ7@AK3:9LA'BNM
O
P@C7:QRA@3
B[Z'B\H^]5U3
Q!n<8% ) 1 )2' %N! + M+2 ) ('i!$587 M # 7T) ;P< 1 (' D
% 7l5 # 7 H F^_ ^H ` o
h
h
h
VW
V| a W Y,cX b d c W pY V| e [f pY | f W SZ gihGkjl
) 587nml< c W
f W
)i>67K) mporq 3 1 !6)D!6# !'Ds +21 !B)D5 %DC,5 1 ! l<#:!
. ! +1 3 1 !B)ut v } t w} +2 ) M 3S' 1 . !B% (' G x ) . !$# 7 + ) 5L!B) I <8J,U )
5 !6<'7l3,7 +2+ #:!6J4>$7 3,7 +2+ #:!$J4>67 3 + <yB!65L! 5L!@)i!! 5L! (' + !65L! M ! + !
7=) !4' + !6)x7PW
) z j M 7l5 % ) ,+ 5 ' ,+ % 1 "!$587=) !B"!$# 1 ' 1 34!6% (' M ! + !
{ | 3,7P% 7
h 
_
f
Y
|
e }
a h e dt } | b } t }
w
v
}~[~60m X
gihG€6l
h
h
Y
a } h
h
} ~~ Y, X ‚e a a e } Y h a a } } e t w} | a b } t v }
} ~ v 0 m X

h
} ~ v Y, X b t v } [
Q! ! ) ;P< 1 (' m0<"!6J4>$7 5 + ; +2 )x)i>67 o
h
h
W
| a VW pY dX b c W Y,V| ƒ i[
†ˆ‡&‰Š.‹ŒŠŽ[‘k’“”•‡0‰Š–‹[Œ—–˜p™0‰šd›œž&ž&Ÿ¡ £¢• ž&ž G
gih …„>l
i) !B587 gihG…„>l
M+ ))i!
g }~
h v
} v ~
_Y,?X
h
h Y, X
} ~~$
Y, j
h
} ~ v
g h
Y,S ! m0<"!$J4>67 7 + %N!6# M 7l5 ) ,+
m h } vv 0m g a Z
} ~~$0m
} ~ v 0m j
b j
G
} ~ v 0
gih pl
) 587 m0< 7 ml< M +2 %<#s' 1&M # 1 34! 7 .( '7 + 5 M ! + % ' + 7P) CT! %@!4' +21 y
5 3,7 . ! +21 3 1 ! ~ v G H ) 7P# <J4>67 5 gihGpl C
h
h
e h t  } _Y
a } w
a X
a
_Y| e } a e d t w} | b } t v }
b X
b [
!6l a )2'i! +- 7 + %N!6# % 0' M 7P# ! +21 yB!6587
O+l b l<834! )2'i! +-M 7m#:! +1 yB!$587 G
3 l M ! + ! S.1 'i! +M 7m#:! +1 yB!$J4>67"! )2' 1 %@!4' 1s. ! 5 a (<8)i!B587 E ) 7 %D7 E
5 # 7 5 +2 ; +2 )x) >$7 gihG…„>l 7 ) ' 1 %N!6587 + _
lC 3 )) -6+1 7 # 1 % 1 E
"! + 7 ,++ 7 % gihG jl 5 I 7 + %N! !n;0! + !6(' 1 + t w} X T7=< e X G
+
",#&%'
%'(-)
.–
r7:9;:Q S ;‚7JH&Qr;IHJ7
AK3NB CFEG;IHJ7@A@3:9
M
O
) ' 1 %N!6587 + 5 % & 1 % P7 ) m0<"!65 + !6587P) ' % ! % 7 +@. ! +21 3 1 !
5 (' +2 '7l587P) 7P) )2' 1 %N!6587 +2 ) # 1 ! +2 ) ">67 M 7m#:! +1 yB!$587=) m0<"!B587 7
x
.( '7 + 5 ,++ 7 5 + ; + ))i>67 C + < 587 O + !B3,78G A 7=%D7 h 1 5 1 34!$587 "!
) J4>67 hGGjP 1 )x)x73,7 ++2 ) M 7=5 ! M+ 7 . ! + ml< t } e C
) % 1 E 5 1 5L! h M 7P) 1 ' 1 . !G
X e ' % E ) h
h
X h e h e X e ue | ue]gi[hG6l
~)x3,7m# 587 X e 3,7=5 1 J4>67 X li ' % E ) g
ue X
76' 0m < )2'i! )3,7P#"! ) !4' 1 ) I !y !
