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Файл:Современные проблемы металлургии и материаловедения гидродинамика и массообмен в многофазных системах металлургии. Учебное пособие
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ɇɚɱɚɥɶɧɵɟ ɭɫɥɨɜɢɹ:
c ɫ
CC
°
t
ɩɪɢ 0
ii
®
ɞɞ
CC
°
ii
¯
0
0
const,
const.
Ƚɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ: (4.249)
kt
ɩɪɢ
r of
ɩɪɢ
ɩɪɢ
cc
C ɋ e
ii
c
rr
,rr
0
Ch
0
0T
i
C ɋ e
1
0
ɞ
ɋ
i
0
;
cc
0
ii
;
kt
1
.
Ɉɫɨɛɟɧɧɨɫɬɶ ɪɟɲɟɧɢɹ ɭɪɚɜɧɟɧɢɹ (4.247) ɫ ɭɫɥɨɜɢɹɦɢ ɨɞɧɨɡɧɚɱɧɨɫɬɢ (4.249) ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɩɨɫɥɟɞɧɢɟ ɫɨɞɟɪɠɚɬ ɡɚɜɢɫɢɦɨɫɬɶ
ɨɬ ɜɪɟɦɟɧɢ. ɍɤɚɡɚɧɧɨɟ ɪɟɲɟɧɢɟ ɩɪɢɜɨɞɢɬɫɹ ɞɥɹ ɞɜɭɯ ɢɧɬɟɪɜɚɥɨɜ
ɜɪɟɦɟɧɢ:
– ɩɪɢ
tD
2
r
0
,
cc
i
ɝɞɟ
c
Pe
*
c
Pe ,
*
*
Ur
P
c
*c
P
1
f
0
ɩɥɨɬɧɨɫɬɶ ɩɨɬɨɤɚ
D
i
ɦɚɫɫɵ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɩɪɢ ɧɚɥɢɱɢɢ ɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ ɩɟɪɜɨɝɨ ɩɨɪɹɞɤɚ ɜ ɫɩɥɨɲɧɨɣ ɮɚɡɟ ɪɚɜɧɚ
ɞɞ
ªº
§·
cc
mD C ke kt
ii i
11
Re erf
00
ii
«»
¨¸
hh
«»
©¹
¬¼
CC
kt kt
1
011
S
t
; (4.250)
2
r
tD!!
– ɩɪɢ
cc
mD
ii
Pe .
0
cc
i
ªº
«»
«»
«»
c
*
«»
«»
«»
¬¼
ɷɬɚ ɜɟɥɢɱɢɧɚ ɪɚɜɧɚ
c
Pe
*
ɞ 22
Cr r
i
00 0
u
kk
11
h
u
23cos 3cos
cc cc
DD
i
3sin
T
T T
erf
cc
Pe Pe
*i*
§·
2
3
ɞ
C
¨¸
¨¸
¨¸
©¹
k
i
0
eCe
h
1
D
1
2
2
r
0
cc
c
Pe
i
*
S
kt
c
1
i
0
(4.251)
ɉɨɬɨɤ ɦɚɫɫɵ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɬɚɤɠɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɞɥɹ ɪɚɡɧɵɯ
ɢɧɬɟɪɜɚɥɨɜ ɜɪɟɦɟɧɢ ɩɨ-ɪɚɡɧɨɦɭ:
121
2
M
r
tD
– ɩɪɢ
S
ii i
rD C ke kt
4Re erf,
0011
0
cc
i
2c c
ɢɦɟɟɦ
c
Pe
*
ɞɞ
ªº
§·
CC
kt kt
ii
11
00
«»
¨¸
hh
«»
©¹
¬¼
1
S
t
(4.252)
2
r
tD!!
– ɩɪɢ
MrD
S
ii
2c c
4Pe .
0*
0
Pe
ɢɦɟɟɦ
c
*
cc
i
ªº
«»
«»
«»
c
«»
«»
«»
¬¼
ɞ 22
Cr r
00 0
i
kk
u
11
h
u
2 3 cos 3 cos
cc cc
DD
ii
3sin
T
T T
erf
cc
Pe Pe
**
§·
2
3
ɞ
C
0
i
¨¸
eCe
¨¸
h
¨¸
©¹
k
1
2
r
0
cc
D
Pe
i
1
6
S
c
*
kt
c
1
0
i
(4.253)
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɢ ɧɚɥɢɱɢɢ ɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ ɦɟɠɞɭ ɤɨɦɩɨɧɟɧɬɚɦɢ, ɧɚɯɨɞɹɳɢɦɢɫɹ ɜ ɤɚɩɥɟ ɢ ɜ ɧɟɫɭɳɟɦ ɩɨɬɨɤɟ, ɢ ɩɪɨɬɟɤɚɸɳɟɣ
ɜ ɧɟɫɭɳɟɦ ɩɨɬɨɤɟ, ɦɚɫɫɨɨɛɦɟɧ ɧɨɫɢɬ ɧɟɫɬɚɰɢɨɧɚɪɧɵɣ ɯɚɪɚɤɬɟɪ, ɢ
ɟɝɨ ɩɚɪɚɦɟɬɪɵ ɢɡɦɟɧɹɸɬɫɹ ɜɨ ɜɪɟɦɟɧɢ. ɂɡ ɩɨɫɥɟɞɧɢɯ ɞɜɭɯ ɭɪɚɜɧɟɧɢɣ ɫɥɟɞɭɟɬ ɬɚɤɠɟ, ɱɬɨ ɫɧɚɱɚɥɚ ɩɨɬɨɤ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɜɨɡɪɚɫɬɚɟɬ, ɚ ɡɚɬɟɦ, ɩɨ ɨɤɨɧɱɚɧɢɢ ɩɟɪɜɨɝɨ
ɩɟɪɢɨɞɚ, ɧɚɱɢɧɚɟɬ ɫɨɤɪɚɳɚɬɶɫɹ,
ɩɪɢɛɥɢɠɚɹɫɶ ɤ ɧɟɤɨɬɨɪɨɦɭ ɫɬɚɰɢɨɧɚɪɧɨɦɭ ɡɧɚɱɟɧɢɸ.
