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ɉɨɩɪɚɜɨɱɧɵɟ ɦɧɨɠɢɬɟɥɢ
Ɍ ɚ ɛ ɥ ɢ ɰ ɚ 1.5
ɍɫɥɨɜɢɹ ɩɪɢɜɟɞɟɧɢɹ
ɨɛɴɟɦɧɨɝɨ ɪɚɫɯɨɞɚ
ɝɚɡɚ
0 °ɋ
ɢ
760 ɦɦ
ɪɬ. ɫɬ.
15 °ɋ
ɢ
760 ɦɦ
ɪɬ. ɫɬ.
20 °ɋ
ɢ
760 ɦɦ
ɪɬ. ɫɬ.
15 °ɋ
ɢ 1 ɛɚɪ
20 °ɋ
ɢ 1 ɛɚɪ
0 °ɋ ɢ 760 ɦɦ ɪɬ. ɫɬ. 1,0 1,0549 1,0732 1,0688 1,0874
15 °ɋ ɢ 760 ɦɦ ɪɬ. ɫɬ. 0,9479 1,0 1,0174 1,0132 1,0308
20 °ɋ ɢ 760 ɦɦ ɪɬ. ɫɬ. 0,9318 0,9829 1,0 0,9959 1,0132
15 °ɋ ɢ 1 ɛɚɪ 0,9355 0,9869 1,0041 1,0 1,0174
20 °ɋ ɢ 1 ɛɚɪ 0,9196 0,9700 0,9869 0,9829 1,0
ɉɪɢɦɟɱɚɧɢɟ: ɞɥɹ ɩɟɪɟɫɱɟɬɚ ɪɚɫɯɨɞɚ ɢɡ ɡɚɞɚɧɧɵɯ ɫɬɚɧɞɚɪɬɧɵɯ ɭɫɥɨɜɢɣ (ɥɟɜɵɣ ɫɬɨɥɛɟɰ ɬɚɛɥɢɰɵ) ɜ ɬɪɟɛɭɟɦɵɟ (ɜɟɪɯɧɹɹ ɫɬɪɨɤɚ ɬɚɛɥɢɰɵ) ɧɟɨɛɯɨɞɢɦɵɣ ɦɧɨɠɢɬɟɥɶ ɧɚɯɨɞɹɬ ɧɚ ɩɟɪɟɫɟɱɟɧɢɢ
ɫɬɪɨɤ ɢ ɫɬɨɥɛɰɨɜ. ɇɚɩɪɢɦɟɪ, ɱɬɨɛɵ ɡɚɞɚɧɧɵɣ ɩɪɢ 20 °ɋ ɢ 760 ɦɦ ɪɬ. ɫɬ. ɪɚɫɯɨɞ ɩɟɪɟɫɱɢɬɚɬɶ ɜ
ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɩɪɢ 0 °ɋ ɢ 760 ɦɦ ɪɬ. ɫɬ., ɧɟɨɛɯɨɞɢɦɨ ɟɝɨ ɜɟɥɢɱɢɧɭ ɭɦɧɨɠɢɬɶ ɧɚ 0,9318.
Ɉɛɴɟɦɧɵɣ ɪɚɫɯɨɞ ɫɭɯɨɝɨ ɝɚɡɚ ɜ ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ QHom, ɩɪɢɧɹɬɵɯ ɜ
ɨɬɟɱɟɫɬɜɟɧɧɨɣ ɩɪɚɤɬɢɤɟ, ɩɪɢɜɨɞɹɬ ɤ ɞɪɭɝɢɦ ɫɬɚɧɞɚɪɬɧɵɦ ɭɫɥɨɜɢɹɦ, ɜɜɨɞɹ ɩɨɩɪɚɜɨɱɧɵɟ ɦɧɨɠɢɬɟɥɢ (ɬɚɛɥ. 1.5), ɂɡɜɟɫɬɧɵɣ ɩɪɢ ɪɚɛɨɱɢɯ ɭɫɥɨɜɢɹɯ ɪɚɫɯɨɞ ɩɟɪɟɫɱɢɬɵɜɚɸɬ ɜ ɪɚɫɯɨɞ ɩɪɢ ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ ɩɨ ɜɵɪɚɠɟɧɢɸ
283,73
QQ
ɧɨɦ 0
P
, (26)
TK
ɝɞɟ Ɋ – ɚɛɫɨɥɸɬɧɨɟ ɞɚɜɥɟɧɢɟ ɝɚɡɚ ɩɪɢ ɪɚɛɨɱɢɯ ɭɫɥɨɜɢɹɯ: Ɍ – ɬɟɦɩɟɪɚɬɭɪɚ ɝɚɡɚ ɜ
ɪɚɛɨɱɢɯ ɭɫɥɨɜɢɹɯ; Ʉ – ɤɨɷɮɮɢɰɢɟɧɬ ɫɠɢɦɚɟɦɨɫɬɢ ɝɚɡɚ.
Ʉɨɷɮɮɢɰɢɟɧɬ ɫɠɢɦɚɟɦɨɫɬɢ Ʉ ɪɚɜɟɧ ɨɬɧɨɲɟɧɢɸ ɩɥɨɬɧɨɫɬɢ ȡ
ɩɨɞɫɱɢɬɚɧ-
ɲ
ɧɨɣ ɩɨ ɡɚɤɨɧɚɦ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ, ɤ ɞɟɣɫɬɜɢɬɟɥɶɧɨɣ ɩɥɨɬɧɨɫɬɢ ɝɚɡɚ ɜ ɪɚɛɨɱɟɦ
ɫɨɫɬɨɹɧɢɢ ɩɪɢ ɞɚɧɧɵɯ Ɋ ɢ Ɍ.
Ɋɚɫɯɨɞ ɜɥɚɠɧɨɝɨ ɝɚɡɚ ɩɟɪɟɫɱɢɬɵɜɚɸɬ ɜ ɪɚɫɯɨɞ ɧɚ ɫɭɯɨɣ ɝɚɡ ɩɪɢ ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ ɩɨ ɜɵɪɚɠɟɧɢɸ
PP
ɝɞɟ Q
– ɨɛɴɟɦɧɵɣ ɪɚɫɯɨɞ ɜɥɚɠɧɨɝɨ ɝɚɡɚ ɩɪɢ ɪɚɛɨɱɢɯ ɭɫɥɨɜɢɹɯ; P
ɜ.ɝ.
283,73 .
QQ
ɧɨɦ ɜ.ɝ
§·
¨¸
TK TK
©¹
ɜ.ɩ.max
M
, (27)
ɜ.ɩ.max
ɧɚɢɛɨɥɶɲɟɟ ɜɨɡɦɨɠɧɨɟ ɞɚɜɥɟɧɢɟ ɜɨɞɹɧɨɝɨ ɩɚɪɚ ɜɨ ɜɥɚɠɧɨɦ ɝɚɡɟ ɩɪɢ ɬɟɦɩɟɪɚ-
2
ɬɭɪɟ t, ɤɝɫ/ɫɦ
.
Ɋɚɫɯɨɞ ɜɥɚɠɧɨɝɨ ɝɚɡɚ ɩɟɪɟɫɱɢɬɵɜɚɸɬ ɜ ɪɚɫɯɨɞ ɟɝɨ ɧɚ ɫɭɯɨɣ ɝɚɡ ɩɪɢ ɪɚɛɨɱɢɯ ɭɫɥɨɜɢɹɯ ɩɨ ɮɨɪɦɭɥɟ
–
31
P
U
U
U
U
M
§·
QQ
ɫ.ɝ. ɜ.ɝ
.1
¨¸
©¹
M
ɜ.ɩ.max
, (28)
P
ɝɞɟ ij – ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɜɥɚɠɧɨɫɬɶ.
Ƚɚɡɵ ɢ ɢɯ ɫɦɟɫɢ ɹɜɥɹɸɬɫɹ ɫɭɯɢɦɢ, ɤɨɝɞɚ ɢɯ ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɜɥɚɠɧɨɫɬɶ ɩɪɢ
ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ ɧɚɯɨɞɢɬɫɹ ɜ ɩɪɟɞɟɥɚɯ 0 < ij < 0,1.
