Баллистическое проектирование ракет 5-696-00672-8
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Russian Pages 92 Year 1996
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p
p P
p p
p
p
623.451.8
. .
ИC ИЧ C И
И
1996
2
623.451.8 ч
.C. .—
:
: .
, 1996. — 92 .
. , . p
.
.5,
.12,
.—8
p
.
-
p
p p
P
:
p p
ISBN 5-696-00672-8
.
. . . .
© ©
, 1996. . .
p p . ____________________________________________________________________ P N 020364 20.01.92. 20.11.96 . p 60 84 1/16. . . . . 6,74. .- . . 6,22. p 150 . 353. p . ____________________________________________________________________ p p p . 454080, . , p. . . . , 76. 2
3
И …………………………………………………………………………
5
…………………………………………………………... ……………………….. …………………………………... . p p ………………………………………... p n0 ………………………………………………………. p pk pa P ………………………………………….. p pk pa P …………………………………………. …………………… p P .. ………………………………
6 6 10 12 19 20 21 22 22 23 23
1. 1.1. 1.2. 1.3. 1.4.
p p 1.4.1. 1.4.2. 1.4.3. 1.4.4. 1.4.5. 1.4.6. 2. Х p
p
2.1.
…………………………………………………….. 25 …………………………. 25
2.1.1. p
…………………………………………………..
25
p
…………………………………………………. ……………………………………. ………… …………………… …………………..
27 27 29 33 36
2.1.2. 2.1.3. 2.2. 2.3. 2.4.
,
…………………………………………………………... 40 ………………………………………… 40 ………………………………………………... 42
3. 3.1. 3.2. 4.
p
p
4.1. 4.1.1. 4.1.2. 4.1.3.
-
p 4.1.4. 4.1.5. 4.1.6. 4.1.7. 4.1.8.
46 ... 46 p ……… 48 ………………………… 48
………………………………………………………….. …………………….. …………………. …………………………… …………………….. ………………………………
48 50 51 51 53 54
4 4.2. 4.2.1. 4.2.2. 4.2.3.
-
p 4.2.4. 4.2.5. 4.2.6. 4.2.7. 4.2.8. 4.3. p 4.3.1. 4.3.2. 4.3.3.
.. 54 ……… 55 ………………………… 57
…………………………………………………………... …………………….. …………………. …………………………… …………………….. ……………………………… -
57 57 58 59 62 62 63 ……… 64 ………………………… 64
p
………………………………………………………….. …………………….. ………………….. ………………………………………... ……………………………. …………………….. ……………………………… P ……… ………………………..
64 65 66 67 67 67 68 69 69 69
p
………………………………………………………….. …………………….. …………………. ………………………………………... ………. ……………………………… ………
70 70 71 73 73 74 76
я ……………………………………………………………………. p 1. p p p p p ……………………………………….. p 2. p p p p p …………………………………. p 3. p p p p p p …………………... p 4. p p p p p p ……………..
78
4.3.4. 4.3.5. 4.3.6. 4.3.7. 4.3.8. 4.3.9. 4.4. p 4.4.1. 4.4.2. 4.4.3. 4.4.4. 4.4.5. 4.4.6. 4.4.7. 4.4.8. 4.5.
78 81 84 88
……………………………………………………………………... 92 4
5
И . :
m
,
.
. :
m
p
.
,
. ,
m0 . -
, ,
,
,
, . . , , (
),
(
).
, (
). .
.
L max )
m0
m
.
(
m
.
( ).
L max .
m0 min
, . . . .
.
.
6
1.
P
PЫ
1.1
, .
,
, ,
.
C
.
m V& = P − X − mg sin ϑ
C
,
[1]
P X V& = − − g sin ϑ . m m , . , . . g ≈ g0 .
(1.1)
, V x 0 = V cosϑ ; (1.1) (1.2)
:
V =
P X dt − ∫m ∫ m dt − g0 ∫ sin ϑ dt ; 0 0 0
t
t
X = ∫ V cos ϑ dt ; t
0
V , X , Y ; ϑ (t ) —
m0 —
6
V y 0 = V sin ϑ . ,
(1.2) :
t
(1.3)
Y = ∫V sin ϑ dt . t
(1.4)
0
— . m& m = m0 − m& t = m0 1 − m0 ; m& — µ = m m0 . m& µ =1− t. m0
t , . (1.5)
7
m&
C
µ: µ = 1; µ =µ =m
.
, (1.5)
,
t
p t=0 t =t m
— ''
C
'' . ,
,
V =−
µ
∫
1
1 V = m&
µ
∫
0
p
P m0 dµ + m m&
µ
µ
∫
µ
∫
0
dt = −( m 0 m& ) dµ .
(1.5)
X m0 dµ + g0 m m&
1
1 P dµ1 − 1 − µ1 m&
µ =1− µ = m C
m0,
µ
∫
1
m0 sin ϑ dµ . m&
µ1 = 1− µ µ
m X dµ1 − 0 g 0 ∫ sin ϑ dµ1 . 1 − µ1 m& 0
m0 —
.
X = qC x S , ; Cx — S .
o
q —
(1.6)
P = P − (P − P0 )
(1.7) ,
ph . p0
P , P0 —
; p0 , ph — h.
J∞
J0 .
J∞ =
P , m&
J0 =
P0 , m&
P = m& J ∞ − m& ( J ∞ − J 0 )
m& = P0 J 0
, V =J
∞
µ
ph . p0
(1.7), (1.8) (1.6),
p 1 1 ln − (J ∞ − J 0 ) ∫ h dµ1 − 1− µ µ p − 1 0 1 0
(1.8)
8 −
P = m0 S n0 = P0 m 0 g0 — (1.9)
J0
µ
g0 P n 0
0
∫
0 µ
∫ sin ϑ dµ1 ,
J qC x dµ1 − 1 − µ1 n0
(1.9)
0
, . V = V − ∆V p − ∆V x − ∆V g .
: (1.10)
, (
). ,
,
p
.
p
.
, ,
. ,
-
. (1.9)
,
V
V = V ( µ , d 0 , n0 , J ∞ , J 0 , m 0 ) ,
d0 —
(1.11)
,
S .
(1.4), .C
,
p
L = L(V , l , h ,ϑ ) = L( µ , d 0 , n0 , J ∞ , J 0 , m0 ,ϑ ) .
(1.12)
;ϑ —
ϑ
l ,h —
( J
. J0
∞
,
, p
C
, (
, :
8
).
L = L ( µ , d 0 , n0 , pa , p , m 0 ,ϑ ) ; m 0 = m 0 ( µ , d 0 , n0 , pa , p , L ,ϑ ) ; n0 d0 .
)
pa . ,
(1.13) (1.14)
9
,
µ =
,
m m . =1− m0 m0
(1.15)
m
µ
.
,
,
. . m
.
,
, , . .
,
,
[1,
..., 8]. , m0 , m
.
µ = µ (m0 , m
, d 0 , n0 , pa , p , . .
, d 0 , n0 , pa , p ) . (1.13) (1.16) ,
p
(1.16)
.
m0
m
.
n0 ,
: p ,
d0 .
pa
, ,
-
.
,
(
,
)
, -
. ,
, m0 , m
(
.
L max )
( (
( m 0 ) min ). .
)
10
,
, .
, ,
, p
.
.
-
, . х
1.2.
,
, .C J J
ρ .
ρ (c) ,
(
V
). ,
, .
( ) .
,
—
.
ρ = (m
+ m ) (V
+V ) ,
; V ,V — =m ρ ;
m ,m — V =m
ρ .
;V (1.17) ρ =
K m = m&
m& = m
ρ
m (m
+m ) + (m
ρ )
=
(1.17)
(1 + K m ) ρ ρ , ρ +Kmρ
(1.18)
m —
.
.
, ,
1
,
K m0 . , , 10
.
, .
11
α :
,
α
.
, α 1.1
= K m K m0 .
. 1.2
(1.19) Km ,
α ,
.
Jp.
C .
pa .
p ,
. 1.1
-
№
Km
1 2 3
-1 (H 2 ) , α
(O2 )
(H 2 ) , α
4 5 6 7
ρ , /
3
T , ˚K
R , ⋅
k ,
J
p
.
/
=0,6
3702 3610 3227
344 385 729
1,135 1,153 1,211
2975 3075 3855
=1
7,937 1135
71
424
3616
516
1,125
3591
2,765 1443 2,015 1443 2,252 1443
786 899 874
1181 1193 1202
3423 3353 3384
345 366 359
1,159 1,176 1,170
2829 2858 2853
3,011 4,403 5,068 2,748 3,101 4,389
786 840 830 786 786 786
1270 1368 1385 1149 1273 1247
3170 3172 3184 3451 3434 2967
349 316 316 351 345 393
1,178 1,153 1,150 1,171 1,174 1,169
2709 2615 2619 2847 2810 2797
-02
-50 -2
* * * * * * * *
/
3
1033 975 315
-1
2
ρ ,
830 786 71
-
-27
/
3
2,726 1135 1,710 1135 4,762 1135
-50
8 9 10 11 12 13
ρ ,
2
: 2N + N(C
1596 1596 1596 1382 1590 1440
— ; 3)2, ; — N2 4, -50 — 50% + 50% ; -27 — 73% + 27% ; -50 — 73% + 27% NO; -2 — 70% + 30% ; -02 — 50% + 50% m – ; p =8 ; p / pa = 80:1; T p = 20˚C.
