Беспалов В.И. Системы и источники энергоснабжения
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ɝɞɟ ɚ – ɧɨɪɦɚ ɪɚɫɯɨɞɚ ɝɨɪɹɱɟɣ ɜɨɞɵ ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ
ɝ
t
= 55 °ɋ, ɤɝ
(ɥ) ɧɚ 1 ɱɟɥ. ɜ ɫɭɬɤɢ; ɡɧɚɱɟɧɢɹ ɚ ɩɪɢɜɟɞɟɧɵ ɜ ɩɪɢɥɨɠɟɧɢɢ 5; b – ɪɚɫɯɨɞ
ɝɨɪɹɱɟɣ ɜɨɞɵ ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ
ɝ
t
= 55 °ɋ, ɤɝ (ɥ) ɞɥɹ ɨɛɳɟɫɬɜɟɧɧɵɯ ɡɞɚ-
ɧɢɣ, ɨɬɧɟɫɟɧɧɵɣ ɤ ɨɞɧɨɦɭ ɠɢɬɟɥɸ ɪɚɣɨɧɚ; ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɛɨɥɟɟ ɬɨɱ-
ɧɵɯ ɞɚɧɧɵɯ ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɩɪɢɧɢɦɚɬɶ b = 25 ɤɝ (ɥ) ɧɚ 1 ɱɟɥ. ɜ ɫɭɬɤɢ;
m – ɤɨɥɢɱɟɫɬɜɨ ɥɸɞɟɣ;
ɫɪ
p
c
= 4190 Ⱦɠ/(ɤɝ·Ʉ) – ɬɟɩɥɨɟɦɤɨɫɬɶ ɜɨɞɵ;
t
ɯ
– ɬɟɦɩɟɪɚɬɭɪɚ ɯɨɥɨɞɧɨɣ ɜɨɞɵ, °ɋ; ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɞɚɧɧɵɯ ɨ ɬɟɦɩɟɪɚ-
ɬɭɪɟ ɯɨɥɨɞɧɨɣ ɜɨɞɨɩɪɨɜɨɞɧɨɣ ɜɨɞɵ ɟɟ ɩɪɢɧɢɦɚɸɬ ɜ ɨɬɨɩɢɬɟɥɶɧɵɣ ɩɟ-
ɪɢɨɞ 5 °ɋ ɢ ɜ ɥɟɬɧɢɣ ɩɟɪɢɨɞ 15 °ɋ;
ɫ
n
– ɪɚɫɱɟɬɧɚɹ ɞɥɢɬɟɥɶɧɨɫɬɶ ɩɨɞɚɱɢ
ɬɟɩɥɨɬɵ ɧɚ ɝɨɪɹɱɟɟ ɜɨɞɨɫɧɚɛɠɟɧɢɟ, ɫ/ɫɭɬ; ɩɪɢ ɤɪɭɝɥɨɫɭɬɨɱɧɨɣ ɩɨɞɚɱɟ
ɫ
n
= 24 · 3600 = 86 400 ɫ; ɤɨɷɮɮɢɰɢɟɧɬ 1,2 ɭɱɢɬɵɜɚɟɬ ɜɵɫɬɵɜɚɧɢɟ ɝɨɪɹ-
ɱɟɣ ɜɨɞɵ ɜ ɚɛɨɧɟɧɬɫɤɢɯ ɫɢɫɬɟɦɚɯ ɝɨɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ.
ɉɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɫɪɟɞɧɟɧɟɞɟɥɶɧɨɝɨ ɪɚɫɯɨɞɚ ɬɟɩɥɨɬɵ ɧɚ ɝɨɪɹɱɟɟ
ɜɨɞɨɫɧɚɛɠɟɧɢɟ ɬɨɥɶɤɨ ɠɢɥɵɯ ɡɞɚɧɢɣ ɛɟɡ ɭɱɟɬɚ ɪɚɫɯɨɞɚ ɝɨɪɹɱɟɣ ɜɨɞɵ ɜ
ɨɛɳɟɫɬɜɟɧɧɵɯ ɡɞɚɧɢɹɯ ɜ ɮɨɪɦɭɥɟ (2.12) ɩɪɢɧɢɦɚɸɬ b = 0.
Ɍɟɦɩɟɪɚɬɭɪɚ ɝɨɪɹɱɟɣ ɜɨɞɵ ɜ ɦɟɫɬɚɯ ɜɨɞɨɪɚɡɛɨɪɚ ɞɨɥɠɧɚ ɩɨɞɞɟɪ-
ɠɢɜɚɬɶɫɹ ɜ ɫɥɟɞɭɸɳɢɯ ɩɪɟɞɟɥɚɯ:
x ɜ ɨɬɤɪɵɬɵɯ
ɫɢɫɬɟɦɚɯ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ ɢ ɜ ɫɢɫɬɟɦɚɯ ɦɟɫɬɧɨɝɨ ɝɨ-
ɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ ɧɟ ɧɢɠɟ 55 ɢ ɧɟ ɜɵɲɟ 80 °ɋ;
x ɜ ɡɚɤɪɵɬɵɯ ɫɢɫɬɟɦɚɯ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ ɧɟ ɧɢɠɟ 50 ɢ ɧɟ ɜɵɲɟ 75 °ɋ.
ɇɨɪɦɵ ɪɚɫɯɨɞɚ ɝɨɪɹɱɟɣ ɜɨɞɵ, ɩɪɢɜɟɞɟɧɧɵɟ ɜ ɩɪɢɥɨɠɟɧɢɢ 5, ɨɬ-
ɧɨɫɹɬɫɹ ɤ ɬɟɦɩɟɪɚɬɭɪɟ
ɝ
t
= 55 °ɋ.
ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɞɥɹ ɛɵɬɨɜɨɝɨ ɝɨɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ ɜɨɞɵ ɫ
ɞɪɭɝɨɣ ɬɟɦɩɟɪɚɬɭɪɨɣ
ɝ
t
ɧɨɪɦɚ ɟɟ ɪɚɫɯɨɞɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɭɫɥɨɜɢɹ ɩɨɞɚ-
ɱɢ ɚɛɨɧɟɧɬɚɦ ɧɨɪɦɢɪɨɜɚɧɧɨɝɨ ɤɨɥɢɱɟɫɬɜɚ ɬɟɩɥɨɬɵ ɩɨ ɮɨɪɦɭɥɟ
ɯɝ
ɯ
55
tt
t
aa
i
i
.
(2.13)
ɉɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɪɚɫɱɟɬɧɨɣ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ ɝɨɪɹɱɟɝɨ ɜɨɞɨ-
ɫɧɚɛɠɟɧɢɹ ɪɚɣɨɧɚ ɰɟɧɬɪɚɥɢɡɨɜɚɧɧɨɝɨ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ ɋɇɢɉ 2.04.07-86
ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɭɱɢɬɵɜɚɬɶ ɧɚɝɪɭɡɤɭ ɝɨɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ ɜɫɟɯ ɫɭ-
ɳɟɫɬɜɭɸɳɢɯ ɡɞɚɧɢɣ, ɜ ɬɨɦ ɱɢɫɥɟ ɧɟ ɢɦɟɸɳɢɯ ɰɟɧɬɪɚɥɢɡɨɜɚɧɧɵɯ ɫɢɫ-
ɬɟɦ ɝɨɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ ɢɥɢ ɨɛɨɪɭɞɨɜɚɧɧɵɯ ɝɚɡɨɜɵɦɢ ɤɨɥɨɧɤɚɦɢ.
ɋɪɟɞɧɟɧɟɞɟɥɶɧɵɣ ɪɚɫɯɨɞ ɬɟɩɥɨɬɵ ɧɚ ɝɨɪɹɱɟɟ ɜɨɞɨɫɧɚɛɠɟɧɢɟ ɧɚ
ɨɞɧɨɝɨ ɠɢɬɟɥɹ ɪɚɣɨɧɚ
ɫɪ.ɧ
ɝ
q ɜɵɱɢɫɥɹɟɬɫɹ ɩɨ (2.12) ɩɪɢ m = 1. Ⱦɥɹ ɡɞɚ-
ɧɢɣ, ɧɟ ɨɛɨɪɭɞɨɜɚɧɧɵɯ ɰɟɧɬɪɚɥɢɡɨɜɚɧɧɨɣ ɫɢɫɬɟɦɨɣ ɝɨɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛ-
ɠɟɧɢɹ, a = 0.