4.2.7. Ɇɚɫɫɨɨɛɦɟɧ ɦɟɠɞɭ ɝɚɡɨɜɵɦ ɩɭɡɵɪɶɤɨɦ ɢ ɩɨɬɨɤɨɦ
ɜɹɡɤɨɣ ɠɢɞɤɨɫɬɢ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɯɢɦɢɱɟɫɤɨɣ
ɪɟɚɤɰɢɢ
4.2.7.1. ɋɨɩɪɨɬɢɜɥɟɧɢɟ ɦɚɫɫɨɩɟɪɟɧɨɫɭ ɫɨɫɪɟɞɨɬɨɱɟɧɨ
ɜɧɭɬɪɢ ɩɭɡɵɪɹ
Ɉɫɨɛɟɧɧɨɫɬɶɸ ɩɪɨɰɟɫɫɨɜ ɦɚɫɫɨɨɛɦɟɧɚ ɜ ɫɢɫɬɟɦɟ ɝɚɡ–ɠɢɞɤɨɫɬɶ ɩɨ
ɫɪɚɜɧɟɧɢɸ ɫ ɫɢɫɬɟɦɨɣ ɠɢɞɤɨɫɬɶ–ɠɢɞɤɨɫɬɶ ɹɜɥɹɟɬɫɹ ɬɨ ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ, ɱɬɨ, ɤɚɤ ɨɬɦɟɱɚɥɨɫɶ ɪɚɧɟɟ, ɞɥɹ ɛɨɥɶɲɢɧɫɬɜɚ ɯɢɦɢɱɟɫɤɢɯ ɷɥɟɦɟɧɬɨɜ ɡɧɚɱɟɧɢɟ ɤɪɢɬɟɪɢɹ ɒɦɢɞɬɚ ɜ ɝɚɡɨɜɨɣ ɫɪɟɞɟ ɛɥɢɡɤɨ ɤ ɟɞɢɧɢɰɟ
122
D
§·
¨¸
©¹
ɱɢɫɥɚ ɉɟɤɥɟ ɞɥɹ ɝɚɡɚ
Sc
Q
. ȼ ɫɜɹɡɢ ɫ ɷɬɢɦ ɩɪɢ ɞRe 1 ɡɧɚɱɟɧɢɟ ɞɢɮɮɭɡɢɨɧɧɨɝɨ
i
i
ɞɞ
c
Pe Re Sc
ɨɤɚɡɵɜɚɟɬɫɹ ɦɟɧɶɲɟ ɟɞɢɧɢɰɵ,
ɬ.ɟ. ɜ ɭɤɚɡɚɧɧɵɯ ɫɥɭɱɚɹɯ ɤɨɧɜɟɤɬɢɜɧɵɣ ɩɟɪɟɧɨɫ, ɜɨ ɜɫɹɤɨɦ ɫɥɭɱɚɟ, ɧɟ
ɩɪɟɜɚɥɢɪɭɟɬ ɧɚɞ ɦɨɥɟɤɭɥɹɪɧɵɦ, ɢ ɩɨɫɥɟɞɧɢɦ ɧɟɥɶɡɹ ɩɪɟɧɟɛɪɟɝɚɬɶ.
ɉɨɷɬɨɦɭ ɪɚɫɫɦɚɬɪɢɜɚɟɦɚɹ ɡɚɞɚɱɚ ɪɟɲɚɟɬɫɹ ɞɥɹ ɞɜɭɯ ɤɪɚɣɧɢɯ ɡɧɚ-
ɱɟɧɢɣ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɱɢɫɥɚ ɉɟɤɥɟ:
ɞ
c
Pe
*
(ɦɨɞɟɥɶ Ʉɪɨɧɢɝɚ – Ȼɪɢɧɤ [5]).
of
Pe 0
(ɦɨɞɟɥɶ ɇɶɸɦɟɧɚ [1]) ɢ
*
ɞ
c
o
ȼ ɞɚɧɧɨɦ ɩɚɪɚɝɪɚɮɟ ɛɭɞɭɬ ɪɚɫɫɦɨɬɪɟɧɵ ɨɛɟ ɷɬɢ ɦɨɞɟɥɢ ɢ ɨɩɪɟɞɟɥɟɧɵ ɝɪɚɧɢɰɵ ɩɪɢɦɟɧɟɧɢɹ ɤɚɠɞɨɣ ɢɡ ɧɢɯ ɞɥɹ ɪɚɫɱɺɬɚ ɫɪɟɞɧɟɣ ɤɨɧɰɟɧɬɪɚɰɢɢ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɜ ɝɚɡɨɜɨɣ ɮɚɡɟ.
Ⱦɪɭɝɨɣ ɨɫɨɛɟɧɧɨɫɬɶɸ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɮɚɡ ɜ ɫɢɫɬɟɦɟ ɝɚɡ–
ɠɢɞɤɨɫɬɶ ɹɜɥɹɟɬɫɹ ɬɨ ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ, ɱɬɨ, ɜ ɨɬɥɢɱɢɟ ɨɬ ɫɢɫɬɟɦɵ
ɠɢɞɤɨɫɬɶ–ɠɢɞɤɨɫɬɶ, ɜ ɫɢɫɬɟɦɟ ɝɚɡ–
ɠɢɞɤɨɫɬɶ ɮɢɡɢɱɟɫɤɢɟ ɩɚɪɚɦɟɬɪɵ
ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ ɮɚɡ, ɩɥɨɬɧɨɫɬɶ ɢ ɜɹɡɤɨɫɬɶ, ɨɬɥɢɱɚɸɬɫɹ ɞɪɭɝ ɨɬ
ɞɪɭɝɚ ɧɚ ɧɟɫɤɨɥɶɤɨ ɩɨɪɹɞɤɨɜ. ɗɬɨɬ ɮɚɤɬ ɜɧɨɫɢɬ ɨɩɪɟɞɟɥɺɧɧɵɟ ɢɡɦɟɧɟɧɢɹ ɜ ɩɨɫɬɚɧɨɜɤɭ ɢ ɪɟɲɟɧɢɹ ɡɚɞɚɱ. ȼ ɱɚɫɬɧɨɫɬɢ, ɜ ɤɚɱɟɫɬɜɟ ɛɟɡɪɚɡɦɟɪɧɨɝɨ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ ɜɹɡɤɨɫɬɢ ɢɫɩɨɥɶɡɭɟɬɫɹ ɜɟɥɢ-
ɱɢɧɚ
ɞ
P
, ɚ ɧɟ ɨɛɪɚɬɧɚɹ ɟɣ ɜɟɥɢɱɢɧɚ
ɫ
P
ɫ
P
, ɤɚɤ ɜ ɫɢɫɬɟɦɟ ɠɢɞɤɨɫɬɶ–
ɞ
P
ɠɢɞɤɨɫɬɶ.