,
12
,
p =4
3000.
. . 1.1 p p p p =8 , pa = 0,1 , 1.2 — , pa = 0,1 . (O2 ) + (H 2 ) , , p / pa = 80 . (O2 ) + (H 2 ) = 0,7; K m = 5,556; ρ = 345 / 3; T ( p / pa = 3000): α
=3483˚K; R
= 671
/ ·
;k
p
= 1,214; J
= 4540 / .
.
C
=
u .
, :
T .
p
1.2 p ρ , / — 51,5%; — 43%; — 5,5% — 80%; — 20% — 72%; — 18%; l — 10% — 68%; — 17%; l — 15%
T , ˚K
3
k
J
p
⋅
u ( p ),
,
/c
/
3060
313
1,21
2400
4,36 p
0,69
1720
2790
326
1,22
2300
4,37 p
0,40
1770
3290
300
1,17
2440
10,12 p
1800
3300
290
1,16
2460
5,75 p
p =4 u = a pν ,
m& ,
0,12
0,40
; p / pa = 40:1; T p = 20˚C.
u = b + a pν .
(1.20)
я
1.3.
p .
.
1622
.P
12
R ,
х
p
ч
х
13
(1
J : J
)
,
=J m .
(1.21)
Р t ,
,
, J =P t .
=Pt
J m& , p
(1.22)
(1.22), m = P m& . ,
P = m& ua + S a ( pa − ph ) ,
(1.24)
Sa — ; ph — (1.24)
C
J
; ua — .
= ua +
S a pa S a ph − , m& m&
(1.25)
, 1ε=p
J :
pa . ,
:
p ρ k = const , ; p, ρ —
1)
k— 2)
p ρ = RT , ;Т—
R— 3)
p
(1.23)
(1.26) ; (1.27) ;
u2 k = const . RT + 2 k −1 (1.25)
,
(1.28)
pa = ph .
J p = ua .
(1.29) ua
(1.28),
,
u = 0: u2 k k RT + RT = . k −1 k −1 2
(1.30)
14
u = (1.26)
C
, J
p
Ta 1 − T
2k RT k −1
(1.27),
k −1 pa k
Ta = T p
.
(1.31)
k −1 =ε k .
(1.32)
k −1 2k RT 1 − ε k . = k −1
(1.33)
J∞
ph = 0:
J ∞ =J p +
C
C
(1.25)
S a pa . m&
(1.34) ,
Sa ,
m& = S a ρ a ua = S a ρ a J p . (1.34}) 1 p J ∞ = J p + p a . J ρa ,
1 pa J p ρa ph = p0 = 0,1 : 1 p = J ∞ – p a J ρa (1.27)
J h =J ∞ –
ph . pa
J0
0,1 . pa
k −1 pa k
= RT a = RT ρa p pa
(1.35)
(1.36) h (1.37)
(1.38) (1.32),
= RT
k −1 ε k .
(1.39)
: — J
∞
=J
p
1
+ J
14
p
RT
k −1 ε k .
(1.40)
15
– J
0
=J
∞
1
– J
p
RT ε
k −1 k 0,1 .
p a
(1.41)
. 1.1, 1.2, k R
.
ε
,
.
: — p
=ϕ J
p
(0,67 − 0,016 p + 0,163 p
0,5
(1 − ε n ) p n )⋅ n p − 0,1n ;
0,5
,
(1.42)
n = (k−1)/k; J p . — — J p = ϕ J p . + 190,3 + 76 p − 3,058 p 2 − 7000 pa + 25484 pa2 ,
(1.43)
J
Jp.
.
—
(
.
ϕ
. 1.2). ( ).
(
) Jp. .
ϕ
0,95...0,99 ,
,
. : —
T =T 10 − 2 (86,9 − 0,578 p + 6,27 p 0,5 ) ;
— T =T T
—
(1.44)
+ 11,42( p − 3,923) ;
(1.45)
,
. 1.1, 1.2.
p
. J ∞ (J 0 )
ε
( ). ,
(
),
. p
,
16
P . P .
P , ,
,
, .
.
J
h
m& , m&
.oc
=
P m&
+P
≈
+ m&
1 + m&
k −1 ph 1 ∞ k J − , RT ε Jp pa
1 m&
(1.46)
— . .
ua
(
ua m& Jh
.oc ( p
N =η L
[5]
L
—
. .
,
m& ,
(η
,
—
1
L
1
.
.
)
,
η
m&
)
—
(1.47) = 0,4...0,5);
,
k −1 k p k RT 1 − 2 = ; p k −1 1
(1.48) ;
, . .
.
(1.47)
, , ).
(
p ,
16
η —
N =
2—
η
1
H ( m&
+ m& ) ,
, H =(p
−p ) ρ ;
[5] (η
(1.49) = 0,6...0,9);
—
17
p ,p .
—
∆p = p
− p = 1,5 p . (1.47) (1.49) : ∆p m& = . −6 L η η ρ 10 − ∆p
m&
∆p
; ρ —
/ 3; L
—
(1.50)
/ .
L 20...50, . . 1000...1200° . . 1.1
k
Т0 700...800°
= (2...5) 10-2.
2/ 1
R .
J
=
.
P +P m&
,
(1.51)
; m& = m& + m&
—
P ,P
m&
m&
α ,
. m& = α m& ;
C (
m& = (1 − α )m& .
, )
α
,
α = 0,12; J
J
.
J
.
= (1 − α )J
.
+α J
.
,
(1.52)
,
α = 0,075. (1.40), (1.41), (1.46)
.
. . u*
C
a = kRT . C
—
,
.
18
u ∗ = kRT ∗ . , ∗2 k k ∗ u RT + RT = . 2 k −1 k −1 (1.53), : k RT . u∗ = 2 k +1 (1.54) T∗ 2 = . T k +1 (1.32), p (1.55)
p
(1.53)
,
∗
k k −1
p 2 = p k + 1
ρ∗ p
∗
k +1 2 ( k −1)
Sa = S
2 εk
m& S
18
m& = 0,98 S 2
,
—
:
K 0 p 10 6
, RТ —
K0 p
RT
,
(1.57)
k.
k −1 2
( k +1) −ε k
ϕ .
p∗ .
(1.57)
k +1 2( k −1)
2 k + 1
(1.55)
(1.56)
p ∗u ∗ = S
2 K0 = k + 1 (1.35) :
(1.54)
, p
m& = S ρ ∗u ∗ = S
(1.53)
.
µ
RT .
/ .
(1.58) m&
(1.59)
19 1.4.
х
p p
C
p
p
V = ∑ J ∞ i ln s
i =1
∆V
—
1− µ
− ∆V
1
,
(1.60)
i
p
, .
[1]
ϑ
L = 222,4 arctg
V 2 tg ϑ
62,57(1 + tg 2ϑ ) − V 2
,
(1.61)
— . (1.61) — .
/ ,
V
arctg —
,
, V = J ∞ ln
∆V µ .
1 , 1− µ
.
J∞
(1.62) V
J∞
. ≈ 3500
J∞
/ ,
J ∞ ≈ 3000 / .
5000 / .
µ
, ,
,
,
. ,
µ L
µ (m0/m . ).
m0/m
.
. C ≈ 50.
,
mo
20 p n0
1.4.1.
n0 = P0 m 0 g0 . p
(1.63) .
n0 m 0 ( n0 )
L
m . . m 0 ( n0 )
V
sin ϑ
1
— (1.64)
V, (1.9), . .
1 = J 0 1 (1 + k p ) ln 1− µ sin ϑ
− 1
1 µ 1 sin ϑ n0
J ∞ 1 = J 0 1 (1 + k p ) .
n0 ),
µ
, —
p , m0 d0 :
n01 = t
ej, u n0 j 20
j
j
(
n0 ,
. p , p ,
,
m0 , m . n0 = 1,8...2,2 [1]. ee , : n01 = 1,8...2; n02 = 1,1...1,4; n03 =
µ
,
:
n0 L
.C
0,9...1.
(1.64) .
m 0 ( n0 )
n0 ,
,
m
µ 1J 0 g0 t
, n0
.
n0 j =
;
1
—
-
µ jJ ∞ j g0 t
;
(j=2, 3 …).
(1.65)
j
, t j=
—
ej u
,
(j=1, 2, 3, …);
(1.66)
j
. , p
.
21
15...30 n02 ≤ 3...4;
: n01 ≤ 2...2,5; , , . .
. C
n03 ≤ 4...5. n0 , p , .
p p
1.4.2.
pa
P
, m0
m p . p
∂ ∂p
.
V :
∞ 1 J ln 1− µ
= 0 .
(1.67)
( p ) opt1 = 20...25 10...12 —
.
, . . ( p ) opt1 = 10...12 2...3 .
,
C .
p p ,
.
µ
pa ( pa ) opt1 ( pa ) opt1
∂ ∂pa1
t
∫ P(t)dt 1
, : = 0.
0
( pa ) opt , pa .
, 0,01...0,02
( pa ) opti
1 ∂ ∞ = 0. J i ln 1 − µ i ∂pa i ( pa ) opt1 = 0,045...0,07
; ( pa ) opt 3 = 0,005...0,015
.