ɋɪɟɞɧɢɣ ɪɚɫɯɨɞ ɬɟɩɥɨɬɵ ɧɚ ɛɵɬɨɜɨɟ ɝɨɪɹɱɟɟ ɜɨɞɨɫɧɚɛɠɟɧɢɟ ɡɚ
ɫɭɬɤɢ ɧɚɢɛɨɥɶɲɟɝɨ ɜɨɞɨɩɨɬɪɟɛɥɟɧɢɹ.
ɫɪ.ɧ
ɝɧ
ɫɪ.ɝ
ɝ
QQ F
(2.14)
ɝɞɟ
ɧ
F
– ɤɨɷɮɮɢɰɢɟɧɬ ɧɟɞɟɥɶɧɨɣ ɧɟɪɚɜɧɨɦɟɪɧɨɫɬɢ ɪɚɫɯɨɞɚ ɬɟɩɥɨɬɵ.
ɉɪɢ ɨɬɫɭɬɫɬɜɢɢ ɨɩɵɬɧɵɯ ɞɚɧɧɵɯ ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɩɪɢɧɢɦɚɬɶ ɞɥɹ ɠɢɥɵɯ
ɢ ɨɛɳɟɫɬɜɟɧɧɵɯ ɡɞɚɧɢɣ
ɧ
F
= 1,2, ɚ ɞɥɹ ɩɪɨɦɵɲɥɟɧɧɵɯ ɡɞɚɧɢɣ ɢ ɩɪɟɞ-
ɩɪɢɹɬɢɣ
ɧ
F
= 1.
ɇɚɝɪɭɡɤɚ ɝɨɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ ɠɢɥɵɯ ɞɨɦɨɜ ɢɦɟɟɬ, ɤɚɤ ɩɪɚɜɢ-
ɥɨ, ɜ ɪɚɛɨɱɢɟ ɞɧɢ ɩɢɤɢ ɜ ɭɬɪɟɧɧɢɟ ɢ ɜɟɱɟɪɧɢɟ ɱɚɫɵ ɢ ɩɪɨɜɚɥɵ ɜ ɞɧɟɜ-
ɧɵɟ ɢ ɩɨɡɞɧɢɟ ɧɨɱɧɵɟ ɱɚɫɵ. ȼ ɞɨɦɚɯ ɫ ɜɚɧɧɚɦɢ ɩɢɤɨɜɚɹ ɧɚɝɪɭɡɤɚ ɝɨɪɹ-
ɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ ɩɪɟɜɵɲɚɟɬ ɫɪɟɞɧɟɫɭɬɨɱɧɭɸ ɧɚɝɪɭɡɤɭ ɜ 2–3 ɪɚɡɚ. ȼ
ɜɵɯɨɞɧɵɟ ɞɧɢ ɫɭɬɨɱɧɵɣ ɝɪɚɮɢɤ ɝɨɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ ɢɦɟɟɬ ɛɨɥɟɟ
ɪɚɜɧɨɦɟɪɧɨɟ ɡɚɩɨɥɧɟɧɢɟ.
ɋɭɬɨɱɧɵɣ ɝɪɚɮɢɤ ɝɨɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ ɪɚɣɨɧɚ (ɪɢɫ. 2.2) ɢɦɟɟɬ
ɛɨɥɟɟ ɪɚɜɧɨɦɟɪɧɵɣ ɯɚɪɚɤɬɟɪ ɛɥɚɝɨɞɚɪɹ ɜɡɚɢɦɧɨɦɭ ɫɝɥɚɠɢɜɚɧɢɸ ɧɟɪɚɜ-
ɧɨɦɟɪɧɨɫɬɟɣ ɝɪɚɮɢɤɨɜ ɨɬɞɟɥɶɧɵɯ ɡɞɚɧɢɣ.
ɋɪɟɞɧɟɫɭɬɨɱɧɵɣ
ɪɚɫɯɨɞ
%
80
60
40
20
048
12
16
20 0 4
8
12 16 20
ɑɚɫɵ
ɋɪɟɞɧɟɫɭɬɨɱɧɵɣ
ɪɚɫɯɨɞ
ȼɬɨɪɧɢɤ
ɋɭɛɛɨɬɚ
Ɋɢɫ. 2.2. ɋɭɬɨɱɧɵɣ ɝɪɚɮɢɤ ɝɨɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ ɠɢɥɨɝɨ ɪɚɣɨɧɚ
Ɋɚɫɱɟɬɧɵɣ (ɦɚɤɫɢɦɚɥɶɧɨ-ɱɚɫɨɜɨɣ) ɪɚɫɯɨɞ ɬɟɩɥɨɬɵ ɧɚ ɛɵɬɨɜɨɟ ɝɨ-
ɪɹɱɟɟ ɜɨɞɨɫɧɚɛɠɟɧɢɟ, Ⱦɠ/ɫ ɢɥɢ ɤɤɚɥ/ɱ, ɪɚɜɟɧ ɫɪɟɞɧɟɱɚɫɨɜɨɦɭ ɪɚɫɯɨɞɭ
ɬɟɩɥɨɬɵ ɡɚ ɫɭɬɤɢ ɧɚɢɛɨɥɶɲɟɝɨ ɜɨɞɨɩɨɬɪɟɛɥɟɧɢɹ, ɭɦɧɨɠɟɧɧɨɦɭ ɧɚ ɤɨɷɮ-
ɮɢɰɢɟɧɬ ɫɭɬɨɱɧɨɣ ɧɟɪɚɜɧɨɦɟɪɧɨɫɬɢ:
ɫɪ.ɧ
ɝɫɧ
ɪ
ɝ
QQ FF ,
(2.15)
ɝɞɟ
ɫ
F
– ɤɨɷɮɮɢɰɢɟɧɬ ɧɟɪɚɜɧɨɦɟɪɧɨɫɬɢ ɪɚɫɯɨɞɚ ɬɟɩɥɨɬɵ ɡɚ ɫɭɬɤɢ ɧɚɢ-
ɛɨɥɶɲɟɝɨ ɜɨɞɨɩɨɬɪɟɛɥɟɧɢɹ. ɉɪɢ ɨɪɢɟɧɬɢɪɨɜɨɱɧɵɯ ɪɚɫɱɟɬɚɯ ɦɨɠɧɨ
ɩɪɢɧɢɦɚɬɶ ɞɥɹ ɝɨɪɨɞɨɜ ɢ ɧɚɫɟɥɟɧɧɵɯ ɩɭɧɤɬɨɜ
ɫ
F
= 1,7–2,0 ɞɥɹ ɩɪɨ-
ɦɵɲɥɟɧɧɵɯ ɩɪɟɞɩɪɢɹɬɢɣ
ɫ
F
= 1.
ȼ ɩɪɢɥɨɠɟɧɢɢ 5 ɩɪɢɜɟɞɟɧɵ ɧɨɪɦɵ ɪɚɫɯɨɞɚ ɝɨɪɹɱɟɣ ɜɨɞɵ: ɫɪɟɞɧɟ-
ɧɟɞɟɥɶɧɚɹ, ɫɪɟɞɧɹɹ ɡɚ ɫɭɬɤɢ ɧɚɢɛɨɥɶɲɟɝɨ ɜɨɞɨɩɨɬɪɟɛɥɟɧɢɹ, ɦɚɤɫɢɦɚɥɶ-
ɧɨ-ɱɚɫɨɜɚɹ.
Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɪɚɫɯɨɞɚ ɬɨɩɥɢɜɚ, ɪɚɡɪɚɛɨɬɤɢ ɪɟɠɢɦɨɜ ɢɫɩɨɥɶɡɨ-
ɜɚɧɢɹ ɨɛɨɪɭɞɨɜɚɧɢɹ, ɝɪɚɮɢɤɨɜ ɟɝɨ ɪɟɦɨɧɬɚ ɢ ɬ. ɩ. ɧɟɨɛɯɨɞɢɦɨ ɡɧɚɬɶ ɝɨ-
ɞɨɜɨɣ ɪɚɫɯɨɞ ɬɟɩɥɨɬɵ ɧɚ ɬɟɩɥɨɫɧɚɛɠɟɧɢɟ, ɚ ɬɚɤɠɟ ɟɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨ
ɫɟɡɨɧɚɦ (ɡɢɦɚ, ɥɟɬɨ) ɢɥɢ ɩɨ
ɨɬɞɟɥɶɧɵɦ ɦɟɫɹɰɚɦ. Ƚɨɞɨɜɨɣ ɪɚɫɯɨɞ ɬɟɩɥɨ-
ɬɵ ɩɨɬɪɟɛɢɬɟɥɹɦɢ ɪɚɣɨɧɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ:
ɝɨɞ
ɬ
ɝɨɞ
ɝ
ɝɨɞ
ɜ
ɝɨɞ
ɨ
ɝɨɞ
QQQQQ ,
(2.16)
ɝɞɟ
ɝɨɞ
ɬ
ɝɨɞ
ɝ
ɝɨɞ
ɜ
ɝɨɞ
ɨ
,,, QQQQ – ɝɨɞɨɜɵɟ ɪɚɫɯɨɞɵ ɬɟɩɥɨɬɵ ɧɚ ɨɬɨɩɥɟɧɢɟ,
ɜɟɧɬɢɥɹɰɢɸ, ɝɨɪɹɱɟɟ ɜɨɞɨɫɧɚɛɠɟɧɢɟ, ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɟ ɧɭɠɞɵ.