ɋɮɨɪɦɭɥɢɪɭɟɦ ɦɚɬɟɦɚɬɢɱɟɫɤɭɸ ɦɨɞɟɥɶ ɢ ɪɚɫɫɦɨɬɪɢɦ ɪɟɲɟɧɢɹ
ɩɨɫɬɚɜɥɟɧɧɨɣ ɡɚɞɚɱɢ.
Ɉɫɬɚɧɨɜɢɦɫɹ ɧɚ ɩɟɪɜɨɦ ɤɪɚɣɧɟɦ ɫɥɭɱɚɟ: ɩɟɪɟɧɨɫ ɦɚɫɫɵ ɰɟɥɟɜɨɝɨ
ɞ
c
Pe 1
ɤɨɦɩɨɧɟɧɬɚ ɜ ɨɛɴɺɦɟ ɩɭɡɵɪɹ ɩɪɨɢɫɯɨɞɢɬ ɜ ɭɫɥɨɜɢɹɯ, ɤɨɝɞɚ
ɂɡ ɷɬɨɝɨ ɫɥɟɞɭɟɬ, ɱɬɨ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɩɟɪɟɧɨɫɚ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɜ
ɨɛɴɺɦɟ ɩɭɡɵɪɹ ɡɚ ɫɱɺɬ ɤɨɧɜɟɤɰɢɢ ɧɢɱɬɨɠɧɨ ɦɚɥɚ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɢɧɬɟɧɫɢɜɧɨɫɬɶɸ ɟɺ ɩɟɪɟɧɨɫɚ ɡɚ ɫɱɺɬ ɦɨɥɟɤɭɥɹɪɧɨɣ ɞɢɮɮɭɡɢɢ. ɉɨɷɬɨɦɭ
ɜ ɭɪɚɜɧɟɧɢɢ ɤɨɧɜɟɤɬɢɜɧɨɣ ɞɢɮɮɭɡɢɢ
ɞ
w
C
G
i
wCDɋ
t
w
ɞɞ2 ɞ
grad
ii i
.
ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ ɫɥɚɝɚɟɦɵɦɢ, ɨɩɢɫɵɜɚɸɳɢɦɢ ɤɨɧɜɟɤɬɢɜɧɵɣ ɩɟɪɟɧɨɫ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ, ɩɨɫɥɟ ɱɟɝɨ ɭɪɚɜɧɟɧɢɟ ɩɪɢɧɢɦɚɟɬ ɜɢɞ
123
ɞ 2 ɞ
C ɋ
ww
w
ɞ
ii
D
i
t
(4.254)
.
2
r
w
ɋɮɨɪɦɭɥɢɪɭɟɦ ɧɚɱɚɥɶɧɵɟ ɢ ɝɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ ɞɥɹ ɭɪɚɜɧɟɧɢɹ
(4.254)
ɩɪɢ 0
t
ɞɞ
ɋ C ; (4.255)
ii
0
const
ɩɪɢ
ɩɪɢ 0
rr
0
r
ɞɞ
ɋ C ; (4.256)
iis
ɞ
ɋ f. (4.257)
i
ɍɫɥɨɜɢɟ (4.255) ɜɵɪɚɠɚɟɬ ɞɨɩɭɳɟɧɢɟ ɨ ɬɨɦ, ɱɬɨ ɜ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɤɨɧɰɟɧɬɪɚɰɢɹ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɜ ɨɛɴɺɦɟ ɩɭɡɵɪɹ
ɛɵɥɚ ɨɞɢɧɚɤɨɜɨɣ ɜɨ ɜɫɟɯ ɬɨɱɤɚɯ. ɋɨɝɥɚɫɧɨ (4.256) ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ
ɩɭɡɵɪɹ ɤɨɧɰɟɧɬɪɚɰɢɹ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɨɫɬɚɺɬɫɹ ɩɨɫɬɨɹɧɧɨɣ ɢ
ɪɚɜɧɚ ɟɺ ɪɚɜɧɨɜɟɫɧɨɦɭ ɡɧɚɱɟɧɢɸ. ɍɫɥɨɜɢɟ (4.257) ɨɬɪɚɠɚɟɬ ɬɨɬ ɮɚɤɬ,
ɱɬɨ ɤɨɧɰɟɧɬɪɚɰɢɹ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɜ ɰɟɧɬɪɟ ɩɭɡɵɪɹ ɜɫɟɝɞɚ ɹɜɥɹ-
ɤɨɧɟɱɧɨɣ ɜɟɥɢɱɢɧɨɣ. ȼɜɟɞɺɦ ɜ ɪɚɫɫɦɨɬɪɟɧɢɟ ɛɟɡɪɚɡɦɟɪɧɭɸ
ɟɬɫɹ
ɤɨɧɰɟɧɬɪɚɰɢɸ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɜ ɝɚɡɨɜɨɦ ɩɭɡɵɪɟ, ɨɛɨɡɧɚɱɢɜ ɟɺ
ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
ɞɞ
CC
ɞ
)
i
0
ii
ɞɞ
CC
0
is i
.
