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Файл:Современные проблемы металлургии и материаловедения гидродинамика и массообмен в многофазных системах металлургии. Учебное пособие
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ɩɨɥɭɱɢɦ ɫɥɟɞɭɸɳɟɟ ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɬɨɥɳɢɧɵ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɝɪɚ-
M
ɧɢɱɧɨɝɨ ɫɥɨɹ:
sin(2 )
T
c2
Dr
4
i
m
i
3
1,1 6 .
0
3sin
T
w
f
T
2
(4.158)
ɂɡ (4.158) ɫɥɟɞɭɟɬ, ɱɬɨ ɬɨɥɳɢɧɚ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɝɪɚɧɢɱɧɨɝɨ
ɫɥɨɹ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɫ ɪɨɫɬɨɦ ɭɝɥɚ
, ɨɛɪɚɳɚɹɫɶ ɜ ɛɟɫɤɨɧɟɱɧɨɫɬɶ ɩɪɢ
T
T S. ȼ ɞɟɣɫɬɜɢɬɟɥɶɧɨɫɬɢ ɠɟ ɩɪɢ T S ɬɨɥɳɢɧɚ ɞɢɮɮɭɡɢɨɧɧɨɝɨ
ɩɨɝɪɚɧɢɱɧɨɝɨ ɫɥɨɹ ɧɟ ɨɛɪɚɳɚɟɬɫɹ ɜ ɛɟɫɤɨɧɟɱɧɨɫɬɶ, ɚ ɩɥɨɬɧɨɫɬɶ ɩɨɬɨɤɚ ɦɚɫɫɵ
m ɜ ɧɭɥɶ. ɗɬɨ ɩɪɨɬɢɜɨɪɟɱɢɟ ɫɜɹɡɚɧɨ ɫ ɬɟɦ, ɱɬɨ, ɤɚɤ ɢ
i
ɩɪɢ ɢɫɫɥɟɞɨɜɚɧɢɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɝɪɚɧɢɱɧɨɝɨ ɫɥɨɹ,
ɦɵ ɩɪɟɞɩɨɥɚɝɚɥɢ, ɱɬɨ ɟɝɨ ɬɨɥɳɢɧɚ ɦɧɨɝɨ ɦɟɧɶɲɟ ɪɚɡɦɟɪɨɜ ɱɚɫɬɢɰɵ.
Ɉɞɧɚɤɨ ɢɡ (4.158) ɫɥɟɞɭɟɬ, ɱɬɨ ɩɪɢ ɨɩɪɟɞɟɥɺɧɧɵɯ ɡɧɚɱɟɧɢɹɯ ɭɝɥɚ
T,
ɛɥɢɡɤɢɯ ɤ T S, ɬɨɥɳɢɧɚ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɝɪɚɧɢɱɧɨɝɨ ɫɥɨɹ ɞɨɫɬɢɝɚɟɬ ɡɧɚɱɟɧɢɣ, ɫɪɚɜɧɢɦɵɯ ɫ ɪɚɞɢɭɫɨɦ ɱɚɫɬɢɰɵ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɜ ɷɬɨɣ
ɨɛɥɚɫɬɢ ɡɧɚɱɟɧɢɣ ɭɝɥɚ T ɩɨɥɭɱɟɧɧɵɟ ɭɪɚɜɧɟɧɢɹ ɞɥɹ ɪɚɫɱɺɬɨɜ ɤɨɧɰɟɧɬɪɚɰɢɢ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ, ɩɥɨɬɧɨɫɬɢ ɩɨɬɨɤɚ ɟɝɨ ɦɚɫɫɵ ɢ ɬɨɥɳɢɧɵ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɝɪɚɧɢɱɧɨɝɨ ɫɥɨɹ ɫɬɚɧɨɜɹɬɫɹ ɧɟɩɪɢɝɨɞɧɵɦɢ.
Ɉɞɧɚɤɨ ɩɨɫɤɨɥɶɤɭ ɱɚɫɬɶ ɩɨɜɟɪɯɧɨɫɬɢ ɱɚɫɬɢɰɵ, ɝɞɟ ɩɪɨɹɜɥɹɟɬɫɹ ɭɤɚɡɚɧɧɨɟ ɩɪɨɬɢɜɨɪɟɱɢɟ, ɧɟɜɟɥɢɤɚ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫɨ ɜɫɟɣ ɟɺ ɩɨɜɟɪɯɧɨɫɬɶɸ, ɨɧɚ ɧɟ ɜɧɨɫɢɬ ɡɚɦɟɬɧɨɝɨ ɢɫɤɚɠɟɧɢɹ ɜ ɫɪɟɞɧɟɟ ɩɨ ɩɨɜɟɪɯɧɨɫɬɢ
ɡɧɚɱɟɧɢɟ ɩɥɨɬɧɨɫɬɢ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɬɨɤɚ ɦɚɫɫɵ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ. ȼ ɫɜɹɡɢ ɫ ɷɬɢɦ ɩɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɬɨɤɚ ɦɚɫɫɵ
ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɢɫɩɨɥɶɡɭɸɬ ɜɵɪɚɠɟɧɢɟ ɩɥɨɬɧɨɫɬɢ ɩɨɬɨɤɚ ɦɚɫɫɵ (4.154), ɢɧɬɟɝɪɢɪɭɹ ɟɝɨ ɩɨ ɜɫɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɱɚɫɬɢɰɵ:
214
c ɫ
mdS D w r C
|
ii i i
³
S
7,9 ( ) .
333
ff
0
(4.159)
4.2.3.2. Ɉɫɧɨɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɦɚɫɫɨɩɟɪɟɧɨɫɭ
ɫɨɫɪɟɞɨɬɨɱɟɧɨ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɱɚɫɬɢɰɵ (Pe 1;
c
!!
Re 1
)
Ɋɚɫɫɦɨɬɪɢɦ ɫɥɭɱɚɣ ɦɟɠɮɚɡɧɨɝɨ ɦɚɫɫɨɨɛɦɟɧɚ, ɤɨɝɞɚ ɫɤɨɪɨɫɬɶ
ɩɪɨɰɟɫɫɚ ɩɟɪɟɧɨɫɚ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɟɝɨ ɤɨɧɰɟɧɬɪɚɰɢɟɣ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɱɚɫɬɢɰɵ. Ɍɚɤɨɣ ɪɟɠɢɦ ɦɚɫɫɨɨɛɦɟɧɚ ɢɦɟɟɬ
ɦɟɫɬɨ, ɧɚɩɪɢɦɟɪ, ɩɪɢ ɪɚɫɬɜɨɪɟɧɢɢ ɱɚɫɬɢɰɵ ɤɜɚɪɰɚ ɜ ɪɚɫɩɥɚɜɟ.
