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Файл:Основы трансформации теплоты. Учебное пособие
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ȼ ɫɥɭɱɚɟ ɪɟɝɟɧɟɪɚɬɢɜɧɨɝɨ ɰɢɤɥɚ (ɫɦ. ɪɢɫ. 3.4) ɬɨɱɤɚ 3 ɨɩɪɟɞɟɥɢɬɫɹ ɢɡ
ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ ɪɟɝɟɧɟɪɚɬɢɜɧɨɝɨ ɬɟɩɥɨɨɛɦɟɧɧɢɤɚ:
h1 – h1' = h3' – h3,
ɝɞɟ ɬɨɱɤɢ 1' ɢ 1 ɡɚɞɚɸɬɫɹ. Ɍɨɱɤɚ 1' ɜɵɛɢɪɚɟɬɫɹ, ɤɚɤ ɩɪɚɜɢɥɨ, ɧɚ ɩɪɚɜɨɣ ɩɨɝɪɚɧɢɱɧɨɣ ɤɪɢɜɨɣ ɥɢɛɨ ɧɚ ɢɡɨɛɚɪɟ ɪ
ɫ ɩɟɪɟɝɪɟɜɨɦ ɧɚ 23 °ɋ.
0
ɍɞɟɥɶɧɚɹ ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ q0 = h1' – h4. Ⱦɚɥɶɧɟɣɲɢɣ ɪɚɫɱɟɬ
ɪɟɝɟɧɟɪɚɬɢɜɧɨɝɨ ɰɢɤɥɚ ɧɢɱɟɦ ɧɟ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɪɚɫɱɟɬɚ ɨɛɵɱɧɨɝɨ ɰɢɤɥɚ.
Ʉɨɧɬɪɨɥɶɧɚɹ ɡɚɞɚɱɚ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ
Ɂɚɞɚɱɚ 3.2. ȼɵɩɨɥɧɢɬɶ ɬɟɩɥɨɜɨɣ ɪɚɫɱɟɬ ɨɞɧɨɫɬɭɩɟɧɱɚɬɨɣ ɩɚɪɨɜɨɣ ɯɨ-
ɥɨɞɢɥɶɧɨɣ ɦɚɲɢɧɵ (ɪɢɫ. 3.6) (ɨɩɪɟɞɟɥɢɬɶ ɭɞɟɥɶɧɭɸ ɦɚɫɫɨɜɭɸ ɢ ɨɛɴɟɦɧɭɸ ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ, ɭɞɟɥɶɧɭɸ ɪɚɛɨɬɭ ɤɨɦɩɪɟɫɫɨɪɚ ɢ ɬɟɩɥɨɜɭɸ ɧɚɝɪɭɡɤɭ ɧɚ ɤɨɧɞɟɧɫɚɬɨɪ, ɦɚɫɫɨɜɵɣ ɪɚɫɯɨɞ ɢ ɞɟɣɫɬɜɢɬɟɥɶɧɵɣ ɨɛɴɟɦ
ɩɚɪɚ ɪɚɛɨɱɟɝɨ ɜɟɳɟɫɬɜɚ, ɨɛɪɚɡɨɜɚɜɲɟɝɨɫɹ ɜ ɢɫɩɚɪɢɬɟɥɟ, ɬɟɨɪɟɬɢɱɟɫɤɭɸ
(ɢɡɨɷɧɬɪɨɩɧɭɸ) ɢ ɞɟɣɫɬɜɢɬɟɥɶɧɭɸ ɪɚɛɨɬɚ ɤɨɦɩɪɟɫɫɨɪɚ, ɬɟɨɪɟɬɢɱɟɫɤɭɸ
ɨɛɴɟɦɧɭɸ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɤɨɦɩɪɟɫɫɨɪɚ, ɯɨɥɨɞɢɥɶɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ)
ɩɨ
ɫɥɟɞɭɸɳɢɦ ɢɫɯɨɞɧɵɦ ɞɚɧɧɵɦ:
ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ Q
ɬɟɦɩɟɪɚɬɭɪɚ ɤɢɩɟɧɢɹ t
;
0
ɬɟɦɩɟɪɚɬɭɪɚ ɤɨɧɞɟɧɫɚɰɢɢ t
;
0
;
Ʉ
ɪɚɛɨɱɟɟ ɜɟɳɟɫɬɜɨ R-22.
ȼɚɪɢɚɧɬɵ ɤɨɧɬɪɨɥɶɧɵɯ ɡɚɞɚɧɢɣ ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥɢɰɟ 3.3.
Ʉɞ
3
2
p
3
ɪ
, Ɍ
Ʉ
Ʉ
2
Ⱦɜ
4
ɂ
Ʉ
ɪ0, Ɍ
0
4
1
ɚ ɛ
Ɋɢɫ. 3.6. ɉɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ (ɚ) ɢ ɰɢɤɥ ɜ ɞɢɚɝɪɚɦɦɟɪ-h (ɛ)
ɨɞɧɨɫɬɭɩɟɧɱɚɬɨɣ ɉɏɆ ɫ ɞɪɨɫɫɟɥɶɧɵɦ ɜɟɧɬɢɥɟɦ
41
1
Ɍ
Ɉɋ
h
Ɍɚɛɥɢɰɚ 3.3
ɉɚɪɚɦɟɬɪɵ
Q0, ɤȼɬ 40 50 60 70 80 90 100 40 50 60 70 80
t0, °C
tɄ, °C 40 35 30 25 20 40 35 30 25 20 40 35
1 2 3 4 5 6 7 8 9 10 11 12
40 35 30 25 20 15 10 5
ȼɚɪɢɚɧɬɵ ɤɨɧɬɪɨɥɶɧɵɯ ɡɚɞɚɧɢɣ
0 0
5 10
ɉɚɪɚɦɟɬɪɵ
Q0, ɤȼɬ 90 100 40 50 60 70 80 90 100 40 50 60
t0, °C
tɄ, °C 30 25 20 40 35 30 25 20 40 35 30 25
13 14 15 16 17 18 19 20 21 22 23 24
15 20 25 30 35
ȼɚɪɢɚɧɬɵ ɤɨɧɬɪɨɥɶɧɵɯ ɡɚɞɚɧɢɣ
0
5 10 15 20 25 30
Ʉɨɧɬɪɨɥɶɧɚɹ ɡɚɞɚɱɚ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ
Ɂɚɞɚɱɚ 3.3. ȼɵɩɨɥɧɢɬɶ ɬɟɩɥɨɜɨɣ ɪɚɫɱɟɬ ɨɞɧɨɫɬɭɩɟɧɱɚɬɨɣ ɩɚɪɨɜɨɣ ɯɨ-
ɥɨɞɢɥɶɧɨɣ ɦɚɲɢɧɵ ɫ ɪɟɝɟɧɟɪɚɬɢɜɧɵɦ ɬɟɩɥɨɨɛɦɟɧɧɢɤɨɦ (ɪɢɫ. 3.7) ɩɨ ɫɥɟɞɭɸɳɢɦ ɢɫɯɨɞɧɵɦ ɞɚɧɧɵɦ:
– ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ Q
– ɬɟɦɩɟɪɚɬɭɪɚ ɤɢɩɟɧɢɹ t
;
0
– ɬɟɦɩɟɪɚɬɭɪɚ ɤɨɧɞɟɧɫɚɰɢɢ t
;
0
;
Ʉ
– ɪɚɛɨɱɟɟ ɜɟɳɟɫɬɜɨ R-22.