ɉɥɨɬɧɨɫɬɶ ɝɚɡɨɜɨɝɨ ɩɨɬɨɤɚ ɞɨɥɠɧɚ ɛɵɬɶ ɢɡɦɟɪɟɧɚ ɢɥɢ ɨɩɪɟɞɟɥɟɧɚ ɜ ɩɪɨɰɟɫɫɟ ɢɡɦɟɪɟɧɢɹ ɪɚɫɯɨɞɚ ɝɚɡɚ. ɉɪɢɟɦɥɟɦ ɥɸɛɨɣ ɦɟɬɨɞ ɢɡɦɟɪɟɧɢɹ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɣ ɩɨɥɭɱɟɧɢɟ ɞɨɫɬɨɜɟɪɧɵɯ ɞɚɧɧɵɯ ɩɨ ɩɥɨɬɧɨɫɬɢ ɝɚɡɚ ɩɪɢ
ɧɨɪɦɚɥɶɧɵɯ ɢɥɢ
ɪɚɛɨɱɢɯ ɭɫɥɨɜɢɹɯ. ɉɥɨɬɧɨɫɬɶ ɫɭɯɢɯ ɝɚɡɨɜ ɢ ɢɯ ɫɦɟɫɟɣ ɨɩɪɟɞɟɥɹɸɬ ɥɚɛɨɪɚɬɨɪɧɵɦɢ ɦɟɬɨɞɚɦɢ ɢɥɢ ɚɧɚɥɢɬɢɱɟɫɤɢɦ ɪɚɫɱɟɬɨɦ ɩɨ ɢɡɜɟɫɬɧɨɦɭ ɤɨɦɩɨɧɟɧɬɧɨɦɭ
ɫɨɫɬɚɜɭ ɫɦɟɫɢ.
ɉɥɨɬɧɨɫɬɶ ɫɭɯɨɝɨ ɝɚɡɚ ɜ ɪɚɛɨɱɢɯ ɭɫɥɨɜɢɹɯ ɩɪɢ ɢɡɜɟɫɬɧɨɣ ɩɥɨɬɧɨɫɬɢ ɜ
ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ ɜɵɱɢɫɥɹɸɬ ɩɨ ɭɪɚɜɧɟɧɢɸ
PT P
UU
. (29)
ɧɨɦ
ɧɨɦ ɧɨɦ
PTK TK
ɧɨɦ
283,73
Ʉɨɷɮɮɢɰɢɟɧɬ ɫɠɢɦɚɟɦɨɫɬɢ Ʉ ɭɱɢɬɵɜɚɟɬ ɨɬɤɥɨɧɟɧɢɟ ɫɜɨɣɫɬɜ ɪɟɚɥɶɧɵɯ ɝɚɡɨɜ ɨɬ ɫɜɨɣɫɬɜ ɢɯ ɫɦɟɫɟɣ ɢ ɫɜɨɣɫɬɜ ɢɞɟɚɥɶɧɵɯ ɝɚɡɨɜ. Ɂɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɚ
ɫɠɢɦɚɟɦɨɫɬɢ ɧɟɤɨɬɨɪɵɯ ɢɧɞɢɜɢɞɭɚɥɶɧɵɯ ɝɚɡɨɜ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ
ɢ ɞɚɜɥɟɧɢɹ ɦɨɝɭɬ ɛɵɬɶ ɨɩɪɟɞɟɥɟɧɵ ɩɨ ɝɪɚɮɢɤɚɦ.
ɉɥɨɬɧɨɫɬɶ ɝɚɡɚ ɡɚɦɟɬɧɨ ɡɚɜɢɫɢɬ ɨɬ ɜɥɚɝɨɫɨɞɟɪɠɚɧɢɹ. Ƚɚɡɵ ɢ ɢɯ ɫɦɟɫɢ ɫɱɢɬɚɸɬɫɹ ɜɥɚɠɧɵɦɢ, ɟɫɥɢ ɡɧɚɱɟɧɢɟ ɢɯ ɨɬɧɨɫɢɬɟɥɶɧɨɣ
ɜɥɚɠɧɨɫɬɢ ɩɪɢ ɧɨɪɦɚɥɶ-
ɧɵɯ ɭɫɥɨɜɢɹɯ ɥɟɠɢɬ ɜ ɩɪɟɞɟɥɚɯ 0,1 < ij < 1,0.
ɉɥɨɬɧɨɫɬɶ ɜɥɚɠɧɨɝɨ ɝɚɡɚ ȡ
ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɨɩɪɟɞɟɥɹɸɬ ɤɚɤ ɫɭɦɦɭ ɩɥɨɬ-
ɜ.ɩ.
ɧɨɫɬɟɣ ɟɝɨ ɫɭɯɨɣ ɱɚɫɬɢ ɢ ɜɨɞɹɧɨɝɨ ɩɚɪɚ ɩɪɢ ɢɯ ɩɚɪɰɢɚɥɶɧɵɯ ɞɚɜɥɟɧɢɹɯ ɢ ɬɟɦɩɟɪɚɬɭɪɟ
ɝɞɟ
– ɩɥɨɬɧɨɫɬɶ ɫɭɯɨɣ ɱɚɫɬɢ ɜɥɚɠɧɨɝɨ ɝɚɡɚ ɩɪɢ ɟɟ ɩɚɪɰɢɚɥɶɧɨɦ ɞɚɜɥɟɧɢɢ ɢ
ɫ.ɝ.
ɬɟɦɩɟɪɚɬɭɪɟ t,
– ɩɥɨɬɧɨɫɬɶ ɜɨɞɹɧɨɝɨ ɩɚɪɚ ɩɪɢ ɟɝɨ ɩɚɪɰɢɚɥɶɧɨɦ ɞɚɜɥɟɧɢɢ ɢ
ɜ.ɩ.
UU
, (30)
ɜ.ɝ. ɫ.ɝ. ɜ.ɩ.
ɬɟɦɩɟɪɚɬɭɪɟ.
ɉɥɨɬɧɨɫɬɶ ɫɭɯɨɣ ɱɚɫɬɢ ɜɥɚɠɧɨɝɨ ɝɚɡɚ ɜ ɪɚɛɨɱɢɯ ɭɫɥɨɜɢɹɯ ɧɚɯɨɞɹɬ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɩɨ ɜɵɪɚɠɟɧɢɸ
()
ɝɞɟ ȡ
– ɩɥɨɬɧɨɫɬɶ ɫɭɯɨɝɨ ɝɚɡɚ (ɢɥɢ ɫɭɯɨɣ ɱɚɫɬɢ ɜɥɚɠɧɨɝɨ ɝɚɡɚ) ɜ ɧɨɪɦɚɥɶɧɨɦ
ɧɨɦ
ɫɨɫɬɨɹɧɢɢ; P
TPP PP
, (31)
UU U
ɫ.ɝ. ɧɨɦ ɧɨɦ
ɜ.ɩ – ɞɚɜɥɟɧɢɟ ɜɨɞɹɧɨɝɨ ɩɚɪɚ ɜɨ ɜɥɚɠɧɨɦ ɝɚɡɟ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ t.
ɧɨɦ ɜ.ɩ.max ɜ.ɩ.max
PTK TK
ɧɨɦ
283,73
M
32
ɉɥɨɬɧɨɫɬɶ ɜɨɞɹɧɨɝɨ ɩɚɪɚ ɜɨ ɜɥɚɠɧɨɦ ɝɚɡɟ ɜ ɪɚɛɨɱɢɯ ɭɫɥɨɜɢɹɯ ɜ ɨɛɳɟɦ
M
U
ɫɥɭɱɚɟ ɨɩɪɟɞɟɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
TP
UU MU
. (32)
ɜ.ɩ. ɜ.ɩ. ɜ.ɩ.max
ɧɨɦ ɜ.ɩ.max
PTK
ɧɨɦ
ɉɥɨɬɧɨɫɬɶ ɠɢɞɤɨɫɬɟɣ ɞɨɥɠɧɚ ɛɵɬɶ ɢɡɦɟɪɟɧɚ ɢɥɢ ɨɩɪɟɞɟɥɟɧɚ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɞɚɜɥɟɧɢɹ ɢ ɬɟɦɩɟɪɚɬɭɪɵ. ȿɫɥɢ ɢɡɜɟɫɬɧɚ ɩɥɨɬɧɨɫɬɶ ȡ ɠɢɞɤɨɫɬɢ ɩɪɢ ɧɟɤɨɬɨɪɨɣ ɬɟɦɩɟɪɚɬɭɪɟ t ɨɬɥɢɱɧɨɣ ɨɬ ɪɚɛɨɱɟɣ ɬɟɦɩɟɪɚɬɭɪɵ, ɬɨ ɩɥɨɬɧɨɫɬɶ ȡ ɩɪɢ
ɬɟɦɩɟɪɚɬɭɪɟ t ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
[1 ( ')]tt
UE
, (33)
t'
ɝɞɟ ȕ – ɫɪɟɞɧɢɣ ɤɨɷɮɮɢɰɢɟɧɬ ɨɛɴɟɦɧɨɝɨ ɬɟɩɥɨɜɨɝɨ ɪɚɫɲɢɪɟɧɢɹ ɠɢɞɤɨɫɬɢ ɜ ɢɧɬɟɪɜɚɥɟ.
Ɂɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ, ɜɯɨɞɹɳɢɯ ɜ ɩɪɢɜɟɞɟɧɧɵɟ ɜɵɲɟ ɮɨɪɦɭɥɵ, ɛɟɪɭɬ ɢɡ
ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɫɩɪɚɜɨɱɧɨɣ ɥɢɬɟɪɚɬɭɪɵ.
Ⱦɥɹ ɬɜɟɪɞɵɯ ɫɵɩɭɱɢɯ ɬɟɥ ɩɨɥɶɡɭɸɬɫɹ ɩɨɧɹɬɢɟɦ ɧɚɫɵɩɧɨɣ ɢɥɢ ɨɛɴɟɦɧɨɣ
ɦɚɫɫɵ.
ɇɚɫɵɩɧɚɹ ɦɚɫɫɚ ɬɜɟɪɞɨɝɨ ɫɵɩɭɱɟɝɨ ɦɚɬɟɪɢɚɥɚ ɧɟ ɢɦɟɟɬ ɞɥɹ ɞɚɧɧɨɝɨ ɜɟɳɟɫɬɜɚ ɩɨɫɬɨɹɧɧɨɝɨ ɡɧɚɱɟɧɢɹ; ɨɧɚ ɡɚɜɢɫɢɬ ɨɬ ɝɪɚɧɭɥɨɦɟɬɪɢɱɟɫɤɨɝɨ ɫɨɫɬɚɜɚ
ɫɵɩɭɱɟɝɨ ɦɚɬɟɪɢɚɥɚ, ɬ. ɟ. ɨɬ ɪɚɡɦɟɪɚ ɱɚɫɬɢɰ ɢ ɤɨɥɢɱɟɫɬɜɟɧɧɨɝɨ ɫɨɞɟɪɠɚɧɢɹ ɱɚɫɬɢɰ
ɪɚɡɥɢɱɧɨɣ ɜɟɥɢɱɢɧɵ ɜ ɨɛɳɟɣ ɦɚɫɫɟ ɫɵɩɭɱɟɝɨ ɦɚɬɟɪɢɚɥɚ. ɉɨɷɬɨɦɭ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɛɨɥɟɟ ɬɨɱɧɵɯ ɪɟɡɭɥɶɬɚɬɨɜ ɩɪɢ ɢɡɦɟɪɟɧɢɢ ɤɨɥɢɱɟɫɬɜɨ ɫɵɩɭɱɟɝɨ ɦɚɬɟɪɢɚɥɚ
ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɡɜɟɲɢɜɚɧɢɟɦ.
ɉɪɢɛɨɪɵ, ɢɡɦɟɪɹɸɳɢɟ ɤɨɥɢɱɟɫɬɜɨ ɜɟɳɟɫɬɜɚ, ɧɚɡɵɜɚɸɬɫɹ ɫɱɟɬɱɢɤɚɦɢ.
ɋɱɟɬɱɢɤɢ ɢɡɦɟɪɹɸɬ ɩɪɨɬɟɤɚɸɳɢɣ ɱɟɪɟɡ ɧɢɯ ɨɛɴɟɦ ɜɟɳɟɫɬɜɚ ɡɚ ɥɸɛɨɣ ɩɪɨɦɟ-
ɜɪɟɦɟɧɢ: ɫɭɬɤɢ, ɦɟɫɹɰ ɢ ɬ. ɞ. Ʉɨɥɢɱɟɫɬɜɨ ɜɟɳɟɫɬɜɚ ɩɪɢ ɷɬɨɦ ɨɩɪɟɞɟɥɹɟɬ-
ɠɭɬɨɤ
ɫɹ ɤɚɤ ɪɚɡɧɨɫɬɶ ɩɨɤɚɡɚɧɢɣ ɫɱɟɬɱɢɤɚ. ɋɱɟɬɱɢɤɢ, ɤɚɤ ɩɪɚɜɢɥɨ, ɹɜɥɹɸɬɫɹ ɩɪɢɛɨɪɚɦɢ ɩɪɹɦɨɝɨ ɢɡɦɟɪɟɧɢɹ, ɢ ɨɬɫɱɟɬ ɩɨ ɢɯ ɲɤɚɥɟ ɞɚɟɬ ɡɧɚɱɟɧɢɟ ɢɡɦɟɪɹɟɦɨɣ ɜɟɥɢɱɢɧɵ ɛɟɡ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɜɵɱɢɫɥɟɧɢɣ.
Ɋɚɫɯɨɞɨɦ ɧɚɡɵɜɚɟɬɫɹ ɤɨɥɢɱɟɫɬɜɨ ɜɟɳɟɫɬɜɚ, ɩɪɨɯɨɞɹɳɟɟ ɱɟɪɟɡ ɞɚɧɧɨɟ ɫɟɱɟɧɢɟ ɤɚɧɚɥɚ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ. Ɇɚɫɫɨɜɵɣ ɪɚɫɯɨɞ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜ ɤɢɥɨɝɪɚɦɦɚɯ ɜ ɫɟɤɭɧɞɭ, ɚ ɨɛɴɟɦɧɵɣ ɪɚɫɯɨɞ ɜ ɤɭɛɢɱɟɫɤɢɯ ɦɟɬɪɚɯ ɡɚ ɫɟɤɭɧɞɭ. ɉɪɢɛɨɪɵ,
ɢɡɦɟɪɹɸɳɢɟ ɪɚɫɯɨɞ, ɧɚɡɵɜɚɸɬɫɹ ɪɚɫɯɨɞɨɦɟɪɚɦɢ. ɗɬɢ ɩɪɢɛɨɪɵ ɦɨɝɭɬ ɛɵɬɶ
ɫɧɚɛɠɟɧɵ ɫɱɟɬɱɢɤɚɦɢ (ɢɧɬɟɝɪɚɬɨɪɚɦɢ), ɬɨɝɞɚ ɨɧɢ ɧɚɡɵɜɚɸɬɫɹ ɪɚɫɯɨɞɨɦɟɪɚɦɢ
ɫɨ ɫɱɟɬɱɢɤɨɦ. Ɍɚɤɢɟ ɪɚɫɯɨɞɨɦɟɪɵ ɩɨɡɜɨɥɹɸɬ ɢɡɦɟɪɹɬɶ ɪɚɫɯɨɞ ɢ ɤɨɥɢɱɟɫɬɜɨ
ɜɟɳɟɫɬɜɚ.
ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɩɪɢɧɹɬɨɝɨ ɦɟɬɨɞɚ ɢɡɦɟɪɟɧɢɹ ɩɪɢɛɨɪɵ ɞɥɹ ɢɡɦɟɪɟɧɢɹ
ɪɚɫɯɨɞɚ ɢ ɤɨɥɢɱɟɫɬɜɚ ɩɨɞɪɚɡɞɟɥɹɸɬɫɹ ɧɚ: ɪɚɫɯɨɞɨɦɟɪɵ ɩɟɪɟɦɟɧɧɨɝɨ ɩɟɪɟɩɚɞɚ
ɞɚɜɥɟɧɢɹ – ɨɫɧɨɜɚɧɧɵɟ ɧɚ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɪɚɫɯɨɞɚ ɜɟɳɟɫɬɜɚ ɩɟɪɟɩɚɞɚ ɞɚɜɥɟ-
33
ɧɢɹ, ɫɨɡɞɚɜɚɟɦɨɝɨ ɧɟɩɨɞɜɢɠɧɵɦ ɭɫɬɪɨɣɫɬɜɨɦ, ɭɫɬɚɧɨɜɥɟɧɧɵɦ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ,
U
ɢɥɢ ɷɥɟɦɟɧɬɨɦ ɬɪɭɛɨɩɪɨɜɨɞɚ; ɪɚɫɯɨɞɨɦɟɪɵ ɩɨɫɬɨɹɧɧɨɝɨ ɩɟɪɟɩɚɞɚ ɞɚɜɥɟɧɢɣ,
ɨɫɧɨɜɚɧɧɵɟ ɧɚ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɪɚɫɯɨɞɚ ɜɟɳɟɫɬɜɚ ɜɟɪɬɢɤɚɥɶɧɨɝɨ ɩɟɪɟɦɟɳɟɧɢɹ
ɬɟɥɚ (ɩɨɩɥɚɜɤɚ), ɢɡɦɟɧɹɸɳɟɝɨ ɩɪɢ ɷɬɨɦ ɩɥɨɳɚɞɶ ɩɪɨɯɨɞɧɨɝɨ ɨɬɜɟɪɫɬɢɹ ɩɪɢɛɨɪɚ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨ ɩɟɪɟɩɚɞ ɞɚɜɥɟɧɢɹ ɩɨ ɨɛɟ ɫɬɨɪɨɧɵ ɩɨɩɥɚɜɤɚ ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɵɦ; ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɟ ɪɚɫɯɨɞɨɦɟɪɵ – ɨɫɧɨɜɚɧɧɵɟ ɧɚ ɡɚɜɢɫɢɦɨɫɬɢ ɪɟɡɭɥɶɬɚɬɚ
ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɞɜɢɠɭɳɟɣɫɹ ɠɢɞɤɨɫɬɢ ɫ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ ɨɬ ɪɚɫɯɨ-
ɞɚ; ɫɱɟɬɱɢɤɢ, ɫɥɭɠɚɳɢɟ ɞɥɹ ɢɡɦɟɪɟɧɢɹ ɤɨɥɢɱɟɫɬɜɚ ɜɟɳɟɫɬɜ.