; ( pa ) opt 2 =
22 p p
1.4.3.
pa P ,
( p ) opt p
P ,
∞ J
∂ ∂p
= 0 .
: 1 ln 1− µ
,
p
:
,
p . .
p .
( p ) opt : ( p ) opt1 = 7...10
; ( p ) opt 2 = 6...9
; ( p )opt 3 = 5...8
(
pa ,
. ,
.
pa . 1 ∂ ∞ J i ln 1− µ ∂pa i
o
: ( pa ) opt1 = 0,05...0,08 0,008...0,014 .
i
= 0 .
; ( pa ) opt 2 = 0,015...0,025
; ( pa ) opt 3 =
х
1.4.4.
lp = lp d 0
d0 , P .
d0
lp = 4 m 01 (π ρ cp d 03 ) .
ρ cp —
(
)
,
. lp = 8...12
(1.68)
— ρ cp = 630...650
ρ cp =790...850 / 3. n
22
/ 3;
23
lp = lc.p + 5d 0 3 n . lc.p —
(1.69)
. p
m 01 — C
d 0 = 0,54 3 m 01 ,
(1.70)
. P = 4 m 0 (πd 02 ) . 12 000...16 000 / 2.
P
(1.71)
я
1.4.5.
я
P
(1.65), (1.66).
, ,
l . (u = const) :
V i ≈ J ∞ i ln
1 − µ i (l i ) 1
− J∞i
µ i (l i ) n0i (l i )
sin ϑ
. i
.
: — (l ) opt1 = 2...3; (l ) opt 2 = 1...2; — (l ) opt1 = 2...3; (l ) opt 2 = 1...2; (l ) opt 3 = 0,5...1. : u 1 = 7...8 = 8,5...10,5 1.4.6.
/ ; u 2 = 7,5...10
/ . ч
. : L max = 1000...4000 m .
1) ;
= 500...1000
/ ;u3=
24
2)
L max = 4000...10 000 m . = 500...1000 ;
3)
L max = 8000...10 000 , ,
—
,
.
. , :
1 V ≈ ∑ J ∞ i ln 1− µ i =1 m 0 , m . , J ∞ i , n0 i
−J∞i
ks
(m 0i +1
i
µ
i
n0 i
sin ϑ
i
.
µ
i
,
∂V =0 ∂m 0i
m 0i )opt .
: — m 02 = 0,23m 01 ; — m 03 = 0,33m 02 ; m 02 = 0,33m 01 . p p p : — m 02 = m . m 01 ; —
m 03 = 3 m 2
µ
24
.
µ
3
1
.
:
2
= 1,1µ 2 ;
µ
m 02 = 3 m
m 01
=µ
— = 1,1µ 1 ; —
µ
2
2
= 1,1µ 1 ;
=…= µ
n.
m 2 01 .
(1.72)
µ i,
25
2. Х
И ч
2.1.
И И
х
p
p
p
p .
p
p
p
p
ч
2.1.1.
p
(
. 2.1) l
l
l
.
.o
= 1,02 = 1,02
d
π
, . =l
.
+l
.
4m0 µ
d 02 ρ
(1 + K m )
4 K m m0 µ
π d 02 ρ (1 + K m )
( ,
lc ≈ d а ;
1 l = l 4
4m& RT
0,98π K 0 p 10
m& 1 = P0 J 0 1 ;
6
p .
+ 0,3d 0 ;
(2.2)
+ 0,3d 0 .
(2.3)
lc ,
.
d
. 2.1).
2 k + 1 fa =
ε
1.3
l
.
: fa ;
k +1 2( k −1)
2 K0 = k + 1
m& j = P0 j J ∞ j ;
k −1 2
k +1 2 k−ε k
l ,
da = d
;
;
k +1 2( k −1)
),
(2.1)
d / d = 2,
d2 =
.
,
,
dа
l
β c = 22 ,
.
;
k;
(j=2, 3 …);
ε = pa p .
.
'' = 2,0...2,5 .
—
'' (
(2.4)
26
0,2...1,0 . l
. 2.1. P 26
= 1,05(l + l ) .
p
(2.5)
27 ч
2.1.2.
p
, , l ,
l , p l ,
(
. 2.2): lc
p d
l , p
l , ,
d
d .
d
l = (0,3…0,6)lа ;
: = 0,3d 0 ;
l = 0,1d 0 ;
lc = la − l ;
la = 1,6ψ ( f a ) 0,5(0,829 + 0,298k ) d ; 2
l ≈ d0 ; l
= 0,8d
;
l ( f a − 1,5) ; d = 1,5d . d = 0,2d 0 ; d = d 1,5 + la d fa (2.4); ψ = 0,4...0,5 — . m& m& = m t = S u ρ S = m eρ — .
da = d
C
l
,
da
p
l ≈ 1,15l d 0 ;
l ,
fa ;
=l +l .
l я
2.1.3.
, ).
lc. = 2l
. lc. = k
.
l . , p
k .
.
p
.
(l
.
—
28
. 2.2. P 28
p
29 2.2.
я
,
-
, ,
. . .
,
, .
,
. 2.1
:
,
1)
-
,
2)
,
p -
, , -
, p
C
,
, ,
.C
(
,
),
,
, , ,
(σ
.
ρ ).
( E ρ ). . 2.1 p p
p
. p
, p . 2.2,
p ,
. 2.2. , ,
. ,
, ,
,
30
, , , ).
(
,
2.2 p
p
p
σ ,
№ / 1 2 3
-
4
-
5 6
-
C
7 8
ρ ,
/
Е,
3
2100 1700 300
8000 7850 2700
185 220 75
500
2400
135
1100 1100
4700 2050
110 40
1300 1400
1500 1400
130 80 p
№ /
σ
1 2 3
-
4
-
5 6
C
7 8
, 30
-
ρ ,
103 E / ρ ,
⋅ 3/
. 2.2
°
0,26 0,22 0,11
⋅ 3/ 1,7 1,9 3,2
280 300 100
0,21
4,8
100
0,23 0,54
2,2 3,1
300 350
0,87 1,0
7,6 6,4
2000 80
.
,
31
400°C, . : σ ≤ 2,4
. 2,4 . .
(
. 2.3), . 2.3
, : 1)
,
-
2)
c
p -
-
p : ,
1) , , 2) -
p
: ,
, C 1) 2) -
: p
: C
, ,
-
-
,
32
,
, , : .
-
,
''
''
4 ,
,
16
. ,
,
. -
.
. C .
( ,
) .
, . . . . 2.4. 2.4 p
p
p
ρ
№ /
,
/
3
u, / 1
p
2 3 4
600 400
200 100
1200
50
1300
200
1600
100
-
5
2.3.
ч
хх
: m 32
=m
.
+m
.
+m
.
+m
.
+ m∗ ,
(2.8)
33
m
— ;m .
;m
.
—
—
.
;m
; m∗ —
—
.
. .
=m
: m
.
.
+m
.
.
(2.9)
.
: +m
.
,
(2.10)
, m
=а
: m m
=m
.
.
.
+b
m
;а
= 150
.
.
.
.
.
(2.11)
= 30
;b
.
= 0,005.
, ,
. 5...10%
. m
=d
.
.
m∗ .
(2.12)
πd 03 ρ 4δ ρ d . = 1,1 1+ ρ 4 ⋅ 1,02m0 µ δ = 1,5⋅10-3; δ = 3⋅10-3. m
. .
,
m
.
m
.
: b
.
.
(2.13)
m
=b
.
m .
.
.
(2.14)
= 0,016. , P0 , p
m
.
=m
+m
+m +m
p . +m
:
+m
.
(2.15)
34
m
—
;m ;m
—
m
—
—
;m ;m
—
—
;
. ,
γ
=
.
m
.
P0
=γ
+γ
γ
m& 1 = P0 [H ] J 0 [ /c];
γ
=
+γ
+γ
+γ
+γ
.
(2.16) :
0,51 m& 1,068 ; P0 pa0, 288 p 0,313
m& i = P0i [H ] J ∞ i [ /c];
i=2,3,…;
= 1,327 ⋅ 10 − 5 p (9 + 0,102 p ) P00,5 + 2,075 P00,5 ; γ = (0,5K0,6)(0,102 + 0,0104 p ) ;
γ
γ
γ
= 8 P0−1 + 9,35 ⋅ 10 − 4 ( p
= 23P0−1 + 3,12 ⋅ 10 − 4 ( p
=0,102
/
;
p
(2.17)
P0 ) 0,5 ; P0 ) 0,5 ; =2 p +7.
γ
1,1...1,2.
γ
m m0 — ; ∆m
p : γ = 0,1γ ; : = m0 + ∆m ; ;m —
∆m = ∆m
=d m —
; ∆m = d m —
(2.17) =1,5 p .
(2.18)
m ∗ = m + ∆m , ,
(2.19)
p
+ ∆m + ∆m + ∆m
; ∆m
; ∆m = d m —
=d
,
; ∆m
+ ∆m
=d
;
(2.20)
m —
m —
,
,
. C d =d 34
, m
+d +d +d
= m0 + d m ; +d
m∗ = m + d m ,
= 0,017 …0,031; d
= 0,003…0,006.