ɉɟɪɟɨɯɥɚɠɞɟɧɢɟ ɠɢɞɤɨɫɬɢ ɩɪɢɧɹɬɶ ɪɚɜɧɵɦ 5 °ɋ, ɩɟɪɟɝɪɟɜ ɩɚɪɚ – 20 °ɋ.
ɉɚɪɚɦɟɬɪɵ t
, tɄ ɢ Q0 ɜɡɹɬɶ ɩɨ ɡɚɞɚɧɧɨɦɭ ɜɚɪɢɚɧɬɭ ɢɡ ɬɚɛɥɢɰɵ 3.3.
0
ɪ
Ʉ
ɪ0, Ɍ
, Ɍ
2
Ʉ
0
1'
2'
1
h
ɊɌɈ
Ʉɞ
Ʉ
p
3'
3
4
3'
3
Ⱦɜ
4
1'
ɂ
2
1
ɚ ɛ
Ɋɢɫ. 3.7. ɉɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ (ɚ) ɢ ɰɢɤɥ ɜ ɪh-ɞɢɚɝɪɚɦɦɟ (ɛ)
ɨɞɧɨɫɬɭɩɟɧɱɚɬɨɣ ɉɏɆ ɫ ɪɟɝɟɧɟɪɚɰɢɟɣ
42
4. ɊȺȻɈɑɂɃ ɉɊɈɐȿɋɋ ȼ ɄɈɆɉɊȿɋɋɈɊȿ
4.1. ɉɪɢɧɰɢɩ ɪɚɛɨɬɵ ɩɨɪɲɧɟɜɨɝɨ ɤɨɦɩɪɟɫɫɨɪɚ
Ʉɨɦɩɪɟɫɫɨɪ – ɨɞɢɧ ɢɡ ɨɫɧɨɜɧɵɯ ɷɥɟɦɟɧɬɨɜ ɯɨɥɨɞɢɥɶɧɨɣ ɦɚɲɢɧɵ
(ɪɢɫ. 4.1). Ɉɧ ɩɪɟɞɧɚɡɧɚɱɟɧ ɞɥɹ ɫɠɚɬɢɹ ɯɨɥɨɞɢɥɶɧɨɝɨ ɚɝɟɧɬɚ ɨɬ ɞɚɜɥɟɧɢɹ
ɤɢɩɟɧɢɹ ɪ
ɞɨ ɞɚɜɥɟɧɢɹ ɤɨɧɞɟɧɫɚɰɢɢ ɪɄ, ɨɬɫɚɫɵɜɚɧɢɹ ɩɚɪɚ ɢɡ ɢɫɩɚɪɢɬɟɥɹ,
0
ɱɬɨ ɨɛɟɫɩɟɱɢɜɚɟɬ ɩɨɧɢɠɟɧɧɨɟ ɞɚɜɥɟɧɢɟ ɢ ɬɟɦɩɟɪɚɬɭɪɭ ɤɢɩɟɧɢɹ ɯɨɥɨɞɢɥɶɧɨɝɨ ɚɝɟɧɬɚ, ɢ ɧɚɝɧɟɬɚɧɢɹ ɩɚɪɚ ɜ ɤɨɧɞɟɧɫɚɬɨɪ.
ɉɨɪɲɧɟɜɨɣ ɤɨɦɩɪɟɫɫɨɪ ɫɨɫɬɨɢɬ ɢɡ
ɰɢɥɢɧɞɪɚ 1, ɜ ɤɨɬɨɪɨɦ ɜɨɡɜɪɚɬɧɨ-ɩɨɫ-
ȼ ɤɨɧɞɟɧɫɚɬɨɪ
5
ɪ
1 2 3
Ʉ
ɬɭɩɚɬɟɥɶɧɨ ɞɜɢɠɟɬɫɹ ɩɨɪɲɟɧɶ 2. ɉɨɪɲɟɧɶ ɩɪɢɜɨɞɢɬɫɹ ɜ ɞɟɣɫɬɜɢɟ ɨɬ ɜɚɥɚ ɩɨɫɪɟɞɫɬɜɨɦ ɤɪɢɜɨɲɢɩɧɨ-ɲɚɬɭɧɧɨɝɨ ɦɟɯɚ-
ɪ
ɧɢɡɦɚ 3. ȼɚɥ ɜɪɚɳɚɟɬɫɹ ɨɬ
ɞɜɢɝɚɬɟɥɹ.
ȼ ɤɪɵɲɤɟ ɰɢɥɢɧɞɪɚ ɪɚɫɩɨɥɨɠɟɧɵ ɜɫɚɫɵɜɚɸɳɢɣ 4 ɢ ɧɚɝɧɟɬɚɬɟɥɶɧɵɣ 5 ɤɥɚɩɚɧɵ.
Ɋɚɛɨɱɢɣ ɩɪɨɰɟɫɫ ɜ ɤɨɦɩɪɟɫɫɨɪɟ ɫɨɜɟɪɲɚɟɬɫɹ ɡɚ ɨɞɢɧ ɨɛɨɪɨɬ ɜɚɥɚ (ɡɚ ɞɜɚ
ɯɨɞɚ ɩɨɪɲɧɹ). ɉɪɢ ɞɜɢɠɟɧɢɢ ɩɨɪɲɧɹ
Ɋɢɫ. 4.1. ɋɯɟɦɚ ɩɨɪɲɧɟɜɨɝɨ
4
0
ɂɡ ɢɫɩɚɪɢɬɟɥɹ
ɤɨɦɩɪɟɫɫɨɪɚ
ɫɥɟɜɚ ɧɚɩɪɚɜɨ ɩɚɪ ɜɫɚɫɵɜɚɟɬɫɹ ɜ ɰɢɥɢɧɞɪ ɱɟɪɟɡ ɤɥɚɩɚɧ 4 ɢɡ ɢɫɩɚɪɢɬɟɥɹ,
ɩɪɢ ɞɜɢɠɟɧɢɢ ɩɨɪɲɧɹ ɫɩɪɚɜɚ ɧɚɥɟɜɨ ɩɚɪɵ ɫɠɢɦɚɸɬɫɹ ɢ ɱɟɪɟɡ ɧɚɝɧɟɬɚɬɟɥɶɧɵɣ
ɤɥɚɩɚɧ 5 ɜɵɬɚɥɤɢɜɚɸɬɫɹ ɜ ɤɨɧɞɟɧɫɚɬɨɪ. Ⱦɚɥɟɟ ɤɨɦɩɪɟɫɫɨɪ ɜɧɨɜɶ
ɦɨɠɟɬ ɡɚɫɚɫɵɜɚɬɶ ɩɚɪɵ, ɢ ɭɤɚɡɚɧɧɵɟ ɩɪɨɰɟɫɫɵ ɩɨɜɬɨɪɹɸɬɫɹ. Ɉɬɫɨɫ ɩɚɪɚ
ɢɡ ɢɫɩɚɪɢɬɟɥɹ, ɨɛɪɚɡɨɜɚɜɲɟɝɨɫɹ ɜ ɧɟɦ ɩɪɢ ɜɨɫɩɪɢɹɬɢɢ ɬɟɩɥɨɬɵ ɨɬ ɨɛɴɟɤɬɚ
ɨɯɥɚɠɞɟɧɢɹ, ɹɜɥɹɟɬɫɹ ɨɛɹɡɚɬɟɥɶɧɵɦ ɭɫɥɨɜɢɟɦ ɞɥɹ ɫɨɡɞɚɧɢɹ ɡɚɞɚɧɧɨɝɨ ɩɨɧɢɠɟɧɧɨɝɨ ɞɚɜɥɟɧɢɹ ɢ ɬɟɦɩɟɪɚɬɭɪɵ ɤɢɩɟɧɢɹ ɜ ɢɫɩɚɪɢɬɟɥɟ.
ɉɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɯɨɥɨɞɢɥɶɧɨɝɨ ɤɨɦɩɪɟɫɫɨɪɚ ɜɵɪɚɠɚɟɬɫɹ ɦɚɫɫɨɣ G,
ɨɛɴɟɦɨɦ V ɡɚɫɚɫɵɜɚɟɦɨɝɨ
ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ ɩɚɪɚ ɢ ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶɸ ɦɚɲɢɧɵ Q0, ɬ. ɟ. ɤɨɥɢɱɟɫɬɜɨɦ ɬɟɩɥɨɬɵ, ɜɨɫɩɪɢɧɹɬɨɣ ɨɬ ɨɯɥɚɠɞɚɟɦɨɣ ɫɪɟɞɵ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ, ɤɨɬɨɪɨɟ ɜɵɡɜɚɥɨ ɨɛɪɚɡɨɜɚɧɢɟ ɩɚɪɚ.
Ɇɚɫɫɚ ɡɚɫɚɫɵɜɚɟɦɨɝɨ ɤɨɦɩɪɟɫɫɨɪɨɦ ɩɚɪɚ G ɩɪɢ ɡɚɞɚɧɧɨɣ ɯɨɥɨɞɨɩɪɨ-
ɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ Q
ɢ ɦɚɫɫɨɜɨɣ ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ q0 ɨɩɪɟɞɟɥɹɟɬ-
0
ɫɹ ɩɨ ɮɨɪɦɭɥɟ:
G = Q
/ q0.
0
43
ɪ
ɪ
ɪ
ɪ
Ʉ
ɛ
ɚ
ɪ
0
2
1
V
h
V
ɚ
ɪ
3
ɪ
Ʉ
2
ɪ
0
ɋ
4
ɋ
1
V
1
V
h
1
V
ɛ
ɪ
3
ɪ
2
ɪ
H
ɪ
Ʉ
ɪ
0
ɪ
ȼɋ
ɪ
1
4
ɋ
1
ɋ
2
'
Ʉ
1'
'
V
2
V
h
1
ɋ
2
ɜ
0
V
Ɋɢɫ. 4.2. Ɋɚɛɨɱɢɣ ɩɪɨɰɟɫɫ ɤɨɦɩɪɟɫɫɨɪɚ:
ɚ – ɬɟɨɪɟɬɢɱɟɫɤɢɣ; ɛ – ɫ ɦɟɪɬɜɵɦ ɩɪɨɫɬɪɚɧɫɬɜɨɦ;
ɜ – ɞɟɣɫɬɜɢɬɟɥɶɧɵɣ
44
Ɉɛɴɟɦ ɡɚɫɚɫɵɜɚɟɦɨɝɨ ɤɨɦɩɪɟɫɫɨɪɨɦ ɩɚɪɚ V ɩɪɢ ɭɞɟɥɶɧɨɦ ɨɛɴɟɦɟ
X
1
ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɦ ɫɨɫɬɨɹɧɢɸ ɩɚɪɚ ɜɨ ɜɫɚɫɵɜɚɸɳɟɦ ɩɚɬɪɭɛɤɟ ɤɨɦɩɪɟɫɫɨɪɚ:
V = G
X
.
1
ɏɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɤɨɦɩɪɟɫɫɨɪɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ
Q0 = G q0 = V q0 /
ɝɞɟ qX ɭɞɟɥɶɧɚɹ ɨɛɴɟɦɧɚɹ ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ.
X
= V qX,
1
ɏɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɤɨɦɩɪɟɫɫɨɪɚ ɡɚɜɢɫɢɬ ɧɟ ɬɨɥɶɤɨ ɨɬ ɦɚɫɫɵ
ɢ ɨɛɴɟɦɚ, ɧɨ ɢ ɨɬ ɩɚɪɚɦɟɬɪɨɜ ɩɚɪɚ, ɤɨɬɨɪɵɣ ɨɧ ɡɚɫɚɫɵɜɚɟɬ.
ȼ ɬɟɨɪɟɬɢɱɟɫɤɨɦ ɪɚɛɨɱɟɦ ɩɪɨɰɟɫɫɟ ɤɨɦɩɪɟɫɫɨɪɚ (ɪɢɫ. 4.2, ɚ) ɥɢɧɢɹ ɚ1 ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɜɫɚɫɵɜɚɧɢɟ ɩɚɪɚ, ɩɪɨɬɟɤɚɸɳɟɝɨ ɩɪɢ ɪ
ɚɞɢɚɛɚɬɧɨɟ ɫɠɚɬɢɟ; 2ɛ – ɜɵɬɚɥɤɢɜɚɧɢɟ ɩɚɪɚ ɜ ɤɨɦɩɪɟɫɫɨɪ ɩɪɢ ɪ
Ɉɛɴɟɦ ɩɚɪɚ, ɡɚɫɚɫɵɜɚɟɦɨɝɨ ɤɨɦɩɪɟɫɫɨɪɨɦ, ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɨɛɴɟɦɭ V
= const; 12
0
= const.
Ʉ
, ɨɩɢ-
h
ɫɵɜɚɟɦɨɦɭ ɩɨɪɲɧɟɦ.