Ƚɨɞɨɜɵɟ ɪɚɫɯɨɞɵ ɬɟɩɥɨɬɵ ɧɚ ɨɬɞɟɥɶɧɵɟ ɜɢɞɵ ɬɟɩɥɨɜɨɝɨ ɩɨɬɪɟɛ-
ɥɟɧɢɹ ɦɨɝɭɬ ɛɵɬɶ ɪɚɫɫɱɢɬɚɧɵ ɩɨ ɫɥɟɞɭɸɳɢɦ ɮɨɪɦɭɥɚɦ [5.1].
Ƚɨɞɨɜɨɣ ɪɚɫɯɨɞ ɬɟɩɥɨɬɵ ɧɚ ɨɬɨɩɥɟɧɢɟ
»
»
¼
º
«
«
¬
ª
ɫɪ.ɨ
ɧɜ.ɪ
ɫɪ.ɨ
ɧɜ.ɞ
ɞɞɨ
ɫɪ
ɨ
ɝɨɞ
ɨ
)(
tt
tt
nnnQQ
,
(2.17)
ɝɞɟ
ɫɪ
ɨ
Q
– ɫɪɟɞɧɢɣ ɪɚɫɯɨɞ ɬɟɩɥɨɬɵ ɡɚ ɨɬɨɩɢɬɟɥɶɧɵɣ ɩɟɪɢɨɞ, Ⱦɠ/ɫ ɢɥɢ
ɤɤɚɥ/ɱ; n
ɨ
– ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɪɚɛɨɬɵ ɫɢɫɬɟɦɵ ɨɬɨɩɥɟɧɢɹ, ɫ/ɝɨɞ ɢɥɢ
ɱ/ɝɨɞ; ɞɥɹ ɠɢɥɵɯ ɢ ɨɛɳɟɫɬɜɟɧɧɵɯ ɡɞɚɧɢɣ n
ɨ
– ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɨɬɨ-
ɩɢɬɟɥɶɧɨɝɨ ɩɟɪɢɨɞɚ (ɫɦ. ɩɪɢɥɨɠɟɧɢɟ 1) (ɞɥɹ ɩɪɨɦɵɲɥɟɧɧɵɯ ɡɞɚɧɢɣ ɩɪɢ
ɧɚɥɢɱɢɢ ɜɧɭɬɪɟɧɧɢɯ ɬɟɩɥɨɜɵɞɟɥɟɧɢɣ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɪɚɛɨɬɵ ɫɢɫ-
ɬɟɦɵ ɨɬɨɩɥɟɧɢɹ ɦɟɧɶɲɟ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɢ ɨɬɨɩɢɬɟɥɶɧɨɝɨ ɩɟɪɢɨɞɚ);
n – ɞɥɢɬɟɥɶɧɨɫɬɶ ɪɚɛɨɬɵ ɞɟɠɭɪɧɨɝɨ ɨɬɨɩɥɟɧɢɹ, ɫ/ɝɨɞ ɢɥɢ ɱ/ɝɨɞ;
ɜ.ɞ
t
– ɬɟɦɩɟɪɚɬɭɪɚ ɜɧɭɬɪɟɧɧɟɝɨ ɜɨɡɞɭɯɚ ɩɪɢ ɪɚɛɨɬɟ ɞɟɠɭɪɧɨɝɨ ɨɬɨɩɥɟ-
ɧɢɹ, °ɋ.
ɋɪɟɞɧɢɣ ɪɚɫɯɨɞ ɬɟɩɥɨɬɵ ɡɚ ɨɬɨɩɢɬɟɥɶɧɵɣ ɩɟɪɢɨɞ
ɧ.ɨɜ.ɪ
ɫɪ.ɨ
ɧɜ.ɪ
ɨ
ɫɪ
ɨ
tt
tt
QQ
c
,
(2.18)
ɝɞɟ
ɫɪ.ɨ
ɧ
t
– ɫɪɟɞɧɹɹ ɬɟɦɩɟɪɚɬɭɪɚ ɨɬɨɩɢɬɟɥɶɧɨɝɨ ɩɟɪɢɨɞɚ ɞɥɹ ɠɢɥɵɯ ɢ
ɨɛɳɟɫɬɜɟɧɧɵɯ ɡɞɚɧɢɣ (ɫɦ. ɩɪɢɥɨɠɟɧɢɟ 1); ɞɥɹ ɩɪɨɦɵɲɥɟɧɧɵɯ ɡɞɚɧɢɣ
ɫɪ.ɨ
ɧ
t – ɫɪɟɞɧɹɹ ɬɟɦɩɟɪɚɬɭɪɚ ɧɚɪɭɠɧɨɝɨ ɜɨɡɞɭɯɚ ɡɚ ɩɟɪɢɨɞ ɪɚɛɨɬɵ ɨɬɨ-
ɩɥɟɧɢɹ.
Ⱦɥɹ ɠɢɥɵɯ ɢ ɨɛɳɟɫɬɜɟɧɧɵɯ ɡɞɚɧɢɣ
ɨ
Q
c
= Q', ɝɞɟ Q' – ɪɚɫɱɟɬɧɵɟ
ɬɟɩɥɨɩɨɬɟɪɢ ɡɞɚɧɢɹ ɩɪɢ ɧɚɪɭɠɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ t
ɧ.ɨ
. Ⱦɥɹ ɩɪɨɦɵɲɥɟɧɧɵɯ
ɡɞɚɧɢɣ
ɨ
Q
c
= Q'– Q
ɬ.ɜ
, ɝɞɟ Q
ɬ.ɜ
– ɜɧɭɬɪɟɧɧɢɟ ɬɟɩɥɨɜɵɞɟɥɟɧɢɹ.
ɋɪɟɞɧɹɹ ɬɟɦɩɟɪɚɬɭɪɚ ɧɚɪɭɠɧɨɝɨ ɜɨɡɞɭɯɚ ɡɚ ɥɸɛɨɣ ɢɧɬɟɪɜɚɥ ɨɬɨ-
ɩɢɬɟɥɶɧɨɝɨ ɩɟɪɢɨɞɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ ɱɚɫɬɧɨɟ ɨɬ ɞɟɥɟɧɢɹ ɚɥ-
ɝɟɛɪɚɢɱɟɫɤɨɣ ɫɭɦɦɵ ɩɪɨɢɡɜɟɞɟɧɢɣ ɫɪɟɞɧɢɯ ɬɟɦɩɟɪɚɬɭɪ ɨɬɞɟɥɶɧɵɯ ɩɟ-
ɪɢɨɞɨɜ ɷɬɨɝɨ ɢɧɬɟɪɜɚɥɚ ɧɚ ɞɥɢɬɟɥɶɧɨɫɬɶ ɷɬɢɯ ɩɟɪɢɨɞɨɜ:
m
mm
nnnn
tntntntn
t
...
...