ɂɡɦɟɪɟɧɢɟ ɪɚɫɯɨɞɚ ɦɟɬɨɞɨɦ ɩɟɪɟɦɟɧɧɨɝɨ ɩɟɪɟɩɚɞɚ ɞɚɜɥɟɧɢɹ
ɂɡ ɜɫɟɝɨ ɩɚɪɤɚ ɫɭɳɟɫɬɜɭɸɳɢɯ ɪɚɫɯɨɞɨɦɟɪɨɜ ɨɤɨɥɨ 80 % ɫɨɫɬɚɜɥɹɸɬ ɪɚɫɯɨɞɨɦɟɪɵ ɩɟɪɟɦɟɧɧɨɝɨ ɩɟɪɟɩɚɞɚ ɞɚɜɥɟɧɢɹ. Ɍɚɤɨɟ ɲɢɪɨɤɨɟ ɩɪɢɦɟɧɟɧɢɟ ɨɛɴɹɫɧɹɟɬɫɹ ɧɢɡɤɨɣ ɫɬɨɢɦɨɫɬɶɸ ɢɯ, ɩɪɨɫɬɨɬɨɣ ɤɨɧɫɬɪɭɤɰɢɢ ɢ ɷɤɫɩɥɭɚɬɚɰɢɢ, ɚ ɬɚɤɠɟ
ɬɟɦ, ɱɬɨ ɞɥɹ
ɝɪɚɞɭɢɪɨɜɤɢ ɬɚɤɢɯ ɪɚɫɯɨɞɨɦɟɪɨɜ ɧɟ ɬɪɟɛɭɸɬɫɹ ɞɨɪɨɝɨɫɬɨɹɳɢɟ ɨɛɪɚɡɰɨɜɵɟ ɭɫɬɚɧɨɜɤɢ. Ɋɚɫɯɨɞɨɦɟɪɵ ɩɟɪɟɦɟɧɧɨɝɨ ɩɟɪɟɩɚɞɚ ɞɚɜɥɟɧɢɹ ɹɜɥɹɸɬɫɹ
ɟɞɢɧɫɬɜɟɧɧɵɦɢ ɧɨɪɦɚɥɢɡɨɜɚɧɧɵɦɢ ɫɪɟɞɫɬɜɚɦɢ ɢɡɦɟɪɟɧɢɹ ɪɚɫɯɨɞɚ ɢɡ ɜɫɟɯ ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɦɢɪɨɜɨɣ ɩɪɚɤɬɢɤɟ.
ɂɡɦɟɪɟɧɢɟ ɪɚɫɯɨɞɚ ɩɨ ɦɟɬɨɞɭ ɩɟɪɟɦɟɧɧɨɝɨ ɩɟɪɟɩɚɞɚ ɞɚɜɥɟɧɢɹ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɤɨɫɜɟɧɧɵɦ ɩɭɬɟɦ, ɬ. ɟ. ɢɡɦɟɪɹɟɬɫɹ ɩɟɪɟɩɚɞ ɞɚɜɥɟɧɢɹ ɧɚ ɫɭɠɚɸɳɟɦ
ɭɫɬɪɨɣɫɬɜɟ, ɭɫɬɚɧɨɜɥɟɧɧɨɦ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ. ɉɪɢ ɩɪɨɯɨɠɞɟɧɢɢ
ɠɢɞɤɨɫɬɢ ɢɥɢ
ɝɚɡɚ ɱɟɪɟɡ ɫɭɠɚɸɳɟɟ ɭɫɬɪɨɣɫɬɜɨ ɫɨɡɞɚɟɬɫɹ ɩɟɪɟɩɚɞ ɞɚɜɥɟɧɢɹ, ɤɨɬɨɪɵɣ ɩɪɢ ɩɪɨɱɢɯ ɪɚɜɧɵɯ ɭɫɥɨɜɢɹɯ ɡɚɜɢɫɢɬ ɨɬ ɪɚɫɯɨɞɚ. ɂɡɜɟɫɬɧɨ, ɱɬɨ ɨɛɴɟɦɧɵɣ ɪɚɫɯɨɞ
Q ɜɟɳɟɫɬɜɚ, ɩɪɨɬɟɤɚɸɳɟɝɨ ɩɨ ɬɪɭɛɨɩɪɨɜɨɞɭ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ ɩɪɨɢɡɜɟɞɟɧɢɟ
ɫɤɨɪɨɫɬɢ ɩɨɬɨɤɚ v ɧɚ ɩɥɨɳɚɞɶ ɨɬɜɟɪɫɬɢɹ ɢɫɬɟɱɟɧɢɹ F
QvF . (34)
Ɇɚɫɫɨɜɵɣ ɪɚɫɯɨɞ G ɩɨɥɭɱɚɸɬ ɭɦɧɨɠɟɧɢɟɦ ɨɛɴɟɦɧɨɝɨ ɪɚɫɯɨɞɚ Q ɧɚ ɩɥɨɬ-
ɧɨɫɬɶ ȡ ɠɢɞɤɨɫɬɢ, ɝɚɡɚ ɢɥɢ ɩɚɪɚ
GQ
. (35)
ɋɤɨɪɨɫɬɶ ɜɟɳɟɫɬɜɚ ɩɪɢ ɩɪɨɯɨɠɞɟɧɢɢ ɱɟɪɟɡ ɫɭɠɚɸɳɟɟ ɭɫɬɪɨɣɫɬɜɨ ɭɜɟɥɢ-
ɱɢɜɚɟɬɫɹ, ɷɬɨ ɫɥɟɞɭɟɬ ɢɡ ɭɫɥɨɜɢɹ ɧɟɪɚɡɪɵɜɧɨɫɬɢ ɫɬɪɭɢ
QvFvf , (36)
12
ɝɞɟ F ɢ f – ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɩɥɨɳɚɞɢ ɫɟɱɟɧɢɹ ɬɪɭɛɨɩɪɨɜɨɞɚ ɢ ɫɭɠɚɸɳɟɝɨ
ɭɫɬɪɨɣɫɬɜɚ; v
ɢ v2 – ɫɪɟɞɧɢɟ ɫɤɨɪɨɫɬɢ ɞɜɢɠɟɧɢɹ ɜɟɳɟɫɬɜɚ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ ɢ ɜ
1
ɫɭɠɚɸɳɟɦ ɭɫɬɪɨɣɫɬɜɟ.
ɍɜɟɥɢɱɟɧɢɟ ɫɤɨɪɨɫɬɢ v
ɩɨ ɫɪɚɜɧɟɧɢɸ ɫɨ ɫɤɨɪɨɫɬɶɸ v1 ɨɛɭɫɥɨɜɥɟɧɨ ɩɟɪɟɯɨ-
2
ɞɨɦ ɱɚɫɬɢ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ ɩɨɬɨɤɚ ɜ ɤɢɧɟɬɢɱɟɫɤɭɸ. ɂɡ ɭɪɚɜɧɟɧɢɹ (36)
ɫɥɟɞɭɟɬ, ɱɬɨ
34
f
f
F
, (37)
vv
21
ɬ. ɟ. ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɨɬɧɨɲɟɧɢɢ F/f ɫɤɨɪɨɫɬɶ v2 ɬɟɦ ɛɨɥɶɲɟ, ɱɟɦ ɜɵɲɟ ɫɤɨ-
ɪɨɫɬɶ
v
ɜɟɳɟɫɬɜɚ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ, ɢɥɢ ɱɟɦ ɛɨɥɶɲɟ ɪɚɫɯɨɞ. Ɉɬɧɨɲɟɧɢɟ f/F
1
ɧɚɡɵɜɚɸɬ ɦɨɞɭɥɟɦ ɫɭɠɚɸɳɟɝɨ ɭɫɬɪɨɣɫɬɜɚ ɢ ɨɛɨɡɧɚɱɚɸɬ ɱɟɪɟɡ
m
2
d
, (38)
2
F
D
m, ɬ. ɟ.
ɝɞɟ d ɢ D – ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɞɢɚɦɟɬɪɵ ɩɪɨɯɨɞɧɵɯ ɫɟɱɟɧɢɣ ɫɭɠɚɸɳɟɝɨɫɹ ɭɫɬɪɨɣɫɬɜɚ ɢ ɬɪɭɛɨɩɪɨɜɨɞɚ.