91
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɢɦɟɟɬ ɦɟɫɬɨ ɩɟɪɟɧɨɫ ɦɚɫɫɵ ɫ ɩɨɜɟɪɯɧɨɫɬɢ ɪɚɫɬɜɨ-
ɪɹɸɳɟɣɫɹ ɱɚɫɬɢɰɵ ɪɚɞɢɭɫɨɦ
ɤɨɫɬɢ ɩɪɢ ɭɫɥɨɜɢɢ, ɱɬɨ Pe 1c!! ɢ
r ɜ ɨɛɬɟɤɚɸɳɢɣ ɟɺ ɩɨɬɨɤ ɜɹɡɤɨɣ ɠɢɞ-
0
Re 1 . Ɍɟɱɟɧɢɟ, ɤɚɤ ɢ ɩɪɟɠɞɟ,
ɫɬɚɰɢɨɧɚɪɧɨɟ, ɨɫɟɫɢɦɦɟɬɪɢɱɧɨɟ ɢ ɩɪɨɢɫɯɨɞɢɬ ɩɪɢ ɩɨɫɬɨɹɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ.
ɉɨɦɟɳɚɟɦ ɧɚɱɚɥɨ ɫɮɟɪɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ ɜ ɰɟɧɬɪ ɱɚɫɬɢɰɵ.
Ʉɚɤ ɛɵɥɨ ɩɨɤɚɡɚɧɨ ɪɚɧɶɲɟ, ɩɪɢ Pe 1c!! ɭ ɩɨɜɟɪɯɧɨɫɬɢ ɱɚɫɬɢɰɵ
ɮɨɪɦɢɪɭɟɬɫɹ ɞɢɮɮɭɡɢɨɧɧɵɣ ɩɨɝɪɚɧɢɱɧɵɣ ɫɥɨɣ, ɤɨɧɰɟɧɬɪɚɰɢɹ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɜ ɤɨɬɨɪɨɦ ɢɡɦɟɧɹɟɬɫɹ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɭɪɚɜɧɟɧɢɟɦ:
cc
CC
ww
wT w\ w\
c2 2
ii
Dr w
T \
sin 3 .
0
i
§·
w
¨¸
f
©¹
(4.160)
ɋɮɨɪɦɭɥɢɪɭɟɦ ɝɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ ɤ ɭɪɚɜɧɟɧɢɸ (4.160). ɍɫɥɨɜɢɹ
ɧɚ ɛɟɫɤɨɧɟɱɧɨɫɬɢ (ɬ.ɟ. ɡɚ ɩɪɟɞɟɥɚɦɢ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɝɪɚɧɢɱɧɨɝɨ
ɫɥɨɹ) ɢ ɜ ɬɨɱɤɟ ɧɚɛɟɝɚɧɢɹ ɩɨɬɨɤɚ ɧɚ ɱɚɫɬɢɰɭ (ɜ ɩɟɪɜɨɣ ɤɪɢɬɢɱɟɫɤɨɣ
ɬɨɱɤɟ), ɨɱɟɜɢɞɧɨ, ɢɦɟɸɬ ɬɨɬ ɠɟ ɜɢɞ, ɱɬɨ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɝɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ ɜ ɩɪɟɞɵɞɭɳɟɦ ɫɥɭɱɚɟ:
ɩɪɢ 0
\ ɢ 0T
ɩɪɢ \of
c
ɋ Cf (4.161)
ii
c
ɋ Cf (4.162)
ii
,
.
ɇɨ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɪɚɫɬɜɨɪɹɸɳɟɣɫɹ ɱɚɫɬɢɰɵ ɝɪɚɧɢɱɧɨɟ ɭɫɥɨɜɢɟ
ɛɭɞɟɬ ɨɬɥɢɱɚɬɶɫɹ ɨɬ ɚɧɚɥɨɝɢɱɧɨɝɨ ɭɫɥɨɜɢɹ ɜ ɩɪɟɞɵɞɭɳɟɦ ɪɚɡɞɟɥɟ:
c ɞ
ɩɪɢ 0\
ɞ
ɝɞɟ
C – ɤɨɧɰɟɧɬɪɚɰɢɹ ɧɚɫɵɳɟɧɢɹ ɪɚɫɬɜɨɪɚ ɰɟɥɟɜɵɦ ɤɨɦɩɨɧɟɧɬɨɦ.
ɧi
ɋ C (4.163)
,
ii
ɧ
ɍɪɚɜɧɟɧɢɟ (4.160) ɫ ɝɪɚɧɢɱɧɵɦɢ ɭɫɥɨɜɢɹɦɢ (4.161) – (4.163)
ɩɪɟɞɫɬɚɜɥɹɸɬ ɡɚɦɤɧɭɬɭɸ ɦɚɬɟɦɚɬɢɱɟɫɤɭɸ ɦɨɞɟɥɶ ɩɪɨɰɟɫɫɚ ɦɚɫɫɨɩɟɪɟɧɨɫɚ ɨɬ ɩɨɜɟɪɯɧɨɫɬɢ ɪɚɫɬɜɨɪɹɸɳɟɣɫɹ ɱɚɫɬɢɰɵ ɜ ɨɦɵɜɚɸɳɢɣ ɟɺ
ɩɨɬɨɤ ɩɪɢ ɨɝɨɜɨɪɟɧɧɵɯ ɭɫɥɨɜɢɹɯ ɨɦɵɜɚɧɢɹ.
Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɢɫɩɨɥɶɡɨɜɚɬɶ ɪɟɡɭɥɶɬɚɬɵ ɪɟɲɟɧɢɹ ɩɪɟɞɵɞɭɳɟɣ
ɡɚɞɚɱɢ, ɧɟɨɛɯɨɞɢɦɨ ɧɟɫɤɨɥɶɤɨ ɢɡɦɟɧɢɬɶ ɧɚɩɢɫɚɧɢɟ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. Ⱦɥɹ ɷɬɨɝɨ ɜɜɟɞɺɦ ɜ ɪɚɫɫɦɨɬɪɟɧɢɟ ɧɨɜɭɸ ɩɟɪɟɦɟɧɧɭɸ
c ɞ
c
ɝɞɟ
ɋ – ɬɟɤɭɳɟɟ ɡɧɚɱɟɧɢɟ ɤɨɧɰɟɧɬɪɚɰɢɢ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ.