(2.21)
35
p m0 = d m = m ,
(
+d
.
)
.
(1 + d )m + b
P0 = n0 g 0 m010 − 3
m0 (1 − b
,
.
)=m
.
m0 + b
p
p d m +γ
.
,
+ (1,014 + d (2.13),
.
p
, p
.
.
P0 + (1 + d )m . d − d =0,014:
)m + γ . n0 m010 − 2 . (2.22)
1,1δ ρ π d 03 m 1 m . = − −γ 1− µ = m0 D m0 1,02 m0 :
D = 1,014 +
(2.8)
4,4δ ρ
ρ
.
n0 10 − 2 − b
.o ,
.
(2.22)
(2.23)
(2.24)
(2.22)...(2.24) . C
, , ,
, . .
≤ 40
( P0
γ m&
.
=
),
(18…20) + (1,8…1,9)m& P0
= (0,11...0,13) m& — .
, m&
-
)
P01 = n 01 m01 g 0 ;
P0 j =n 0 j m0 j g 0 ;
m i = m0i µ i ; m& 1 = P01 J 0 1 ,
(2.25)
= (0,07…0,08) m& —
µ .
(2.23) :
( .
m& j = P0 j J ∞ j , (j = 2, 3, …);
36
m&
i
= m& i
= m& i ρ i ; t i = m i m& i .
V&
i
-
ч
2.4.
) =m
m m
.
1 ; 1 + K mi
V& i = m&
i
ρ i;
хх
( m
m& i = m& i
K mi , 1 + K mi
.
−m . −m . , (2.9), (2.14).
(2.26)
µ .
l
=m
m
.
+ m∗ .
,
. : (2.27)
, m
.
=m +m
+m
+m
+m +m , ;m
m —
;m
m = ω l d 03 ,
1) K —
/ 3;
—
36
—
— .
ω = K K tπ f ρ p 2σ t ,
(2.29) ;f—
/ 2; ρ — ,
; l = l d0 .
= q d 03 , q = ω 2 . p m = q d 03 + ω l d 03 ,
m
3)
;m
, f = 1,2; σ t — t° = 200...300°C),
( 2)
;m
, K = 1,2; K t —
,
,
—
—
;m — ,
,
(2.28)
(2.30) (2.31)
37
π
=ξ
q
d0
ξ
ea ρ u
=ε
,
υ
d0
, = ξ πα ρ
0,04...0,1 5)
. a
2
/
(2.32) .
m
K u ;ω
= q d 03 + ω l d 03 ,
= ε πα ρ
: K = 2, ξ
= - 0,11, ε
ρ : (2.33)
K u .
α
= 0,6.
/
= .
mc = nc (m
nc —
;m ;m
= 1⋅10-6 u
4)
q
ea ρ u
d . e ≤ 0,51 − 1,15 d 0 d = 1 − 2e
≥ 1,15d .
d
π
=ε
= 0,5. . e : e = e d 0 ; u = apυ . . 1.2
—
а
ω
,
c
+m
+ m ),
—
;m
—
p
— .
m = ω l d 03 ,
p
ωc =
(2.34)
π (1 − e )u ρ
RTк
0,98 K 0 p 10 6 sin β
( f a − 1)(δ c ρ + δ ρ
k +1 2( k −1)
2 k + 1 fa =
(2.35)
2 εk
k −1 2
k +1 −ε k
;
);
38 k +1 2( k −1)
2 K0 = k + 1
β = 20° —
—
ε = pa p .
k;
; δ c = (4...8) 10-3 — ; δ = (1,0...1,4) 10-2 — , / 3; ρ c ; ρ — / 3; ρ —
, 3
/ .
,
=ξ m
6) m
= (0,16…0,25) K t p m .
(2.39)
m = ω l d 03 ,
7)
ω = e (1 − e )πρ . C (2.28)
:
(2.40)
, (2.27).
m
.
=d
:
.
mc = m
m∗ = d .
+m
.
.
(1 + d )m . +m
.
+ m∗ .
p , m0 + d c m = m . + d . (1 + d )m + b . m0 + b . d c m + (1 + d )m . d = d + d + d = 0,013...0,022, d = = 0,003...0,006. p d − d = 0,01.
µ =
d
.
=
(ω + ω
ω
1
m 1 m = 1 − . − b m0 D m0
+ω
D = 1,01 + d +ω ) +
.
;
(2.41)
+q
+q ) ,
e = 0,5(1 − 1 M ) ,
:
38
,
1 ((1 + ξ )q ω l
,
M = d0 d ,
.
:
—
. ,e
39
µ = 0,46
ε
.
M ≤ 20 p
max
m i = m0i µ i ; t i = ei u i ;
: -
P01 = m& 1 J 0 1 ;
-
(t = +20°C) Е = 40 ε = 0,08, .
m& i = m
i
t i;
P0 j = m& j J ∞ j ;
n01 =
µ 1 J 0 1u g 0 e1
1
,
n0 j =
µ j J ∞ ju g 0e j
j
,
(j = 2, 3, …).
,
40
И
3.
И я
3.1.
: ( g 0 );
; ;
µ , J , n0 , Θ .
.
∞
,
,
ϑ (t ) . C
V
,
, V ,
µ , J ∞ , n0 , Θ . ,
, ,
. . : 1)
max ;
V
2) 3) 4) 5)
;
ϑ&
; (
ϑ&& );
. , . ,
, ,
.
,
, .
, ,
,
L max .
, ,
. .
40
, -
41
. 3.1. p
, ,
p
p
t=0ϑ
. = 90°.
.
, . ,
(
. ,
≈ 1),
.
42
α ≠0
,
(
α.
≈ 1).
,
. , .
ϑ
, 9°)
π 2, π ϑ = 4 − ϑ 0,55 − µ ∗ 2 ϑ , µ∗ — p
(
(
ч
,
(
)2 + ϑ ,
. 3.1),
0 ≤ µ ∗ ≤ 0,05;
0,05 < µ ∗ ≤ 0,55;
(3.1)
µ ∗ > 0,55;
,
µ ∗ = m& t m01 .
3.2.
,
ч
C( F
.
. 3.1).
FC. ,
,
80...100
,
. (
)
,
, . 80
.
, ,
1%.
-
. , . ,
. x
: 42
y
43
y = ∫0 V sin ϑ dt .
x = ∫0 V cos ϑ dt ;
t
t
-
x = (R0 + y )tg η ;
h ,
R
y = R sin η ;
h = R − R0 .
,
, .
, Y, ,
( ,Y) —
.
: L
V
.max
h .
ϑ∗, .
β ϑ∗:
ϑ .
ϑ ,
V 2 (1 + h ) ν = ; g 0 R0
h =
ν 2 − (2 + h )ν . 2 (ν + 2h )
tgϑ ∗ =
h ; R0
:
V
βc =
L L−l ; = R0 R0 V (
.
.p
min
h = = 11,2
tg 2ϑ =
h ; R0 1
1+ h
tg
βc 2
sin β c
(1 + h ) − cos β c
tgϑ .
h ,l
[1]: ; (3.3)
3.1), ,
min
h .
L
ϑ .
(3.2)
ϑ
44
.
,
V .
, h ,l
. 3.1 p
ϑ
h ,l p
p L
n0i
= 2 [1]. h ,l ,ϑ ,V L, h ,
.
l ,
ϑ∗,
ϑ , V
min ,
Lv′ ,
hmax , T ,
/
3.1
Lv′
L
1 70
2 90
4 140
6 170
8 200
10 225
12 250
14 270
60
110
195
285
380
480
590
740
41
39
35
31,5
28
25
23
20
41
39
35
31,5
27
23
19
15
2810
3920
5200
6000
6500
6900
7150
7400
0,67
1,06
1,88
2,90
4,00
5,22
6,62
8,20
260
480
870
1200
1400
1600
1800
1900
8
11
16
21
27
33
39
45
/
0,29 0 ≤ M < 0,800, C x = M − 0,51 0,800 ≤ M < 1,068, 0,091 + 0,5M −1 M ≥ 1,068,
[2]
,
. 3.1
ϑ
ϑ .
(3.2).
-
,
ϑ
.C . ,h .
44
ϑ ,
ϑ∗,
6000 ∗
(3.4)
h
l l ,
Kn = 2 n ,
n
, —
45
.
n02 .
n n . l = 0,1L n ;
:
h = (40 L ⋅ 10 −3 + 100) n ;
0,7854 − L 22918, 0,6545 − L 45837
ϑ =
tg
(3.5)
L ≤ 6000; L > 6000.
(3.6)
L = β R0 ,
β
= b + b 2 + ac a ; a = 2(1 + tg 2ϑ ) − (2 + h )ν ; 2 c =ν h . b = ν tgϑ ; L = L +l .
,
: Lv′ = ∂L ∂V .
Lv′
:
∇L = Lv′ ∇V .
(3.7)
hmax = r − R0 , r =
p ; 1− e
p = ν ( R0 + h ) cos 2 ϑ ;
e = (1 − ν ) 2 cos 2 ϑ + sin 2 ϑ ; T =
2( R0 + h ) V
1 sin ϑ + ⋅ 2 − ν (2 − ν )ν
ν
(3.8)
R0 = 6371
.
π − arcsin 1 − ν 2 e
.