ȼ ɞɟɣɫɬɜɢɬɟɥɶɧɨɦ ɩɪɨɰɟɫɫɟ ɤɨɦɩɪɟɫɫɨɪɚ ɢɦɟɸɬɫɹ ɩɨɬɟɪɢ: ɨɛɴɟɦɧɵɟ,
ɫɧɢɠɚɸɳɢɟ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɤɨɦɩɪɟɫɫɨɪɚ, ɢ ɷɧɟɪɝɟɬɢɱɟɫɤɢɟ, ɭɜɟɥɢɱɢɜɚɸɳɢɟ ɪɚɫɯɨɞ ɷɧɟɪɝɢɢ. Ʉ ɨɛɴɟɦɧɵɦ ɨɬɧɨɫɹɬɫɹ ɩɨɬɟɪɢ, ɜɵɡɜɚɧɧɵɟ ɧɚɥɢɱɢɟɦ ɦɟɪɬɜɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɞɟɩɪɟɫɫɢɟɣ ɩɪɢ ɜɫɚɫɵɜɚɧɢɢ ɢ ɧɚɝɧɟɬɚɧɢɢ,
ɩɨɞɨɝɪɟɜɨɦ ɩɚɪɚ ɨɬ ɫɬɟɧɨɤ ɰɢɥɢɧɞɪɚ ɩɪɢ ɜɫɚɫɵɜɚɧɢɢ ɢ ɭɬɟɱɤɢ ɱɟɪɟɡ ɧɟɩɥɨɬɧɨɫɬɢ ɜ ɤɥɚɩɚɧɚɯ ɢ ɩɨɪɲɧɟɜɵɯ ɤɨɥɶɰɚɯ.
Ɇɟɪɬɜɨɟ ɩɪɨɫɬɪɚɧɫɬɜɨ. Ɂɚɡɨɪ ɋ (ɪɢɫ. 4.2, ɛ) ɦɟɠɞɭ ɞɧɢɳɟɦ ɩɨɪɲɧɹ ɜ
ɜɟɪɯɧɟɣ ɦɟɪɬɜɨɣ ɬɨɱɤɟ ɢ ɤɥɚɩɚɧɧɨɣ ɩɥɢɬɨɣ ɧɚɡɵɜɚɟɬɫɹ ɥɢɧɟɣɧɨɟ ɦɟɪɬɜɨɟ
ɩɪɨɫɬɪɚɧɫɬɜɨ. ɗɬɨɬ ɡɚɡɨɪ ɩɪɟɞɭɫɦɚɬɪɢɜɚɟɬɫɹ ɞɥɹ ɤɨɦɩɟɧɫɚɰɢɢ ɬɟɦɩɟɪɚɬɭɪɧɨɝɨ ɪɚɫɲɢɪɟɧɢɹ ɞɟɬɚɥɟɣ ɤɨɦɩɪɟɫɫɨɪɚ ɜ ɩɪɨɰɟɫɫɟ ɟɝɨ ɪɚɛɨɬɵ.
ɉɪɨɫɬɪɚɧɫɬɜɨ ɦɟɠɞɭ ɩɨɪɲɧɟɦ ɢ ɤɪɵɲɤɨɣ ɰɢɥɢɧɞɪɚ, ɜɤɥɸɱɚɹ ɳɟɥɢ ɞɨ
ɩɥɚɫɬɢɧ ɤɥɚɩɚɧɨɜ, ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɨɛɴɟɦɧɨɟ ɦɟɪɬɜɨɟ ɩɪɨɫɬɪɚɧɫɬɜɨ.
Ɋɚɛɨɱɢɣ
ɩɪɨɰɟɫɫ ɤɨɦɩɪɟɫɫɨɪɚ ɫ ɦɟɪɬɜɵɦ ɩɪɨɫɬɪɚɧɫɬɜɨɦ ɩɪɟɞɫɬɚɜɥɟɧ
ɧɚ ɪɢɫɭɧɤɟ 4.2, ɛ. ɉɪɨɰɟɫɫ ɜɵɬɚɥɤɢɜɚɧɢɹ ɡɚɤɚɧɱɢɜɚɟɬɫɹ ɜ ɬɨɱɤɟ 3, ɢ ɜ
ɦɟɪɬɜɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ ɨɫɬɚɟɬɫɹ ɧɟɤɨɬɨɪɨɟ ɤɨɥɢɱɟɫɬɜɨ ɫɠɚɬɨɝɨ ɩɚɪɚ ɩɪɢ
ɞɚɜɥɟɧɢɢ ɪ
. ɉɪɢ ɨɛɪɚɬɧɨɦ ɞɜɢɠɟɧɢɢ ɩɨɪɲɧɹ ɩɪɨɰɟɫɫ ɜɫɚɫɵɜɚɧɢɹ ɧɚɱɢ-
Ʉ
ɧɚɟɬɫɹ ɩɨɫɥɟ ɬɨɝɨ, ɤɚɤ ɫɠɚɬɵɣ ɩɚɪ, ɨɫɬɚɜɲɢɣɫɹ ɜ ɦɟɪɬɜɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ,
ɪɚɫɲɢɪɢɬɫɹ (ɩɪɨɰɟɫɫ 34) ɢ ɩɨɧɢɡɢɬ ɫɜɨɟ ɞɚɜɥɟɧɢɟ ɞɨ ɞɚɜɥɟɧɢɹ ɜɫɚɫɵɜɚ-
ɧɢɹ. ɗɬɨɬ ɩɚɪ ɡɚɣɦɟɬ ɱɚɫɬɶ ɩɨɥɟɡɧɨɝɨ ɨɛɴɟɦɚ ɰɢɥɢɧɞɪɚ ɋ
ɱɟɝɨ ɨɛɴɟɦ ɜɫɚɫɵɜɚɧɢɹ ɧɨɜɨɣ ɩɨɪɰɢɢ ɩɚɪɚ V
ɭɦɟɧɶɲɢɬɫɹ:
1
, ɜ ɪɟɡɭɥɶɬɚɬɟ
1
,
45
ɝɞɟ Vh – ɬɟɨɪɟɬɢɱɟɫɤɢɣ ɨɛɴɟɦ ɜɫɚɫɵɜɚɧɢɹ, ɢɥɢ ɨɛɴɟɦ, ɨɩɢɫɵɜɚɟɦɵɣ
ɩɨɪɲɧɟɦ.
Ɇɟɪɬɜɨɟ ɩɪɨɫɬɪɚɧɫɬɜɨ ɜɵɪɚɠɚɸɬ ɜ ɩɪɨɰɟɧɬɚɯ ɨɛɴɟɦɚ, ɨɩɢɫɵɜɚɟɦɨɝɨ
ɩɨɪɲɧɟɦ:
V1 = Vh – C1,
C
100 %
cV
h
.
ȼ ɫɨɜɪɟɦɟɧɧɵɯ ɛɵɫɬɪɨɯɨɞɧɵɯ ɤɨɦɩɪɟɫɫɨɪɚɯ ɦɟɪɬɜɨɟ ɩɪɨɫɬɪɚɧɫɬɜɨ ɫɨɫɬɚɜɥɹɟɬ 35 %. ɑɟɦ ɛɨɥɶɲɟ ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɜɟɥɢɱɢɧɚ ɦɟɪɬɜɨɝɨ ɩɪɨɫɬɪɚɧ-
ɫɬɜɚ, ɬɟɦ ɜɵɲɟ ɨɛɴɟɦɧɵɟ ɩɨɬɟɪɢ. Ɉɛɴɟɦɧɵɟ ɩɨɬɟɪɢ ɜɨɡɪɚɫɬɚɸɬ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɨɬɧɨɲɟɧɢɹ ɞɚɜɥɟɧɢɹ ɧɚɝɧɟɬɚɧɢɹ ɤ ɞɚɜɥɟɧɢɸ ɜɫɚɫɵɜɚɧɢɹ ɪ
/ ɪ0.