i
ɋ CC (4.164)
ii i
,
ɧ
92
ɉɟɪɟɩɢɲɟɦ ɝɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ (4.161) – (4.163) ɫ ɭɱɺɬɨɦ (4.164):
ɩɪɢ \of
ɫɞ
ɋ CC
, (4.165)
ɧii i
f
ɩɪɢ 0\ ɢ 0T
ɩɪɢ 0\ 0
ɋ . (4.167)
ɫɞ
ɋ CC
, (4.166)
f
ɧii i
i
ɉɨɫɤɨɥɶɤɭ ɭɪɚɜɧɟɧɢɟ (4.160) ɫɨɞɟɪɠɢɬ ɬɨɥɶɤɨ ɩɪɨɢɡɜɨɞɧɵɟ ɨɬ
,
ɮɭɧɤɰɢɢ
ɨɛɪɚɡɨɦ, ɜ ɬɟɪɦɢɧɚɯ ɮɭɧɤɰɢɢ
ɋ \T , ɡɚɦɟɧɚ (4.164) ɧɟ ɦɟɧɹɟɬ ɜɢɞɚ ɭɪɚɜɧɟɧɢɹ. Ɍɚɤɢɦ
i
,
ɋ \T ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɪɚɫ-
i
ɫɦɚɬɪɢɜɚɟɦɨɣ ɡɚɞɚɱɢ ɜɤɥɸɱɚɟɬ ɜ ɫɟɛɹ ɭɪɚɜɧɟɧɢɟ (4.160), ɡɚɩɢɫɚɧɧɨɟ
ɞɥɹ ɮɭɧɤɰɢɢ
,
ɋ \T, ɢ ɝɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ (4.165) – (4.167).
i
ȿɞɢɧɫɬɜɟɧɧɨɟ ɨɬɥɢɱɢɟ ɜ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɩɨɫɬɚɧɨɜɤɚɯ ɡɚɞɚɱ ɜ
ɩɟɪɜɨɦ ɢ ɜɬɨɪɨɦ ɩɚɪɚɝɪɚɮɚɯ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɜ ɝɪɚɧɢɱɧɵɯ
ɭɫɥɨɜɢɹɯ (4.165) ɢ (4.166) ɫɬɨɢɬ ɩɨɫɬɨɹɧɧɚɹ
ɫɞ
()
CC
, ɚ ɧɟ
ɧ
ii
f
ɫ
Cf, ɤɚɤ
i
ɜ ɝɪɚɧɢɱɧɵɯ ɭɫɥɨɜɢɹɯ ɩɪɟɞɵɞɭɳɟɝɨ ɩɚɪɚɝɪɚɮɚ. ɉɨɷɬɨɦɭ ɞɥɹ ɬɨɝɨ
ɱɬɨɛɵ ɩɨɥɭɱɢɬɶ ɮɨɪɦɭɥɭ, ɨɩɢɫɵɜɚɸɳɭɸ ɡɚɜɢɫɢɦɨɫɬɶ
c
C ɨɬ ɚɪɝɭ-
i
ɦɟɧɬɨɜ ɢ ɩɚɪɚɦɟɬɪɨɜ ɡɚɞɚɱɢ, ɧɟɨɛɯɨɞɢɦɨ ɜ ɩɪɚɜɨɣ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ
(4.152) ɡɚɦɟɧɢɬɶ ɩɨɫɬɨɹɧɧɭɸ
ɬɚɬɟ ɞɥɹ ɮɭɧɤɰɢɢ
ɋ ɩɨɥɭɱɢɦ ɫɥɟɞɭɸɳɟɟ ɜɵɪɚɠɟɧɢɟ:
i
0,86 ( ) exp ,
ɋ CC d
[[
iii
ɫɞ 3
f
ɫ
Cf ɧɚ ɜɟɥɢɱɢɧɭ
i
[
ɧ
³
0
4
§·
¨¸
9
©¹
ɫɞ
()
CC
. ȼ ɪɟɡɭɥɶ-
ɧ
ii
f
(4.168)
ɝɞɟ ɜɟɥɢɱɢɧɚ [ ɨɩɪɟɞɟɥɹɟɬɫɹ ɮɨɪɦɭɥɨɣ (4.153).
ɋ ɭɱɺɬɨɦ (4.164) ɩɨɥɭɱɢɦ ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɤɨɧɰɟɧɬɪɚɰɢɢ ɰɟɥɟɜɨɝɨ
ɤɨɦɩɨɧɟɧɬɚ ɜ ɠɢɞɤɨɫɬɢ, ɨɤɪɭɠɚɸɳɟɣ ɱɚɫɬɢɰɭ:
c ɞɫɞ 3
CC C C d
[[
ii i i
0,86 ( ) exp .
ɧɧ
f
[
³
0
4
§·
¨¸
9
©¹
(4.169)
ȼɟɥɢɱɢɧɭ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɬɨɤɚ ɦɚɫɫɵ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɨɬ
ɩɨɜɟɪɯɧɨɫɬɢ ɪɚɫɬɜɨɪɹɟɦɨɣ ɱɚɫɬɢɰɵ ɨɩɪɟɞɟɥɢɦ ɩɨ ɮɨɪɦɭɥɟ
24 1
c ɞɫ
7,9 ( ) ( ).
MDrwCC
(4.170)
ii ii
33 3
0 ɧ
ff
93
ȼɜɟɞɹ ɛɟɡɪɚɡɦɟɪɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɦɚɫɫɨɨɬɞɚɱɢ (ɱɢɫɥɨ ɒɟɪɜɭɞɚ)
D
M
ɩɨ ɮɨɪɦɭɥɟ
Sh
i
2()
S
rD C C
i
c ɞɫ
ii i
0 ɧ
, ɭɪɚɜɧɟɧɢɟ (4.170) ɦɨɠɧɨ
f
ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɛɟɡɪɚɡɦɟɪɧɨɦ ɜɢɞɟ:
11
cc
Sh 1,25 ( ) (Re ) .
ii
SC (4.171)
33
4.2.4. Ɇɚɫɫɨɨɛɦɟɧ ɦɟɠɞɭ ɬɜɺɪɞɨɣ ɱɚɫɬɢɰɟɣ ɢ ɩɨɬɨɤɨɦ
ɜɹɡɤɨɣ ɠɢɞɤɨɫɬɢ ɩɪɢ ɧɚɥɢɱɢɢ ɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ ɧɚ
ɩɨɜɟɪɯɧɨɫɬɢ ɱɚɫɬɢɰɵ
Ɋɚɫɫɦɨɬɪɢɦ ɩɨɫɬɚɧɨɜɤɭ ɢ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ ɨ ɩɟɪɟɧɨɫɟ ɦɚɫɫɵ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɧɚ ɩɨɜɟɪɯɧɨɫɬɶ ɱɚɫɬɢɰɵ ɢɡ ɩɨɬɨɤɚ ɜɹɡɤɨɣ ɠɢɞɤɨɫɬɢ
ɩɪɢ ɭɫɥɨɜɢɢ, ɱɬɨ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɩɪɨɬɟɤɚɟɬ ɯɢɦɢɱɟɫɤɚɹ ɪɟɚɤɰɢɹ ɩɟɪɜɨɝɨ ɩɨɪɹɞɤɚ. Ʉɚɤ ɢ ɩɪɟɠɞɟ, ɫɱɢɬɚɟɦ, ɱɬɨ Re 1 , ɬɟɱɟɧɢɟ ɫɬɚɰɢɨ-
ɧɚɪɧɨɟ ɢ ɨɫɟɫɢɦɦɟɬɪɢɱɧɨɟ, ɩɪɨɢɫɯɨɞɢɬ ɩɪɢ ɩɨɫɬɨɹɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ.
