1
!
"# $%
"&'() $*+((
,- $./01234536+((
7849:;)
<=,->?4&
,- $./0>?4&@9AB
7-C-&D)((.()E"F
7#&C#&D)((
7G(H&
77IJ2J?,&
7< K&
7L5M
<5>NO>/P>&>QR
<SD1TQR
<./12'5>N
L"-.U12'V$
WXYZ"Y[\
5
]
^
'
^
,,8_Y`G
a
'?
^
ZbY(
]
Yc
^
2
de./0 .2'$16 T(2fg13*>&I+&
25>be./0) 2,2)CfM'
.()e./0'b3)bI&)( /0bh?,-de./0)
,T4.22((& Ki.? 41&D4>&I/
ZbjbG&>bh
k11'Vl$U>+TC-b_'gK>>mn
CCe12V)C-1Te./0b(C&de
./0,T4JfC5 + &>!KC&b_'o.0-.2
P7EEEC'pIcde./0.26JdJ2(_/-1T1q#
q.=2,b_'(2(2I3lJde./0_2n
e'f ?,bC&e./0 /02/D?'
_ T2r-C-12'5>N.()E"Fsbt:'
u-C-.()2,3((f41.() u /0.v>V
wm'bJ(5,F:3FJ3m36bi CI''36x
>/P>&>QR?,.2'$ T26,b.cD*-,c ?,
g.2'$ T2'1M1U,(D&.2' d&t:'C5&
CNn3312)-1TC-!t:'6'(U /03*>=
12 &&+&f,5&(($'5
5
]
^
'
^
,,8_Y`G
a
'?
^
ZbY(
]
Yc
^
3
_TPmI.():(TM!C&`:(6)(
() $b:(536,:(34&D),cI:
:(.()Pm3 ?,`:12: !
YM:
?,.()>S-cq/p
- 536>& i12e'F -12F
- Rm1U4() $i<'y3zL'y3
- T($4{'@.()536NB|E'@.()536.B
- 84&D)z7&D)
- 9&C#&D)i7'z<L'
- 841oD,&D)E|<E1oy>t
34 K I'+`
- ?,.2.()36(6
- #0>1T1U4C&
- YMJ)12C#/.c oN}34(2(
- ,4 T}/ I ~(1•)VD,
6 c}#0>(/P1U4S q
5
]
^
'
^
,,8_Y`G
a
'?
^
ZbY(
]
Yc
^
4
YM8P d6)(
a
YM7: !
?,.2.()'>&I(pf ?,
- Rm1U4() $7z<E'y3
- T(J/7E'
- 84&D)z<&
- 9&C#&D)J/E'
K I'`
- Rm1U4() $.2C&$
5
]
^
'
^
,,8_Y`G
a
'?
^
ZbY(
]
Yc
^
5
- () $C5>$12(/+1U4JoC#cI
.v> KV1q#1U4(1Jom,C5S q
- ,c36+}OLE€3(1C()
$Vk1U4
!"#
$%&'(")*''
YM8*, S&>36121U4D:
?,.23P d'cm&- S+Jom,C D •((_&
534
∞ , d , w
.f./0 K/(Jom,V~15k>#/((b
)((b12~15kV>#3((
‚ƒ q.Um((2C4./0(Jom,D(()7-JV~15
k>#/b>#312,)((`
ρ . A
∞
. U
∞
„
ρ . A
d
. U
d
„
ρ . A
w
. U
w
K
U
d
=U
∞
(1−a)
@B
,12(I!c /0`
5
]
^
'
^
,,8_Y`G
a
'?