Ʉ
ɋɨɩɪɨɬɢɜɥɟɧɢɟ ɩɪɢ ɜɫɚɫɵɜɚɧɢɢ ɢ ɧɚɝɧɟɬɚɧɢɢ. Ʉɥɚɩɚɧɵ ɞɟɣɫɬɜɢɬɟɥɶɧɨɝɨ ɤɨɦɩɪɟɫɫɨɪɚ ɨɬɤɪɵɜɚɸɬɫɹ ɢ ɡɚɤɪɵɜɚɸɬɫɹ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɪɚɡɧɨɫɬɢ ɞɚɜɥɟɧɢɣ ɜ ɰɢɥɢɧɞɪɟ ɢ ɬɪɭɛɨɩɪɨɜɨɞɚɯ. ɉɚɪ ɩɪɢ ɩɪɨɯɨɞɟ ɩɨ ɬɪɭɛɨɩɪɨɜɨɞɚɦ ɢ, ɨɫɨɛɟɧɧɨ ɜ ɫɭɠɟɧɧɵɯ ɫɟɱɟɧɢɹɯ ɤɥɚɩɚɧɨɜ, ɩɪɟɨɞɨɥɟɜɚɟɬ ɫɨɩɪɨɬɢɜɥɟɧɢɟ, ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɩɨɬɟɪɟ ɞɚɜɥɟɧɢɹ. ɉɨɷɬɨɦɭ ɞɚɜɥɟɧɢɟ ɜɨ ɜɫɚɫɵɜɚɸɳɟɦ ɬɪɭɛɨɩɪɨɜɨɞɟ ɩɟɪɟɞ ɤɨɦɩɪɟɫɫɨɪɨɦ ɪ
ɪɢɬɟɥɟ ɪ
, ɚ ɞɚɜɥɟɧɢɟ ɜ ɰɢɥɢɧɞɪɟ ɤɨɦɩɪɟɫɫɨɪɚ ɪ1 ɧɢɠɟ ɪȼɋ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ,
0
ɧɢɠɟ, ɱɟɦ ɞɚɜɥɟɧɢɟ ɜ ɢɫɩɚ-
ȼɋ
ɜ ɞɟɣɫɬɜɢɬɟɥɶɧɨɦ ɪɚɛɨɱɟɦ ɩɪɨɰɟɫɫɟ (ɪɢɫ. 4.2, ɜ) ɜɫɚɫɵɜɚɧɢɟ 41 ɩɪɨɬɟɤɚɟɬ
ɩɪɢ ɛɨɥɟɟ ɧɢɡɤɨɦ ɞɚɜɥɟɧɢɢ, ɱɟɦ ɜ ɢɫɩɚɪɢɬɟɥɟ.
ɉɨ ɚɧɚɥɨɝɢɱɧɵɦ ɩɪɢɱɢɧɚɦ ɧɚɝɧɟɬɚɧɢɟ (ɩɪɨɰɟɫɫ 23) ɩɪɨɢɫɯɨɞɢɬ ɩɨɞ
ɞɚɜɥɟɧɢɟɦ ɪ2 ɜ ɰɢɥɢɧɞɪɟ. ɗɬɨ ɞɚɜɥɟɧɢɟ ɜɵɲɟ ɞɚɜɥɟɧɢɹ ɜ ɧɚɝɧɟɬɚɬɟɥɶɧɨɦ
ɬɪɭɛɨɩɪɨɜɨɞɟ ɪ
, ɤɨɬɨɪɨɟ, ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɜɵɲɟ ɞɚɜɥɟɧɢɹ ɜ ɤɨɧɞɟɧɫɚɬɨɪɟ ɪɄ.
ɇ
ɉɨɬɟɪɢ (ɞɟɩɪɟɫɫɢɹ) ɩɪɢ ɜɫɚɫɵɜɚɧɢɢ ɪ0 ɞɨɫɬɢɝɚɸɬ 0,03 Ɇɉɚ, ɚ ɩɪɢ ɧɚɝɧɟɬɚɧɢɢ ɞɨ 0,050,07 Ɇɉɚ.
ɋ ɩɨɧɢɠɟɧɢɟɦ ɞɚɜɥɟɧɢɹ ɩɪɢ ɜɫɚɫɵɜɚɧɢɢ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɭɞɟɥɶɧɵɣ
ɨɛɴɟɦ ɜɯɨɞɹɳɟɝɨ ɜ ɰɢɥɢɧɞɪ ɩɚɪɚ ɢ ɭɦɟɧɶɲɚɟɬɫɹ ɦɚɫɫɚ ɜɫɚɫɵɜɚɟɦɨɝɨ ɩɚɪɚ.
ɉɪɢ ɞɜɢɠɟɧɢɢ ɩɨɪɲɧɹ ɫɩɪɚɜɚ ɧɚɥɟɜɨ (ɪɢɫ. 4.2, ɜ) ɱɚɫɬɶ ɯɨɞɚ ɢɫɩɨɥɶɡɭɟɬɫɹ ɬɨɥɶɤɨ ɞɥɹ ɞɨɜɟɞɟɧɢɹ ɞɚɜɥɟɧɢɹ ɜ ɰɢɥɢɧɞɪɟ ɞɨ ɪ
(ɩɪɨɰɟɫɫ 1–1'),
ȼɋ
ɚ ɷɬɨ ɩɪɢɜɨɞɢɬ ɤ ɨɛɴɟɦɧɵɦ ɩɨɬɟɪɹɦ. ɍɦɟɧɶɲɟɧɢɟ ɨɛɴɟɦɚ ɜɫɚɫɵɜɚɧɢɹ, ɜɵɡɜɚɧɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ ɩɪɢ ɜɫɚɫɵɜɚɧɢɢ, ɧɚ ɞɢɚɝɪɚɦɦɟ ɩɨɤɚɡɚɧɨ ɨɬɪɟɡɤɨɦ ɋ
, ɤɨɬɨɪɵɣ ɜɨɡɪɚɫɬɚɟɬ ɫ ɭɜɟɥɢɱɟɧɢɟɦ 'ɪȼɋ = ɪȼɋ – ɪ1. Ʉɪɨɦɟ ɬɨɝɨ,
2
ɜ ɪɟɡɭɥɶɬɚɬɟ ɩɨɧɢɠɟɧɢɹ ɞɚɜɥɟɧɢɹ ɩɪɢ ɜɫɚɫɵɜɚɧɢɢ ɢ ɩɨɜɵɲɟɧɢɹ ɩɪɢ
ɧɚɝɧɟɬɚɧɢɢ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɨɬɧɨɲɟɧɢɟ ɞɚɜɥɟɧɢɹ ɪ
/ ɪ1 ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ,
2
ɜɨɡɪɚɫɬɚɸɬ ɩɨɬɟɪɢ ɋ1, ɨɛɭɫɥɨɜɥɟɧɧɵɟ ɦɟɪɬɜɵɦ ɩɪɨɫɬɪɚɧɫɬɜɨɦ.