X
X
ue
e e u
e SZ
) 587 m0< ! M + 7 M+1 5L!$5 e X
# 7P;0!6% (' C M 7P)) .0 # .0,+21 34! + m0< ue
X
ue
e
G
gih …h>l
e e I 7 1 <' 1 # 1 yB!65L! G H "! E
ue ][
G
gih 6l
7 + 'i!B0'7 )x<8O8)2' 1 '< 1 587 E ) gihG…h>l h gihG>l % gihG6lS ' % E ) X e [
gihG>l
1 "!6# % 0' ! M # 1 34!B587 E ) ! ) My,+ !BJ4! %N!' % - ' 1 34!"!$##s' 1 %@! m0<"! E
J4>67887PO'C % E ) X
X
t
}
h
h
t
}
e Z
G
gih >l
) 587m0< ! @
% !4' +1 y 587 #:!6587 ) m0< ,+ 587 5L! 1 ;P<"!6# 5L!65 C ) % 1 5 1 5L!
M 7=) 1 ' 1 . ! M 7 + ,3 7P8) ' + <J4>678G
+
",#&%'
%'(-)
.. S ;Q S ;‚7
A@3
B CFEG;&HJ7KA@3:9
M
O
A =7 8) 1 5 ,+2 ! )i!! 5L! 5 <8% M+ 7l3 )x)x7 M ! + !6% ' +21 yB!6587 5L!N) iE
;P< 1 (' I 7 + %@! X | ƒ `) 587 m0< 7 ,+2+ 7 ƒ CD7 +RE
%N!6#&% (' 5 1 ) ' +21 O8< 587 3,7P% % C,5 1 !y ,+ 7 5 ) . 1 7 M !65 + >67 1 ;P<"!$# !2t
h
h
h
t } )( e '&
*
$
#

Z
% '& ,+
t v X "!
[ gihGjz>l
(.t
(
4
6
3
8
5
7
} / 21 }
0
' 1 # 1 yB!B587 ghG jz>l98;
' : % E 6) :
h
h
,+ (.h
<&
 '&
.
(
qsrdt v X qsr e } | qsr t } e }
h =  , + h = 
h '& h  't & } h qsr qsr t } X
Z
t }
gihG j>jl
>'?A@[‹Œ—•‘B—@DC6”"?EB•0F’ ‰Dœ•kž<G0ž ¢ H<IKJi );: 587 0m <: I 7 1 <8) !$587
5 1 )x)7 9
{ qsrft ?v
{
1
#&%
/
DX
21
7=;w7
Z
X
"1
& |
|
G H # C %
/
*
*
G
gih j€6l
'
: ;: 9
9 X tY
}
[
5 : ) 1 ;m< # 5 5 : 5 : A + %DC +E2F 7 );: '7 +
h
"
t
}
#
e
0< C M :,3 1 : : 3,7 .21 3 1 587
5 587 g . : Q ! : m0< J4>67 gihGkjl[liG
m :
/
h  {
h
h
&
&
X
#&
{
h  t Y } h
h
&
& |
X
#
h  tY } h 
h
'&
* [
X
#
t }
{ } sq rft v
{}
X
# e
1 85 7 5
: }Z
* t
:
G
gih j„>l
1 7 m0< E
+
M
",#&%'
%'(-)
., 3:Q>B9 \Q S ;i7LB
S 3:Q C\; CFEQ S ;‚7
A@3
B CFEG;IHJ7@A@3:9
O
:
Q
X
:
h
X
Y |
ue
ƒ G
gih j pl
[
&
Z
G
gih j 6l
H : m0< 4J >$7 gihGkj 'l M 7 5 : : < 5 M ; : : m0< J4>67 1 3 1 X | 9 : 8< O 1 < 1
85 7 E : : ml< J4>67 : gihGj 6l 9 : < : &
X
X
587
ƒ e
(
ue Y
|
h
Y
(
=
h
Yƒ
h
e g Y
Y j
=
<
!#"ˆš•Š%$Dœ•kž<G'&‚ £¢• (&)&i h
(
Yƒ
Z
G
y
j
gh kj h>l
1 5 : ,3 7 .21 3 1 G : : Q pE : =
9 M {
| G
: c 6
> 7 M 7 : 7 : 7 7 m0<:
(
h
Y
=
c c vv Z X =
{
vv Z
{
g Y
| =
X
: |
G
:
gih j 6l
M = { | G : : 7 9 { : : ;P< 5 M : 85 7 587
5 : 7 5 :JghGjh>l ,7 : ; : M 7=O O 5 5 : M G 7 E
7 9
X
0< 7
,: 5 5 ml<: =
m :
: {
|
|
ue
Z
=
{
587 : Q S 3:Q C\; CFEBQ!EB 95
G H ,7 5 J,U : >678o
|
[
: :
E:
G
gih j >l
: {
Q >67 ;P< G 7 c : ƒ 5 : : : 5 : M : 5 : : : c 5 : : : M : : : : : : :
7 5 : < : : : : : : 5 O+l^ƒ C < 587 O ,7 G : : 7 X  87=<
l c :Wƒ : h Q 5 : M : 5 : : : >67 Q : ; : 7 : h
5 : Y 97=< : Q 9 .~kX  : g€G…€6l9 C 5 : M : 5 : : 5 :ƒ G
l
:
!
E
5
5
:
Y