^
ZbY(
]
Yc
^
6
A
∞
.U
∞
=
(
1−a
)
. A
d
.U
∞
@B
6,O1((J#
A
d
M/P!1>fJ#
A
∞
=
(
1−a
)
. A
d
+JoC5C#.2( Se./01((Y34
a
/0
%.234…>+Jom,?,.234 K/(3*( Se
./0nJoC5C#12((
+,"-./01%234*''
R('K/12'K3((/m,1T&>36c36.*12.*
2,.,c?, S $./0+JoC#D((
p
¿
−¿
+¿− p
d
¿
. A
d
F=¿
¿
„@
U
∞
z
U
w
B
ρ . A
d
. U
d
@7B
G/PM9:.(Jom,
1
2
. ρ .U
2
+ p+ ρ . g .h=constant
†>J(Jom,/ •
+¿+ρ
d
.g. h
d
1
2
.ρ
∞
. U
∞
2
+ρ
∞ .
g. h
∞
=
1
2
. ρ
d
.U
d
2
+ p
d
¿
+¿
1
2
. ρU
∞
2
=
1
2
ρ . U
d
2
+ p
d
¿
@<B
/P*/1U,(Jom,3 •
−¿
1
2
. ρU
w
2
=
1
2
ρ .U
d
2
+ p
d
¿
@LB
"-0>@77B12@7<B
p
¿
−¿
+¿−p
d
¿
=
1
2
ρ .(U
∞
2
−U
w
2
)
¿
¿
5
]
^
'
^
,,8_Y`G
a
'?
^
ZbY(
]
Yc
^
7
,12(>/PM@7B /0
1
2
. ρ
(
U
∞
2
−U
w
2
)
. A
d
=
(
U
∞
−U
w
)
. ρ. A
d
. U
d
2
U
d
=U
∞
(1−a)
c
U
w
=
(
1−2 a
)
.U
∞
@{B
T2,•.21U412(((121U4V~15k>#3(( T
m' ./0
a .U
∞
,12(I!@<B
F=
(
U
∞
−U
w
)
. ρ . A
d
.U
d
=2.ρ . A
d
U
∞
2
a(1−a)
@‡B
536,T(((#.25uV+JoC#
1−a ¿
2
P=F . U
d
=2. ρ . A
d
U
∞
3
a¿
@ˆB
Y34536+((.2‰34n5,T(((12 $eJo
C# DJ#Dƒ+((( P1qp
η=
P
1
2
. ρ. U
∞
3
. A
d
,12(c
1−a ¿
2
η=4 a¿
@7ˆB
562789:(
)(2'I!@7ˆB:(
a
5
]
^
'
^
,,8_Y`G
a
'?
^
ZbY(
]
Yc
^
8
d η
da
=4
(
1−a
) (
1−3. a
)
=0
6,O
a=
1
3
Š
η
max
=
16
27
=0,593
!.236+(('~?,g#.2$J q.U9:; /0
21U.=/p!Z.:9:;M'12(e'‹{_'%.()M T
C5I ) /034536.62,"5>m3*)C-
C-'2.2Jom,+C5C#12(q…> 3(1Jom,*J(
DT'K((
_2 T2, u /0!'(*-& )2,,
T36} )7Ez<L€
;<=+,>?2$
*&J.c>?4&>$12,-4I, S /0.2C#
/&126p3*~& q1U4/P 41&2>f1U
4,I $J%:(&C#+&(((/C5 &CI
9- /0MJ&>?4&I~& q /0&34.*?12.*
m
C
l
,C
d
12-c+t:(6
‚ƒD,11U4.2
Ω
121U4JoC#.2
U
∞
5
]
^
'
^
,,8_Y`G
a
'?
^
ZbY(
]
Yc
^
9
&b&C#Œ12TJ2J?,.2 K&.2
β
.2
n /pC# $&12'K>xD,+ •
m,-4
c , β
TI-c:(&C#&D)
)>?4&b1U4->,-+>?4&.2
Ωr
121U4->
,-+1-.2
a
'
Ωr
R( 1U4->,-/P 4+JoC#1>?
5&.2
1+a
(¿¿')Ωr
¿
5
]
^
'
^
,,8_Y`G
a
'?
^
ZbY(
]
Yc
^
10
'&1U4(1U4/P 4+Jom,1>?4&
1+a
'
¿
2
1−a ¿
2
+Ω
2
r
2
¿
U
∞
2
¿
W=
√
¿
@‹B
_2
ϕ
/0~& qVI!`
sin ϕ=
U
∞
.(1−a)
W
cos ϕ=
Ωr (1+ a ')
W
6+>?4&`
α=ϕ−β
" .*?12.*m.c>?4&.2`
L=
1
2
.W
2
. c .C
l
.r
D=
1
2
.W
2
. c . C
d
.r
5
]
^
'
^
,,8_Y`G
a
'?