46
Ɉɛɴɟɦɧɵɟ ɩɨɬɟɪɢ, ɨɛɭɫɥɨɜɥɟɧɧɵɟ ɦɟɪɬɜɵɦ ɩɪɨɫɬɪɚɧɫɬɜɨɦ ɋ1 ɢ ɫɨɩɪɨ-
X
ɬɢɜɥɟɧɢɟɦ ɜ ɤɥɚɩɚɧɚɯ ɋ
, ɜɢɞɧɵ ɧɚ ɢɧɞɢɤɚɬɨɪɧɨɣ ɞɢɚɝɪɚɦɦɟ (ɪɢɫ. 4.2, ɜ).
2
Ɉɛɴɟɦɧɵɟ ɩɨɬɟɪɢ ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɨɛɴɟɦɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɢɧɞɢɤɚɬɨɪ-
ɧɨɣ ɞɢɚɝɪɚɦɦɵ:
O
= V2 / Vh,
i
ɝɞɟ V2 – ɞɟɣɫɬɜɢɬɟɥɶɧɵɣ ɨɛɴɟɦ ɜɫɚɫɵɜɚɧɢɹ, ɜɡɹɬɵɣ ɢɡ ɢɧɞɢɤɚɬɨɪɧɨɣ ɞɢɚɝɪɚɦɦɵ.
ɉɨɞɨɝɪɟɜ ɩɚɪɚ ɩɪɢ ɜɫɚɫɵɜɚɧɢɢ. ɏɨɥɨɞɢɥɶɧɵɣ ɚɝɟɧɬ ɩɪɢ ɜɫɚɫɵɜɚɧɢɢ, ɧɚɝɪɟɜɚɹɫɶ ɨɬ ɫɬɟɧɨɤ ɰɢɥɢɧɞɪɚ, ɪɚɫɲɢɪɹɟɬɫɹ, ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɭɜɟɥɢɱɟɧɢɸ ɭɞɟɥɶɧɨɝɨ ɨɛɴɟɦɚ ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɤ ɭɦɟɧɶɲɟɧɢɸ ɦɚɫɫɵ ɩɨɫɬɭɩɚɸɳɟɝɨ ɜ ɰɢɥɢɧɞɪ ɯɨɥɨɞɢɥɶɧɨɝɨ ɚɝɟɧɬɚ. ɉɨɬɟɪɢ, ɜɵɡɜɚɧɧɵɟ ɬɟɩɥɨɨɛɦɟɧɨɦ ɜ ɰɢɥɢɧɞɪɟ, ɯɚɪɚɤɬɟɪɢɡɭɸɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɩɨɞɨɝɪɟɜɚ
O
.
w
ɋ ɰɟɥɶɸ ɭɦɟɧɶɲɟɧɢɹ ɩɨɞɨɝɪɟɜɚ ɩɚɪɚ ɨɬ ɫɬɟɧɨɤ ɰɢɥɢɧɞɪɚ ɩɪɟɞɭɫɦɚɬɪɢɜɚɸɬ ɨɯɥɚɠɞɟɧɢɟ ɰɢɥɢɧɞɪɨɜ ɤɨɦɩɪɟɫɫɨɪɚ ɜɨɞɨɣ ɢɥɢ ɜɨɡɞɭɯɨɦ, ɞɥɹ ɱɟɝɨ
ɫɥɭɠɚɬ ɜɨɞɹɧɵɟ ɨɯɥɚɠɞɚɸɳɢɟ ɪɭɛɚɲɤɢ ɢɥɢ ɪɟɛɪɚ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɰɢɥɢɧɞɪɚ ɢ ɤɪɵɲɤɚɯ.
ɍɬɟɱɤɢ ɩɚɪɚ ɱɟɪɟɡ ɧɟɩɥɨɬɧɨɫɬɶ. ȼ ɩɪɨɰɟɫɫɟ ɪɚɛɨɬɵ ɤɨɦɩɪɟɫɫɨɪɚ
ɢɦɟɸɬ ɦɟɫɬɨ ɩɟɪɟɬɟɱɤɢ ɩɚɪɚ ɱɟɪɟɡ ɪɚɡɥɢɱɧɵɟ ɤɨɧɫɬɪɭɤɬɢɜɧɵɟ ɡɚɡɨɪɵ:
ɜ ɪɚɡɴɟɦɚɯ ɩɨɪɲɧɟɜɵɯ ɤɨɥɟɰ;
ɜ ɡɚɡɨɪɚɯ ɦɟɠɞɭ ɩɨɪɲɧɟɦ ɢ ɩɨɪɲɧɟɜɵɦɢ
ɤɨɥɶɰɚɦɢ; ɱɟɪɟɡ ɧɟɩɥɨɬɧɨɫɬɶ ɜ ɤɥɚɩɚɧɚɯ ɢ ɞɪ. Ɉɛɴɟɦɧɵɟ ɩɨɬɟɪɢ, ɜɵɡɜɚɧɧɵɟ ɭɬɟɱɤɚɦɢ, ɯɚɪɚɤɬɟɪɢɡɭɸɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɩɥɨɬɧɨɫɬɢ
O
.
ɉɅ
Ʉɨɷɮɮɢɰɢɟɧɬ ɩɨɞɚɱɢ. ȼɫɟ ɨɛɴɟɦɧɵɟ ɩɨɬɟɪɢ ɜ ɞɟɣɫɬɜɢɬɟɥɶɧɨɦ ɩɪɨɰɟɫɫɟ ɤɨɦɩɪɟɫɫɨɪɚ, ɜɵɡɵɜɚɸɳɢɟ ɭɦɟɧɶɲɟɧɢɟ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ, ɭɱɢɬɵɜɚɸɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɩɨɞɚɱɢ:
O
= V / Vh,
ɝɞɟ V – ɞɟɣɫɬɜɢɬɟɥɶɧɚɹ ɨɛɴɟɦɧɚɹ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ;
V
– ɨɛɴɟɦ, ɨɩɢɫɚɧɧɵɣ ɩɨɪɲɧɟɦ.
h
Ʉɨɷɮɮɢɰɢɟɧɬ ɩɨɞɚɱɢ ɦɨɠɧɨ ɜɵɪɚɡɢɬɶ ɨɬɧɨɲɟɧɢɟɦ ɞɟɣɫɬɜɢɬɟɥɶɧɨɣ
ɦɚɫɫɨɜɨɣ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ ɤɨɦɩɪɟɫɫɨɪɚ G ɤ ɟɝɨ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ G
ɌȿɈɊ
:
V
/
O
V
/
X
G
1
1
G
ɌȿɈɊh
ɢɥɢ
47
Gq
OOO
O
O
Vq
0
qG
0
Q
X
qV
X
0
.