(4.258)
ȼɜɟɞɺɦ (4.258) ɜ ɭɪɚɜɧɟɧɢɟ (4.254) ɢ ɭɫɥɨɜɢɹ ɨɞɧɨɡɧɚɱɧɨɫɬɢ
(4.255) – (4.257):
ɞ 2 ɞ
w) w )
ɩɪɢ
w
ɞ
ii
D
i
t
0t
(4.259)
,
2
r
w
ɞ
0,
) (4.260)
i
ɩɪɢ
ɩɪɢ
rr
0r
ɞ
1,
) (4.261)
0
i
ɞ
)f (4.262)
.
i
ɍɪɚɜɧɟɧɢɟ (4.259) ɫ ɤɪɚɟɜɵɦɢ ɭɫɥɨɜɢɹɦɢ (4.260) – (4.262) ɪɟɲɚɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɦɟɬɨɞɚ Ɏɭɪɶɟ. ɉɪɢ ɷɬɨɦ ɪɟɲɟɧɢɟ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜ
124
ɜɢɞɟ ɩɪɨɢɡɜɟɞɟɧɢɹ ɞɜɭɯ ɮɭɧɤɰɢɣ, ɤɚɠɞɚɹ ɢɡ ɤɨɬɨɪɵɯ ɡɚɜɢɫɢɬ ɨɬ ɨɞɧɨɝɨ ɚɪɝɭɦɟɧɬɚ – ɜɪɟɦɟɧɢ ɢɥɢ ɤɨɨɪɞɢɧɚɬɵ. Ɉɤɨɧɱɚɬɟɥɶɧɨ ɤɨɧɰɟɧɬɪɚɰɢɹ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɜ ɝɚɡɨɜɨɦ ɩɭɡɵɪɟ ɜɵɪɚɠɚɟɬɫɹ ɫɥɟɞɭɸɳɢɦ ɭɪɚɜɧɟɧɢɟɦ:
ɞ 22
) S
i
f
,1 sin exp .
rt n
¦
n
1
22
n
1
S
nr r
§·
rDt
0
S
r
¨¸
0
©¹
§·
¨¸
©¹
ɞ
i
2
r
0
(4.263)
ɋɪɟɞɧɹɹ ɩɨ ɨɛɴɺɦɭ ɝɚɡɨɜɨɝɨ ɩɭɡɵɪɹ ɤɨɧɰɟɧɬɪɚɰɢɹ ɰɟɥɟɜɨɝɨ ɤɨɦ-
ɩɨɧɟɧɬɚ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ:
ɇ
ɞ 22 ɞ
) S
1expFo,
i
f
61
¦
22
S
n
1
n
n
(4.264)
ɝɞɟ ɢɧɞɟɤɫ «ɇ» ɨɡɧɚɱɚɟɬ, ɱɬɨ ɭɪɚɜɧɟɧɢɟ (4.264) ɞɥɹ ɫɪɟɞɧɟɝɨ ɡɧɚɱɟ-
ɧɢɹ ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɨɥɭɱɟɧɨ ɜ ɪɚɦɤɚɯ ɦɨɞɟɥɢ ɦɚɫɫɨɩɟɪɟɧɨɫɚ
ɇɶɸɦɟɧɚ;
ɞ
Dtr
ɞ
Fo
i
– ɱɢɫɥɨ Ɏɭɪɶɟ, ɛɟɡɪɚɡɦɟɪɧɨɟ ɜɪɟɦɹ.
2
0
Ɇɨɞɟɥɶ ɇɶɸɦɟɧɚ, ɨɩɢɫɵɜɚɸɳɚɹ ɦɚɫɫɨɩɟɪɟɧɨɫ ɜ ɝɚɡɨɜɨɣ ɮɚɡɟ
ɬɨɥɶɤɨ ɡɚ ɫɱɺɬ ɦɨɥɟɤɭɥɹɪɧɨɣ ɞɢɮɮɭɡɢɢ, ɦɨɠɟɬ ɛɵɬɶ ɩɪɢɦɟɧɟɧɚ ɞɥɹ
ɩɭɡɵɪɶɤɨɜ, ɞɢɚɦɟɬɪ ɤɨɬɨɪɵɯ ɧɟ ɩɪɟɜɵɲɚɟɬ 0,3 ɦɦ. ɋɨɝɥɚɫɧɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɞɚɧɧɵɦ [5], ɜ ɩɭɡɵɪɶɤɚɯ ɞɢɚɦɟɬɪɨɦ ɛɨɥɟɟ 0,3 ɦɦ ɫɭɳɟɫɬɜɭɟɬ ɪɚɡɜɢɬɨɟ ɬɟɱɟɧɢɟ ɝɚɡɚ, ɩɪɟɞɫɬɚɜɥɹɸɳɟɟ ɫɨɛɨɣ ɜɢɯɪɢ ɏɢɥɥɚ.
Ɋɚɫɫɦɨɬɪɢɦ ɜɬɨɪɭɸ ɤɪɚɣɧɸɸ ɦɨɞɟɥɶ ɦɚɫɫɨɩɟɪɟɧɨɫɚ ɜ
ɫɢɫɬɟɦɟ
ɝɚɡ–ɠɢɞɤɨɫɬɶ, ɭɱɢɬɵɜɚɸɳɭɸ ɧɚɥɢɱɢɟ ɰɢɪɤɭɥɹɰɢɨɧɧɨɝɨ ɬɟɱɟɧɢɹ
ɜɧɭɬɪɢ ɝɚɡɨɜɵɯ ɩɭɡɵɪɶɤɨɜ – ɦɨɞɟɥɶ Ʉɪɨɧɢɝɚ – Ȼɪɢɧɤ.
ɉɨɥɚɝɚɟɦ, ɱɬɨ
Pe
. Ɍɨɝɞɚ ɩɪɨɰɟɫɫ ɩɟɪɟɧɨɫɚ ɦɚɫɫɵ ɰɟɥɟɜɨɝɨ
of
ɞ
c
ɤɨɦɩɨɧɟɧɬɚ ɜ ɨɛɴɺɦɟ ɝɚɡɨɜɨɝɨ ɩɭɡɵɪɹ ɡɚɜɢɫɢɬ, ɪɟɲɚɸɳɢɦ ɨɛɪɚɡɨɦ,
ɨɬ ɟɺ ɤɨɧɜɟɤɰɢɢ ɜ ɩɭɡɵɪɟ ɢ ɨɩɢɫɵɜɚɟɬɫɹ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɦ ɭɪɚɜɧɟɧɢɟɦ ɤɨɧɜɟɤɬɢɜɧɨɣ ɞɢɮɮɭɡɢɢ, ɤɨɬɨɪɨɟ ɜ ɫɮɟɪɢɱɟɫɤɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ ɢɦɟɟɬ ɜɢɞ
ɞɞɞɞ2 ɞ
CCwC ɋ
ww w w
ww wT
ɞɞ
ii i i
wD
ri
trr
T
T
.
