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Файл:Основы трансформации теплоты. Учебное пособие
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Ɉɬɜɨɞ ɬɟɩɥɨɬɵ ɨɬ «ɩɪɹɦɨɝɨ» ɩɨɬɨɤɚ ɩɪɨɢɫɯɨɞɢɬ ɜ ɪɟɝɟɧɟɪɚɬɨɪɟ ɡɚ
ɫɱɟɬ ɩɨɞɨɝɪɟɜɚ ɜ ɩɪɨɰɟɫɫɟ 61 «ɨɛɪɚɬɧɨɝɨ» ɩɨɬɨɤɚ, ɜɵɯɨɞɹɳɟɝɨ ɢɡ ɬɟɩɥɨɨɛɦɟɧɧɨɝɨ ɚɩɩɚɪɚɬɚ ɌɈ. Ⱥɧɚɥɢɡ ɪɢɫɭɧɤɚ 8.2, ɛ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ, ɩɨɞɨɛɪɚɜ
ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦ ɨɛɪɚɡɨɦ ɝɥɭɛɢɧɭ ɪɟɝɟɧɟɪɚɰɢɢ, ɦɨɠɟɦ ɩɨɥɭɱɢɬɶ ɧɢɡɤɢɟ
ɬɟɦɩɟɪɚɬɭɪɵ Ɍ
ɢ Ɍ6, ɧɟ ɭɜɟɥɢɱɢɜɚɹ ɨɬɧɨɲɟɧɢɹ ɞɚɜɥɟɧɢɣ ɜ ɤɨɦɩɪɟɫɫɨɪɟ.
5
Ɋɚɛɨɬɚ ɪɟɝɟɧɟɪɚɬɢɜɧɨɝɨ ɰɢɤɥɚ:
l = q – q0 = (h2 – h3) – (h6 – h5) = lK – lȾ = (h2 – h1) – (h4 – h5).
ɏɨɥɨɞɢɥɶɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɪɟɝɟɧɟɪɚɬɢɜɧɨɝɨ ɰɢɤɥɚ:
q
0
H
qq
0
hh
56
.
)()(
hhhh
5632
Ɋɚɡɨɦɤɧɭɬɵɟ ɰɢɤɥɵ. ȿɫɥɢ ɪɚɛɨɱɢɦ ɜɟɳɟɫɬɜɨɦ ȽɏɆ ɹɜɥɹɟɬɫɹ ɜɨɡɞɭɯ,
ɬɨ ɨɬɜɨɞ ɬɟɩɥɨɬɵ ɜ ɨɤɪɭɠɚɸɳɭɸ ɫɪɟɞɭ ɦɨɠɧɨ ɨɫɭɳɟɫɬɜɥɹɬɶ ɩɭɬɟɦ ɬɟɩɥɨɢ ɦɚɫɫɨɨɛɦɟɧɚ. ɉɪɢ ɷɬɨɦ ɨɬɩɚɞɚɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɜ ɩɪɨɦɟɠɭɬɨɱɧɨɦ ɯɨɥɨɞɢɥɶɧɢɤɟ.
Ɋɚɡɨɦɤɧɭɬɵɣ ɰɢɤɥ ɫ ɬɟɩɥɨɦɚɫɫɨɨɛɦɟɧɨɦ. ȼ ɫɯɟɦɟ ɬɚɤɨɣ ȽɏɆ ɨɬɫɭɬɫɬɜɭɟɬ ɩɪɨɦɟɠɭɬɨɱɧɵɣ ɯɨɥɨɞɢɥɶɧɢɤ (ɪɢɫ. 8.3, ɚ).