ɂɡ ɭɫɥɨɜɢɹ Pe 1c!! ɫɥɟɞɭɟɬ, ɱɬɨ ɡɚɞɚɱɚ
ɫɜɨɞɢɬɫɹ ɤ ɫɥɭɱɚɸ ɩɟɪɟɧɨɫɚ
ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɜ ɩɪɟɞɟɥɚɯ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɝɪɚɧɢɱɧɨɝɨ ɫɥɨɹ.
ȼ ɫɮɟɪɢɱɟɫɤɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ ɫ ɧɚɱɚɥɨɦ ɜ ɰɟɧɬɪɟ ɱɚɫɬɢɰɵ ɷɬɨɬ
ɩɪɨɰɟɫɫ ɨɩɢɫɵɜɚɟɬɫɹ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɦ ɭɪɚɜɧɟɧɢɟɦ
cc2c
CwC C
www
wD
ri
wwT
0
ii i
rr
0
c
.
(4.172)
2
r
w
ɋɮɨɪɦɭɥɢɪɭɟɦ ɝɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ ɤ ɷɬɨɦɭ ɭɪɚɜɧɟɧɢɸ. Ʉɨɧɰɟɧɬɪɚɰɢɹ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɜ ɠɢɞɤɨɫɬɢ ɡɚ ɩɪɟɞɟɥɚɦɢ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɝɪɚɧɢɱɧɨɝɨ ɫɥɨɹ ɩɨɫɬɨɹɧɧɚ:
ɩɪɢ
r of
c ɫ
CC
(4.173)
ii
f
const.
ɉɪɢɧɢɦɚɟɦ, ɱɬɨ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɬɜɺɪɞɨɣ ɱɚɫɬɢɰɵ ɩɪɨɬɟɤɚɟɬ ɪɟɚɤɰɢɹ ɩɟɪɜɨɝɨ ɩɨɪɹɞɤɚ. ɉɪɢ ɫɬɚɰɢɨɧɚɪɧɨɦ ɪɟɠɢɦɟ ɦɚɫɫɨɨɛɦɟɧɚ ɷɬɨɬ
ɩɪɨɰɟɫɫ, ɤɚɤ ɛɵɥɨ ɩɨɤɚɡɚɧɨ ɪɚɧɟɟ, ɨɩɢɫɵɜɚɟɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
c
§·
w
C
cc
ɩɪɢ
k
ɝɞɟ
– ɤɨɧɫɬɚɧɬɚ ɫɤɨɪɨɫɬɢ ɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ.
i
94
rr
0
i
w
r
¨¸
iii
©¹
kC
,
(4.174)
Ʉɪɨɦɟ (4.173) ɢ (4.174) ɫɮɨɪɦɭɥɢɪɭɟɦ ɝɪɚɧɢɱɧɨɟ ɭɫɥɨɜɢɟ ɞɥɹ
ɩɟɪɜɨɣ ɤɪɢɬɢɱɟɫɤɨɣ ɬɨɱɤɢ:
ɩɪɢ
rr ɢ
0
0T
CC
c ɫ
ii
.
(4.175)
f
ɍɪɚɜɧɟɧɢɟ (4.172) ɫ ɝɪɚɧɢɱɧɵɦɢ ɭɫɥɨɜɢɹɦɢ (4.173) – (4.175)
ɩɪɟɞɫɬɚɜɥɹɟɬ ɦɚɬɟɦɚɬɢɱɟɫɤɭɸ ɦɨɞɟɥɶ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ ɩɪɨɰɟɫɫɚ.
Ⱥɧɚɥɢɬɢɱɟɫɤɨɟ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ ɩɨɞɪɨɛɧɨ ɢɡɥɨɠɟɧɨ ɜ [4]. ȼɨɫɩɨɥɶɡɭɟɦɫɹ ɪɟɡɭɥɶɬɚɬɚɦɢ ɷɬɨɝɨ ɪɟɲɟɧɢɹ ɞɥɹ ɚɧɚɥɢɡɚ ɦɟɯɚɧɢɡɦɚ ɢ ɨɫɨɛɟɧɧɨɫɬɟɣ ɩɪɨɰɟɫɫɚ ɦɚɫɫɨɩɟɪɟɧɨɫɚ ɜ ɢɡɭɱɚɟɦɨɦ ɫɥɭɱɚɟ.
ɉɥɨɬɧɨɫɬɶ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɬɨɤɚ ɦɚɫɫɵ ɤɚɤ ɮɭɧɤɰɢɹ ɩɨɥɹɪɧɨɝɨ
ɭɝɥɚ ɨɩɢɫɵɜɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ
f
ɫ
kC
ii
k – ɤɨɧɫɬɚɧɬɚ ɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ;
ɝɞɟ
i
T JU U U
med
i
§·
Ƚ
¨¸
©¹
f
exp ,
³
2
0
3
21
§·
¨¸
¨¸
©¹
U
33
(4.176)
U ɢ J – ɜɫɩɨɦɨɝɚɬɟɥɶɧɵɟ ɮɭɧɤɰɢɢ;
1
½
i
3
0
2
§·
¨¸
3
©¹
°
°
,
°
°
(4.177)
¾
°
°
,
°
°
¿
1
§·
T T
sin 2
2
sin
1
§·
¨¸
3
©¹
2
3
kr
1
3
f
T
¨¸
©¹
J H
12
33
3 Ƚ
H
c
Dw
2 Ƚ
i
U
– ɜɟɥɢɱɢɧɚ, ɨɩɪɟɞɟɥɹɟɦɚɹ ɢɡ ɝɪɚɧɢɱɧɵɯ ɭɫɥɨɜɢɣ.
Ɋɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ (4.176) ɧɚɯɨɞɢɬɫɹ ɩɭɬɺɦ ɪɚɡɥɨɠɟɧɢɹ ɜ ɪɹɞ
ɩɨɞɵɧɬɟɝɪɚɥɶɧɨɣ ɮɭɧɤɰɢɢ ɢ ɟɝɨ ɨɤɨɧɱɚɬɟɥɶɧɵɣ ɜɢɞ ɡɚɜɢɫɢɬ ɨɬ ɡɧɚɱɟɧɢɹ ɤɨɧɫɬɚɧɬɵ ɫɤɨɪɨɫɬɢ ɪɟɚɤɰɢɢ.