ɂɡ ɭɪɚɜɧɟɧɢɣ (37) ɢ (38) ɩɨɥɭɱɢɦ
v
1
. (39)
vm
2
ɉɪɢ ɞɜɢɠɟɧɢɢ ɠɢɞɤɨɫɬɢ ɢɥɢ ɝɚɡɚ ɩɨ ɬɪɭɛɨɩɪɨɜɨɞɭ ɤɚɠɞɨɣ ɫɤɨɪɨɫɬɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɨɩɪɟɞɟɥɟɧɧɨɟ ɫɬɚɬɢɱɟɫɤɨɟ ɞɚɜɥɟɧɢɟ
ɞɚɜɥɟɧɢɟ ɦɟɧɶɲɟ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɞɚɜɥɟɧɢɟ
ɫɟɱɟɧɢɢ
f.
P; ɱɟɦ ɜɵɲɟ ɫɤɨɪɨɫɬɶ, ɬɟɦ ɷɬɨ
P ɜ ɫɟɱɟɧɢɢ F ɜɫɟɝɞɚ ɛɨɥɶɲɟ, ɱɟɦ ɜ
ɇɚ ɪɢɫ. 2 ɩɨɤɚɡɚɧɵ ɜɢɞ ɩɨɬɨɤɚ ɢ ɢɡɦɟɧɟɧɢɟ ɞɚɜɥɟɧɢɹ ɢɡɦɟɪɹɟɦɨɣ ɫɪɟɞɵ
ɩɪɢ ɩɪɨɯɨɠɞɟɧɢɢ ɟɟ ɱɟɪɟɡ ɫɭɠɚɸɳɟɟ ɭɫɬɪɨɣɫɬɜɨ. ȿɫɥɢ ɞɨ ɫɭɠɚɸɳɟɝɨ ɭɫɬɪɨɣɫɬɜɚ ɫɬɚɬɢɱɟɫɤɨɟ ɞɚɜɥɟɧɢɟ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ ɪɚɜɧɨ
Ɋ, ɬɨ ɜ ɫɭɠɚɸɳɟɦ ɭɫɬɪɨɣɫɬɜɟ
ɨɧɨ ɪɟɡɤɨ ɩɚɞɚɟɬ, ɡɚɬɟɦ ɩɨɫɬɟɩɟɧɧɨ ɜɨɡɪɚɫɬɚɟɬ ɞɨ ɧɨɜɨɝɨ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɡɧɚɱɟɧɢɹ. ɉɪɢ ɷɬɨɦ ɞɚɜɥɟɧɢɟ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ ɡɚ ɫɭɠɚɸɳɢɦ ɭɫɬɪɨɣɫɬɜɨɦ ɧɟ ɞɨɫɬɢɝɚɟɬ ɡɧɚɱɟɧɢɹ
P, ɩɨɫɤɨɥɶɤɭ ɱɚɫɬɶ ɷɧɟɪɝɢɢ ɬɟɪɹɟɬɫɹ ɧɚ ɬɪɟɧɢɟ ɨ ɫɬɟɧɤɢ ɫɭɠɚɸ-
ɳɟɝɨ ɭɫɬɪɨɣɫɬɜɚ ɢ ɡɚɜɢɯɪɟɧɢɹ ɩɨɬɨɤɚ ɩɨɫɥɟ, ɫɭɠɚɸɳɟɝɨ ɭɫɬɪɨɣɫɬɜɚ.
Ɋɢɫ. 2. ȼɢɞ ɩɨɬɨɤɚ ɢ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɞɚɜɥɟɧɢɹ ɩɪɢ ɭɫɬɚɧɨɜɤɟ ɫɭɠɚɸɳɟɝɨ ɭɫɬɪɨɣɫɬɜɚ
ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ
35
ȼɟɥɢɱɢɧɚ ɛɟɡɜɨɡɜɪɚɬɧɵɯ ɩɨɬɟɪɶ ɪɚɜɧɚ Pɩ. ɉɟɪɟɞ ɫɭɠɟɧɢɟɦ ɞɚɜɥɟɧɢɟ ɨɤɨɥɨ
ɫɬɟɧɨɤ ɬɪɭɛɨɩɪɨɜɨɞɚ ɧɟɫɤɨɥɶɤɨ ɜɨɡɪɚɫɬɚɟɬ ɞɨ
ɬɨɤɚ ɩɟɪɟɞ ɫɭɠɚɸɳɢɦ ɭɫɬɪɨɣɫɬɜɨɦ. Ɇɢɧɢɦɚɥɶɧɨɟ ɞɚɜɥɟɧɢɟ
Pi, ɬɚɤ ɤɚɤ ɜɨɡɧɢɤɚɟɬ ɩɨɞɩɨɪ ɩɨ-
Ɋ
ɧɚɛɥɸɞɚɟɬɫɹ ɧɚ
2
ɧɟɤɨɬɨɪɨɦ ɪɚɫɫɬɨɹɧɢɢ ɨɬ ɫɭɠɚɸɳɟɝɨ ɭɫɬɪɨɣɫɬɜɚ. Ⱦɚɜɥɟɧɢɟ ɜ ɩɪɨɯɨɞɧɨɦ ɫɟɱɟɧɢɢ ɫɭɠɚɸɳɟɝɨ ɭɫɬɪɨɣɫɬɜɚ ɪɚɜɧɨ
Ɋ
. Ɋɚɡɧɨɫɬɶ ɞɚɜɥɟɧɢɣ P1–Ɋ2 ɹɜɥɹɟɬɫɹ ɩɟɪɟ-
2
ɩɚɞɨɦ, ɡɚɜɢɫɹɳɢɦ ɨɬ ɪɚɫɯɨɞɚ ɫɪɟɞɵ, ɩɪɨɬɟɤɚɸɳɟɣ ɱɟɪɟɡ ɬɪɭɛɨɩɪɨɜɨɞ. ɇɚɣɞɟɦ
ɡɚɜɢɫɢɦɨɫɬɶ ɦɟɠɞɭ ɩɟɪɟɩɚɞɨɦ ɞɚɜɥɟɧɢɹ ɧɚ ɫɭɠɚɸɳɟɦ ɭɫɬɪɨɣɫɬɜɟ ɢ ɪɚɫɯɨɞɨɦ.
ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɭɪɚɜɧɟɧɢɟɦ Ȼɟɪɧɭɥɥɢ ɞɥɹ ɫɟɱɟɧɢɣ I–I ɢ II–II ɞɥɹ ɝɨɪɢɡɨɧɬɚɥɶɧɨɝɨ ɭɱɚɫɬɤɚ ɬɪɭɛɨɩɪɨɜɨɞɚ (ɫɦ. ɪɢɫ. 2):
ɢɥɢ
22
Pv Pv
21 12
(40)
22
UU
22
PPvv
1221
UU
12
22
, (41)
2
ɝɞɟ ȡ1 ɢ ȡ2 – ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɩɥɨɬɧɨɫɬɢ ɢɡɦɟɪɹɟɦɨɣ ɫɪɟɞɵ ɜ ɫɟɱɟɧɢɹɯ I–I ɢ II–II.
Ⱦɥɹ ɧɟɫɠɢɦɚɟɦɨɣ ɠɢɞɤɨɫɬɢ
Ɋ
= Ɋ2 = P, ɬɨɝɞɚ
1
22
vv
PP
. (42)
12
21
2
ɂɡ ɭɪɚɜɧɟɧɢɹ (39) ɫɥɟɞɭɟɬ, ɱɬɨ v1 = mv2. ɉɨɞɫɬɚɜɥɹɹ ɜ ɭɪɚɜɧɟɧɢɟ (42) ɡɧɚɱɟɧɢɟ v
ɢɡ (39), ɩɨɥɭɱɢɦ
1
Ɋɟɲɚɹ ɭɪɚɜɧɟɧɢɟ (43) ɨɬɧɨɫɢɬɟɥɶɧɨ v2, ɧɚɯɨɞɢɦ
PP v
(43)
12 2
222 2
vmv m
22
U
22
v
12( )
2
2
1
m
(1 )
U
PP
12
U
2
.
. (44)
ɂɡɦɟɪɢɬɶ ɞɚɜɥɟɧɢɟ ɜ ɫɟɱɟɧɢɢ II–II ɩɪɚɤɬɢɱɟɫɤɢ ɧɟɜɨɡɦɨɠɧɨ.