ɂɡ ɚɬɦɨɫɮɟɪɵ ȼ ɚɬɦɨɫɮɟɪɭ
ɄɄ
1
6
Ɍ
Ɉɋ
Ɋ
2
5
ɄɄ
2
2
Ⱦɜ
1
Ʉ
Ⱦ
Ɋ
1
Q
0
3
4
ɌɈ
Ɍ
Ɍ
Ɍ
Ɉɋ
ɂɇɌ
3
4
2
1
5
ɪ
1
ɪ
2
6
s
ɚ ɛ
Ɋɢɫ. 8.3. ɉɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ (ɚ) ɢ ɰɢɤɥ (ɛ) ɪɟɝɟɧɟɪɚɬɢɜɧɨɣ
ɝɚɡɨɜɨɣ ɯɨɥɨɞɢɥɶɧɨɣ ɦɚɲɢɧɵ ɫ ɬɟɩɥɨɦɚɫɫɨɨɛɦɟɧɨɦ
ȼɨɡɞɭɯ ɩɨɫɬɭɩɚɟɬ ɜ ɤɨɦɩɪɟɫɫɨɪ Ʉ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɢɡ ɚɬɦɨɫɮɟɪɵ, ɫɠɢɦɚɟɬɫɹ ɜ ɩɪɨɰɟɫɫɟ 12 (ɪɢɫ. 8.3, ɛ) ɢ, ɩɪɨɣɞɹ ɱɟɪɟɡ
ɫɪɚɡɭ ɩɨɩɚɞɚɟɬ ɜ ɪɟɝɟɧɟɪɚɬɨɪ Ɋ
, ɜ ɤɨɬɨɪɨɦ ɨɯɥɚɠɞɚɟɬɫɹ ɜ ɩɪɨɰɟɫɫɟ 23,
1
91
ɤɥɚɩɚɧɧɭɸ ɤɨɪɨɛɤɭ ɄɄ1,
ɨɬɞɚɜɚɹ ɬɟɩɥɨɬɭ ɧɚɫɚɞɤɟ ɪɟɝɟɧɟɪɚɬɨɪɚ, ɫɧɚɱɚɥɚ ɞɨ ɬɟɦɩɟɪɚɬɭɪɵ ɌɈɋ, ɚ ɡɚɬɟɦ ɞɨ Ɍ
. ɂɡ ɪɟɝɟɧɟɪɚɬɨɪɚ, ɩɪɨɣɞɹ ɤɥɚɩɚɧɧɭɸ ɤɨɪɨɛɤɭ ɄɄ2, ɜɨɡɞɭɯ ɩɨɩɚ-
3
ɞɚɟɬ ɜ ɞɟɬɚɧɞɟɪ Ⱦ, ɝɞɟ ɪɚɫɲɢɪɹɟɬɫɹ, ɫɨɜɟɪɲɚɹ ɜɧɟɲɧɸɸ ɩɨɥɟɡɧɭɸ ɪɚɛɨɬɭ,
ɢ ɨɯɥɚɠɞɚɟɬɫɹ ɞɨ ɬɟɦɩɟɪɚɬɭɪɵ Ɍ
. ɉɨɫɥɟ ɷɬɨɝɨ ɜɨɡɞɭɯ ɧɚɩɪɚɜɥɹɟɬɫɹ ɜ ɬɟɩ-
4
ɥɨɨɛɦɟɧɧɵɣ ɚɩɩɚɪɚɬ ɌɈ, ɝɞɟ ɨɬɜɨɞɢɬ ɬɟɩɥɨɬɭ ɨɬ ɨɯɥɚɠɞɚɟɦɨɝɨ ɢɫɬɨɱɧɢɤɚ,
ɧɚɝɪɟɜɚɹɫɶ ɩɪɢ ɷɬɨɦ ɞɨ ɬɟɦɩɟɪɚɬɭɪɵ Ɍ5, ɡɚɬɟɦ ɩɨɬɨɤ ɜɨɡɞɭɯɚ ɱɟɪɟɡ ɤɥɚɩɚɧɧɭɸ ɤɨɪɨɛɤɭ ɄɄ
ɩɨɩɚɞɚɟɬ ɜ ɪɟɝɟɧɟɪɚɬɨɪ Ɋ2, ɝɞɟ ɨɯɥɚɠɞɚɟɬ ɧɚɫɚɞɤɭ,
2
ɨɬɧɢɦɚɹ ɨɬ ɧɟɟ ɬɟɩɥɨɬɭ, ɚ ɫɚɦ ɧɚɝɪɟɜɚɟɬɫɹ ɞɨ ɬɟɦɩɟɪɚɬɭɪɵ Ɍ6 = Ɍ2 > ɌɈɋ.