(4.265)
2
r
w
ɋɨɫɬɚɜɥɹɸɳɢɟ ɜɟɤɬɨɪɚ ɫɤɨɪɨɫɬɢ ɝɚɡɚ ɜ ɨɛɴɺɦɟ ɩɭɡɵɪɶɤɚ ɨɩɪɟɞɟ-
ɥɹɸɬɫɹ ɩɨ ɮɨɪɦɭɥɚɦ [5]:
125
2
]
gr
ɞ
w
T
r
'U
0
c*
P P
323
2
§·
r
1cos
¨¸
2
r
0
©¹
, (4.266)
2
gr
ɞ
w
T
T
'U
0
c*
323
P P
§·
12 sin.
¨¸
©¹
2
r
2
r
0
(4.267)
ɂɡ (4.266) ɢ (4.267) ɜɢɞɧɨ, ɱɬɨ ɫɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ ɝɚɡɚ ɜɧɭɬɪɢ ɩɭɡɵɪɶɤɨɜ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɫɤɨɪɨɫɬɢ ɨɦɵɜɚɸɳɟɝɨ ɩɨɬɨɤɚ, ɤɚɤ ɜ ɫɥɭɱɚɟ
ɨɛɬɟɤɚɧɢɹ ɤɚɩɥɢ, ɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɞɟɣɫɬɜɢɟɦ ɫɢɥɵ ɬɹɠɟɫɬɢ ɫ ɭɱɺɬɨɦ
ɜɵɬɚɥɤɢɜɚɸɳɟɣ ɫɢɥɵ Ⱥɪɯɢɦɟɞɚ. ɋɥɚɛɨɟ ɜɥɢɹɧɢɟ ɨɤɪɭɠɚɸɳɟɝɨ ɩɭ-
ɡɵɪɶ ɩɨɬɨɤɚ ɜɹɡɤɨɣ ɠɢɞɤɨɫɬɢ ɫɜɹɡɚɧɨ ɫ ɨɬɧɨɫɢɬɟɥɶɧɨ ɦɚɥɵɦ ɡɧɚɱɟ-
ɧɢɟɦ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ ɜɹɡɤɨɫɬɢ ɝɚɡɚ. Ɋɟɲɟɧɢɟ
ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɛɭɞɟɦ ɢɫɤɚɬɶ ɩɨ ɦɟɬɨɞɢɤɟ, ɢɡɥɨɠɟɧɧɨɣ ɪɚɧɟɟ. ɋ ɷɬɨɣ ɰɟɥɶɸ ɢɫɩɨɥɶɡɭɟɦ ɤɪɢɜɨɥɢɧɟɣɧɭɸ ɫɢɫɬɟɦɭ
ɤɨɨɪɞɢɧɚɬ, ɝɟɨɦɟɬɪɢɱɟɫɤɨɟ ɢɡɨɛɪɚɠɟɧɢɟ ɤɨɬɨɪɨɣ ɩɪɟɞɫɬɚɜɥɟɧɨ ɧɚ
ɪɢɫ. 4.11. ɋɟɦɟɣɫɬɜɨ ɤɨɨɪɞɢɧɚɬɧɵɯ ɥɢɧɢɣ
[ ɡɞɟɫɶ ɜɵɛɪɚɧɨ ɬɚɤɢɦ
ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɨɧɨ ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɩɨɫɬɨɹɧɧɨɝɨ ɦɧɨɠɢɬɟɥɹ ɫɨɜɩɚɞɚ-
ɥɨ ɫ ɥɢɧɢɹɦɢ ɬɨɤɚ
const\ . ȼɬɨɪɨɟ ɫɟɦɟɣɫɬɜɨ ɤɨɨɪɞɢɧɚɬ const
ɞ
ɨɪɬɨɝɨɧɚɥɶɧɨ ɩɟɪɜɨɦɭ:
22
§·
Ɍɚɤ ɤɚɤ
rr
[ T
41 sin,
¨¸
22
rr
00
©¹
4
§·
r
T
¨¸
©¹
]
ɞ
Pecof, ɬɨ ɦɨɠɧɨ ɭɬɜɟɪɠɞɚɬɶ, ɱɬɨ ɜɞɨɥɶ ɥɢɧɢɣ ɬɨɤɚ ɰɟ-
cos
r
0
2
r
2
2
r
0
2
(4.268)
4
.
(4.269)
1
ɥɟɜɨɣ ɤɨɦɩɨɧɟɧɬ ɩɟɪɟɧɨɫɢɬɫɹ ɜ ɨɫɧɨɜɧɨɦ ɡɚ ɫɱɺɬ ɤɨɧɜɟɤɬɢɜɧɨɣ ɞɢɮɮɭɡɢɢ, ɚ ɜ ɧɚɩɪɚɜɥɟɧɢɢ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɦ ɥɢɧɢɹɦ ɬɨɤɚ, ɟɝɨ ɩɟɪɟɧɨɫ
ɩɪɨɢɫɯɨɞɢɬ ɡɚ ɫɱɺɬ ɦɨɥɟɤɭɥɹɪɧɨɣ ɞɢɮɮɭɡɢɢ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɜɵɪɚɜɧɢɜɚɧɢɟ ɤɨɧɰɟɧɬɪɚɰɢɢ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɜ ɨɛɴɺɦɟ ɩɭɡɵɪɹ ɜɞɨɥɶ
ɥɢɧɢɣ ɬɨɤɚ ɩɪɨɢɫɯɨɞɢɬ ɡɧɚɱɢɬɟɥɶɧɨ ɛɵɫɬɪɟɟ, ɱɟɦ ɜ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɦ
ɧɢɦ ɧɚɩɪɚɜɥɟɧɢɢ, ɢ ɟɝɨ ɤɨɧɰɟɧɬɪɚɰɢɹ ɜɞɨɥɶ ɥɢɧɢɣ ɬɨɤɚ ɩɨɫɬɨɹɧɧɚ.
ɤ
Ⱥɧɚɥɢɬɢɱɟɫɤɢ ɫɞɟɥɚɧɧɵɟ ɞɨɩɭɳɟɧɢɹ ɜɵɪɚɠɚɸɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
126
B
B
G
wC
ɞ
grad 0,
i
ɞɞ
CC t [
ii
,.