ɂɫɫɥɟɞɭɟɦ ɯɚɪɚɤɬɟɪ ɩɪɨɬɟɤɚɧɢɹ ɩɪɨɰɟɫɫɚ ɦɚɫɫɨɨɛɦɟɧɚ ɜ ɪɚɡɥɢɱɧɵɯ ɡɨɧɚɯ ɩɨɜɟɪɯɧɨɫɬɢ ɱɚɫɬɢɰɵ. ȼɧɚɱɚɥɟ ɪɚɫɫɦɨɬɪɢɦ ɫɥɭɱɚɣ, ɤɨɝɞɚ
ɤɨɧɫɬɚɧɬɚ ɫɤɨɪɨɫɬɢ ɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ ɟɫɬɶ ɜɟɥɢɱɢɧɚ ɤɨɧɟɱɧɚɹ, ɬ.ɟ.
ɜɵɩɨɥɧɹɟɬɫɹ
ɫɨɨɬɧɨɲɟɧɢɟ
const .
k f (4.178)
i
95
ȼ ɨɤɪɟɫɬɧɨɫɬɹɯ ɩɟɪɜɨɣ ɤɪɢɬɢɱɟɫɤɨɣ ɬɨɱɤɢ
0To ɡɧɚɱɟɧɢɟ J
ɫɨɝɥɚɫɧɨ (4.177) ɧɟɜɟɥɢɤɨ ɢ ɪɚɡɥɨɠɟɧɢɟ (4.176) ɞɚɺɬ ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ
ɜɬɨɪɨɝɨ ɱɥɟɧɚ ɪɹɞɚ
ɫ
kC
f
ii
« J»
m
i
§·
Ƚ
¨¸
©¹
2
3
n
ªº
1
!3
n
«»
¬¼
22
§·
Ƚ .
¨¸
©¹
n
n
ɂɥɢ ɞɥɹ 1n
ɩɪɢ
0To
0,66
mkC
| . (4.179)
iii
ɫ
f
ɂɡ (4.179) ɫɥɟɞɭɟɬ, ɱɬɨ ɥɢɦɢɬɢɪɭɸɳɟɣ ɫɬɚɞɢɟɣ ɩɪɨɰɟɫɫɚ ɦɚɫɫɨɨɛɦɟɧɚ ɜ ɨɤɪɟɫɬɧɨɫɬɹɯ ɩɟɪɜɨɣ ɤɪɢɬɢɱɟɫɤɨɣ ɬɨɱɤɢ ɹɜɥɹɟɬɫɹ ɯɢɦɢɱɟɫɤɚɹ ɪɟɚɤɰɢɹ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɝɨɜɨɪɹɬ, ɱɬɨ ɭɤɚɡɚɧɧɚɹ ɨɛɥɚɫɬɶ ɩɨɜɟɪɯɧɨɫɬɢ ɱɚɫɬɢɰɵ ɪɚɛɨɬɚɟɬ ɜ ɤɢɧɟɬɢɱɟɫɤɨɦ ɪɟɠɢɦɟ ɦɚɫɫɨɨɛɦɟɧɚ.
ȼ ɨɤɪɟɫɬɧɨɫɬɹɯ ɜɬɨɪɨɣ ɤɪɢɬɢɱɟɫɤɨɣ ɬɨɱɤɢ ()T S ɡɧɚɱɟɧɢɟ
J
ɫɨ-
ɝɥɚɫɧɨ (4.177) ɦɧɨɝɨ ɛɨɥɶɲɟ ɟɞɢɧɢɰɵ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɪɚɡɥɨɠɟɧɢɟ
ɮɭɧɤɰɢɢ (4.176) ɞɨ ɜɬɨɪɨɝɨ ɱɥɟɧɚ ɪɹɞɚ ɞɚɺɬ
221
ɫ c
333
3()
CD w
ii
m
i
ff
Ƚ r
1
§·
¨¸
3
©¹
2
3
0
sin
T
1
§·
¨¸
©¹
sin 2
T T
2
ɩɪɢ ToS.
ɉɨɫɥɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢɦɟɟɦ
3
w
0,86 .
mDC
iii
c ɫ
f
3
4
f
21
Dr
i
0
§·
¨¸
©¹
sin
T
1
sin 2
T T
2
(4.180)
3
Ɏɨɪɦɭɥɚ (4.180) ɫɨɜɩɚɞɚɟɬ ɫ ɜɵɪɚɠɟɧɢɟɦ ɞɥɹ ɩɥɨɬɧɨɫɬɢ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɬɨɤɚ ɦɚɫɫɵ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɬɜɺɪɞɨɣ ɱɚɫɬɢɰɵ ɜ ɫɥɭɱɚɟ,
ɤɨɝɞɚ ɥɢɦɢɬɢɪɭɸɳɢɦ ɮɚɤɬɨɪɨɦ ɹɜɥɹɟɬɫɹ ɫɤɨɪɨɫɬɶ ɩɨɞɜɨɞɚ ɰɟɥɟɜɨɝɨ
ɤɨɦɩɨɧɟɧɬɚ ɤ ɦɟɠɮɚɡɧɨɣ ɝɪɚɧɢɰɟ. ɍɤɚɡɚɧɧɚɹ ɨɛɥɚɫɬɶ ɩɨɜɟɪɯɧɨɫɬɢ
ɱɚɫɬɢɰɵ ɪɚɛɨɬɚɟɬ ɜ ɞɢɮɮɭɡɢɨɧɧɨɦ ɪɟɠɢɦɟ. Ɉɱɟɜɢɞɧɨ, ɱɚɫɬɶ ɩɨɜɟɪɯɧɨɫɬɢ ɱɚɫɬɢɰɵ, ɪɚɫɩɨɥɨɠɟɧɧɚɹ ɜ ɢɧɬɟɪɜɚɥɟ ɢɡɦɟɧɟɧɢɹ ɩɨɥɹɪɧɨɝɨ
ɭɝɥɚ 0
TS, ɪɚɛɨɬɚɟɬ ɜ ɩɪɨɦɟɠɭɬɨɱɧɨɦ ɪɟɠɢɦɟ ɦɚɫɫɨɨɛɦɟɧɚ. ɉɪɢ
ɷɬɨɦ ɩɥɨɬɧɨɫɬɶ ɩɨɬɨɤɚ ɦɚɫɫɵ ɜ ɩɟɪɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɤɚɤ ɫɪɟɞɧɟɚɪɢɮɦɟɬɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ ɦɟɠɞɭ ɡɧɚɱɟɧɢɹɦɢ
96
m
, ɩɨ-
i
ɥɭɱɟɧɧɵɦɢ ɩɨ ɮɨɪɦɭɥɚɦ (4.179) ɢ (4.180). Ʉɨɝɞɚ ɧɟɨɛɯɨɞɢɦɨ ɨɩɪɟ-
M
ɞɟɥɢɬɶ ɩɥɨɬɧɨɫɬɶ ɩɨɬɨɤɚ ɦɚɫɫɵ ɫ ɛɨɥɟɟ ɜɵɫɨɤɨɣ ɫɬɟɩɟɧɶɸ ɬɨɱɧɨɫɬɢ,
ɧɭɠɧɨ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɧɟɫɤɨɥɶɤɢɦɢ ɱɥɟɧɚɦɢ ɪɚɡɥɨɠɟɧɢɹ ɜ ɪɹɞ
ɮɨɪɦɭɥɵ (4.176).