321
ɫɪ
ɧ
ɫɪ
ɧ3
3
ɫɪ
ɧ2
2
ɫɪ
ɧ1
1
ɫɪ.ɨ
ɧ
,
(2.19)
Ⱦɥɹ ɠɢɥɵɯ ɢ ɨɛɳɟɫɬɜɟɧɧɵɯ ɡɞɚɧɢɣ n
ɞ
= 0 ɢ (2.17) ɩɪɢɧɢɦɚɟɬ ɜɢɞ
ɨ
ɫɪ
ɨ
ɝɨɞ
ɨ
nQQ ,
2.20)
Ƚɨɞɨɜɨɣ ɪɚɫɯɨɞ ɬɟɩɥɨɬɵ ɧɚ ɜɟɧɬɢɥɹɰɢɸ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
»
»
¼
º
«
«
¬
ª
»
»
¼
º
«
«
¬
ª
ɨ
ɜ
ɞ
ɜɨ
ɧ.ɨɜ.ɪ
ɫɪ.ɨ
ɧɜ.ɪ
ɜ
'
ɜ
ɝɨɞ
ɜ
1)(
n
n
nn
tt
tt
nQQ
(2.21)
ɝɞɟ
'
ɜ
Q
– ɪɚɫɱɟɬɧɵɣ ɪɚɫɯɨɞ ɬɟɩɥɨɬɵ ɧɚ ɜɟɧɬɢɥɹɰɢɸ, Ⱦɠ/ɫ ɢɥɢ ɤɤɚɥ/ɱ;
n
ɜ
– ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɨɬɨɩɢɬɟɥɶɧɨɝɨ ɩɟɪɢɨɞɚ ɫ ɬɟɦɩɟɪɚɬyɪɨɣ ɧɚɪɭɠ-
ɧɨɝɨ ɜɨɡɞɭɯɚ t
ɧ
t
ɧ.ɜ
, ɫ/ɝɨɞ ɢɥɢ ɱ/ɝɨɞ (ɩɪɢ
0 ;
ɜɧ.ɨɧ.ɜ
ntt
);
ɜ
ɞ
n
– ɞɥɢɬɟɥɶɧɨɫɬɶ ɨɬɨɩɢɬɟɥɶɧɨɝɨ ɩɟɪɢɨɞɚ, ɤɨɝɞɚ ɜɟɧɬɢɥɹɰɢɹ ɧɟ ɪɚɛɨɬɚ-
ɟɬ, ɫ/ɝɨɞ ɢɥɢ ɱ/ɝɨɞ;
ɫɪ.ɨ
ɧ
t – ɫɪɟɞɧɹɹ ɬɟɦɩɟɪɚɬɭɪɚ ɧɚɪɭɠɧɨɝɨ ɜɨɡɞɭɯɚ ɡɚ ɩɟɪɢɨɞ ɨɬ ɧɚɱɚɥɚ ɨɬɨ-
ɩɢɬɟɥɶɧɨɝɨ ɩɟɪɢɨɞɚ t
ɧ
=t
ɧ.ɤ
ɞɨ t
ɧ
=t
ɧ.ɜ.
.
Ƚɨɞɨɜɨɣ ɪɚɫɯɨɞ ɬɟɩɥɨɬɵ ɧɚ ɝɨɪɹɱɟɟ ɜɨɞɨɫɧɚɛɠɟɧɢɟ
»
»
¼
º
«
«
¬
ª
E )(
ɨɝ
ɯ.ɡɝ
ɯ.ɥɝ
ɨ
ɫɪ.ɧ
ɝ
ɝɨɞ
ɝ
nn
tt
tt
nQQ
,
(2.22)
ɝɞɟ
ɫɪ.ɧ
ɝ
Q
– ɫɪɟɞɧɟɧɟɞɟɥɶɧɵɣ ɪɚɫɯɨɞ ɬɟɩɥɨɬɵ ɧɚ ɝɨɪɹɱɟɟ ɜɨɞɨ-
ɫɧɚɛɠɟɧɢɟ, Ⱦɠ/ɫ ɢɥɢ ɤɤɚɥ/ɱ; n
ɝ
, n
ɨ
– ɞɥɢɬɟɥɶɧɨɫɬɶ ɪɚɛɨɬɵ ɫɢɫɬɟɦɵ ɝɨ-
ɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ ɢ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɨɬɨɩɢɬɟɥɶɧɨɝɨ ɩɟɪɢɨɞɚ,
ɫ/ɝɨɞ ɢɥɢ ɱ/ɝɨɞ; ȕ – ɤɨɷɮɮɢɰɢɟɧɬ, ɭɱɢɬɵɜɚɸɳɢɣ ɢɡɦɟɧɟɧɢɟ ɫɪɟɞɧɟɧɟ-
ɞɟɥɶɧɨɝɨ ɪɚɫɯɨɞɚ ɜɨɞɵ ɧɚ ɝɨɪɹɱɟɟ ɜɨɞɨɫɧɚɛɠɟɧɢɟ ɜ ɧɟɨɬɨɩɢɬɟɥɶɧɵɣ ɩɟ-
ɪɢɨɞ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɨɬɨɩɢɬɟɥɶɧɨɦɭ ɩɟɪɢɨɞɭ; ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɛɨɥɟɟ
ɬɨɱɧɵɯ ɞɚɧɧɵɯ ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɩɪɢɧɢɦɚɬɶ: ȕ = 0,8 ɞɥɹ ɠɢɥɢɳɧɨ-
ɤɨɦɦɭɧɚɥɶɧɨɝɨ ɫɟɤɬɨɪɚ ɜɫɟɯ ɪɚɣɨɧɨɜ, ɤɪɨɦɟ
ɤɭɪɨɪɬɧɵɯ ɢ ɸɠɧɵɯ ɝɨɪɨ-
ɞɨɜ; ȕ = 1,5 ɞɥɹ ɠɢɥɢɳɧɨ-ɤɨɦɦɭɧɚɥɶɧɨɝɨ ɫɟɤɬɨɪɚ ɤɭɪɨɪɬɧɵɯ ɢ ɸɠɧɵɯ
ɝɨɪɨɞɨɜ; ȕ = 1 ɞɥɹ ɩɪɨɦɵɲɥɟɧɧɵɯ ɩɪɟɞɩɪɢɹɬɢɣ.
Ƚɨɞɨɜɨɣ ɪɚɫɯɨɞ ɬɟɩɥɨɬɵ ɧɚ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɟ ɧɭɠɞɵ ɨɩɪɟɞɟɥɹɟɬɫɹ
ɧɚ ɨɫɧɨɜɟ ɝɨɞɨɜɨɝɨ ɝɪɚɮɢɤɚ ɬɟɩɥɨɜɨɝɨ ɩɨɬɪɟɛɥɟɧɢɹ. ɉɪɢɦɟɪɧɵɣ ɝɪɚɮɢɤ
ɪɚɫɯɨɞɚ ɬɟɩɥɨɬɵ ɩɨ ɦɟɫɹɰɚɦ ɩɨ ɤɚɡɚɧ ɧɚ ɪɢɫ. 2.3.
0
4
8
12
IIII
V
VII I
X
XI
10
3
ȽȾɠ/ɦɟɫ
Ɇɟɫɹɰ
Ɋɢɫ. 2.3. ɉɪɢɦɟɪɧɵɣ ɝɪɚɮɢɤ ɪɚɫɯɨɞɚ ɬɟɩɥɨɬɵ ɩɨ ɦɟɫɹɰɚɦ ɝɨɞɚ
ɉɪɢ ɩɨɫɬɪɨɟɧɢɢ ɷɬɨɝɨ ɝɪɚɮɢɤɚ ɪɚɫɯɨɞ ɬɟɩɥɨɬɵ ɧɚ ɨɬɨɩɥɟɧɢɟ ɢ
ɜɟɧɬɢɥɹɰɢɸ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɫɪɟɞɧɟɦɟɫɹɱɧɵɦ ɧɚɪɭɠɧɵɦ ɬɟɦɩɟɪɚɬɭɪɚɦ.
ȼ ɩɪɢɥɨɠɟɧɢɢ 2 ɩɪɢɜɟɞɟɧɵ ɫɪɟɞɧɟɦɟɫɹɱɧɵɟ ɬɟɦɩɟɪɚɬɭɪɵ ɧɚɪɭɠɧɨɝɨ
ɜɨɡɞɭɯɚ ɜ ɪɹɞɟ ɝɨɪɨɞɨɜ Ɋɨɫɫɢɢ ɢ ɛɵɜɲɟɝɨ ɋɋɋɊ.
2.1.5. Ƚɪɚɮɢɤ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɢ ɬɟɩɥɨɜɵɯ ɧɚɝɪɭɡɨɤ.