ɉɟɪɟɯɨɞɹ ɤ ɤɪɢɜɨɥɢɧɟɣɧɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ, ɡɚɩɢɲɟɦ ɭɪɚɜɧɟ-
ɧɢɟ (4.265) ɢ ɤɪɚɟɜɵɟ ɭɫɥɨɜɢɹ (4.260) – (4.262) ɜ ɛɟɡɪɚɡɦɟɪɧɨɦ ɜɢɞɟ:
ªº
w
pg
[ [
«»
w[ w[
¬¼
ɩɪɢ
ɩɪɢ 0
ɩɪɢ 1
ɞ
Dtr
ɞ
Fo
ɝɞɟ
Ƚɪɚɮɢɤɢ ɮɭɧɤɰɢɣ
i
– ɱɢɫɥɨ Ɏɭɪɶɟ, ɛɟɡɪɚɡɦɟɪɧɨɟ ɜɪɟɦɹ.
2
0
p [ ɢ
ɞɞ
w) w)
Fo 0
[
[
1
ii
16
ɞ
g [
ɞ
0;
) (4.271)
i
ɞ
1;
) (4.272)
i
ɞ
)f (4.273)
ɩɨɤɚɡɚɧɵ ɧɚ ɪɢɫ. 4.12. ɍɪɚɜɧɟɧɢɟ
,
i
, (4.270)
ɞ
Fo
w
(4.270) ɹɜɥɹɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ ɫ ɪɚɡɞɟɥɹɸɳɢɦɢɫɹ ɩɟɪɟɦɟɧɧɵɦɢ ɢ ɪɟɲɚɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɦɟɬɨɞɚ Ɏɭɪɶɟ. Ɉɤɨɧɱɚɬɟɥɶɧɨ ɜɵɪɚɠɟɧɢɟ ɞɥɹ
ɫɪɟɞɧɟɣ ɩɨ ɨɛɴɺɦɭ ɝɚɡɨɜɨɝɨ ɩɭɡɵɪɹ ɤɨɧɰɟɧɬɪɚɰɢɢ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨ-
ɤ-ɛ
ɧɟɧɬɚ
ɞ
) ɫ ɭɱɺɬɨɦ ɤɪɚɟɜɵɯ ɭɫɥɨɜɢɣ (4.271) – (4.273) ɢɦɟɟɬ ɜɢɞ
i
ɤ-ɛ
ɝɞɟ
O
ɢ
n
ɞɞ
) O
– ɱɢɫɥɟɧɧɵɟ ɤɨɷɮɮɢɰɢɟɧɬɵ.
n
1 exp 16 Fo ,
inn
ɉɨɫɤɨɥɶɤɭ ɮɭɧɤɰɢɢ
ɚɧɚɥɢɬɢɱɟɫɤɢ, ɡɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ
n
3
¦
8
1
n
p [ ɢ
B
g [ ɧɟ ɦɨɝɭɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɵ
ɢ
n
(4.274)
O ɨɩɪɟɞɟɥɹɸɬɫɹ ɬɨɥɶ-
n
ɤɨ ɱɢɫɥɟɧɧɵɦ ɦɟɬɨɞɨɦ. ȼ ɬɚɛɥ. 4.1 ɩɪɢɜɟɞɟɧɵ ɡɧɚɱɟɧɢɹ ɷɬɢɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɞɥɹ ɫɟɦɢ ɱɥɟɧɨɜ ɪɹɞɚ, ɜɯɨɞɹɳɟɝɨ ɜ (4.274).
127
Ɍɚɛɥɢɰɚ 4.1
n B
1 1,656 1,66
2 9,8 0,335
3 22,2 0,149
4 38,5 0,122
5 63,0 0,078
6 89,8 0,048
7 123,8 0,026
n
Ȝ
n
ɉɪɢɦɟɧɟɧɢɟ ɦɨɞɟɥɢ Ʉɪɨɧɢɝɚ – Ȼɪɢɧɤ ɨɝɪɚɧɢɱɟɧɨ ɞɨɩɭɳɟɧɢɟɦ ɨ
ɩɨɫɬɨɹɧɫɬɜɟ ɤɨɧɰɟɧɬɪɚɰɢɢ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɜɞɨɥɶ ɥɢɧɢɣ ɬɨɤɚ
ɜɧɭɬɪɢ ɝɚɡɨɜɨɝɨ ɩɭɡɵɪɹ, ɤɨɬɨɪɨɟ ɬɪɟɛɭɟɬ ɜɵɩɨɥɧɟɧɢɹ ɫɥɟɞɭɸɳɟɝɨ
ɭɫɥɨɜɢɹ:
ɞ
c
ɝɞɟ
Pe
g
2
ɞ
c
Pe
– ɫɤɨɪɨɫɬɶ ɜɫɩɥɵɬɢɹ ɝɚɡɨɜɨɝɨ ɩɭɡɵɪɹ, ɦ/ɫ.