Ɋɚɫɫɦɨɬɪɢɦ ɞɚɥɟɟ ɫɥɭɱɚɣ, ɤɨɝɞɚ ɤɨɧɫɬɚɧɬɚ ɫɤɨɪɨɫɬɢ ɯɢɦɢɱɟɫɤɨɣ
ɪɟɚɤɰɢɢ ɫɬɪɟɦɢɬɫɹ ɤ ɛɟɫɤɨɧɟɱɧɨɫɬɢ.
Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɩɪɢ ɪɨɫɬɟ ɤɨɧɫɬɚɧɬɵ ɫɤɨɪɨɫɬɢ ɪɟɚɤɰɢɢ ɡɧɚɱɟɧɢɟ
J
ɬɚɤɠɟ ɭɜɟɥɢɱɢɜɚɟɬɫɹ (4.177). ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɢ ɨɛɥɚɫɬɶ ɩɨɜɟɪɯɧɨɫɬɢ ɱɚɫɬɢɰɵ, ɪɚɛɨɬɚɸɳɚɹ ɜ ɞɢɮɮɭɡɢɨɧɧɨɦ ɪɟɠɢɦɟ.
ɉɪɢ
k of
i
Jof ɜɫɹ ɦɟɠɮɚɡɧɚɹ ɩɨɜɟɪɯɧɨɫɬɶ ɪɚɛɨɬɚɟɬ ɜ ɞɢɮɮɭ-
ɡɢɨɧɧɨɦ ɪɟɠɢɦɟ ɦɚɫɫɨɨɛɦɟɧɚ, ɢ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɜɨ ɜɫɺɦ ɢɧɬɟɪɜɚɥɟ
ɡɧɚɱɟɧɢɣ ɭɝɥɚ
0TTS ɩɥɨɬɧɨɫɬɶ ɩɨɬɨɤɚ ɦɚɫɫɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ
ɮɨɪɦɭɥɟ (4.180).
0
ȿɫɥɢ ɠɟ
ɫɤɨɦ ɪɟɠɢɦɟ, ɢ ɜɟɪɧɨ ɪɚɜɟɧɫɬɜɨ (4.179) ɩɪɢ
ɇɚ ɪɢɫ. 4.9 ɩɨɤɚɡɚɧɵ ɨɛɥɚɫɬɢ ɡɧɚɱɟɧɢɣ ɩɚɪɚɦɟɬɪɨɜ T ɢ
k o , ɬɨ ɜɫɹ ɩɨɜɟɪɯɧɨɫɬɶ ɱɚɫɬɢɰɵ ɪɚɛɨɬɚɟɬ ɜ ɤɢɧɟɬɢɱɟ-
i
0 dTdS.
H , ɫɨɨɬ-
ɜɟɬɫɬɜɭɸɳɢɟ ɬɪɺɦ ɪɟɠɢɦɚɦ ɪɚɛɨɬɵ ɨɬɞɟɥɶɧɵɯ ɱɚɫɬɟɣ ɩɨɜɟɪɯɧɨɫɬɢ
ɫɮɟɪɢɱɟɫɤɨɣ ɬɜɺɪɞɨɣ ɱɚɫɬɢɰɵ.
T
S
III
S
2
I
3 101
0 10
Ɋɢɫ. 4.9. Ɋɟɠɢɦɵ ɪɚɛɨɬɵ ɪɚɡɥɢɱɧɵɯ ɡɨɧ ɩɨɜɟɪɯɧɨɫɬɢ
ɬɜɺɪɞɨɣ ɫɮɟɪɢɱɟɫɤɨɣ ɱɚɫɬɢɰɵ:
I – ɤɢɧɟɬɢɱɟɫɤɢɣ ɪɟɠɢɦ; II – ɫɦɟɲɚɧɧɵɣ ɪɟɠɢɦ;
III – ɞɢɮɮɭɡɢɨɧɧɵɣ ɪɟɠɢɦ
II
1 10 10
3
H
ɉɟɪɟɣɞɺɦ ɤ ɜɵɱɢɫɥɟɧɢɸ ɩɨɬɨɤɚ ɦɚɫɫɵ ɧɚ ɩɨɜɟɪɯɧɨɫɬɶ ɱɚɫɬɢɰɵ.
ɂɧɬɟɝɪɢɪɭɹ ɩɨ ɩɨɜɟɪɯɧɨɫɬɢ ɫɮɟɪɵ ɭɪɚɜɧɟɧɢɟ (4.176), ɩɨɥɭɱɚɟɦ ɞɥɹ
ɜɟɥɢɱɢɧɵ
:
i
97
2
M
3
23
S
M
u
i
Ƚ
ɝɞɟ
ªº
«»
fS
«»
uTT
«»
³³
00
«»
§·
«»
¨¸
©¹
¬¼
sin
T
1
sin 2
T T
2
3
;U JU
2
1
3
ɫ c
rC D
ii
f
0
1
§·
¨¸
3
©¹
ªº
§·
U
«»
exp sin ,
¨¸
«»
¨¸
JT
©¹
«»
¬¼
1
3
c
Pe
2
3
dedU
U
(4.181)
Pec – ɞɢɮɮɭɡɢɨɧɧɨɟ ɱɢɫɥɨ ɉɟɤɥɟ.