Ⱦɥɹ ɭɫɬɚɧɨɜɥɟɧɢɹ ɷɤɨɧɨɦɢɱɧɨɝɨ ɪɟɠɢɦɚ ɪɚɛɨɬɵ ɬɟɩɥɨɮɢɤɚɰɢɨɧ-
ɧɨɝɨ ɨɛɨɪɭɞɨɜɚɧɢɹ, ɜɵɛɨɪɚ ɧɚɢɜɵɝɨɞɧɟɣɲɢɯ ɩɚɪɚɦɟɬɪɨɜ ɬɟɩɥɨɧɨɫɢɬɟ-
ɥɹ, ɚ ɬɚɤɠɟ ɞɥɹ ɞɪɭɝɢɯ ɩɥɚɧɨɜɵɯ ɢ ɬɟɯɧɢɤɨ-ɷɤɨɧɨɦɢɱɟɫɤɢɯ ɢɫ-
ɫɥɟɞɨɜɚɧɢɣ ɧɟɨɛɯɨɞɢɦɨ ɡɧɚɬɶ ɞɥɢɬɟɥɶɧɨɫɬɶ ɪɚɛɨɬɵ ɫɢɫɬɟɦɵ ɬɟɩɥɨ-
ɫɧɚɛɠɟɧɢɹ ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɪɟɠɢɦɚɯ ɜ ɬɟɱɟɧɢɟ ɝɨɞɚ. Ⱦɥɹ ɷɬɨɣ ɰɟɥɢ ɫɬɪɨ-
ɹɬɫɹ ɝɪɚɮɢɤɢ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɢ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ (ɝɪɚɮɢɤɢ Ɋɨɫɫɚɧ-
ɞɟɪɚ).
Ɇɟɬɨɞ ɩɨɫɬɪɨɟɧɢɹ ɝɪɚɮɢɤɚ
ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɢ ɫɟɡɨɧɧɨɣ ɬɟɩɥɨ-
ɜɨɣ ɧɚɝɪɭɡɤɢ ɩɨɤɚɡɚɧ ɧɚ ɪɢɫ. 2.4.
ɉɨɫɬɪɨɟɧɢɟ ɜɟɞɟɬɫɹ ɜ ɱɟɬɵɪɟɯ ɤɜɚɞɪɚɧɬɚɯ. ȼ ɥɟɜɨɦ ɜɟɪɯɧɟɦ ɤɜɚɞ-
ɪɚɧɬɟ ɩɨɫɬɪɨɟɧɵ ɝɪɚɮɢɤɢ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɧɚɪɭɠɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ t
ɧ
, ɬɟ-
ɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ ɨɬɨɩɥɟɧɢɹ Q
ɨ
ɜɟɧɬɢɥɹɰɢɢ Q
ɜ
ɢ ɫɭɦɦɚɪɧɨɣ ɫɟɡɨɧɧɨɣ ɧɚ-
ɝɪɭɡɤɢ (Q
ɨ
+Q
ɜ
). ȼ ɧɢɠɧɟɦ ɥɟɜɨɦ ɤɜɚɞɪɚɧɬɟ ɩɪɢɜɟɞɟɧɚ ɤɪɢɜɚɹ ɞɥɢɬɟɥɶ-
ɧɨɫɬɢ ɫɬɨɹɧɢɹ n ɜ ɬɟɱɟɧɢɟ ɨɬɨɩɢɬɟɥɶɧɨɝɨ ɩɟɪɢɨɞɚ ɧɚɪɭɠɧɵɯ ɬɟɦɩɟɪɚɬɭɪ
t
ɧ
, ɪɚɜɧɵɯ ɞɚɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɢɥɢ ɧɢɠɟ. ɗɬɚ ɤɪɢɜɚɹ ɫɬɪɨɢɬɫɹ ɧɚ ɨɫɧɨɜɟ
ɞɚɧɧɵɯ npɢɥɨɠɟɧɢɹ 3.
ȼ ɧɢɠɧɟɦ ɩɪɚɜɨɦ ɤɜɚɞɪɚɧɬɟ ɩɪɨɜɟɞɟɧɚ ɩɪɹɦɚɹ ɥɢɧɢɹ ɩɨɞ ɭɝɥɨɦ
45° ɤ ɜɟɪɬɢɤɚɥɶɧɨɣ ɢ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɨɫɹɦ, ɢɫɩɨɥɶɡɭɟɦɚɹ ɞɥɹ ɩɟɪɟɧɨɫɚ
ɡɧɚɱɟɧɢɣ ɲɤɚɥɵ n ɢɡ ɧɢɠɧɟɝɨ ɥɟɜɨɝɨ ɤɜɚɞɪɚɧɬɚ ɜ ɜɟɪɯɧɢɣ ɩɪɚɜɵɣ ɤɜɚɞ-
ɪɚɧɬ. Ƚɪɚɮɢɤ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɢ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ 5 ɫɬɪɨɢɬɫɹ ɞɥɹ
ɪɚɡɧɵɯ ɧɚɪɭɠɧɵɯ ɬɟɦɩɟɪɚɬɭɪ
t
ɧ
ɩɨ ɬɨɱɤɚɦ ɩɟɪɟɫɟɱɟɧɢɹ ɲɬɪɢɯɨɜɵɯ ɥɢ-
ɧɢɣ, ɨɩɪɟɞɟɥɹɸɳɢɯ ɬɟɩɥɨɜɭɸ ɧɚɝɪɭɡɤɭ ɢ ɞɥɢɬɟɥɶɧɨɫɬɶ ɫɬɨɹɧɢɹ ɧɚɝɪɭ-
ɡɨɤ, ɪɚɜɧɵɯ ɢɥɢ ɛɨɥɶɲɟ ɞɚɧɧɨɣ.
ɉɥɨɳɚɞɶ ɩɨɞ ɤɪɢɜɨɣ 5 ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɢ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ
ɪɚɜɧɚ ɪɚɫɯɨɞɭ ɬɟɩɥɨɬɵ ɧɚ ɨɬɨɩɥɟɧɢɟ ɢ ɜɟɧɬɢɥɹɰɢɸ ɡɚ ɨɬɨɩɢɬɟɥɶɧɵɣ ɫɟ-
ɡɨɧ
ɝɨɞ
ɫ
Q . ȿɫɥɢ ɩɨ ɨɫɢ ɚɛɫɰɢɫɫ ɝɪɚɮɢɤɚ 5 ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɢ ɫɟɡɨɧɧɨɣ
ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ ɩɨɫɬɪɨɢɬɶ ɪɚɜɧɨɜɟɥɢɤɢɣ ɩɪɹɦɨɭɝɨɥɶɧɢɤ 0bcd0 ɩɥɨ-
ɳɚɞɶɸ, ɪɚɜɧɨɣ ɩɥɨɳɚɞɢ ɩɨɞ ɝɪɚɮɢɤɨɦ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɢ, ɬɨ ɜɵɫɨɬɚ
ɷɬɨɝɨ ɩɪɹɦɨɭɝɨɥɶɧɢɤɚ ɛɭɞɟɬ ɪɚɜɧɚ ɫɪɟɞɧɟɦɭ ɪɚɫɯɨɞɭ ɬɟɩɥɨɬɵ ɡɚ ɨɬɨɩɢ-
ɬɟɥɶɧɵɣ ɫɟɡɨɧ:
ɨ
ɝɨɞ
ɫ
ɫɪ
ɫ
/ nQQ ,
(2.23)
ɝ
Ɋ
1
5
ɝ
ɩ
ɭ
ɬ
ɝ
ɝ
ɞ
ɟ
Ɋ
ɢ
ɫ
1
–
5
–
ɝ
ɪ
ɭ
ɩ
ɥ
ɭ
ɝ
ɨ
ɬ
ɟ
ɩ
ɝ
ɞ
ɟ
ɟ
n
ɫ
.
2
–
Q
–
ɝ
ɪ
ɭ
ɡ
ɤ
ɨ
ɳ
ɨ
ɥ
ɶ
ɩ
ɥ
ɨ
ɟ
Q
n
ɨ
–
2
.
4
o
Q
ɪ
ɚ
ɮ
ȿ
ɤ
ɢ
ɳ
ɚ
ɞ
ɶ
ɧ
ɢ
ɨ
ɜ
ɨ
'
ɫ
Q
–
ɞ
4
.
ɉ
f
ɮ
ɢɤ
ȿ
ɫ
ɥ
ɩ
ɨ
ɞ
ɢ
ɢ
ɤ
ɨ
ɣ
Q
ɥ
ɢ
ɉ
ɨ
ɫ
(
t
f
ɩ
ɪ
ɥ
ɢ
ɨ
ɫ
ɬ
ɩ
ɨ
ɚ
ɛ
ɧ
ɚ
'
ɨ
Q
ɢ
ɬɟ
ɫ
ɬɪ
)
ɧ
t
ɪ
ɨɞ
ɧ
ɚ
ɬ
ɪ
ɨ
ɨ
ɞ
ɛ
ɭ
ɞ
ɚ
ɝ
ɪ
ɨ
ɥɶ
ɨɟ
ɧ
;
ɨɥ
ɠ
ɚ
ɨ
ɨ
ɢ
ɬ
ɝ
ɪ
ɞ
ɟ
ɬ
ɪ
ɭ
ɡ
ɜ
Q
ɧ
ɨ
ɧ
ɢ
ɟ
2
–
ɠ
ɢ
ɬ
ɫ
ɢ
ɬ
ɶ
ɪ
ɪ
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ɢ
'
ɜ
.