U
f
f
– ɞɢɮɮɭɡɢɨɧɧɨɟ ɱɢɫɥɨ ɉɟɤɥɟ ɞɥɹ ɝɚɡɨɜɨɣ ɮɚɡɵ;
ɞ
D
i
0,007 0, 007 Pe ,
[! |
0
*
ɞ
P
1
ɫ
P
ɞ
c
(4.275)
ɂɡ ɪɢɫ. 4.12 ɜɢɞɧɨ, ɱɬɨ ɦɢɧɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɮɭɧɤɰɢɢ
g [
ɪɚɜɧɹɟɬɫɹ 2,2. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɫɨɝɥɚɫɧɨ (4.275) ɩɪɢɦɟɧɟɧɢɟ ɦɨɞɟɥɢ
Ʉɪɨɧɢɝɚ – Ȼɪɢɧɤ ɞɥɹ ɫɢɫɬɟɦ ɝɚɡ–ɠɢɞɤɨɫɬɶ ɜɨɡɦɨɠɧɨ ɬɨɥɶɤɨ ɩɪɢ
ɞ
c
Pe 300
. ɇɚ ɩɪɚɤɬɢɤɟ ɱɚɳɟ ɜɫɟɝɨ ɡɧɚɱɟɧɢɹ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɱɢɫɥɚ
ɉɟɤɥɟ ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɶɲɟ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɩɭɡɵɪɶɤɨɜ ɚɡɨɬɚ ɞɢɚɦɟɬɪɨɦ 1 ɦɦ, ɜɫɩɥɵɜɚɸɳɢɯ ɜ ɪɚɫɩɥɚɜɟ ɫɨ ɫɤɨɪɨɫɬɶɸ 0,2 ɦ/ɫ, ɡɧɚɱɟɧɢɟ
ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɱɢɫɥɚ ɉɟɤɥɟ ɞɥɹ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ, ɢɦɟɸɳɟɝɨ
ɤɨɷɮɮɢɰɢɟɧɬ ɦɨɥɟɤɭɥɹɪɧɨɣ ɞɢɮɮɭɡɢɢ ɜ ɚɡɨɬɟ 10
–5
ɦ2/ɫ, ɪɚɜɧɨ 40 ɢ
ɧɟɪɚɜɟɧɫɬɜɨ (4.275) ɧɟ ɜɵɩɨɥɧɹɟɬɫɹ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɞɥɹ ɢɧɠɟɧɟɪɧɵɯ
ɪɚɫɱɺɬɨɜ ɫɪɟɞɧɟɣ ɤɨɧɰɟɧɬɪɚɰɢɢ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɜ ɝɚɡɨɜɨɦ ɩɭɡɵɪɶɤɟ ɭɞɨɛɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɥɟɞɭɸɳɭɸ ɮɨɪɦɭɥɭ:
ɄȻ ɄȻ ɇ
ɞɞ ɞ ɞ ɞ ɞ
) ) ) ) D
ii i i
ªºª º
«»« »
¬¼¬ ¼
exp Pe Fo ,
mn
c
(4.276)
ɝɞɟ
128
ɞ
)
ɢ
i
ɇ
ɞ
) – ɡɧɚɱɟɧɢɹ ɫɪɟɞɧɟɣ ɩɨ ɨɛɴɺɦɭ ɩɭɡɵɪɶɤɚ ɤɨɧ-
i
ɄȻ
ɰɟɧɬɪɚɰɢɢ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ, ɪɚɫɫɱɢɬɚɧɧɵɟ ɩɨ ɦɨɞɟɥɢ Ʉɪɨɧɢɝɚ – Ȼɪɢɧɤ (4.274) ɢ ɇɶɸɦɟɧɚ (4.264) ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ;
,D ,n
m – ɱɢɫɥɟɧɧɵɟ ɤɨɷɮɮɢɰɢɟɧɬɵ: 0,0288D ; 2nm .
ɍɪɚɜɧɟɧɢɟ (4.265) ɢ ɮɨɪɦɭɥɵ ɞɥɹ ɤɨɦɩɨɧɟɧɬ ɫɤɨɪɨɫɬɢ (4.266) ɢ
(4.267) ɫɩɪɚɜɟɞɥɢɜɵ ɞɥɹ ɫɮɟɪɢɱɟɫɤɢɯ ɩɭɡɵɪɶɤɨɜ ɝɚɡɚ ɩɪɢ ɛɟɡɨɬɪɵɜ-
ɧɨɦ ɨɛɬɟɤɚɧɢɢ ɢɯ ɠɢɞɤɨɫɬɶɸ. ɋɨɝɥɚɫɧɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɞɚɧɧɵɦ
ɷɬɢ ɭɫɥɨɜɢɹ ɜɵɩɨɥɧɹɸɬɫɹ ɤɨɝɞɚ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɦɚɫɫɨɩɟɪɟɧɨɫɭ ɫɨɫɪɟɞɨɬɨɱɟɧɨ ɜ ɝɚɡɨɜɨɣ ɮɚɡɟ ɢ ɪɚɡɦɟɪ ɩɭɡɵɪɹ ɧɟ ɩɪɟɜɵɲɚɟɬ 5 ɦɦ. ɉɪɢ
ɷɬɨɦ ɪɚɫɱɺɬɧɵɟ ɡɧɚɱɟɧɢɹ ɤɨɧɰɟɧɬɪɚɰɢɢ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɨɬɥɢɱɚɸɬɫɹ ɨɬ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ
ɨɩɪɟɞɟɥɺɧɧɵɯ ɧɟ ɛɨɥɟɟ ɱɟɦ ɧɚ 10 %.
4.2.7.2. ɋɨɩɪɨɬɢɜɥɟɧɢɟ ɦɚɫɫɨɩɟɪɟɧɨɫɭ ɫɨɫɪɟɞɨɬɨɱɟɧɨ ɜ
ɨɦɵɜɚɸɳɟɦ ɩɨɬɨɤɟ ɜɹɡɤɨɣ ɠɢɞɤɨɫɬɢ
ȿɫɥɢ ɩɪɨɰɟɫɫ ɦɚɫɫɨɨɛɦɟɧɚ ɥɢɦɢɬɢɪɭɟɬɫɹ ɜɧɟɲɧɟɣ ɞɢɮɮɭɡɢɟɣ, ɬɨ
ɧɟɨɛɯɨɞɢɦɨ ɪɟɲɚɬɶ ɡɚɞɚɱɭ ɨ ɪɚɫɩɪɟɞɟɥɟɧɢɢ ɤɨɧɰɟɧɬɪɚɰɢɢ ɰɟɥɟɜɨɝɨ
ɤɨɦɩɨɧɟɧɬɚ ɜ ɩɨɝɪɚɧɢɱɧɨɦ ɫɥɨɟ ɩɨɬɨɤɚ ɠɢɞɤɨɫɬɢ, ɨɤɪɭɠɚɸɳɟɣ ɝɚɡɨɜɵɣ ɩɭɡɵɪɺɤ. ȼ ɞɚɧɧɨɦ ɩɚɪɚɝɪɚɮɟ ɪɚɫɫɦɨɬɪɢɦ ɪɟɲɟɧɢɟ ɬɚɤɨɣ ɡɚɞɚɱɢ ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɡɧɚɱɟɧɢɹɯ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɱɢɫɥɚ
ɉɟɤɥɟ ɞɥɹ
ɫɩɥɨɲɧɨɣ ɫɪɟɞɵ.