ɉɨɫɥɟ ɪɟɝɟɧɟɪɚɬɨɪɚ ɜɨɡɞɭɯ ɩɪɨɯɨɞɢɬ ɤɥɚɩɚɧɧɭɸ ɤɨɪɨɛɤɭ ɄɄ
ɢ ɜɵɛɪɚɫɵ-
1
ɜɚɟɬɫɹ ɜ ɚɬɦɨɫɮɟɪɭ, ɝɞɟ, ɫɦɟɲɢɜɚɹɫɶ ɫ ɨɤɪɭɠɚɸɳɢɦ ɜɨɡɞɭɯɨɦ, ɨɯɥɚɠɞɚɟɬɫɹ ɜ ɩɪɨɰɟɫɫɟ ɬɟɩɥɨɦɚɫɫɨɨɛɦɟɧɚ ɞɨ ɬɟɦɩɟɪɚɬɭɪɵ Ɍ
Ɉɋ
.
Ɉɫɨɛɟɧɧɨɫɬɶɸ ɪɚɛɨɬɵ ȽɏɆ ɫ ɬɟɩɥɨɦɚɫɫɨɨɛɦɟɧɨɦ ɹɜɥɹɟɬɫɹ ɧɟɩɪɟɪɵɜɧɨɟ ɜɫɚɫɵɜɚɧɢɟ ɜ ɤɨɦɩɪɟɫɫɨɪ ɚɬɦɨɫɮɟɪɧɨɝɨ ɜɨɡɞɭɯɚ, ɤɨɬɨɪɵɣ ɜɫɟɝɞɚ ɫɨɞɟɪɠɢɬ ɜɥɚɝɭ. ɉɪɢ ɨɯɥɚɠɞɟɧɢɢ ɜ ɪɟɝɟɧɟɪɚɬɨɪɟ ɷɬɚ ɜɥɚɝɚ ɫɧɚɱɚɥɚ ɜɵɩɚɞɚɟɬ
ɜ ɜɢɞɟ ɠɢɞɤɨɫɬɢ, ɚ ɡɚɬɟɦ ɩɪɢ t < 0 °ɋ – ɜ ɜɢɞɟ ɤɪɢɫɬɚɥɥɨɜ ɥɶɞɚ, ɤɨɬɨɪɵɟ
ɨɫɟɞɚɸɬ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɪɟɝɟɧɟɪɚɬɨɪɚ. Ʉɚɧɚɥɵ ɪɟɝɟɧɟɪɚɬɨɪɚ, ɜɵɩɨɥɧɟɧɧɨɝɨ ɜ ɜɢɞɟ ɪɟɤɭɩɟɪɚɬɢɜɧɨɝɨ ɬɟɩɥɨɨɛɦɟɧɧɢɤɚ (
ɬ. ɟ. ɫ ɬɟɩɥɨɨɛɦɟɧɨɦ ɱɟɪɟɡ
ɩɨɜɟɪɯɧɨɫɬɶ), ɩɨ ɤɨɬɨɪɵɦ ɞɜɢɠɟɬɫɹ ɨɯɥɚɠɞɚɟɦɵɣ ɜɨɡɞɭɯ, ɱɟɪɟɡ ɧɟɫɤɨɥɶɤɨ
ɦɢɧɭɬ ɪɚɛɨɬɵ ɛɭɞɭɬ ɡɚɛɢɬɵ ɥɶɞɨɦ, ɢ ɦɚɲɢɧɚ ɫɬɚɧɟɬ ɧɟɪɚɛɨɬɨɫɩɨɫɨɛɧɨɣ.