ɨ
ɫɬ
ɟ
ɝ
ɪ
–
Q
ɬ
ɟ
ɥ
ɢ
ɨ
ɪ
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ɜ
ɮ
ɢ
ɤ
ɪ
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ɢ
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n
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ɮ
ɜ
Q
ɥ
ɶ
ɧ
ɪ
ɞ
ɜ
ɧ
ɨ
ɤ
ɨ
ɦ
ɧ
ɨ
ɚ
ɨ
ɢ
n
ɨ
ɬ
ɨ
ɮ
ɢ
ɤ
f
ɧ
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ɬ
ɢ
ɧ
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ɦ
ɩ
ɨ
ɞ
ɥ
ɨ
ɬ
ɨ
ɨ
ɩ
ɢ
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ɚ
(
t
f
ɬ
ɢ
ɧ
ɚ
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ɢ
ɩ
ɪ
ɨ
ɥ
ɢ
ɬ
ɨ
ɩ
ɢ
ɝ
ɫ
Q
ɢ
ɬ
ɟ
ɩ
ɪ
)
ɧ
t
ɫɟ
ɡ
ɬ
ɝ
ɪ
ɢɤ
ɨ
ɞ
ɨ
ɬ
ɟ
ɥ
ɢ
ɬ
ɟ
ɝ
ɨ
ɞ
ɫ
ɟ
ɥ
ɶ
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ɞ
)
;
ɡ
ɨ
ɧ
ɪ
ɚ
ɮ
ɤ
ɢ
ɣ
ɨ
ɥ
ɥ
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ɧ
ɟ
ɥ
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Q
ɶ
ɧ
ɨ
ɞ
ɨɥ
ɠ
3
–
ɧ
ɧɨ
ɮɢ
ɣ
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ɪ
ɠ
ɢ
ɧ
ɨ
ɫ
ɶ
ɧ
ɵ
'
ɫ
Q
ɨ
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–
(
Q
ɨ
ɣ
ɬ
ɢ
ɤ
ɚ
ɪ
ɹ
ɦ
ɢ
ɬ
ɟ
ɫ
ɬ
ɢ
ɵ
ɣ
,
ɨ
ɫ
ɢ
ɬɟ
ɥ
o
Q
ɬ
ɟɩ
ɚ
5
ɦɨ
ɟ
ɥ
ɶ
ɢ
ɢ
ɫ
ɟ
ɟɡ
ɨ
ɥ
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ɧ
o
ɥɨ
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ɝ
ɶ
ɧ
ɨ
ɢ
ɫ
ɩ
ɟ
ɡ
ɨ
ɨ
ɧ
ɧ
ɨ
ɫ
ɜ
Q
ɜ
ɨ
ɣ
ɪ
ɨ
ɞ
ɝ
ɨ
ɥ
ɨ
ɫ
ɬ
ɩ
ɨ
ɥ
ɨ
ɧ:
ɚ,
ɫ
ɫ
ɬ
ɢ
)
ɜ
ɣ
ɧ
ɚ
ɞ
ɨ
ɥ
ɥ
ɶ
ɧ
ɬ
ɢ,
ɥ
ɶ
ɡ
ɫ
/
ɝ
ɢ
ɫ
ɟ
f
ɚ
ɝ
ɪ
ɥ
ɠ
ɧ
ɢ
ɤ
ɬ
ɨ
ɡ
ɨ
ɜ
ɝ
ɨ
ɞ
ɟ
ɡ
ɨ
(
t
f
ɪ
ɭɡ
ɤ
ɠ
ɢ
ɬ
ɤ
0
ɨ
ɨ
ɜ
ɚ
ɧ
ɞ
ɢ
ɨ
ɧ
ɧ
)
ɧ
t
ɤ
ɢ
ɬ
ɟ
ɥ
kl
n
ɨ
ɫ
ɧ
ɧ
ɢ
ɹ
ɥ
ɢ
ɧ
ɨ
ɣ
;
ɥ
ɶ
ɧ
n
0
ɧ
ɨ
ɜ
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ɪ
ɢ
ɱ
/
ɣ
ɬ
ɟ
4
–
ɧ
ɨ
ɫ
ɩ
ɥ
ɜ
ɚ
ɧ
ɪ
ɚɫ
/
ɝ
ɨ
ɟ
ɩ
ɥ
–
n
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ɢ
ɥ
ɨ
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ɱɟ
ɬ
ɨ
ɞ.
ɥ
ɨ
ɜ
n
ɢ
ɬ
ɳɚ
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ɣ
(
f
ɬ
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ɨ
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ɚ
(
ɧ
t
ɩ
ɥ
ɨ
ɸ
,
ɝɨ
ɣ
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ɝ
ɪ
);
ɨ
ɜ
ɨ
ɪɚ
ɩ
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ɨ
(
ɪ
ɭɡ
ɨ
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ɨ
ɧ
ɧ
(
2.
ɡ
ɤɢ
ɧ
ɚ
ɧ
ɨ
ɣ
ɦɨ
ɧ
ɨ
ɣ
2
4
ɚ
-
ɣ
ɨ
-
ɣ
4
)
Ʉɨɝɞɚ ɨɬɨɩɢɬɟɥɶɧɚɹ ɢɥɢ ɜɟɧɬɢɥɹɰɢɨɧɧɚɹ ɧɚɝɪɭɡɤɚ ɢɡɦɟɧɹɟɬɫɹ ɩɨ
ɱɚɫɚɦ ɫɭɬɨɤ ɢɥɢ ɞɧɹɦ ɧɟɞɟɥɢ (ɧɚɩɪɢɦɟɪ, ɤɨɝɞɚ ɜ ɧɟɪɚɛɨɱɢɟ ɱɚɫɵ ɩɪɨ-
ɦɵɲɥɟɧɧɵɟ ɩɪɟɞɩɪɢɹɬɢɹ ɩɟɪɟɜɨɞɹɬɫɹ ɧɚ ɞɟɠɭɪɧɨɟ ɨɬɨɩɥɟɧɢɟ ɢɥɢ ɜɟɧ-
ɬɢɥɹɰɢɹ ɩɪɨɦɵɲɥɟɧɧɵɯ ɩɪɟɞɩɪɢɹɬɢɣ ɪɚɛɨɬɚɟɬ ɧɟ ɤɪɭɝɥɨɫɭɬɨɱɧɨ), ɧɚ
ɝɪɚɮɢɤ ɧɚɧɨɫɹɬ ɬɪɢ ɤɪɢɜɵɟ ɪɚɫɯɨɞɨɜ ɬɟɩɥɨɬɵ: ɨɞɧɭ (ɨɛɵɱɧɨ ɫɩɥɨɲɧɚɹ
ɥɢɧɢɹ) ɢɫɯɨɞɹ ɢɡ ɫɪɟɞɧɟɝɨ ɩɪɢ ɞɚɧɧɨɣ ɧɚɪɭɠɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɪɚɫɯɨɞɚ
ɬɟɩɥɨɬɵ ɡɚ ɧɟɞɟɥɸ ɧɚ ɨɬɨɩɥɟɧɢɟ ɢ ɜɟɧɬɢɥɹɰɢɸ; ɞɜɟ (ɨɛɵɱɧɨ ɩɭɧɤɬɢɪ)
ɢɫɯɨɞɹ ɢɡ ɦɚɤɫɢɦɚɥɶɧɨɣ ɢ ɦɢɧɢɦɚɥɶɧɨɣ ɧɚɝɪɭɡɨɤ ɧɚ ɨɬɨɩɥɟɧɢɟ ɢ ɜɟɧ-
ɬɢɥɹɰɢɸ ɩɪɢ ɷɬɨɣ ɠɟ ɧɚɪɭɠɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ t
ɧ
. Ɍɚɤɨɟ ɩɨɫɬɪɨɟɧɢɟ ɩɨ-
ɤɚɡɚɧɨ ɧɚ ɪɢɫ. 2.5.