Ɋɚɫɫɦɨɬɪɢɦ ɫɧɚɱɚɥɚ ɫɥɭɱɚɣ, ɤɨɝɞɚ
ɫ
c
Pe 0
o. ɉɪɢ ɷɬɨɦ
0
f
c
D
i
2
Ur
ɦɨɠɧɨ ɜ ɭɪɚɜɧɟɧɢɢ ɤɨɧɜɟɤɬɢɜɧɨɣ ɞɢɮɮɭɡɢɢ ɩɪɟɧɟɛɪɟɱɶ ɤɨɧɜɟɤɬɢɜɧɵɦɢ ɱɥɟɧɚɦɢ ɢ ɭɪɚɜɧɟɧɢɟ ɩɪɟɨɛɪɚɡɭɟɬɫɹ ɜ ɭɪɚɜɧɟɧɢɟ ɧɟɫɬɚɰɢɨɧɚɪɧɨɣ ɦɨɥɟɤɭɥɹɪɧɨɣ ɞɢɮɮɭɡɢɢ ɜ ɧɟɩɨɞɜɢɠɧɨɣ ɫɪɟɞɟ:
c2c
C ɋ
ww
w
c
ii
D
t
i
(4.277)
.
2
w
r
Ȼɭɞɟɦ ɩɨɥɚɝɚɬɶ, ɱɬɨ ɜ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɤɨɧɰɟɧɬɪɚɰɢɹ
ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɛɵɥɚ ɨɞɢɧɚɤɨɜɨɣ ɜɨ ɜɫɟɯ ɬɨɱɤɚɯ ɨɛɴɺɦɚ ɠɢɞɤɨɫɬɢ, ɚ ɧɚ ɛɟɫɤɨɧɟɱɧɨɦ ɭɞɚɥɟɧɢɢ ɨɬ ɩɨɜɟɪɯɧɨɫɬɢ ɩɭɡɵɪɹ ɨɫɬɚɺɬɫɹ
ɩɨɫɬɨɹɧɧɨɣ ɢ ɜɨ ɜɪɟɦɟɧɢ:
ɩɪɢ
ɩɪɢ
0t
r of
c ɫɫ
ɋ CC
(4.278)
0
ii i
c ɫ
ɋ C
(4.279)
ii
f
f
const.
const
Ⱦɥɹ ɩɨɜɟɪɯɧɨɫɬɢ ɩɭɡɵɪɹ ɫɮɨɪɦɭɥɢɪɭɟɦ ɭɫɥɨɜɢɟ ɪɚɜɧɨɜɟɫɢɹ ɤɨɧɰɟɧɬɪɚɰɢɣ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɜ ɝɚɡɨɜɨɣ ɢ ɠɢɞɤɨɣ ɮɚɡɚɯ ɢ ɭɫɥɨɜɢɟ
129
ɪɚɜɟɧɫɬɜɚ ɩɥɨɬɧɨɫɬɟɣ ɩɨɬɨɤɨɜ ɦɚɫɫɵ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɜɧɟ ɢ
D
D
ɜɧɭɬɪɢ ɝɚɡɨɜɨɝɨ ɩɭɡɵɪɶɤɚ:
ɩɪɢ
ɩɪɢ
h – ɤɨɧɫɬɚɧɬɚ ɪɚɜɧɨɜɟɫɢɹ.
ɝɞɟ
rr
rr
0
0
ɫ c
ɋ hC (4.280)
is i
c ɞ
ɋɋ
ww
c ɞ
ii
DD
ii
rr
ww
,
(4.281)
,
Ɋɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ (4.277) ɫ ɤɪɚɟɜɵɦɢ ɭɫɥɨɜɢɹɦɢ (4.278) –
(4.281) ɧɚɯɨɞɢɬɫɹ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɦɟɬɨɞɨɜ ɨɩɟɪɚɰɢɨɧɧɨɝɨ ɢɫɱɢɫ-
ɥɟɧɢɹ. ɉɪɢ ɷɬɨɦ ɭɪɚɜɧɟɧɢɟ ɩɨɬɨɤɚ ɦɚɫɫɵ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɞɥɹ
ɪɚɡɥɢɱɧɵɯ ɢɧɬɟɪɜɚɥɨɜ ɜɪɟɦɟɧɢ ɢɦɟɟɬ ɜɢɞ
3
ɞ 2
2
§· § ·
i
¨¸ ¨ ¸
DDt
©¹ © ¹
c ɞ
ii
00
(4.282)
,
ɩɪɢ
!!
t
2
r
0
MDChC
iiii
ɞ
i
rh D r
S
ɞɞc
00
3
ɞ c
ChC
ii
00
i
(4.283)
,
t
ɩɪɢ
t
2
r
0
ɞ
i
8
M
i
2c
rD
S
0
c
D
h
i
ɞ
D
i
Ɋɚɫɫɦɨɬɪɢɦ ɦɚɫɫɨɨɛɦɟɧ ɦɟɠɞɭ ɠɢɞɤɨɫɬɶɸ ɢ ɩɭɡɵɪɶɤɨɦ ɩɪɢ
ɫ
Pecof. ɋɱɢɬɚɟɦ ɤɨɧɰɟɧɬɪɚɰɢɸ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɧɚ ɩɨɜɟɪɯ-
ɧɨɫɬɢ ɩɭɡɵɪɹ ɩɨɫɬɨɹɧɧɨɣ ɜɟɥɢɱɢɧɨɣ:
ɞ
ɩɪɢ
rr
0
c ɫ
ɋɋ
(4.284)
iis
C
i
0
.
h
Ɂɚ ɩɪɟɞɟɥɚɦɢ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɝɪɚɧɢɱɧɨɝɨ ɫɥɨɹ ɜɵɩɨɥɧɹɟɬɫɹ
ɭɫɥɨɜɢɟ (4.279). Ɇɚɫɫɨɩɟɪɟɧɨɫ ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ ɫɥɭɱɚɟ ɨɩɢɫɵɜɚ-
ɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ ɫɬɚɰɢɨɧɚɪɧɨɣ ɤɨɧɜɟɤɬɢɜɧɨɣ ɞɢɮɮɭɡɢɢ:
wCDC G (4.285)
ii i
cc2c
grad .
ȼ ɭɪɚɜɧɟɧɢɢ (4.285) ɩɟɪɟɣɞɺɦ ɤ ɛɟɡɪɚɡɦɟɪɧɵɦ ɩɟɪɟɦɟɧɧɵɦ:
c ɫ
CC
130
c
r
r
;
r
0
c
w
;
w
)
U
0
ii
ɞ
C
0
i
C
h
f
.
ɫ
f
i
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