ɉɨɷɬɨɦɭ ɜ ɬɚɤɢɯ ȽɏɆ ɜɫɟɝɞɚ ɩɪɢɦɟɧɹɟɬɫɹ ɩɚɪɚ ɪɟɝɟɧɟɪɚɬɢɜɧɵɯ ɬɟɩɥɨɨɛɦɟɧɧɢɤɨɜ, ɫɨɞɟɪɠɚɳɢɯ ɬɟɩɥɨɟɦɤɭɸ ɧɚɫɚɞɤɭ, ɜɵɩɨɥɧɹɟɦɭɸ ɨɛɵɱɧɨ ɢɡ
ɝɨɮɪɢɪɨɜɚɧɧɨɣ ɚɥɸɦɢɧɢɟɜɨɣ ɥɟɧɬɵ. Ɋɟɝɟɧɟɪɚɬɨɪɵ ɪɚɛɨɬɚɸɬ ɩɨɩɟɪɟɦɟɧɧɨ. ɋɧɚɱɚɥɚ «ɩɪɹɦɨɣ» ɩɨɬɨɤ ɜɨɡɞɭɯɚ, ɜɵɯɨɞɹɳɟɝɨ ɢɡ
ɠɞɚɟɬɫɹ ɜ ɪɟɝɟɧɟɪɚɬɨɪɟ Ɋ
, ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɧɚɫɚɞɤɢ ɤɨɬɨɪɨɝɨ ɜɵɩɚɞɚɟɬ ɠɢɞ-
1
ɤɨɦɩɪɟɫɫɨɪɚ, ɨɯɥɚ-
ɤɨɫɬɶ ɢ ɤɪɢɫɬɚɥɥɵ ɥɶɞɚ. ȼ ɷɬɨ ɜɪɟɦɹ «ɨɛɪɚɬɧɵɣ» ɩɨɬɨɤ ɜɨɡɞɭɯɚ ɩɪɢ ɛɨɥɟɟ
ɧɢɡɤɨɦ ɞɚɜɥɟɧɢɢ ɪ
ɧɚɝɪɟɜɚɟɬɫɹ ɜ ɪɟɝɟɧɟɪɚɬɨɪɟ Ɋ2. ɂɡɜɟɫɬɧɨ, ɱɬɨ ɱɟɦ ɦɟɧɶ-
1
ɲɟ ɞɚɜɥɟɧɢɟ ɜɥɚɠɧɨɝɨ ɜɨɡɞɭɯɚ, ɬɟɦ ɛɨɥɶɲɟ ɟɝɨ ɜɥɚɝɨɫɨɞɟɪɠɚɧɢɟ ɩɪɢ ɨɞɧɨɣ
ɢ ɬɨɣ ɠɟ ɬɟɦɩɟɪɚɬɭɪɟ ɢ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɜɥɚɠɧɨɫɬɢ. ȼɫɥɟɞɫɬɜɢɟ ɷɬɨɝɨ «ɨɛɪɚɬɧɵɣ» ɩɨɬɨɤ ɜɨɡɞɭɯɚ ɜɵɧɨɫɢɬ ɜɫɸ ɜɥɚɝɭ ɢɡ ɪɟɝɟɧɟɪɚɬɨɪɚ Ɋ
ɢ ɩɨɥɧɨɫɬɶɸ
2
ɟɝɨ ɨɫɭɲɚɟɬ. ɑɟɪɟɡ ɨɩɪɟɞɟɥɟɧɧɵɣ ɩɟɪɢɨɞ, ɨɛɵɱɧɨ ɱɟɪɟɡ 12 ɦɢɧ, ɡɚɫɥɨɧɤɢ
ɨɛɟɢɯ ɤɥɚɩɚɧɧɵɯ ɤɨɪɨɛɨɤ ɚɜɬɨɦɚɬɢɱɟɫɤɢ ɩɨɜɨɪɚɱɢɜɚɸɬɫɹ ɧɚ 90° ɢ ɭɫɬɚɧɚɜɥɢɜɚɸɬɫɹ ɜ ɩɨɥɨɠɟɧɢɟ, ɭɤɚɡɚɧɧɨɟ ɧɚ ɪɢɫɭɧɤɟ 8.3, ɚ ɲɬɪɢɯɨɜɨɣ ɥɢɧɢɟɣ.