ɉɟɪɟɩɚɞ ɞɚɜɥɟɧɢɣ ɨɛɵɱɧɨ ɢɡɦɟɪɹɸɬ ɧɚ ɭɱɚɫɬɤɚɯ ɬɪɭɛɨɩɪɨɜɨɞɚ ɩɟɪɟɞ ɢ ɡɚ
ɫɭɠɚɸɳɢɦ ɭɫɬɪɨɣɫɬɜɨɦ, ɝɞɟ ɩɟɪɟɩɚɞ P
ɧɟɫɤɨɥɶɤɨ ɛɨɥɶɲɟ, ɱɟɦ P
ɟɧɬ ȝ, ɩɨɥɭɱɢɦ
. ȼɜɟɞɹ ɜ ɭɪɚɜɧɟɧɢɟ (44) ɩɨɩɪɚɜɨɱɧɵɣ ɤɨɷɮɮɢɰɢ-
1–Ɋ2
v
P
2
1
m
ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ ɢ
1–Ɋ2
2( )
PP
12
2
. (45)
U
36
Ɉɩɪɟɞɟɥɟɧɢɟ ɡɧɚɱɟɧɢɹ ɩɨɩɪɚɜɨɱɧɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ ȝ ɜ ɤɚɠɞɨɦ ɤɨɧɤɪɟɬ-
P
f
ɧɨɦ ɫɥɭɱɚɟ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜɨɡɦɨɠɧɵɦ. Ɉɧ ɡɚɜɢɫɢɬ ɨɬ ɯɚɪɚɤɬɟɪɚ ɞɜɢɠɟɧɢɹ ɠɢɞɤɨɫɬɢ ɢɥɢ ɝɚɡɚ ɢ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɤɪɢɬɟɪɢɹ (ɱɢɫɥɚ) Ɋɟɣɧɨɥɶɞɫɚ (Re). Ⱦɥɹ ɪɚɡɥɢɱɧɵɯ ɬɢɩɨɪɚɡɦɟɪɨɜ ɫɭɠɚɸɳɢɯ ɭɫɬɪɨɣɫɬɜ ɧɚ ɨɫɧɨɜɟ
ɛɨɥɶɲɨɝɨ ɱɢɫɥɚ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɧɚɣɞɟɧɵ ɤɨɷɮɮɢɰɢɟɧɬɵ Ȑ, ɪɚɜɧɵɟ ɩɟɪɜɨɦɭ
ɱɥɟɧɭ ɩɪɚɜɨɣ ɱɚɫɬɢ ɪɚɜɟɧɫɬɜɚ (45), ɬ. ɟ
.
1 m
.
(46)
2
D
ɗɬɨɬ ɤɨɷɮɮɢɰɢɟɧɬ, ɭɱɢɬɵɜɚɸɳɢɣ ɪɚɫɯɨɠɞɟɧɢɟ ɦɟɠɞɭ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɢ
ɞɟɣɫɬɜɢɬɟɥɶɧɨɣ ɫɤɨɪɨɫɬɹɦɢ, ɧɚɡɵɜɚɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɪɚɫɯɨɞɚ. ɉɨɞɫɬɚɜɥɹɹ
ɡɧɚɱɟɧɢɟ ɚ ɢɡ ɭɪɚɜɧɟɧɢɹ (46) ɜ ɭɪɚɜɧɟɧɢɟ (45), ɩɨɥɭɱɢɦ
2
ɝɞɟ P
ɢ Ɋ2 – ɞɚɜɥɟɧɢɟ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ ɩɨ ɨɛɟ ɫɬɨɪɨɧɵ ɫɭɠɚɸɳɟɝɨ ɭɫɬɪɨɣɫɬɜɚ
1
, (47)
212
()vPP
D
U
ɜɛɥɢɡɢ ɧɟɝɨ.
ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (34) ɭɪɚɜɧɟɧɢɹ ɪɚɫɯɨɞɚ ɞɥɹ ɧɟɫɠɢɦɚɟɦɨɣ ɠɢɞɤɨɫɬɢ ɜ
ɨɛɴɟɦɧɵɯ ɢ ɦɚɫɫɨɜɵɯ ɟɞɢɧɢɰɚɯ ɛɭɞɭɬ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɢɦɟɬɶ ɜɢɞ (ɜ ɦ
ɢ ɤɝ/ɫ)
2
Ɂɞɟɫɶ P
D
; (48)
ɢ Ɋ2 ɢɡɦɟɪɹɸɬɫɹ ɜ ɉɚ, ȡ – ɜ ɤɝ/ɦ3, f – ɜ ɦ2.
1
. (49)
ɦ 12
()Qf PP
12
U
2( )Qf PP
DU
3
/ɫ
ȼɟɥɢɱɢɧɚ Į (ɤɨɷɮɮɢɰɢɟɧɬɚ ɪɚɫɯɨɞɚ) ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɦɨɞɭɥɹ m ɫɭɠɚɸɳɟɝɨ ɭɫɬɪɨɣɫɬɜɚ ɢ ɤɪɢɬɟɪɢɹ Ɋɟɣɧɨɥɶɞɫɚ Re
(,Re)
m
D
. (50)
ɉɪɢ ɢɡɦɟɪɟɧɢɢ ɪɚɫɯɨɞɚ ɫɠɢɦɚɟɦɵɯ ɫɪɟɞ (ɝɚɡɨɜ ɢ ɩɚɪɨɜ), ɨɫɨɛɟɧɧɨ ɩɪɢ
ɛɨɥɶɲɢɯ ɩɟɪɟɩɚɞɚɯ ɞɚɜɥɟɧɢɹ ɜ ɫɭɠɚɸɳɟɦ ɭɫɬɪɨɣɫɬɜɟ, ɧɟɨɛɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶ
ɭɦɟɧɶɲɟɧɢɟ ɩɥɨɬɧɨɫɬɢ ȡ, ɜɵɡɜɚɧɧɨɟ ɫɧɢɠɟɧɢɟɦ ɞɚɜɥɟɧɢɹ ɫɪɟɞɵ ɩɪɢ ɩɪɨɯɨɠɞɟɧɢɢ ɱɟɪɟɡ ɫɭɠɚɸɳɟɟ ɭɫɬɪɨɣɫɬɜɨ, ɩɨɷɬɨɦɭ ɦɚɫɫɨɜɵɣ ɪɚɫɯɨɞ (ɚ ɬɚɤɠɟ ɨɛɴɟɦɧɵɣ, ɨɬɧɟɫɟɧɧɵɣ ɤ ɧɚɱɚɥɶɧɨɦɭ ɡɧɚɱɟɧɢɸ ȡ) ɧɟɫɤɨɥɶɤɨ ɭɦɟɧɶɲɚɟɬɫɹ.
ȼɪɟɦɹ ɩɪɨɯɨɠɞɟɧɢɹ ɝɚɡɨɜ ɢ ɩɚɪɨɜ ɱɟɪɟɡ
ɫɭɠɚɸɳɟɟ ɭɫɬɪɨɣɫɬɜɨ ɧɚɫɬɨɥɶɤɨ
ɧɟɡɧɚɱɢɬɟɥɶɧɨ, ɱɬɨ ɢɯ ɫɠɚɬɢɟ ɢ ɩɨɫɥɟɞɭɸɳɟɟ ɪɚɫɲɢɪɟɧɢɟ ɩɪɨɢɫɯɨɞɹɬ ɩɪɚɤɬɢɱɟɫɤɢ ɛɟɡ ɨɛɦɟɧɚ ɬɟɩɥɚ ɫ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɨɣ, ɬ. ɟ. ɚɞɢɚɛɚɬɢɱɟɫɤɢ. ɉɨɷɬɨɦɭ
ɭɪɚɜɧɟɧɢɹ ɪɚɫɯɨɞɚ ɞɥɹ ɝɚɡɨɜ ɢ ɩɚɪɨɜ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɜ ɨɛɴɟɦɧɵɯ (ɦ
ɫɨɜɵɯ (ɤɝ/ɫ) ɞɨɥɹɯ ɪɚɜɧɵ
37
3
/ɫ) ɢ ɦɚɫ-
2
DH
; (51)
DH U
, (52)
ɦ 11 2
()Qf PP
12
U
1
2( )QfPP
ɝɞɟ Į – ɩɨɩɪɚɜɨɱɧɵɣ ɦɧɨɠɢɬɟɥɶ ɧɚ ɪɚɫɲɢɪɟɧɢɟ ɢɡɦɟɪɹɟɦɨɣ ɫɪɟɞɵ, ɧɚɡɵɜɚɟɦɵɣ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɪɚɫɲɢɪɟɧɢɹ;
P
– ɩɥɨɬɧɨɫɬɶ ɩɨɬɨɤɚ ɩɟɪɟɞ ɜɯɨɞɨɦ ɟɝɨ ɜ ɨɬɜɟɪɫɬɢɟ ɫɭɠɚɸɳɟɝɨ ɭɫɬɪɨɣɫɬɜɚ.