Q
0
ɌȿɈɊhɌȿɈɊ
Ʉɨɷɮɮɢɰɢɟɧɬ ɩɨɞɚɱɢ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɤɚɤ ɩɪɨɢɡɜɟɞɟɧɢɟ ɨɛɴɟɦɧɵɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ:
.
ɩɥwi
ɇɚ ɪɢɫɭɧɤɟ 4.3 ɩɪɢɜɟɞɟɧɵ ɡɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɩɨɞɚɱɢ O ɢ ɢɧɞɢ-
K
ɤɚɬɨɪɧɵɯ ɄɉȾ
, ɩɨɥɭɱɟɧɧɵɟ ɩɪɢ ɢɫɩɵɬɚɧɢɢ ɚɦɦɢɚɱɧɵɯ ɢ ɯɥɚɞɨɧɨɜɵɯ
i
ɤɨɦɩɪɟɫɫɨɪɨɜ.
Ɋɢɫ. 4.3. Ɂɚɜɢɫɢɦɨɫɬɢ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɩɨɞɚɱɢ
ɢ ɢɧɞɢɤɚɬɨɪɧɵɯ ɄɉȾ
K
ɨɬ ɨɬɧɨɲɟɧɢɹ ɞɚɜɥɟɧɢɣ pK / p0:
i
O
1 ɞɥɹ ɫɪɟɞɧɢɯ ɤɨɦɩɪɟɫɫɨɪɨɜ; 2 – ɞɥɹ ɤɪɭɩɧɵɯ ɤɨɦɩɪɟɫɫɨɪɨɜ
Ⱥɧɚɥɢɡ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ O ɭɦɟɧɶɲɚɟɬɫɹ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɨɬɧɨɲɟɧɢɹ
ɞɚɜɥɟɧɢɹ ɤɨɧɞɟɧɫɚɰɢɢ ɤ ɞɚɜɥɟɧɢɸ ɤɢɩɟɧɢɹ.
4.2. ɏɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɤɨɦɩɪɟɫɫɨɪɚ
Ʉɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ, ɨɬɧɢɦɚɟɦɨɟ ɯɨɥɨɞɢɥɶɧɨɣ ɦɚɲɢɧɨɣ ɨɬ ɨɯɥɚɠɞɚɟɦɨɣ ɫɪɟɞɵ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ, ɧɚɡɵɜɚɟɬɫɹ ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶɸ Q
0
ɏɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɦɚɲɢɧɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɨɥɢɱɟɫɬɜɨɦ ɯɨɥɨɞɢɥɶɧɨɝɨ ɚɝɟɧɬɚ G, ɩɪɨɯɨɞɹɳɟɝɨ ɩɨ ɢɫɩɚɪɢɬɟɥɸ, ɢ ɦɚɫɫɨɜɨɣ ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶɸ q
:
0
Q0 = G q0 = G (h1 – h2).
.
48
ɏɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɤɨɦɩɪɟɫɫɨɪɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɪɨɢɡɜɟɞɟɧɢɟɦ ɞɟɣɫɬɜɢɬɟɥɶɧɨɝɨ ɨɛɴɟɦɚ ɩɚɪɚ V, ɡɚɫɚɫɵɜɚɟɦɨɝɨ ɤɨɦɩɪɟɫɫɨɪɨɦ, ɢ ɨɛɴ-
ɟɦɧɨɣ ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶɸ q
:
X
Q0 = V q
,
X
ɝɞɟ V = O Vh;
O
ɤɨɷɮɮɢɰɢɟɧɬ ɩɨɞɚɱɢ ɤɨɦɩɪɟɫɫɨɪɚ.
Ɍɨɝɞɚ
q
0
VqVQ
0
X
.
OO
hh
X
1
Ɉɛɴɟɦ, ɨɩɢɫɵɜɚɟɦɵɣ ɩɨɪɲɧɟɦ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɚɡɦɟɪɨɦ ɰɢɥɢɧɞɪɚ ɢ
ɱɚɫɬɨɬɨɣ ɜɪɚɳɟɧɢɹ ɜɚɥɚ:
V
2
D
S
h
,
Snz
4
ɝɞɟ D – ɞɢɚɦɟɬɪ ɰɢɥɢɧɞɪɚ;
S – ɯɨɞ ɩɨɪɲɧɹ;
n – ɱɚɫɬɨɬɚ ɜɪɚɳɟɧɢɹ ɜɚɥɚ;
z – ɱɢɫɥɨ ɰɢɥɢɧɞɪɨɜ.
Ⱦɥɹ ɨɞɧɨɝɨ ɢ ɬɨɝɨ ɠɟ ɤɨɦɩɪɟɫɫɨɪɚ ɩɪɢ ɩɨɫɬɨɹɧɧɨɣ ɱɚɫɬɨɬɟ ɜɪɚɳɟɧɢɹ
ɜɟɥɢɱɢɧɚ V
ɧɨɫɬɢ ɢ ɤɨɷɮɮɢɰɢɟɧɬ ɩɨɞɚɱɢ
ɩɨɫɬɨɹɧɧɚ. Ɉɛɴɟɦɧɚɹ qX ɢ ɦɚɫɫɨɜɚɹ q0 ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶ-
h
O
– ɜɟɥɢɱɢɧɵ ɩɟɪɟɦɟɧɧɵɟ. Ɉɧɢ ɡɚɜɢɫɹɬ ɨɬ
ɬɟɦɩɟɪɚɬɭɪɧɨɝɨ ɪɟɠɢɦɚ ɪɚɛɨɬɵ ɭɫɬɚɧɨɜɤɢ: ɬɟɦɩɟɪɚɬɭɪɵ ɤɢɩɟɧɢɹ t0, ɤɨɧɞɟɧɫɚɰɢɢ tɄ ɢ ɬɟɦɩɟɪɚɬɭɪɵ ɩɟɪɟɞ ɪɟɝɭɥɢɪɭɸɳɢɦ ɜɟɧɬɢɥɟɦ tɉ.
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɤɨɦɩɪɟɫɫɨɪɚ – ɜɟɥɢɱɢɧɚ
ɧɟɩɨɫɬɨɹɧɧɚɹ ɢ ɡɚɜɢɫɢɬ ɨɬ ɰɢɤɥɚ ɪɚɛɨɬɵ ɯɨɥɨɞɢɥɶɧɨɣ ɦɚɲɢɧɵ.