46
4. я
4. 1.
ИP
P я
И
ч
,
ч
я
,
, ,
:
Lmax , (
m
.
). :
-
;
---
; : p i , pai , n0i , ki , d 01
µi;
; ;
µ
. i
,
µi
. ,
µ , p
J
. .
i
, (1.10)
,
V =J
.
—
.
ln
(1 − µ 1 )(1 − µ 2 ) …(1 − µ n ) . 1
µ
.
− ∇V
(4.1)
, 1− µ
46
,
,
,
C
;
,
µ
.
.
.
= (1 − µ 1 )(1 − µ 2 )…(1 − µ n ) . = 1 − (1 − µ 1 )(1 − µ 2 )…(1 − µ n ) . (4.1) :
(4.2)
47
V =J
.
ln
1− µ
− ∇V
1
.
(4.3)
.
C [1] J C
ks J0 1 + J∞1 ∞ = + 2∑J i . 2k s − 1 2 i=2 ∆V
1
.
V + ∆V Kv —
(4.4) ,
= К vV ,
.
(4.5)
,
, . L = 10...14
.
µ
K v = 1,15...1,25. (4.5) (4.3)
µ
(4.2)
µ
µ .
.
К V = 1 − exp − v J .
. , (1.72), (1.73). µ i.
= k1µ 1 . = 1 − (1 − µ 1 )(1 − k1µ 1 ) .
,
(4.6)
,
2
k1µ 21 − (1 − k1 ) µ ,
—
.
1
+µ
= 0.
.
µ. 1 + k1 1 + k1 − µ 1= − 2k1 k1 2k1 µ 2, 2
µ i.
.
(4.7)
, (2.22),
m0i =
1−γ
m0i +1 + 1,078δ ρ π d 03 i n0i 10
−2
−b
. i
− Di µ
.
: . i
(4.8)
48
: = 1500
;
Lm = 11 000 ( )+
: (
;
m
).
4.1.1.
-
ч
х
(
. 4.1).
p
, . , . ,
. х
4.1.2.
. 1.1
: Jp.
-
/ ⋅
= 345
R
-
k
= 1,159;
-
T
= 3423° ;
4.1.3.
ρ
= 1443
ρ = 786
ρ = 1181
= 2829 / ; ;
/ 3;
/ 3; / 3; K m = 2,765.
х
яp
, p
p
. 1.4,
: 48
n01 = 1,8; n02 = 1,4; p 1 = 25 p 2 = 20 p 1 = 0,06
; ; ;
.
49
. 4.1.
-
p
P
50
-
p
2
= 0,015 k1 = 1,2.
;
: p -
(3.1); ,
(3.6);
-
'' ч
4.1.4.
'' C x (M ) (3.4).
х
(1.42) :
J p 1 = 0,96 J p .
n n 0,5 (1 − ε1 ) p 1 (0,67 − 0,016 p 1 + 0,163 p 1 ) ⋅ p n − 0,1n 1
= 0,96⋅2829 (0,67− 0,016⋅25 + 0,163 Jp
2
(1 − 0,4371)1,5552 25 ) 1,5552 − 0,7272
= 0,96 J p . (0,67 − 0,016 p
= 0,96⋅2829 (0,67− 0,016⋅20 + 0,163 J ∞ 1= J p 1+ J∞2=J p 2+
1 Jp1 1 Jp2
2
0 ,5
0 ,5
= 3030 / ;
n n 0,5 (1 − ε 2 ) p 2 + 0,163 p 2 ) ⋅ p n − 0,1n 2
(1 − 0,3726)1,5084 20 ) 1,5084 − 0,7272
RT 1ε1n = 3030 + RT 2ε 2n = 3225 +
=
0,5
=
0 ,5
= 3225 / ;
345 ⋅ 3553 ⋅ 0,4371 = 3207 / ; 3030
(1.40):
345 ⋅ 3558 ⋅ 0,3726 = 3366 / . 3225
(1.41): RT 1ε1n 0,1 345 ⋅ 3553 ⋅ 0,4371 ⋅ 1,635 0 ∞ = 3207− J 1= J 1– = 2918 / . 3030 J p pa1 1
50
51 х
4.1.5.
µ
(4.5).
i
,
, :Кv = 1,2.
. 3.1 : V = 7025 / . (4.4)
J0 1 + J∞1 + 2J ∞ 2 = J . = 2k s − 1 2 1 2918 + 3207 = + 2 ⋅ 3366 = 3265 / . 2 ⋅ 2 − 1 2 µ. : (4.6)
:
1
,
µ
.
К V = 1 − exp − v J .
= 1 − exp − 1,2 ⋅ 7025 = 0,9244. 3265 (4.7})
k1 = 1,2,
1 + 1,2 0,9244 1 + 1,2 = 0,6521. µ 1= − − 2 ⋅ 1,2 1,2 2 ⋅ 1,2 = k1µ 1 =1,2⋅0,6521=0,7826. 2
µ
2
х
4.1.6.
(4.8). p
.
m02
p m01 = 0,275.
p
ρ
l p = 10, = 800
, , =
/ 3. , d 01 = 3 d 01 = 1,9 .
m02 = 11000
; P02 = 151
m01 = 40 . 4m01 4 ⋅ 40000 =3 ⋅ 800 = 1,85 π lpρ π ⋅10 ;γ
: P01 = 706 . 2
;γ
. 1
. = 1,3; D1 = 1,0442;
= 1,12; D2 = 1,0442.
(2.23) : 1 m02 + 1,078δ ρ π d 03 µ 1= 1− −γ D1 m01
.
−2 −b 1n01 10
.o =
52
1 11000 + 188 − 1,3 ⋅ 1,8 ⋅ 10 − 2 − 0,016 = 0,6521; 1 − 1,0442 40000 1 m . + 1,078δ ρ π d 03 1− − γ . 2 n02 10 − 2 − b .o = µ2= D2 m02 1 1500 + 188 − 1,12 ⋅ 1,4 ⋅ 10 − 2 − 0,016 = 0,7804. = 1 − 1,0442 11000 , µ . = 0,9234. µ . = 0,9244 =
C 0,001.
, d 01 = 3
m01 = 50 . 4m01 4 ⋅ 50000 =3 = 1,997 . π lpρ 3,14 ⋅10 ⋅ 800
d 01 = 1,9 . m02 = 13750
;γ
; P02 = 189
: P01 = 883 . 2
;γ
. 1
= 1,35; D1 = 1,0442;
= 1,085; D2 = 1,0442.
(2.23) : 1 13750 + 188 − 1,35 ⋅ 1,8 ⋅ 10 − 2 − 0,016 = 0,6521; µ 1= 1 − 1,0442 50000 1 1500 + 188 − 1,085 ⋅ 1,4 ⋅ 10 − 2 − 0,016 = 0,8102. µ2= 1 − 1,0442 13750 C , µ . = 0,934. µ . = 0,9244 0,0096. p : m01 = 40,6 ; m02 = 11,165 . , p γ . i , 1,1. P1=
4m01
π
2 d 01
=
4 ⋅ 40600
3,14 ⋅ 1,9
2
= 14 320
: / 2.
, : 52
m01 = 40 600 ; m02 = 11 165 ;
∗ = m01 − m02 = 29 435 m01
∗ m02 = m02 − m . = 9665 m 1 = µ 1m01 = 26 477 ;
; ;
53
-
m
"
" ч
4.1.7.
= µ 2 m02 = 8738
;
m = m01 − m 1 − m 2 = 5385 ; [ m − (d − d c )(m 1 + m 2 )] = 4892
-
2
.
х
d 0 = 1,9 . : -
d
d a1 = d
= 0,671 ; -
d
-
l
1
=d
l
1
-
1
d l
2
lc.p = 2l
.
=d
f a1 =
1
= 0,21 ;
4 = 0,5 ; 1
.
1
d a2 = d
-
l
=l 2
= 2d
f a2 =
2
= 0,143 ;
4 = 0,5 ; 2
= 0,733 ; l 2 = 1,05(l 2 + l 2 ) = 1,295 . : l . 2 = 1,633 ; l . 2 = 2,171 ; l . 2 = l . 2 + l . 2 = 3,804 . ( = 3,0 . 2
.
2
2
( = 16,715 .
= 2d
= 0,105 ;
= = 0,671 ; l 1 = 1,05(l 1 + l 1 ) = 1,23 . : l . 1 = 3,79 ; l . 1 = = 5,42 ; l . 1 = l . 1 + l . 1 = = 9,21 . : d 2 = 0,071 ;
= 0,733 ; -
=l
1
1
. p . 4.1) lp = l
1
+l
1
+ 0,75l
2
+l
) 2
+ 0,5l
.
=
54
4.1.8. я
х
) P01 = n01m01 g 0 = 717 ; ) P02 = n02 m02 g 0 = 153,3 ; : m& 1 = P01 J 0 1 = 245,7
: -
( (
-
m& 2 = P02 J ∞ 2 = 45,6
-
t t я
4.2.
я
1 2
=m =m
/ ; / ;
: 1 2
m& 1 = 107,8 ; m& 2 = 192 c.
ч
ч
я
,
. .
, , . : -
-
; : p i , pai , ki , d 0 ;
µ i;
;
;
; p
µ
.
, .