ɉɨɫɥɟ ɷɬɨɝɨ ɩɪɹɦɨɣ ɩɨɬɨɤ ɜɨɡɞɭɯɚ ɢɡ ɤɨɦɩɪɟɫɫɨɪɚ ɩɨɣɞɟɬ ɱɟɪɟɡ ɨɯɥɚɠɞɟɧɧɵɣ ɢ ɨɫɭɲɟɧɧɵɣ ɪɟɝɟɧɟɪɚɬɨɪ Ɋ
, ɚ ɨɛɪɚɬɧɵɣ – ɱɟɪɟɡ ɪɟɝɟɧɟɪɚɬɨɪ Ɋ1,
2
ɢ ɜɟɫɶ ɰɢɤɥ ɩɨɜɬɨɪɢɬɫɹ.
92
Ɋɚɡɨɦɤɧɭɬɵɣ ɜɚɤɭɭɦɧɵɣ ɰɢɤɥ ɫ ɬɟɩɥɨɦɚɫɫɨɨɛɦɟɧɨɦ ɨɬɥɢɱɚɟɬɫɹ
ɨɬ ɪɚɫɫɦɨɬɪɟɧɧɨɝɨ ɜɵɲɟ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶɸ ɪɚɛɨɬɵ ɷɥɟɦɟɧɬɨɜ ɫɯɟɦɵ.
Ɂɞɟɫɶ ɤɨɦɩɪɟɫɫɨɪ Ʉ ɹɜɥɹɟɬɫɹ ɩɨɫɥɟɞɧɢɦ ɷɥɟɦɟɧɬɨɦ ɫɯɟɦɵ (ɪɢɫ. 8.4, ɚ).
ȿɝɨ ɧɚɡɧɚɱɟɧɢɟ – ɫɨɡɞɚɬɶ ɪɚɡɪɹɠɟɧɢɟ ɡɚ ɞɟɬɚɧɞɟɪɨɦ Ⱦ, ɚ ɞɚɜɥɟɧɢɟ ɧɚ ɜɵɯɨɞɟ ɢɡ ɤɨɦɩɪɟɫɫɨɪɚ ɪɚɜɧɨ ɚɬɦɨɫɮɟɪɧɨɦɭ (ɜ ɬɟɨɪɟɬɢɱɟɫɤɨɦ ɰɢɤɥɟ).
Ⱥɬɦɨɫɮɟɪɧɵɣ ɜɨɡɞɭɯ ɩɪɨɯɨɞɢɬ ɤɥɚɩɚɧɧɭɸ ɤɨɪɨɛɤɭ ɄɄ
ɫɪɚɡɭ ɜ ɪɟɝɟɧɟɪɚɬɨɪ Ɋ
, ɝɞɟ ɨɯɥɚɠɞɚɟɬɫɹ ɜ ɩɪɨɰɟɫɫɟ 12 ɫɪɚɡɭ ɞɨ ɧɢɡɲɟɣ
1
ɢ ɩɨɫɬɭɩɚɟɬ
1
ɬɟɦɩɟɪɚɬɭɪɵ ɰɢɤɥɚ Ɍ2. ɉɨɫɥɟ ɷɬɨɝɨ ɯɨɥɨɞɧɵɣ ɜɨɡɞɭɯ ɧɚɩɪɚɜɥɹɟɬɫɹ ɜ ɬɟɩɥɨɨɛɦɟɧɧɵɣ ɚɩɩɚɪɚɬ ɌɈ, ɝɞɟ ɨɧ ɨɬɜɨɞɢɬ ɬɟɩɥɨɬɭ ɨɬ ɨɯɥɚɠɞɚɟɦɨɝɨ ɢɫɬɨɱɧɢɤɚ Q