Ɋɢɫ. 2.5. ɂɧɬɟɝɪɚɥɶɧɵɣ ɝɪɚɮɢɤ ɫɭɦɦɚɪɧɨɣ ɧɚɝɪɭɡɤɢ ɪɚɣɨɧɚ
ɚ – Q= f(t
ɧ
); ɛ – ɝɪɚɮɢɤ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɢ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ; 1 – ɫɪɟɞɧɟɱɚɫɨɜɚɹ ɡɚ
ɧɟɞɟɥɸ ɧɚɝɪɭɡɤɚ; 2 – ɦɚɤɫɢɦɚɥɶɧɨ-ɱɚɫɨɜɚɹ ɫɭɦɦɚɪɧɚɹ ɧɚɝɪɭɡɤɚ; 3 – ɦɢɧɢɦɚɥɶɧɨ-
ɱɚɫɨɜɚɹ ɫɭɦɦɚɪɧɚɹ ɧɚɝɪɭɡɤɚ
Ƚɨɞɨɜɨɣ ɪɚɫɯɨɞ ɬɟɩɥɨɬɵ ɧɚ ɨɬɨɩɥɟɧɢɟ ɦɨɠɧɨ ɢɫɱɢɫɥɹɬɶ ɫ ɧɟ-
ɛɨɥɶɲɨɣ ɩɨɝɪɟɲɧɨɫɬɶɸ ɛɟɡ ɬɨɱɧɨɝɨ ɭɱɟɬɚ ɩɨɜɬɨɪɹɟɦɨɫɬɢ ɬɟɦɩɟɪɚɬɭɪ
ɧɚɪɭɠɧɨɝɨ ɜɨɡɞɭɯɚ ɡɚ ɨɬɨɩɢɬɟɥɶɧɵɣ ɫɟɡɨɧ, ɩɪɢɧɹɜ ɫɪɟɞɧɢɣ ɪɚɫɯɨɞ ɬɟɩ-
ɥɨɬɵ ɧɚ ɨɬɨɩɥɟɧɢɟ ɡɚ ɫɟɡɨɧ ɪɚɜɧɨɣ 50 % ɪɚɫɯɨɞɚ ɬɟɩɥɨɬɵ ɧɚ ɨɬɨɩɥɟɧɢɟ
ɩɪɢ ɪɚɫɱɟɬɧɨɣ ɧɚɪɭɠɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ
ɧ.ɨ
t
. ȿɫɥɢ ɢɡɜɟɫɬɟɧ ɝɨɞɨɜɨɣ ɪɚɫ-
ɯɨɞ ɬɟɩɥɨɬɵ ɧɚ ɨɬɨɩɥɟɧɢɟ, ɬɨ, ɡɧɚɹ ɞɥɢɬɟɥɶɧɨɫɬɶ ɨɬɨɩɢɬɟɥɶɧɨɝɨ ɫɟɡɨɧɚ,
ɥɟɝɤɨ ɨɩɪɟɞɟɥɢɬɶ ɫɪɟɞɧɢɣ ɪɚɫɯɨɞ ɬɟɩɥɨɬɵ. Ɇɚɤɫɢɦɚɥɶɧɵɣ ɪɚɫɯɨɞ ɬɟɩ-
ɥɨɬɵ ɧɚ ɨɬɨɩɥɟɧɢɟ ɦɨɠɧɨ ɞɥɹ ɨɪɢɟɧɬɢɪɨɜɨɱɧɵɯ ɪɚɫɱɟɬɨɜ ɩɪɢɧɢɦɚɬɶ
ɪɚɜɧɵɦ ɭɞɜɨɟɧɧɨɦɭ ɫɪɟɞɧɟɦɭ ɪɚɫɯɨɞɭ.
ȼ ɬɨɦ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɬɟɩɥɨɜɚɹ ɧɚɝɪɭɡɤɚ ɪɚɣɨɧɚ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɬɟ-
ɩɥɨɬɨɣ ɢɡ ɪɚɡɥɢɱɧɵɯ ɢɫɬɨɱɧɢɤɨɜ, ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɫɬɟɩɟɧɢ ɢɯ ɭɱɚɫɬɢɹ ɜ
ɩɨɤɪɵɬɢɢ ɝɨɞɨɜɨɝɨ ɪɚɫɯɨɞɚ ɬɟɩɥɨɬɵ ɭɞɨɛɧɨ ɩɨɥɶɡɨɜɚɬɶɫɹ ɢɧɬɟɝɪɚɥɶɧɵɦ
ɝɪɚɮɢɤɨɦ
),(
ɫɝɨɞ
D D f
ɩɪɟɞɫɬɚɜɥɟɧɧɨɦ ɧɚ ɪɢɫɭɧɤɟ 2.6, ɛ. Ɂɞɟɫɶ
'
ɫɫ
QQ
i
D
– ɨɬɧɨɲɟɧɢɟ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ ɢɫɬɨɱɧɢɤɚ ɤ ɪɚɫɱɟɬɧɨɣ ɧɚ-
ɝɪɭɡɤɟ ɪɚɣɨɧɚ;
ɝɨɞ
ɫ
ɝɨɞ
ɝɨɞ
QQ
i
D
– ɨɬɧɨɲɟɧɢɟ ɤɨɥɢɱɟɫɬɜɚ ɬɟɩɥɨɬɵ, ɨɬ-
ɩɭɫɤɚɟɦɨɣ ɡɚ ɨɬɨɩɢɬɟɥɶɧɵɣ ɫɟɡɨɧ ɢɫɬɨɱɧɢɤɨɦ, ɢɦɟɸɳɢɦ ɪɚɫɱɟɬɧɭɸ
ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɤ ɫɭɦɦɚɪɧɨɦɭ ɪɚɫɯɨɞɭ ɬɟɩɥɨɬɵ ɡɚ ɫɟɡɨɧ.
Ɋɢɫ. 2.6. ɩɨɫɬɪɨɟɧɢɟ ɢɧɬɟɝɪɚɥɶɧɨɝɨ ɝɪɚɮɢɤɚ ɨɬɨɩɢɬɟɥɶɧɨɣ ɧɚɝɪɭɡɤɢ
ɚ – ɝɪɚɮɢɤ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɢ ɨɬɨɩɢɬɟɥɶɧɨɣ ɧɚɝɪɭɡɤɢ
ɫ
D
= f(n); ɛ – ɢɧɬɟɝɪɚɥɶɧɵɣ
ɝɪɚɮɢɤ
ɝɨɞ ɫ
()
f
D
D
ɂɧɬɟɝɪɚɥɶɧɵɣ ɝɪɚɮɢɤ
),(
ɫɝɨɞ
D D f
ɫɬɪɨɢɬɫɹ ɧɚ ɨɫɧɨɜɟ ɝɪɚɮɢɤɚ
ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɢ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ. Ⱦɥɹ ɷɬɨɣ ɰɟɥɢ ɝɪɚɮɢɤ ɩɪɨɞɨɥ-
ɠɢɬɟɥɶɧɨɫɬɢ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ (ɪɢɫ. 2.6, ɚ) ɞɟɥɹɬ ɝɨɪɢɡɨɧɬɚɥɶɧɵɦɢ ɥɢ-
ɧɢɹɦɢ ɱɟɪɟɡ ɪɚɜɧɵɟ ɢɧɬɟɪɜɚɥɵ ɩɨ ɨɫɢ ɨɪɞɢɧɚɬ ɧɚ ɪɹɞ ɩɥɨɳɚɞɨɤ ɢ ɨɩɪɟ-
ɞɟɥɹɸɬ ɨɬɧɨɲɟɧɢɟ ɪɚɡɦɟɪɨɜ ɷɬɢɯ ɩɥɨɳɚɞɨɤ ɤɨ ɜɫɟɣ ɩɥɨɳɚɞɢ ɝɪɚɮɢɤɚ
ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɢ, ɪɚɜɧɨɣ ɪɚɫɯɨɞɭ ɬɟɩɥɨɬɵ ɡɚ ɫɟɡɨɧ. ɉɨɥɭɱɟɧɧɵɟ
ɞɚɧɧɵɟ ɧɚɧɨɫɹɬ
ɧɚ ɢɧɬɟɝɪɚɥɶɧɵɣ ɝɪɚɮɢɤ (ɪɢɫ. 2.6, ɛ).