1
ɍɪɚɜɧɟɧɢɹ (51) ɢ (52) ɫɩɪɚɜɟɞɥɢɜɵ ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɫɤɨɪɨɫɬɶ ɩɨɬɨɤɚ ɜ
ɫɭɠɚɸɳɟɦ ɭɫɬɪɨɣɫɬɜɟ ɨɫɬɚɟɬɫɹ ɦɟɧɶɲɟ ɤɪɢɬɢɱɟɫɤɨɣ, ɬ. ɟ. ɦɟɧɶɲɟ ɫɤɨɪɨɫɬɢ
ɡɜɭɤɚ ɜ ɞɚɧɧɨɣ ɫɪɟɞɟ. ɍɪɚɜɧɟɧɢɹ ɪɚɫɯɨɞɚ ɞɥɹ ɝɚɡɨɜ ɢ ɩɚɪɨɜ ɨɬɥɢɱɚɸɬɫɹ ɨɬ
ɭɪɚɜɧɟɧɢɣ ɪɚɫɯɨɞɚ ɞɥɹ ɧɟɫɠɢɦɚɟɦɨɣ ɠɢɞɤɨɫɬɢ ɬɨɥɶɤɨ ɤɨɷɮɮɢɰɢɟɧɬɨɦ Į. Ʉɨɷɮɮɢɰɢɟɧɬ
ɪɚɫɲɢɪɟɧɢɹ
§·
PP
12
fm
HF
¨¸
P
2
©¹
,
ɝɞɟ Ȥ – ɩɨɤɚɡɚɬɟɥɶ ɚɞɢɚɛɚɬɵ.
ɋɬɚɧɞɚɪɬɧɵɟ ɫɭɠɚɸɳɢɟ ɭɫɬɪɨɣɫɬɜɚ
Ʉ ɫɬɚɧɞɚɪɬɧɵɦ (ɧɨɪɦɚɥɢɡɨɜɚɧɧɵɦ) ɫɭɠɚɸɳɢɦ ɭɫɬɪɨɣɫɬɜɚɦ ɨɬɧɨɫɹɬɫɹ
ɞɢɚɮɪɚɝɦɵ, ɫɨɩɥɚ, ɫɨɩɥɚ ȼɟɧɬɭɪɢ ɢ ɬɪɭɛɵ ȼɟɧɬɭɪɢ, ɩɪɢɦɟɧɹɟɦɵɟ ɞɥɹ ɢɡɦɟɪɟɧɢɹ ɪɚɫɯɨɞɚ ɜɟɳɟɫɬɜɚ ɛɟɡ ɢɧɞɢɜɢɞɭɚɥɶɧɨɣ ɝɪɚɞɭɢɪɨɜɤɢ. Ⱦɨɩɭɫɤɚɸɬɫɹ ɤ ɷɤɫɩɥɭɚɬɚɰɢɢ ɞɢɮɦɚɧɨɦɟɬɪɵ ɢ ɩɪɢɛɨɪɵ ɞɥɹ ɢɡɦɟɪɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɫɪɟɞɵ, ɫɟɪɢɣɧɨ ɜɵɩɭɫɤɚɟɦɵɟ ɩɪɨɦɵɲɥɟɧɧɨɫɬɶɸ ɢɥɢ ɨɩɵɬɧɵɦ ɩɪɨɢɡɜɨɞɫɬɜɨɦ ɢ ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɟ ɬɪɟɛɨɜɚɧɢɹɦ
ɞɟɣɫɬɜɭɸɳɢɯ ɝɨɫɭɞɚɪɫɬɜɟɧɧɵɯ ɫɬɚɧɞɚɪɬɨɜ ɢɥɢ ɩɪɨ-
ɲɟɞɲɢɟ ɝɨɫɭɞɚɪɫɬɜɟɧɧɭɸ ɦɟɬɪɨɥɨɝɢɱɟɫɤɭɸ ɚɬɬɟɫɬɚɰɢɸ.
Ɋɚɫɯɨɞɨɦɟɪɵ ɩɨɫɬɨɹɧɧɨɝɨ ɩɟɪɟɩɚɞɚ ɞɚɜɥɟɧɢɹ
ɇɚɢɛɨɥɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɵɦɢ ɩɪɢɛɨɪɚɦɢ ɝɪɭɩɩɵ ɪɚɫɯɨɞɨɦɟɪɨɜ ɩɟɪɟɦɟɧɧɨɝɨ ɩɟɪɟɩɚɞɚ ɹɜɥɹɸɬɫɹ ɪɚɫɯɨɞɨɦɟɪɵ ɫɨ ɫɜɨɛɨɞɧɨ ɩɟɪɟɦɟɳɚɸɳɢɦɫɹ ɜ ɤɨɪɩɭɫɟ
ɩɨɩɥɚɜɤɨɦ (ɪɨɬɚɦɟɬɪɵ). ɉɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ ɪɨɬɚɦɟɬɪɚ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 3.
ɉɪɨɯɨɞɹɳɢɣ ɱɟɪɟɡ ɪɨɬɚɦɟɬɪ ɫɧɢɡɭ ɩɨɬɨɤ ɠɢɞɤɨɫɬɢ ɢɥɢ ɝɚɡɚ ɩɨɞɧɢɦɚɟɬ ɩɨɩɥɚɜɨɤ ɜɜɟɪɯ ɞɨ ɬɟɯ
ɩɨɪ, ɩɨɤɚ ɪɚɫɲɢɪɹɸɳɚɹɫɹ ɤɨɥɶɰɟɜɚɹ ɳɟɥɶ ɦɟɠɞɭ ɬɟɥɨɦ ɩɨɩɥɚɜɤɚ ɢ ɫɬɟɧɤɚɦɢ ɤɨɧɭɫɧɨɣ ɬɪɭɛɤɢ ɧɟ ɞɨɫɬɢɝɧɟɬ ɬɚɤɨɣ ɜɟɥɢɱɢɧɵ, ɩɪɢ ɤɨɬɨɪɨɣ
ɞɟɣɫɬɜɭɸɳɢɟ ɧɚ ɩɨɩɥɚɜɨɤ ɫɢɥɵ ɭɪɚɜɧɨɜɟɲɢɜɚɸɬɫɹ, ɢ ɨɧ ɨɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɧɚ
ɬɨɣ ɢɥɢ ɢɧɨɣ ɜɵɫɨɬɟ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɜɟɥɢɱɢɧɵ ɪɚɫɯɨɞɚ. ɉɪɢ ɧɟɢɡɦɟɧɧɨɦ
ɪɚɫɯɨɞɟ ɩɨɩɥɚɜɨɤ ɧɟɩɨɞɜɢɠɟɧ.
38
U
U
U
U
U
Ɋɢɫ. 3. ɉɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ ɪɨɬɚɦɟɬɪɚ
ȼ ɪɚɛɨɬɚɸɳɟɦ ɪɨɬɚɦɟɬɪɟ ɩɨɩɥɚɜɨɤ ɩɨɥɧɨɫɬɶɸ ɩɨɝɪɭɠɟɧ ɜ ɢɡɦɟɪɹɟɦɭɸ
ɫɪɟɞɭ. ȼɟɫ ɩɨɝɪɭɠɟɧɧɨɝɨ ɩɨɩɥɚɜɤɚ G
1 ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ
g( )GV
, (53)
1 ɩɩ ɫ
U
ɝɞɟ Vɩ – ɨɛɴɟɦ ɩɨɩɥɚɜɤɚ; ȡɩ ɢ ȡɫ – ɩɥɨɬɧɨɫɬɢ ɩɨɩɥɚɜɤɚ ɢ ɢɡɦɟɪɹɟɦɨɣ ɫɪɟɞɵ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ; g – ɭɫɤɨɪɟɧɢɟ ɫɜɨɛɨɞɧɨɝɨ ɩɚɞɟɧɢɹ.
ɋɢɥɚ G
, ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɩɨɩɥɚɜɨɤ ɫɨ ɫɬɨɪɨɧɵ ɢɡɦɟɪɹɟɦɨɝɨ ɩɨɬɨɤɚ, ɪɚɜɧɚ
2
()GPPF , (54)
2120
ɝɞɟ P1 ɢ Ɋ2 – ɞɚɜɥɟɧɢɹ ɫɪɟɞɵ ɩɟɪɟɞ ɩɨɩɥɚɜɤɨɦ ɢ ɡɚ ɧɢɦ;
– ɧɚɢɛɨɥɶɲɟɟ ɩɨɩɟɪɟɱɧɨɟ ɫɟɱɟɧɢɟ ɩɨɩɥɚɜɤɚ.
F
0
ȼ ɫɨɫɬɨɹɧɢɢ ɪɚɜɧɨɜɟɫɢɹ (ɩɨɩɥɚɜɨɤ ɧɟɩɨɞɜɢɠɟɧ) G
ɢɥɢ
()()
Vg P P F
ɩɩ 120
PP
U
(55)
ɫ
()Vg
. (56)
12
ɩɩɫ
F
U
0
= G2, ɬ. ɪ.