(ɩɪɨɰɟɫɫ 23), ɚ ɞɚɥɟɟ – ɜ ɞɟɬɚɧɞɟɪ Ⱦ. Ɍɚɤ ɤɚɤ ɤɨɦɩɪɟɫɫɨɪ ɧɟɩɪɟ-
0
ɪɵɜɧɨ ɩɨɞɞɟɪɠɢɜɚɟɬ ɩɪɢ ɜɵɯɨɞɟ ɢɡ ɞɟɬɚɧɞɟɪɚ ɩɨɧɢɠɟɧɧɨɟ ɞɚɜɥɟɧɢɟ
ɪ
< ɪ3 = ɪ
4
, ɬɨ ɜɨɡɞɭɯ, ɪɚɫɲɢɪɹɹɫɶ ɜ ɞɟɬɚɧɞɟɪɟ (ɩɪɨɰɟɫɫ 34), ɫɨɜɟɪɲɚɟɬ
ȺɌɆ
ɜɧɟɲɧɸɸ ɪɚɛɨɬɭ, ɚ ɫɚɦ ɩɪɢ ɷɬɨɦ ɨɯɥɚɠɞɚɟɬɫɹ ɞɨ ɬɟɦɩɟɪɚɬɭɪɵ Ɍ4. Ɂɚɬɟɦ,
ɩɪɨɣɞɹ ɤɥɚɩɚɧɧɭɸ ɤɨɪɨɛɤɭ ɄɄ
, ɷɬɨɬ «ɨɛɪɚɬɧɵɣ» ɩɨɬɨɤ ɯɨɥɨɞɧɨɝɨ ɜɨɡɞɭ-
2
ɯɚ ɩɪɨɯɨɞɢɬ ɪɟɝɟɧɟɪɚɬɨɪ Ɋ2, ɝɞɟ ɨɬɜɨɞɢɬ ɬɟɩɥɨɬɭ ɨɬ ɧɚɫɚɞɤɢ ɢ ɜɵɧɨɫɢɬ
ɜɥɚɝɭ, ɧɚɯɨɞɹɳɭɸɫɹ ɧɚ ɟɟ ɩɨɜɟɪɯɧɨɫɬɢ. Ɍɟɦɩɟɪɚɬɭɪɚ ɨɛɪɚɬɧɨɝɨ ɩɨɬɨɤɚ
ɜɨɡɞɭɯɚ ɩɨɜɵɲɚɟɬɫɹ ɞɨ Ɍ
ɩɚɟɬ ɜ ɤɨɦɩɪɟɫɫɨɪ Ʉ, ɝɞɟ ɫɠɢɦɚɟɬɫɹ ɞɨ ɚɬɦɨɫɮɟɪɧɨɝɨ ɞɚɜɥɟɧɢɹ ɪ
. ɉɪɨɣɞɹ ɤɥɚɩɚɧɧɭɸ ɤɨɪɨɛɤɭ ɄɄ1, ɜɨɡɞɭɯ ɩɨɫɬɭ-
5
= ɪ
6
ȺɌɆ
(ɩɪɨɰɟɫɫ 56) ɢ ɜɵɛɪɚɫɵɜɚɟɬɫɹ ɜ ɚɬɦɨɫɮɟɪɭ. Ɍɚɤ ɤɚɤ ɞɚɜɥɟɧɢɟ ɨɛɪɚɬɧɨɝɨ
ɩɨɬɨɤɚ ɜɨɡɞɭɯɚ ɧɢɠɟ ɚɬɦɨɫɮɟɪɧɨɝɨ, ɬɚɤɨɣ ɰɢɤɥ ɧɚɡɵɜɚɸɬ ɜɚɤɭɭɦɧɵɦ.