,
µ
.
= 1 − (1 − µ 1 )(1 − µ 2 )…(1 − µ n ) . K vV = J
54
;
(4.9)
: .
ln
1− µ
1
. .
(4.10)
55
L = 10...14
Кv = 1,15...1,25. C p
1 J = ks
: J
.
(4.10)
0
µ i = 1 − (1 − µ
+ J∞1 2
+ ∑ J i . i =2 ∞
ks
µ i:
, (4.9)
(1.74),
1
.
.
(4.11)
µ
.
.
)1 n , i = 1, 2, 3….
(4.12)
, (2.41).
m0i =
m0i +1 1 − b . i − Di µ
: .
(4.13)
i
: -
m
.
Lmax = 10 000 = 620 ;
;
.
4.2.1.
ч
-
х
, ''
'' (
. 4.2). .C
. . , .C . . . , . , ,
. ,
.
56
. 4.2. 56
-
p
p
P
57
х
4.2.2.
. 1.2
: Jp.
-
= 290
R
/ ⋅
-
k
= 1,16;
-
T
= 3300° ;
ρ = 1800
-
= 2460 / ; ;
/ 3;
u = 5,75 p 0, 4
-
/ .
х
4.2.3.
яp
,
p :
k1 = k 2 = 1 .
1.4, p 1=9 p 2 =8 p 3 =7 pa1 = 0,06 pa2 = 0,015 pa3 = 0,008
; ; ; ; ; ;
d0 ,
u
p e. (3.1). (3.6). Cx( ) (3.4). 4.2.4.
ч
х
(1.43) :
58
J p 1 = 0,96 J p . +190,3 + 76 p
1
J p 2 = 0,96 J p . +190,3 + 76 p
2
J p 3 = 0,96 J p . +190,3 + 76 p
3
2 ,= − 3,058 p 21 − 7000 pa1 + 25484 pa1
=0,96⋅2460 + 190,3 + 76⋅9 − 3,058⋅81 − 7000⋅0,06 + 25484⋅0,0036 = 2660 / ; 2 ,= − 3,058 p 22 − 7000 pa2 + 25484 pa2
=0,96⋅2460 + 190,3 + 76⋅8 − 3,058⋅64 − 7000⋅0,015 + 25484⋅0,000225 = 2865 / ; 2 ,= − 3,058 p 23 − 7000 pa3 + 25484 pa3
=0,96⋅2460 + 190,3 + 76⋅7 − 3,058⋅49 − 7000⋅0,008 + 25484⋅0,000064 = 2880 / ; (1.45): T i =T +11,42( p i − 3,923) , (i=1, 2, 3). (1.40): J ∞ 1= J p 1+
k −1 pa1 k
RT 1 J p1 p 1
k −1 pa2 k
RT J ∞ 2 = J p 2 + p 2 J 2p
2
3
= 2844 / ;
290 ⋅ 3335 0,008 1,16 = 3012 / ; = 2880 + 2880 7
0,16
0,16
(1.41): J 0 1= J ∞ 1–
= 2844 −
9
2660
290 ⋅ 3347 0,015 1,16 = 3008 / ; = 2865 + 2865 8
k −1 pa3 k
RT J ∞ 3 = J p 3 + p 3 J 3p
= 2660 +
0,16 290 ⋅ 3358 0,06 1,16
RT J
1
p 1
k −1 p a1 k
p
1
0,16 290 ⋅ 3358 0,06 1,16
2660
9
0,1 p = a1
0,1 = 2544 / . 0,06
х
4.2.5.
µ
(4.12).
i
,
, , Кv = 1,16.
. 3.1 : V = 6900 / . (4.11)
58
:
59 0 ∞ 1 J 1 + J 1 k s ∞ J . = + ∑J i = 2 ks i=2 1 2544 + 2844 + 3008 + 3012 = 2905 / . = 3 2 , µ 1 = µ 2 = µ 3,
, (4.12)
K vV 3J .
=1 − exp − 1,16 ⋅ 6900 = 0,6007. 3 ⋅ 2905 :
µ i = 1 − exp −
P =
(4.10),
4m01
π
2 d 01
= 12000
:
/ 2.
d 01 = 0,543 m01 ,
m01 :
0,543π P 0,1575 ⋅ 3,14 ⋅ 12 d 01 = = = 1,4833 . 4 4 d 0 = 1,48 . 0,71 , . . do 3 = 0,71 . х
4.2.6.
.
σ = 1100
3
/ .C / 3.
ρ
ρ = 1300
= 1600 -
ρ = 2050 ρ = 4700
/ 3.
/ 3.
.
(4.13) .
p
.
4.1. , 1.
ω = 1,2
1,2πρ p 2σ
3
= 1,44
3,14 ⋅ 2050 ⋅ 7 = 30 2 ⋅ 1100
do /
3
.
3
= 0,71 .
60
2.
q 3.
q
=ω
2 = 15
q
3
.
:
0,5π e3a = ρ d 3 u3
4.
/
0,5 ⋅ 3,14 280 ⋅ 10 − 6 =ω = ⋅ 1600 = 17 0,71 12,52 : π 0,1ρ 3,14 ⋅ 0,1 ⋅ 1300 3 = −0,11 = −0,11 ⋅ = −1,8 / , 2u 3 2 ⋅ 12,52 4.1 N
ω , l
q , u , e
3
/
3
/ /
d0 , e, q , ω , q ,
ω , ωc , 1+ ξ ω ,
/ / /
3 3 3 3
/
fa
d
/
3
/
3
.
µ
D m0 , d0 , J0 , /
J∞ , /
n0 60
I 2,7
II 0,9
III 2,5
38 19 13,85 0,4 1,48 592 11 11 -1,6
34 17 13,21 0,4 1,48 592 11,5 11,5 -1,7
30 15 12,52 0,4 0,71 284 17 17 -1,8
8,9
9,3
9,8
18 19 1,6
49 58 1,57
74 95 1,53
1357 0,07
1357 0,113
1357 0,123
1,08 0,6007 19705 1,478 2544
1,123 0,6007 6606 1,481 —
1,133 0,6007 2044 0,713 —
2844
3008
3012
3,65
4,1
8,14
/ .
61
ω 5.
= 0,6
ωc =
π 0,1ρ 2u
− 3 p
ω
3
( f a3 − 1)(δ c ρ + δ ρ
=
2 0,008 1,16
× 6 ⋅ 10 − 3 ⋅ 4700 + 12 ⋅ 10 − 3 ⋅ 1600 = 95
/
3
= 0,2 p
3
7
(74 − 1) ×
)
3
= 0,2 7 = 0,53. /
3
.
1 ((1 + ξ )q + q + q ) = ω 3 ω 3l 3 1 1 = [(1 + 0,53) ⋅ 15 + 17 − 1,8] = (30 + 17 + 9,8 + 95) + 1357l 3 1357 1 = 0,11186 + 0,02811 . l3 9. (4.13): 1 D3 = 1,01 + d . 3 = 1,12186 + 0,02811 . l3 10. C 3 m 3 ω l 3d 3 m . m03 = = = , µ3 µ3 1 − b . 3 − D3 µ 3
. 3
=
1
+ω
= 74 .
.
= e3 (1 − e3 )π ρ = 0,4 ⋅ (1 − 0,4) ⋅ 3,14 ⋅ 1800 = 1357
(ω + ω
.
2,16 0,008 1,16
7
ξ
3
);
2 2⋅0,16 0,16 2 2,16 −
(
/
2,16
0,6407 ⋅ 7 ⋅ 10 6 ⋅ 0,342
7.
d
k −1 2
3
, 1,885 ⋅ 12,52 ⋅ 10 − 3 ⋅ 1800 ⋅ 290 ⋅ 3335
6.
8.
3 6
k +1 pa3 k
2 pa3 k
ωc =
RT
3,14 ⋅ 0,1 ⋅ 1300 = 9,8 2 ⋅ 12,52
0,98 K 0 p 310 sin 20°
2 k + 1 f a3 =
C
3
π (1 − e )u 3 ρ k +1 2( k −1)
p
= 0,6 ⋅
+ω ) +
1357 ⋅ 0,713 620 = 0,6007 (1 − 0,016 − 0,6007 ⋅ 1,12186)l
3 − 0,6007 ⋅ 0,02811
.
62
l
3
C
= 2,529. ,
e ≤ 0,5(1 − 1,15d ) ,
d . d
2
=
3
1357 ⋅ 0,713 ⋅ 2,529 m03 = = 2044 0,6007 , d = d d0 . e3 = 0,4
.
4 ⋅ 0,6 ⋅ 2,53 ⋅ 12,52 ⋅ 10 − 3 ⋅ 1,8 ⋅ 103 290 ⋅ 3335 0,98 ⋅ 0,6407 ⋅ 7 ⋅ 10 6
= 0,175;
= 0,0306 ,
. ч
4.2.7.
х
( . (2.6), (2.7). ,
. 4.2)
. 4.2.
d d
, .
p p l
p
p
0,5,
p p
,
p
p
l p .
p 0,5; 0,4;
0,3 ,
l
2
p
. lp = l
1
4.2.8. я
+l
( 2
. . 4.2) + 1,1l 3 = 5,2 + 1,905 + 1,1 ⋅ 2,33 = 9,668 .