ȼɜɟɞɺɦ ɱɢɫɥɨ ɒɟɪɜɭɞɚ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɚɜɟɧɫɬɜɨɦ
M
Sh
2
S
i
c ɫ
rDC
0
f
ii
. (4.182)
ɂɫɯɨɞɹ ɢɡ (4.181) ɩɨɥɭɱɢɦ ɧɚ ɨɫɧɨɜɚɧɢɢ (4.182):
ªº
U
JT
2
3
U
dedU
2
3
3sin
Sh Pe exp sin ,
TT
§·
Ƚ
¨¸
©¹
1
3
«»
fS
1
«»
3
c
«»
³³
00
«»
§·
T T
«»
¨¸
©¹
¬¼
T
1
sin 2
2
ªº
§·
«»
1
3
¨¸
«»
¨¸
©¹
«»
¬¼
(4.183)
Ɉɛɨɡɧɚɱɢɦ ɱɟɪɟɡ
Sh ɱɢɫɥɨ ɒɟɪɜɭɞɚ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɞɢɮɮɭ-
0
ɡɢɨɧɧɨɦɭ ɩɨɬɨɤɭ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɱɚɫɬɢɰɵ, ɜ
ɫɥɭɱɚɟ, ɤɨɝɞɚ ɫɤɨɪɨɫɬɶ ɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ ɦɧɨɝɨ ɛɨɥɶɲɟ ɫɤɨɪɨɫɬɢ
ɩɨɞɜɨɞɚ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɤ ɦɟɠɮɚɡɧɨɣ ɝɪɚɧɢɰɟ. ɋɨɨɬɜɟɬɫɬɜɭɸ-
ɳɢɣ
Sh
ɞɢɮɮɭɡɢɨɧɧɵɣ ɩɨɬɨɤ ɦɚɫɫɵ
0
ɧɚɡɵɜɚɟɬɫɹ ɩɪɟɞɟɥɶɧɵɦ
0i
ɞɢɮɮɭɡɢɨɧɧɵɦ ɩɨɬɨɤɨɦ.
ɇɚ ɪɢɫ. 4.10 ɩɪɢɜɟɞɟɧɚ ɡɚɜɢɫɢɦɨɫɬɶ ɨɬɧɨɲɟɧɢɹ
Sh
ɨɬ ɩɚɪɚɦɟɬɪɚ
Sh
0
H , ɩɨɥɭɱɟɧɧɚɹ ɫ ɩɨɦɨɳɶɸ ɱɢɫɥɟɧɧɨɝɨ ɪɚɫɱɺɬɚ ɢɧɬɟɝɪɚɥɚ, ɫɬɨɹɳɟɝɨ ɜ
ɩɪɚɜɨɣ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ (4.183).
98
1,00
Sh
Sh
0
0,75
0,50
0,25
0
3
10
Ɋɢɫ. 4.10. Ɂɚɜɢɫɢɦɨɫɬɶ ɡɧɚɱɟɧɢɹ ɱɢɫɥɚ ɒɟɪɜɭɞɚ ɨɬ ɩɚɪɚɦɟɬɪɚ H :
1 – ɪɟɡɭɥɶɬɚɬɵ ɪɚɫɱɺɬɚ ɩɨ ɭɪɚɜɧɟɧɢɸ (4.182);
2 – ɪɟɡɭɥɶɬɚɬɵ ɪɚɫɱɺɬɚ ɩɨ ɭɪɚɜɧɟɧɢɸ (4.183)
2
1
1011 10 10
3
ȼ ɡɚɤɥɸɱɟɧɢɟ ɨɰɟɧɢɦ ɬɨɥɳɢɧɭ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɝɪɚɧɢɱɧɨɝɨ
ɫɥɨɹ ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɡɧɚɱɟɧɢɹɯ ɩɚɪɚɦɟɬɪɚ
H . ȿɝɨ ɜɟɥɢɱɢɧɚ ɦɨɠɟɬ
ɛɵɬɶ ɜɵɱɢɫɥɟɧɚ ɢɡ ɜɵɪɚɠɟɧɢɹ
c ɫ c
DC C
ii is
G
ɞ
f
m
i
.
(4.184)
ɂɫɩɨɥɶɡɭɹ ɮɨɪɦɭɥɭ ɞɥɹ ɪɚɫɱɺɬɚ ɩɥɨɬɧɨɫɬɢ ɩɨɬɨɤɚ ɦɚɫɫɵ (4.176) ɢ
(4.180) ɢ ɝɪɚɧɢɱɧɨɟ ɭɫɥɨɜɢɟ (4.174), ɩɨɥɭɱɚɟɦ
1
3
(4.185)
ɩɪɢ
0Ho
0,78 Pe ,
G
ɞ
§·
¨¸
1
©¹
3
c
1
T T
sin 2
2
sin
T
1
3
(4.186)
ɩɪɢ
Hof
1
3
1, 0 8 P e
G
ɞ
c
1
§·
¨¸
©¹
sin 2
T T
2
sin
T
Ɏɨɪɦɭɥɚ (4.185) ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɤɢɧɟɬɢɱɟɫɤɨɦɭ ɪɟɠɢɦɭ ɦɚɫɫɨɨɛɦɟɧɚ, ɚ ɮɨɪɦɭɥɚ (4.186) – ɞɢɮɮɭɡɢɨɧɧɨɦɭ. ɉɨɫɥɟɞɧɟɟ ɜɵɪɚɠɟɧɢɟ
ɫɨɜɩɚɞɚɟɬ ɫ ɮɨɪɦɭɥɨɣ, ɨɩɪɟɞɟɥɹɸɳɟɣ ɬɨɥɳɢɧɭ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɝɪɚɧɢɱɧɨɝɨ ɫɥɨɹ ɜ ɫɥɭɱɚɟ ɩɪɟɞɟɥɶɧɨɝɨ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɬɨɤɚ ɦɚɫɫɵ
ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɱɚɫɬɢɰɵ. ɂɡ (4.185) ɢ (4.186)
99
ɫɥɟɞɭɟɬ, ɱɬɨ ɜ ɫɥɭɱɚɟ ɤɢɧɟɬɢɱɟɫɤɨɝɨ ɪɟɠɢɦɚ ɦɚɫɫɨɨɛɦɟɧɚ ɞɢɮɮɭɡɢɨɧɧɵɣ ɩɨɝɪɚɧɢɱɧɵɣ ɫɥɨɣ ɧɟɫɤɨɥɶɤɨ ɬɨɧɶɲɟ, ɱɟɦ ɜ ɫɥɭɱɚɟ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɪɟɠɢɦɚ. Ɋɚɫɱɺɬ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɩɪɢ ɢɡɦɟɧɟɧɢɢ 0
ɬɨɥɳɢɧɚ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɝɪɚɧɢɱɧɨɝɨ ɫɥɨɹ ɪɚɫɬɺɬ ɫ ɭɜɟɥɢɱɟɧɢɟɦ
Hf
H .