^
ZbY(
]
Yc
^
11
@+,"-./>?2$7AB
‚:'/34Jom,
a , a'
.2C5 ScJ#Dƒ+>?4_2
C53*/P&n&JofCT
2>f.*C# $&J.c>?4&:(TD,.2`
L. cos ϕ+ D . sin ϕ=
1
2
.W
2
. N . c.
(
C
l
. cosϕ+C
d
. sinϕ
)
r
@EB
2>f.*&J.c>?4&:(>/P->,-.2`
L. sinФ−D .cos Ф=
1
2
.W
2
. N .c .
(
C
l
.sin ϕ−C
d
.cos ϕ
)
r
@B
8*, S $./0:(+JoC# DJ#Dƒ.2`
m.∆ v=.U
∞
(
1−a
)
.2 . π .r .r .2 .a. U
∞
= 4π .U
∞
2
a
(
1−a
)
r .r
8*'6&>36,c?J(1-D,
2. a
'
. Ω. r ¿
2
∆ p=
1
2
.. ¿
†>362,)(.*&J:(>/PD,.2`
2. a
'
. Ω. r ¿
2
.2. π . r . r
1
2
.. ¿
R( ?O.*:(>/PD,`
L. cos Ф+ D .sinФ=m . ∆ v+∆ p .s
R(2>f
∆ p . s ≪m.∆ v
c I(#(&(
∆ p . s≈ 0
cI!cV2`
1
2
.W
2
. N . c .
(
C
l
.cos ϕ+C
d
.sin ϕ
)
r=4 π . U
∞
2
a
(
1−a
)
r .r
5
]
^
'
^
,,8_Y`G
a
'?
^
ZbY(
]
Yc
^
12
W
2
U
∞
2
.N .
c
R
.
(
C
l
. cosϕ+C
d
.sin ϕ
)
=8 π . x . a .
(
1−a
)
@B
8*, S $./0+JoC#,TDJ#Dƒ+>?4`
ρ .U
∞
.
(
1−a
)
.Ω .2 a
'
r .2 πr .r= 4 π ρ. U
∞
.
(
1−a
)
Ω .a
'
r. r r
?O1.*C# $:(>/P->,-VI!@Bb`
L. sin ϕ−D .cos ϕ=4 π ρ. U
∞
.
(
1−a
)
Ω .a
'
r . r r
Y,`
1
2
.W
2
.N .c.
(
C
l
. sin ϕ−C
d
. cosϕ
)
r =4 π ρ .U
∞
.
(
1−a
)
Ω. a
'
r. r r
W
2
U
∞
2
. N .
c
R
.
(
C
l
. sin ϕ−C
d
. cos ϕ
)
=8π . λ . x
2
a
'
(
1−a
)
@7B
5,C,$D(''-'(E
•c?
]
`
4 $CV $bL'y3
4 $v f>&7'y3
4 $ q'!<'y3
4 $U> 5{'y3
536 q'!E"F
4 $D,Œ((Ez{E1y>
():`7&b
5F
CF
D
''
:536E"F() $V1U4 q'!<'y3R*12(
5!#36+:
5
]
^
'
^
,,8_Y`G
a
'?
^
ZbY(
]
Yc
^
13
7
P
U R
η
ρ π
=
@7B
Y36:* ) ) /0:(.=,-.2EL‹7/&:
2,,M} )&qŽ„E7|EL
_U,&C#&D)((.2`
7
P
R
U
ρ π η
∞
=
@7B
_G„E"F@536 q'!B
ρ
=
bLCy'7@C4./0c+C5C#B
U
∞
„<'y3@_U4 q'!B
,3412( /0Œ„‡L|7LL'
#+#(&2,.2 M'36+: u /03lJ
cC5D?' -&q+536 q'!R( 1•%&
C#+((Œ„L'
%}341U4 f'g&•`
5
]
^
'
^
,,8_Y`G
a
'?
^
ZbY(
]
Yc
^