х
t 1 = e1 u 1 = 592 / 13,85 = 42,74 ; t 2 = e2 u 2 = 592 / 13,21 = 44,8 ; t 3 = e3 u 3 $ = 284 / 12,52 = 22,7 . : m& 1 = m 1 t 1 = 11836 / 42,7 = 277 / ; m& 2 = m 2 t 2 = 3968 / 44,8 = 89 / ; m& 3 = m 3 t 3 = 1228 / 22,7 = 54 / . :
C : 62
l
3
63
-
(
-
(
-
) P01 = m& 1 J 0 1 = 277⋅2544 = 705
) P02 = m& 2 J ∞ 2 = 89⋅3008 = 268
) P03 = m& 3 J ∞ 3 = 54⋅3012 = 163
(
4.2 N m0 , m , d0 , d d , l3 u ,
/
d d f d d d d l l l l l l
4.3.
p
, , , , , , , , , , ,
я
ч
I 19705 11836 1,48 0,2 0,296 2,7 13,85 0,17
II 6606 3968 1,48 0,2 0,296 0,9 13,21 0,1
III 2044 1228 0,71(1,48) 0,2 0,142 2,5 12,52 0,175
0,25
0,15
0,125
18 1,06 0,39 0,72 0,3 1,2 0,6
49 1,05 0,23 0,54 0,3 1,31 0,5
74 1,08 0,19 0,44 0,14 1,4 0,4
0,6 0,2 4,6 5,2
0,81 0,12 1,5 1,905
1,0 0,1 2,0 2,33
ч
, . . :
я
; ; .
64
-
m . = 1500 ; m01 = 42 000 ; :
.
4.3.1.
ч
-
х
(
.
. 4.1).
.
-
6
.
.
, . , . , . . , , .
. х
4.3.2.
. 1.1
: Jp.
-
/ ⋅
= 345
R
-
k
= 1,159;
-
T
= 3423° ;
4.3.3.
ρ
= 1443
ρ = 786
ρ = 1181
= 2829 / ; ;
/ 3;
/ 3; / 3; K m = 2,765.
х
яp
,
p
1.4,
: 64
n01 = 1,8; n02 = 1,4; p 1 = 25
;
65
-
p p p
1 2
p 2 = 20 = 0,06 = 0,015 k1 ,
; ;
&1 Lmax . d 01 = 3
4m01 , π lpρ
ρ
l p = 10, = 800
;
/ 3. d 01 = 3
4 ⋅ 42000 = 1,884 , . π ⋅ 10 ⋅ 800
d 01 = 1,9 . P1=
4m01
π
2 d 01
=
4 ⋅ 42000
3,14 ⋅ 1,9
2
= 14 800
/ 2.
(3.1). (3.6). Cx( ) (3.4). 4.3.4.
ч
х
(1.42) : J p 1 = 3030 / ;
J p 2 = 3225 / ;
J ∞ 1 = 3207 / ;
(
(1.41): J 0 ,
J ∞ 2 = 3366 / ;
)
= 2918 / . '' '' ∞ 0 0 K p1 = J 1 − J 1 J 1 = 0,099. 1
(1.40):
:
=
66
х
4.3.5.
µ
(2.23), (2.24) . m02 = m01 (1 − γ 1
. 1n01 10
−2
−b . 4.3.
.o
− D1µ 1 ) − 1,078δ ρ π d 03
4.3 p p
p
m01 , n01 P01 ,
γ
. 1,
/
bх.о1 D1
µ
1
m02 , n02 P02 ,
γ
. 2,
/
b х.о 2 D2
µ
p
2
µ
k1 &1
1
2
N 3
42 1,8 742 1,3 0,016 1,0442 0,8 5,1 1,4 70 1,353 0,016 1,0442 0,6061 0,76 0,9212 0,121
42 1,8 742 1,3 0,016 1,0442 0,75 7,3 1,4 100 1,211 0,016 1,0442 0,7049 0,94 0,9262 0,174
42 1,8 742 1,3 0,016 1,0442 0,7 9,5 1,4 130 1,143 0,016 1,0442 0,7567 1,08 0,9270 0,226
p 4
5
6
42 1,8 742 1,3 0,016 1,0442 0,65 11,7 1,4 161 1,105 0,016 1,0442 0,7896 1,21 0,9264 0,279
42 1,8 742 1,3 0,016 1,0442 0,6 13,9 1,4 190 1,08 0,016 1,0442 0,8112 1,35 0,9245 0,330
42 1,8 742 1,3 0,016 1,0442 0,55 16,1 1,4 221 1,07 0,016 1,0442 0,8275 1,5 0,9224 0,383
p p
, 1,1.
γ
. 1
L = L(k1). L k1(&1) 66
,
67
,
,
µ
µ
=µ
(k1) (
.
. 4.3).
''
(&1).
''
k1
,
µ ч
4.3.6.
µ
= 1 − (1 − µ 1 )(1 − µ
,
:
2 ).
ч
k1 = 1,08 (&1 = 0,226), = 0,9270. (4.4), (4.6) :
V =
J
.
Кv
ln
1− µ
=
1
. 3.1
Kv = 1,2,
.
3265 1 ln = 7121 / . 1,2 1 − 0,927 L = 11700
.
х
4.3.7.
: -
m01 = 42000 ; m02 = 9500 ;
∗ m01 = m01 − m02 = 32 500
m01 − m 1 − m -
∗ m02 = m02 − m . = 8000 m 1 = µ 1 ⋅ m01 = 29 400 ; m 2 = µ 2 ⋅ m02 = 7180 ;
pp
;
m = 2
= 5420
ч
4.3.8.
;
;
m −( d − d ) ( m 1 + m 2 ) = 4910
.
х
d 0 = 1,9 . :
-
d
1
= 0,108 ;
68
= 0,69 . = 0,676 ; -
d a1 = d d
d
1
= 0,216 ;
= 2d
= 0,132 ;
2
l 2 = l . 2 4 = 0,5 ; l 2 = d 2 = 0,676 ; l 2 = 1,05(l 2 + l 2 ) = 1,235 . : l . 2 = 1,44 ; l . 2 = 1,89 ; l . 2 = l . 2 + l . 2 = 3,33 ; lc.p = 2l . = 3,0 . ( . p . 4.1) lp = l 1 + l 1 + 0,75l 2 + l 2 + 0,5l . = 17,096 . 2
2
х
) P01 = n01m01 g 0 = 742 ; ) P02 = n02 m02 g 0 = 130 ; : m& 1 = P01 J 0 1 = 254
( (
m& 2 = P02 J ∞ 2 = 39
-
68
1
d a2 = d
:
-
f a1 =
l 1 = l . 1 4 = = 0,5 ; l 1 = d 1 = = 0,69 ; l 1 = 1,05(l 1 + l 1 ) = 1,25 . : l . 1 = 4,14 ; l . 1 = 5,95 , l . 1 = l . 1 + l . 1 = 10,09 ; : d 2 = 0,066 ;
4.3.9. я
C -
= 2d
1
t t
1 2
=m =m
: 1 2
m& 1 = 115 ; m& 2 = 185 .
/ ; / ;
f a2 =
69
4.4.
я
p
ч
ч
я
P
,
.
. : m . = 620 ; m01 = 20 000 ; .
4.4.1.
ч
-
х
, ''
'' (
. .C
. 4.2). . . . .C . . . ,
68%
.
, 17%
15%
.
, .
4.4.2. Х
. 1.2
: Jp.
-
= 290
R
/ ⋅
-
k
= 1,16;
-
T
= 3300° ;
-
, .
ρ = 1800
/ 3;
= 2460 / ; ;
70
u = 5,75 p 0, 4
-
/ .
σ = 1100 ρ
: / ;
ρ
3
= 4700
1300
ρ = 2050
3
/ ;
= 1600
/ 3;
ρ
—
3
/ . х
4.4.3.
яp
, -
p :
1.4, p 1=9 p 2 =8 p 3 =7 pa1 = 0,06 pa2 = 0,015 pa3 = 0,008
; ; ; ;
(3.1). (3.6). Cх( ) (3.4). 4.4.4.
ч
х
(1.43) : J p 1 = 2660 / ; T
1
= 3358° ;
J ∞ 1 = 2844 / ;
'' 70
J p 2 = 2865 / ; T
2
= 3347° ;
J ∞ 2 = 3008 / ;
(1.41): J 0 ''
1
= 2544 / .
J p 3 = 2880 / ; (1.45): T 3 = 3335° ; (1.40): J ∞ 3 = 3012 / ;
; ;
=
71
J∞1 − J0
K p1 =
J0
= 0,118 .
1
1
х
4.4.5.
, sin ϑ
1=
sin ϑ
: n01 = n02 = n03 ; [1]:
2=
sin ϑ
3,
µ 1= µ 2 = µ 3 .
m m m = 03 = 02 . m03 m02 m01 m01
m01
m02 = m m01 ,
2 m02 = 3 m m01 ; :
m03 = 3 m 2 m01 .
m02 = 3 620 ⋅ 20000 2 = 6283 m03 = 3 620 2 ⋅ 20000 = 1974
m01 —
d
3
:
; . :
d 0 = 0,54 3 m01 .