4.2.5. Ɇɚɫɫɨɨɛɦɟɧ ɦɟɠɞɭ ɤɚɩɥɟɣ ɢ ɩɨɬɨɤɨɦ ɜɹɡɤɨɣ
ɠɢɞɤɨɫɬɢ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ
Ɍɚɤɢɟ ɡɚɞɚɱɢ ɯɚɪɚɤɬɟɪɧɵ, ɜ ɱɚɫɬɧɨɫɬɢ, ɩɪɢ ɨɩɢɫɚɧɢɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɲɥɚɤɨɜɨɣ ɢ ɦɟɬɚɥɥɢɱɟɫɤɨɣ ɮɚɡ ɜ ɩɥɚɜɢɥɶɧɵɯ ɢ ɪɚɮɢɧɢɪɨɜɨɱɧɵɯ ɩɟɱɚɯ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɢɯ ɪɟɲɟɧɢɹ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɢɧɮɨɪɦɚɰɢɸ ɨ
ɫɤɨɪɨɫɬɢ ɦɚɫɫɨɩɟɪɟɧɨɫɚ, ɤɨɬɨɪɚɹ ɫɭɳɟɫɬɜɟɧɧɨ ɡɚɜɢɫɢɬ ɨɬ ɪɟɠɢɦɨɜ
ɬɟɱɟɧɢɹ ɠɢɞɤɨɫɬɟɣ ɜ ɫɩɥɨɲɧɨɣ ɫɪɟɞɟ ɢ ɜɧɭɬɪɢ ɤɚɩɥɢ, ɨɬ ɫɨɨɬɧɨɲɟɧɢɹ ɢɧɬɟɧɫɢɜɧɨɫɬɟɣ ɤɨɧɜɟɤɬɢɜɧɨɝɨ ɢ ɦɨɥɟɤɭɥɹɪɧɨɝɨ ɦɟɯɚɧɢɡɦɨɜ ɩɟ
ɪɟɧɨɫɚ ɦɚɫɫɵ ɜ ɨɛɳɟɦ ɩɨɬɨɤɟ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ, ɨɬ ɬɨɝɨ, ɜ ɤɚɤɨɣ
ɢɡ ɮɚɡ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɦɚɫɫɨɩɟɪɟɧɨɫɭ ɛɨɥɟɟ ɡɧɚɱɢɬɟɥɶɧɨ, ɢ ɬ.ɩ.
ɉɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɦɟɯɚɧɢɡɦɨɜ ɦɚɫɫɨɨɛɦɟɧɚ ɤɚɩɟɥɶ ɢ ɩɭɡɵɪɟɣ ɫ
ɩɨɬɨɤɨɦ ɫɩɥɨɲɧɨɣ ɫɪɟɞɵ ɜɚɠɧɨ ɡɧɚɬɶ, ɤɚɤɚɹ ɢɡ ɮɚɡ, ɫɩɥɨɲɧɚɹ ɢɥɢ
ɞɢɫɩɟɪɫɧɚɹ, ɥɢɦɢɬɢɪɭɟɬ ɩɪɨɰɟɫɫ ɩɟɪɟɧɨɫɚ. ȿɫɥɢ ɥɢɦɢɬɢɪɭɸɳɟɣ ɹɜɥɹɟɬɫɹ ɫɩɥɨɲɧɚɹ ɫɪɟɞɚ, ɬɨ ɜɟɥɢɱɢɧɚ
ɩɨɬɨɤɚ ɦɚɫɫɵ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɝɢɞɪɨɞɢɧɚɦɢɤɨɣ ɧɟɫɭɳɟɝɨ ɩɨɬɨɤɚ. ȼ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɨɫɧɨɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɦɚɫɫɨɩɟɪɟɧɨɫɭ ɫɨɫɪɟɞɨɬɨɱɟɧɨ ɜ ɞɢɫɩɟɪɫɧɨɣ ɮɚɡɟ, ɨɩɪɟɞɟɥɹɸɳɟɟ ɜɥɢɹɧɢɟ ɧɚ ɦɚɫɫɨɨɛɦɟɧ ɨɤɚɡɵɜɚɟɬ ɯɚɪɚɤɬɟɪ ɩɟɪɟɦɟɲɢɜɚɧɢɹ ɠɢɞɤɨɫɬɟɣ ɢɥɢ ɝɚɡɚ ɜɧɭɬɪɢ ɞɢɫɩɟɪɫɧɨɣ ɱɚɫɬɢɰɵ (ɤɚɩɥɢ ɢɥɢ ɩɭɡɵɪɹ). ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɩɪɨɰɟɫɫ ɦɚɫɫɨɨɛɦɟɧɚ ɧɨɫɢɬ
ɧɟɫɬɚɰɢɨɧɚɪɧɵɣ ɯɚɪɚɤɬɟɪ ɢ ɢɫɤɨɦɵɟ ɜɟɥɢɱɢɧɵ – ɩɨɬɨɤ
ɦɚɫɫɵ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɢ ɤɨɧɰɟɧɬɪɚɰɢɹ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ – ɫɬɚɧɨɜɹɬɫɹ
ɮɭɧɤɰɢɹɦɢ ɜɪɟɦɟɧɢ. ȼ ɩɟɪɜɨɦ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɨɫɧɨɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɫɨɫɪɟɞɨɬɨɱɟɧɨ ɜ ɧɟɫɭɳɟɦ ɩɨɬɨɤɟ, ɩɪɨɰɟɫɫ ɦɚɫɫɨɨɛɦɟɧɚ ɫɬɚɰɢɨɧɚɪɟɧ ɢ ɞɥɹ ɟɝɨ ɨɩɢɫɚɧɢɹ ɢɫɩɨɥɶɡɭɸɬɫɹ ɭɪɚɜɧɟɧɢɹ ɞɢɮɮɭɡɢɨɧɧɨɝɨ
ɩɨɝɪɚɧɢɱɧɨɝɨ ɫɥɨɹ.
-
4.2.5.1. Ɉɫɧɨɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɦɚɫɫɨɩɟɪɟɧɨɫɭ
ɫɨɫɪɟɞɨɬɨɱɟɧɨ ɜ ɨɦɵɜɚɸɳɟɦ ɤɚɩɥɸ ɩɨɬɨɤɟ
(Re 1;
Pe 1)
c
!!
ȼ ɧɚɫɬɨɹɳɟɦ ɩɚɪɚɝɪɚɮɟ ɩɪɟɞɩɨɥɚɝɚɟɦ, ɱɬɨ ɩɨɥɹ ɫɤɨɪɨɫɬɟɣ ɬɟɱɟɧɢɹ ɠɢɞɤɨɫɬɟɣ ɜɧɭɬɪɢ ɢ ɫɧɚɪɭɠɢ ɤɚɩɥɢ ɨɩɢɫɵɜɚɸɬɫɹ ɫɥɟɞɭɸɳɢɦɢ
ɮɨɪɦɭɥɚɦɢ:
– ɞɥɹ ɠɢɞɤɨɫɬɢ ɜɧɭɬɪɢ ɤɚɩɥɢ
100
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