1
ɂɡ ɩɨɥɭɱɟɧɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɜɢɞɧɨ, ɱɬɨ ɧɟɡɚɜɢɫɢɦɨ ɨɬ ɩɨɥɨɠɟɧɢɹ ɩɨɩɥɚɜɤɚ
ɩɟɪɟɩɚɞ ɞɚɜɥɟɧɢɹ ɧɚ ɧɟɦ ɩɨɫɬɨɹɧɟɧ ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɢɡɦɟɪɹɟɦɨɝɨ ɪɚɫɯɨɞɚ. ɗɬɨ
ɨɛɴɹɫɧɹɟɬɫɹ ɩɨɫɬɨɹɧɫɬɜɨɦ ɫɤɨɪɨɫɬɢ ɢɡɦɟɪɹɟɦɨɣ ɫɪɟɞɵ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɟɟ ɪɚɫɯɨɞɚ, ɱɬɨ ɨɛɭɫɥɨɜɥɟɧɨ ɢɡɦɟɧɟɧɢɟɦ ɩɥɨɳɚɞɢ ɤɨɥɶɰɟɜɨɝɨ ɡɚɡɨɪɚ ɦɟɠɞɭ ɩɨɩɥɚɜɤɨɦ ɢ ɬɪɭɛɤɨɣ. ɗɬɚ ɫɤɨɪɨɫɬɶ ɪɚɜɧɚ
2( ) 2 ( )PP gV
v
12 ɩɩ ɫ
. (57)
UU
ɫ 0
U
F
Ɉɛɴɟɦɧɵɣ ɪɚɫɯɨɞ ɫ ɭɱɟɬɨɦ ɤɨɷɮɮɢɰɢɟɧɬɚ ɪɚɫɯɨɞɚ Į ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ
QF
ɝɞɟ F
– ɩɥɨɳɚɞɶ ɤɨɥɶɰɟɜɨɝɨ ɡɚɡɨɪɚ ɦɟɠɞɭ ɩɨɩɥɚɜɤɨɦ ɢ ɬɪɭɛɤɨɣ.
ɤ
, (58)
2( )gV
D
ɤ
39
U
ɩɩ ɫ
F
U
ɫ 0
Ɇɚɫɫɨɜɵɣ ɪɚɫɯɨɞ
U
H
H
H
GF
. (59)
2( )gV
D
ɤ
UU
ɩɩ ɫɫ
F
0
ɂɡ ɭɪɚɜɧɟɧɢɹ (59) ɫɥɟɞɭɟɬ, ɱɬɨ ɞɥɹ ɨɩɪɟɞɟɥɟɧɧɨɣ ɢɡɦɟɪɹɟɦɨɣ ɫɪɟɞɵ ɜɫɟ
ɜɟɥɢɱɢɧɵ ɩɪɚɜɨɣ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ, ɤɪɨɦɟ F
ɧɢɟ ɦɨɠɧɨ ɩɟɪɟɩɢɫɚɬɶ ɜ ɜɢɞɟ
ɝɞɟ
ɉɨɫɤɨɥɶɤɭ ɜɵɫɨɬɚ ɩɨɞɴɟɦɚ ɩɨɩɥɚɜɤɚ ɨɩɪɟɞɟɥɹɟɬ ɜɟɥɢɱɢɧɭ ɩɥɨɳɚɞɢ F
k
FkQ , (60)
ɤ 1
1/
1
2( )
gV
DUU
ɝɞɟ
– ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ.
k
2
ɉɨɞɫɬɚɜɢɜ ɭɪɚɜɧɟɧɢɟ (60) ɜ ɭɪɚɜɧɟɧɢɟ (62), ɩɨɥɭɱɢɦ
, ɩɨɫɬɨɹɧɧɵ. ɉɨɷɬɨɦɭ ɷɬɨ ɭɪɚɜɧɟ-
ɤ
F
U
ɫ 0
ɩɩ ɫ
kF , (62)
2 ɤ
kkQ (63)
22
. (61)
ɤ
ɢɥɢ
ɝɞɟ k = k
1k2
.
kQ , (64)
ɂɡ ɭɪɚɜɧɟɧɢɹ (64) ɫɥɟɞɭɟɬ, ɱɬɨ ɡɚɜɢɫɢɦɨɫɬɶ ɩɨɥɨɠɟɧɢɹ ɩɨɩɥɚɜɤɚ ɪɨɬɚɦɟɬɪɚ ɨɬ ɢɡɦɟɪɹɟɦɨɝɨ ɪɚɫɯɨɞɚ ɥɢɧɟɣɧɚ, ɱɬɨ ɢ ɨɩɪɟɞɟɥɹɟɬ ɪɚɜɧɨɦɟɪɧɨɫɬɶ ɲɤɚɥɵ
ɪɨɬɚɦɟɬɪɚ.
Ɋɨɬɚɦɟɬɪɵ ɜɵɩɨɥɧɹɸɬ ɫɨ ɫɬɟɤɥɹɧɧɨɣ ɢɥɢ ɦɟɬɚɥɥɢɱɟɫɤɨɣ ɬɪɭɛɤɨɣ. ɇɚ
ɪɢɫ. 4 ɩɨɤɚɡɚɧɨ ɭɫɬɪɨɣɫɬɜɨ ɪɨɬɚɦɟɬɪɚ ɫɨ ɫɬɟɤɥɹɧɧɨɣ ɤɨɧɢɱɟɫɤɨɣ ɬɪɭɛɤɨɣ 3, ɡɚɤɪɟɩɥɟɧɧɨɣ ɜ ɞɜɭɯ ɦɟɬɚɥɥɢɱɟɫɤɢɯ ɝɨɥɨɜɤɚɯ 1 ɢ 6, ɫɧɚɛɠɟɧɧɵɯ ɫɚɥɶɧɢɤɚɦɢ ɢ
ɮɥɚɧɰɚɦɢ ɞɥɹ ɜɤɥɸɱɟɧɢɹ
ɜ ɜɟɪɬɢɤɚɥɶɧɵɣ ɭɱɚɫɬɨɤ ɬɪɭɛɨɩɪɨɜɨɞɚ.
Ƚɨɥɨɜɤɢ ɩɪɢɬɹɧɭɬɵ ɨɞɧɚ ɤ ɞɪɭɝɨɣ ɧɟɫɤɨɥɶɤɢɦɢ ɬɹɝɚɦɢ 4, ɨɛɪɚɡɭɸɳɢɦɢ
ɜɦɟɫɬɟ ɫ ɩɨɩɟɪɟɱɢɧɚɦɢ 5 ɡɚɳɢɬɧɭɸ ɪɟɲɟɬɤɭ ɜɨɤɪɭɝ ɫɬɟɤɥɹɧɧɨɣ ɬɪɭɛɤɢ. ȼɧɭɬɪɢ ɬɪɭɛɤɢ 3 ɫɜɨɛɨɞɧɨ ɩɟɪɟɦɟɳɚɟɬɫɹ ɩɨɩɥɚɜɨɤ 2, ɢɦɟɸɳɢɣ ɮɨɪɦɭ ɜɨɥɱɤɚ.
ȼ ɧɢɠɧɟɣ ɝɨɥɨɜɤɟ ɢɦɟɟɬɫɹ ɫɟɞɥɨ, ɧɚ ɤɨɬɨɪɨɟ ɨɩɭɫɤɚɟɬɫɹ ɩɨɩɥɚɜɨɤ ɩɪɢ ɩɪɟɤɪɚɳɟɧɢɢ ɩɨɬɨɤɚ. ȼɟɪɯɧɹɹ ɝɨɥɨɜɤɚ ɫɧɚɛɠɟɧɚ ɨɝɪɚɧɢɱɢɬɟɥɟɦ ɯɨɞɚ
ɩɨɩɥɚɜɤɚ. ɋɟɞɥɨ
ɢ ɨɝɪɚɧɢɱɢɬɟɥɶ ɯɨɞɚ ɧɟ ɩɨɡɜɨɥɹɸɬ ɩɨɩɥɚɜɤɭ ɜɵɣɬɢ ɡɚ ɩɪɟɞɟɥɵ ɫɬɟɤɥɹɧɧɨɣ
ɬɪɭɛɤɢ. ɒɤɚɥɚ 7 ɩɪɢɛɨɪɚ ɜɵɬɪɚɜɥɟɧɚ ɧɚ ɫɚɦɨɣ ɫɬɟɤɥɹɧɧɨɣ ɬɪɭɛɤɟ; ɨɬɫɱɟɬ ɜɟɞɟɬɫɹ ɩɨ ɜɟɪɯɧɟɣ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ ɩɨɩɥɚɜɤɚ.
40
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