: d 0 = 0,54 3 20 = 1,47 . d 01 = 1,5 ,
—
= 0,7 . P =
4m01
2 π d 01
=
4 ⋅ 20000
π ⋅ 1,52
= 11323
/
2
. p
.
72 = m01 − m02 − m
m
m∗
=m
m
: = 20000 − 6283 − 0,016 ⋅ 20000 = 13397
.
m d :
+ (1 + d − d c )m = (ω + ω
+ [(1+ ξ )q .
+ω
3 + ω )l d 01 +
3 3 + q ]d 01 + 1,01ω l d 01 . ,
+q
.
(4.14)
l . :
µ = p
1.
ω = 1,2
1,2πρ p 2σ
2. q 3.
ω
q
ω
72
=q
= −0,11
ω 5.
.
(4.15)
1
.
= 1,44
=ω
3,14 ⋅ 2050 ⋅ 9 = 38 2 ⋅ 1100
2 = 19
3
/
0,5π d 01
4(1 − e ) l u ρ 0,98 K 0 p 10
RT 6
.
(4.16)
.
.
0,5π = 1,5
π 0,1ρ
= 0,6
/ 3.
.
e1a ρ u1 e e ≤ 0,5(1 − 1,15d ) , =
e1 = e1d 01 = 0,4 ⋅ 1,5 = 600
,
4.
m0
p
=q
d 2p = e1 = 0,4.
3 ω l d 01
2u 1 π 0,1ρ 2u
1
600 ⋅ 10 − 6 1600 = 11 / 3. 13,85 : 3,14 ⋅ 0,1 ⋅ 1300 = −1,6 / = −0,11 ⋅ 2 ⋅ 13,85 = 0,6 ⋅
3,14 ⋅ 0,1 ⋅ 1300 = 8,9 2 ⋅ 12,52
/
3
.
3
,
73
ωc = =
π (1 − e )u 1 ρ
RT
K 0 p 110 sin 20° 1
( f a1 − 1)(δ c ρ + δ ρ
1
6
3,14 ⋅ 0,6 ⋅ 13,85 ⋅ 10 − 3 ⋅ 1,8 ⋅ 103 ⋅ 290 ⋅ 3358 0,6407 ⋅ 9 ⋅ 10 6 ⋅ 0,342
× (18 − 1)(6 ⋅ 10 − 3 ⋅ 4700 + 12 ⋅ 10 − 3 ⋅ 1600) = 19
ξ
6.
ω
7.
1
= 0,2 p
1
)= ×; / 3.
= 0,2 9 = 0,6.
= e (1 − e )π ρ = 0,4 ⋅ (1 − 0,4) ⋅ 3,14 ⋅ 1800 = 1357
8.
/
3
.
(4.14)
m
= (38 + 11 + 8,9 + 19)3,375 l 1 + (1,6 ⋅ 19 + 11 − 1,6)3,375 +
+ 1,01 ⋅ 1357 ⋅ 3,375l 1 = 4885l 1 + 134,3. 13397 . 4885l 1 + 134,3 = 13397 . e1 = 0,4 , l 1 = 2,715 . (4.16) 1
=
d 2p1 d
p1
4 ⋅ 0,6 ⋅ 2,715 ⋅ 13,85 ⋅ 10 − 3 ⋅ 1,8 ⋅ 103 290 ⋅ 3358 0,98 ⋅ 0,6407 ⋅ 9 ⋅ 10 6
= 0,169 ,
, 0,5 (1−1,15⋅0,69) = 0,403, . . e1 ≤ 0,403.
µ
(4.15): 1357 ⋅ 2,715 ⋅ 3,375 = 0,6217. µ 1= 20000 p . 4.4.
p ч
4.4.6.
1
ч
(4.9), (4.10) V =
J
.
Кv
ln
1− µ
=
1 .
. 3.1 4.4.7.
= 0,0285.
ч
(4.11). :
Kv = 1,16,
1 2905 ln = 6954 / . 1,16 1 − 0,9378 L = 10432
.
х
. 4.5. , p
p
. 2.1, 2.4.
74
, lc 2
p
.
lc 3 lp = l
1
+l
( 2
. . 4.2): + 1,1 l 3 = 5,29 + 1,84 + 1,1 ⋅ 2,33 = 9,693 . 4.4
p
1 20 000 13 397
2 6283 4209
3 1974 1322
d ,
13,85 38 19 0,169
13,21 34 17 0,095
12,52 30 15 0,174
e d0 , e, q , ω , q ,
0,4 1,5 600 11 11 -1,6
0,4 1,5 600 11,5 11,5 -1,7
0,4 0,7 280 17 17 -1,8
8,9
9,3
9,8
18 19 1,6
49 58 1,57
74 95 1,53
1357 2,715
1357 0,82
1357 2,507
/
12434,4 0,6217 2544
3756 0,5977 —
1167 0,5910 —
/
2844
3008
3012
3,722
4,04
8,11
m0 , m , u , ω , q ,
ω , ω , 1+ ξ ω ,
/ / /
/ / /
3 3
3 3 3 3
/
fa
/
3
/
3
l m ,
µ
J0 , J∞ ,
n0 4.4.8. я 74
№
p
х
75
t 1 = e1 u 1 = 600 / 13,85 = 43,3 ; t 2 = e2 u 2 = 600 / 13,21 = 45,4 ; t 3 = e3 u 3 = 280 / 12,52 = 22,4 . : m& 1 = m 1 t 1 = 287 / ; m& 2 = m 2 t 2 = 83 / ; m& 3 = m 3 t 3 = 52 / . :
C : -
(
-
(
-
) P01 = m& 1 J 0 1 = 277⋅2544 = 705
;
) P02 = m& 2 J ∞ 2 = 89⋅3008 = 268
;
) P03 = m& 3 J ∞ 3 = 54⋅3012 = 163
(
. 4.5
p
№
p 1 20 000 12434 1,5 0,2
2 6283 3756 1,5 0,2
3 1974 1167 0,7 0,2
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2,715
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2,507
d
13,85 0,169
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0,26
0,14
0,122
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d ,
18 1,1 0,39 0,72 0,3
49 0,98 0,21 0,54 0,3
74 1,05 0,19 0,43 1,14
la , l ,
1,23 0,6
1,23 0,5
1,4 0,4
l ,
0,63
0,73
1,0
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/
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l ,
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0,11
0,1
l , l ,
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1,47 1,84
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ч
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2829.0 345.0 1.159
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82
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3
p
p
p
, ,
p
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p " , p
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p "
3423.0 1443.0 786.0 1181.0 2.765
3423.0 1443.0 786.0 1181.0 2.765
0.0 0.0 0.0 0.0 0.0
1.800 — 25.00 0.060
1.400 0.280 20.00 0.015
0.0 0.0 0.0 0.0
p
p
III , 0.0 0.0 p , 0.0 p p , 0.0 0.0 0.0 µk , / 3 0.0 , / — , / 0.0 p p 5460.7 ……………………………………..……………… 4949.2
p
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II 9660.0 7338.9 821.1 718.3 1.9 0.7597 2700.0 — 3366.3
0.199 0.203 0.095 0.381 0.209 0.102 1.309
0.171 0.134 0.198 0.279 0.255 0.102 1.139
0.0 0.0 0.0 0.0 0.0 0.0 0.0
p p
, , 82
I 0.107 0.682
II 0.066 0.682
III 0.0 0.0
83
,
0.214 0.133 0.0 , 0.500 0.500 0.0 , 0.682 0.682 0.0 , 1.241 1.241 0.0 , 4.122 1.463 0.0 , 5.919 1.914 0.0 , 10.041 3.377 0.0 …………………………………………………. 3.000 ………………………………………………………. 18.900 p p
p
p
p
p
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, p p
p
p p
, p
, p
,
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,
/
I 741.6 21 444.6 7755.7 186.68 67.51 254.19 114.88
II 132.7 5389.7 1949.3 28.94 10.47 39.41 186.21
III 0.0 0.0 0.0 0.0 0.0 0.0 0.0
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: 09/08/96; 12:17:11. . . : Omega. , . . . . ,
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:
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:
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; ; . :
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p p
2460.0 290.0 1.160 3300.0 1800.0 5.75
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0.40
0.40
0.40
1100.0 2050.0 1300.0 4700.0 1600.0
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9.000 0.060
8.000 0.015
7.000 0.008
p p
p p p p p p
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p , 3 , / , / 3
p
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3
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p
p p
,
I II 20 231.1 6331.1
III 1981.2
86
, , p
p
12 596.7 3791.15 13 576.4 4248.5 1303.4 558.7
1170.76 1329.5 190.5
1177.4
520.8
178.8
1.48 2543.47 2843.37 0.6226
1.48 — 3007.40 0.5988
0.71 — 3011.63 0.5909
13.847 3.87
13.210 3.71
12.523 8.16
, p
p , , , / , /
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p p p …………………………………………………………………… 2672.55 " " …………………………………………………… 2496.96 w, q, /
p p
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3
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p
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29.508 14.75 16.69 16.69 9.78 -1.79 97.73 1347.97 1.56
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p
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p p
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87
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p p
p
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:
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; ;
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2460.0 290.0 1.160 3300.0 1800.0 5.75
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9.000 0.060
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p p
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p
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p
p p
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1164.02 1322.1 189.6
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