ɂɧɬɟɝɪɚɥɶɧɵɟ ɝɪɚɮɢɤɢ ɫɟɡɨɧɧɨɣ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ ɨɛɥɚɞɚɸɬ
ɫɜɨɣɫɬɜɨɦ ɭɧɢɜɟɪɫɚɥɶɧɨɫɬɢ. ɂɧɬɟɝɪɚɥɶɧɵɣ ɝɪɚɮɢɤ, ɩɨɫɬɪɨɟɧɧɵɣ ɞɥɹ
ɨɞɧɨɝɨ ɤɚɤɨɝɨ-ɥɢɛɨ ɝɟɨɝɪɚɮɢɱɟɫɤɨɝɨ ɩɭɧɤɬɚ, ɦɨɠɟɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧ ɫ
ɞɨɫɬɚɬɨɱɧɨɣ ɞɥɹ ɩɪɚɤɬɢɱɟɫɤɢɯ ɰɟɥɟɣ ɬɨɱɧɨɫɬɶɸ ɞɥɹ ɜɫɟɝɨ ɤɥɢɦɚɬɢɱɟ-
ɫɤɨɝɨ ɩɨɹɫɚ. ɇɚɩɪɢɦɟɪ, ɩɪɢɜɟɞɟɧɧɵɣ ɧɚ ɪɢɫ. 2.6, ɛ ɢɧɬɟɝɪɚɥɶɧɵɣ ɝɪɚ-
ɮɢɤ, ɩɨɫɬɪɨɟɧɧɵɣ ɞɥɹ ɨɬɨɩɢɬɟɥɶɧɨɣ ɧɚɝɪɭɡɤɢ Ɇɨɫɤɜɵ, ɦɨɠɟɬ ɛɵɬɶ ɢɫ-
ɩɨɥɶɡɨɜɚɧ ɞɥɹ ɜɫɟɣ ɫɪɟɞɧɟɣ ɩɨɥɨɫɵ ɟɜɪɨɩɟɣɫɤɨɣ ɱɚɫɬɢ Ɋɨɫɫɢɢ.
ɋ ɩɨɦɨɳɶɸ ɢɧɬɟɝɪɚɥɶɧɨɝɨ ɝɪɚɮɢɤɚ ɥɟɝɤɨ ɭɫɬɚɧɨɜɢɬɶ ɝɨɞɨɜɭɸ ɩɨ
-
ɞɚɱɭ ɬɟɩɥɨɬɵ ɪɚɡɥɢɱɧɵɦɢ ɢɫɬɨɱɧɢɤɚɦɢ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ. ɇɚɩɪɢɦɟɪ, ɟɫ-
ɥɢ ɨɬɨɩɢɬɟɥɶɧɚɹ ɧɚɝɪɭɡɤɚ ɪɚɣɨɧɚ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɞɜɭɦɹ ɢɫɬɨɱɧɢɤɚɦɢ
ɬɟɩɥɨɬɵ, ɢɡ ɤɨɬɨɪɵɯ ɨɞɢɧ, ɛɨɥɟɟ ɷɤɨɧɨɦɢɱɧɵɣ, ɢɦɟɟɬ ɦɨɳɧɨɫɬɶ, ɪɚɜ-
ɧɭɸ 60 % ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɬɟɩɥɨɜɨɝɨ ɩɨɬɪɟɛɥɟɧɢɹ ɪɚɣɨɧɚ (Į
ɫ
= 0,6), ɚ
ɞɪɭɝɨɣ, ɦɟɧɟɟ ɷɤɨɧɨɦɢɱɧɵɣ, ɫɩɨɫɨɛɟɧ ɩɨɤɪɵɬɶ ɧɟɞɨɫɬɚɸɳɢɟ 40 % ɦɚɤ-
ɫɢɦɚɥɶɧɨɝɨ ɬɟɩɥɨɜɨɝɨ ɩɨɬɪɟɛɥɟɧɢɹ, ɬɨ, ɤɚɤ ɜɢɞɧɨ ɢɡ ɪɢɫ. 2.6, ɩɟɪɜɵɣ
ɦɨɠɟɬ ɨɛɟɫɩɟɱɢɬɶ 92 % ɝɨɞɨɜɨɝɨ ɪɚɫɯɨɞɚ ɬɟɩɥɨɬɵ (Į
ɝɨɞ
= 0,92) (ɩɥɨ-
ɳɚɞɶ 0klbc0 ɝɪɚɮɢɤɚ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɢ), ɚ ɜɬɨɪɨɣ – ɬɨɥɶɤɨ 8 % ɝɨɞɨ-
ɜɨɝɨ ɪɚɫɯɨɞɚ ɬɟɩɥɨɬɵ (ɩɥɨɳɚɞɶ kplk).
Ɋɚɫɯɨɞ ɬɟɩɥɨɬɵ ɧɚ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɟ ɧɭɠɞɵ ɢ ɝɨɪɹɱɟɟ ɜɨɞɨɫɧɚɛ-
ɠɟɧɢɟ ɜ ɨɬɥɢɱɢɟ ɨɬ ɪɚɫɯɨɞɚ ɧɚ ɨɬɨɩɥɟɧɢɟ ɢ ɜɟɧɬɢɥɹɰɢɸ ɧɟ ɹɜɥɹɟɬɫɹ
ɮɭɧɤɰɢɟɣ ɧɚɪɭɠɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ.
Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ ɝɪɚɮɢɤɚ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɢ ɫɭɦɦɚɪɧɨɣ ɧɚɝɪɭɡɤɢ
ɡɚ ɨɬɨɩɢɬɟɥɶɧɵɣ ɫɟɡɨɧ ɧɚɯɨɞɹɬ ɞɥɹ ɪɚɡɧɵɯ ɧɚɪɭɠɧɵɯ ɬɟɦɩɟɪɚɬɭɪ
ɫɭɦ-
ɦɚɪɧɭɸ ɫɪɟɞɧɟ ɧɟɞɟɥɶɧɭɸ ɧɚɝɪɭɡɤɭ ɩɨ ɜɫɟɦ ɜɢɞɚɦ ɬɟɩɥɨɜɨɝɨ ɩɨɬɪɟɛ-
ɥɟɧɢɹ:
ɫɪ.ɧ
ɬ
ɫɪ.ɧ
ɝ
ɫɪ.ɧ
ɜ
ɫɪ.ɧ
ɨ
ɫɪ.ɧ
QQQQQ
.
(2.25)
ɇɚ ɨɫɧɨɜɟ ɧɚɣɞɟɧɧɵɯ ɡɧɚɱɟɧɢɣ Q
ɫɪ.ɧ
ɞɥɹ ɪɚɡɧɵɯ ɧɚɪɭɠɧɵɯ ɬɟɦ-
ɩɟɪɚɬɭɪ ɢ ɤɥɢɦɚɬɨɥɨɝɢɱɟɫɤɢɯ ɞɚɧɧɵɯ ɨ ɞɥɢɬɟɥɶɧɨɫɬɢ ɫɬɨɹɧɢɹ ɪɚɡɥɢɱ-
ɧɵɯ ɧɚɪɭɠɧɵɯ ɬɟɦɩɟɪɚɬɭɪ ɫɬɪɨɢɬɫɹ ɩɨ ɢɡɥɨɠɟɧɧɨɣ ɜɵɲɟ ɦɟɬɨɞɢɤɟ
ɝɪɚɮɢɤ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɢ ɫɭɦɦɚɪɧɨɣ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ ɡɚ ɨɬɨɩɢ-
ɬɟɥɶɧɵɣ ɫɟɡɨɧ.
ȼ ɥɟɬɧɢɣ ɩɟɪɢɨɞ ɨɫɧɨɜɧɵɦ ɜɢɞɨɦ ɬɟɩɥɨɜɨɝɨ ɩɨɬɪɟɛɥɟɧɢɹ ɹɜɥɹɸɬ-
ɫɹ ɬɟɯɧɨɥɨɝɢɱɟɫɤɚɹ ɧɚɝɪɭɡɤɚ ɢ ɝɨɪɹɱɟɟ ɜɨɞɨɫɧɚɛɠɟɧɢɟ. ɋɪɟɞɧɟ ɧɟɞɟɥɶ-
ɧɨɟ ɡɧɚɱɟɧɢɟ ɷɬɨɣ ɧɚɝɪɭɡɤɢ ɩɨɫɬɨɹɧɧɨ.
ɋɪɟɞɧɟ ɧɟɞɟɥɶɧɚɹ ɧɚɝɪɭɡɤɚ ɝɨɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ ɪɚɣɨɧɚ ɜ ɥɟɬ-
ɧɢɣ ɩɟɪɢɨɞ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ:
,
ɨɝɨɞ
ɪɨɝɨɞ
ɡ
ɯɝ
ɥ
ɯɝ
ɥ
ɝ
ɫɪ.ɧ
ɝ.ɡ
ɫɪ.ɧ
ɝ.ɥ
nn
nnn
tt
tt
QQ
M
(2.26)