ɇɚ ɪɢɫɭɧɤɟ 4.4, ɚ ɩɪɟɞɫɬɚɜɥɟɧɵ ɞɜɚ ɰɢɤɥɚ (1234 ɢ 1'2'34') c
ɨɞɢɧɚɤɨɜɨɣ ɬɟɦɩɟɪɚɬɭɪɨɣ ɤɨɧɞɟɧɫɚɰɢɢ ɢ ɪɚɡɥɢɱɧɵɦɢ ɬɟɦɩɟɪɚɬɭɪɚɦɢ ɤɢɩɟɧɢɹ. Ⱥɧɚɥɢɡ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɫ ɩɨɧɢɠɟɧɢɟɦ t
ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ q
= q0 /
X
X
ɭɦɟɧɶɲɚɟɬɫɹ, ɬɚɤ ɤɚɤ ɭɦɟɧɶɲɚɟɬɫɹ ɦɚɫɫɨ-
1
(t'0 < t0) ɨɛɴɟɦɧɚɹ ɯɨɥɨɞɨ-
0
ɜɚɹ ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ q'0 < q0. Ɍɚɤɠɟ ɫ ɩɨɧɢɠɟɧɢɟɦ t0 ɪɟɡɤɨ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɭɞɟɥɶɧɵɣ ɨɛɴɟɦ ɜɫɚɫɵɜɚɟɦɨɝɨ ɤɨɦɩɪɟɫɫɨɪɨɦ ɩɚɪɚ
X
'1 >
X
ɜɫɥɟɞɫɬɜɢɟ ɩɨɧɢɠɟɧɢɹ ɞɚɜɥɟɧɢɹ ɜ ɢɫɩɚɪɢɬɟɥɟ (ɪ'0 < p0). Ʉɨɷɮɮɢɰɢɟɧɬ ɩɨ-
O
ɞɚɱɢ
ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɫɬɟɩɟɧɶ ɫɠɚɬɢɹ ɪ
ɤɨɦɩɪɟɫɫɨɪɚ ɫ ɩɨɧɢɠɟɧɢɟɦ t0 ɬɚɤɠɟ ɭɦɟɧɶɲɚɟɬɫɹ, ɬɚɤ ɤɚɤ ɩɪɢ ɷɬɨɦ
/ ɪ0.
Ʉ
49
1
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫ ɩɨɧɢɠɟɧɢɟɦ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɞɚɜɥɟɧɢɹ ɜ ɢɫɩɚɪɢɬɟɥɟ
ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɤɨɦɩɪɟɫɫɨɪɚ ɭɦɟɧɶɲɚɟɬɫɹ.
ɚ ɛ
Ɋɢɫ. 4.4. ɐɢɤɥɵ ɯɨɥɨɞɢɥɶɧɵɯ ɦɚɲɢɧ:
ɚ – ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɬɟɦɩɟɪɚɬɭɪɚɯ ɤɢɩɟɧɢɹ;
ɛ – ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɬɟɦɩɟɪɚɬɭɪɚɯ ɤɨɧɞɟɧɫɚɰɢɢ
ɇɚ ɪɢɫɭɧɤɟ 4.4, ɛ ɩɪɟɞɫɬɚɜɥɟɧɵ ɞɜɚ ɰɢɤɥɚ (1234 ɢ 12'3'4')
c ɨɞɢɧɚɤɨɜɨɣ ɬɟɦɩɟɪɚɬɭɪɨɣ ɤɢɩɟɧɢɹ ɢ ɪɚɡɥɢɱɧɵɦɢ ɬɟɦɩɟɪɚɬɭɪɚɦɢ ɤɨɧɞɟɧɫɚɰɢɢ. Ⱥɧɚɥɢɡ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɨɛɴɟɦɧɚɹ ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ
q
= q0 /
X
ɧɟ ɢɡɦɟɧɹɟɬɫɹ, ɤɨɷɮɮɢɰɢɟɧɬ ɩɨɞɚɱɢ ɫ ɩɨɜɵɲɟɧɢɟɦ t
X
ɫ ɩɨɜɵɲɟɧɢɟɦ tɄ (t'K > tK) ɭɦɟɧɶɲɚɟɬɫɹ, ɬɚɤ ɤɚɤ q'0 < q0, ɚ
1
ɬɚɤɠɟ ɭɦɟɧɶɲɚɟɬɫɹ.
K
X
1
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɫ ɩɨɜɵɲɟɧɢɟɦ ɬɟɦɩɟɪɚɬɭɪɵ ɤɨɧɞɟɧɫɚɰɢɢ (ɩɟɪɟɞ ɪɟɝɭɥɢɪɭɸɳɢɦ ɜɟɧɬɢɥɟɦ) ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɤɨɦɩɪɟɫɫɨɪɨɜ ɭɦɟɧɶɲɚɟɬɫɹ. Ɍɚɤɨɟ ɠɟ ɜɥɢɹɧɢɟ ɨɤɚɡɵɜɚɟɬ ɬɟɦɩɟɪɚɬɭɪɚ ɩɟɪɟɨɯɥɚɠɞɟɧɢɹ ɠɢɞɤɨɫɬɢ
ɩɟɪɟɞ ɪɟɝɭɥɢɪɭɸɳɢɦ ɜɟɧɬɢɥɟɦ t
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɢ ɪɚɡɧɵɯ ɬɟɦɩɟɪɚɬɭɪɚɯ t
.
ɉ
, tK ɢ tɉ ɯɨɥɨɞɢɥɶɧɚɹ ɦɚ-
0
ɲɢɧɚ ɫ ɨɞɧɢɦ ɢ ɬɟɦ ɠɟ ɤɨɦɩɪɟɫɫɨɪɨɦ ɞɚɟɬ ɪɚɡɧɭɸ ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ Q
. ɋ ɩɨɜɵɲɟɧɢɟɦ t0 ɢ ɩɨɧɢɠɟɧɢɟɦ tɄ ɢ tɉ ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶ-
0
ɧɨɫɬɶ ɦɚɲɢɧɵ ɭɜɟɥɢɱɢɜɚɟɬɫɹ, ɚ ɫ ɩɨɧɢɠɟɧɢɟɦ t0 ɢ ɫ ɩɨɜɵɲɟɧɢɟɦ tɄ ɢ tɉ
ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɭɦɟɧɶɲɚɟɬɫɹ. ɇɚɢɛɨɥɟɟ ɪɟɡɤɨɟ ɜɥɢɹɧɢɟ ɧɚ ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɨɤɚɡɵɜɚɟɬ ɬɟɦɩɟɪɚɬɭɪɚ ɤɢɩɟɧɢɹ ɯɨɥɨɞɢɥɶɧɨɝɨ
ɚɝɟɧɬɚ.
ɍɫɬɚɧɨɜɥɟɧɨ, ɱɬɨ ɩɨɜɵɲɟɧɢɟ t
ɧɚ 1 °ɋ ɜ ɚɦɦɢɚɱɧɵɯ ɦɚɲɢɧɚɯ ɩɪɢɜɨ-
0
ɞɢɬ ɤ ɭɜɟɥɢɱɟɧɢɸ Q0 ɩɪɢɦɟɪɧɨ ɧɚ 6 %, ɜ ɯɥɚɞɨɧɨɜɵɯ – ɧɚ 4 %.
50
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