ɂɡ ɚɬɦɨɫɮɟɪɵ ȼ ɚɬɦɨɫɮɟɪɭ
ɄɄ
1
1
5
Ɋ
Ɋ
1
2
Ɍ
ɂɇɌ
4
Ⱦɜ
Ʉ
Ⱦ
Ɍ
Ɍ
Ɉɋ
6
Ɍ
ɂɇɌ
3
= ɪ
ɪ
1
1
3
6
ȺɌɆ
5
ɄɄ
2
2
ɌɈ
Q
0
2
4
ɪ5< ɪ
ȺɌɆ
s
ɚ ɛ
Ɋɢɫ. 8.4. ɉɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ (ɚ) ɢ ɜɚɤɭɭɦɧɵɣ ɰɢɤɥ (ɛ) ɪɟɝɟɧɟɪɚɬɢɜɧɨɣ
ɝɚɡɨɜɨɣ ɯɨɥɨɞɢɥɶɧɨɣ ɦɚɲɢɧɵ ɫ ɬɟɩɥɨɦɚɫɫɨɨɛɦɟɧɨɦ
93
ɍɫɬɚɧɨɜɤɚ ɞɥɹ ɤɨɦɩɥɟɤɫɧɨɝɨ ɩɪɨɢɡɜɨɞɫɬɜɚ ɬɟɩɥɨɬɵ ɢ ɬɜɟɪɞɨɝɨ
ɞɢɨɤɫɢɞɚ ɭɝɥɟɪɨɞɚ. ɍɫɬɚɧɨɜɤɚ ɫɨɫɬɨɢɬ (ɪɢɫ. 8.5) ɢɡ ɝɚɡɨɬɭɪɛɨɝɟɧɟɪɚɬɨɪɚ I,
ɬɟɩɥɨɭɬɢɥɢɡɚɰɢɨɧɧɨɣ ɱɚɫɬɢ II ɢ ɯɨɥɨɞɢɥɶɧɨɣ ɱɚɫɬɢ III [1–4]. Ƚɚɡɨɬɭɪɛɨɝɟɧɟɪɚɬɨɪ ɩɪɟɞɧɚɡɧɚɱɟɧ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɝɚɡɨɜɨɡɞɭɲɧɨɣ ɫɦɟɫɢ ɫ ɜɵɫɨɤɨɣ
ɬɟɦɩɟɪɚɬɭɪɨɣ ɢ ɢɡɛɵɬɨɱɧɵɦ ɞɚɜɥɟɧɢɟɦ, ɬɟɩɥɨɭɬɢɥɢɡɚɰɢɨɧɧɚɹ ɱɚɫɬɶ – ɞɥɹ
ɩɨɥɭɱɟɧɢɹ ɩɚɪɚ ɢ ɝɨɪɹɱɟɣ ɜɨɞɵ ɡɚ ɫɱɟɬ ɬɟɩɥɨɜɨɣ ɷɧɟɪɝɢɢ ɝɚɡɨɜɨɡɞɭɲɧɨɣ
ɫɦɟɫɢ, ɯɨɥɨɞɢɥɶɧɚɹ ɱɚɫɬɶ – ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɬɜɟɪɞɨɝɨ
ɞɢɨɤɫɢɞɚ ɭɝɥɟɪɨɞɚ
ɩɪɢ ɪɚɫɲɢɪɟɧɢɢ ɩɪɨɞɭɤɬɨɜ ɫɝɨɪɚɧɢɹ ɬɨɩɥɢɜɚ, ɢɦɟɸɳɢɯ ɢɡɛɵɬɨɱɧɨɟ ɞɚɜɥɟɧɢɟ.
I
Ʉɋ
4
Ʉ
II
3
ȼɨɞɚ
ɉɏ
III
2
ɇ
1
ȼɨɡɞɭɯ ɢɡ
ɚɬɦɨɫɮɟɪɵ
Ɍɨɩɥɢɜɨ
ɗ
7
ɌȾ
9
Ɍɜɟɪɞɵɣ
5
ȽɌ
ȼɈ
ɋɈ
ɚ
6
ɉɚɪ, ɜɨɞɚ
~
2
Ɋ
ɗȾ
10
ȼ ɚɬɦ.
8
ɋ
10
11
Ɍ
Ɍ
Ɉɋ
8
9
10
5
4
3
7
2
1
11
6
s
ɛ
Ɋɢɫ. 8.5. ɉɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ (ɚ) ɢ ɰɢɤɥ (ɛ)
ɬɟɩɥɨɯɥɚɞɨɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɚɝɪɟɝɚɬɚ:
ɇ – ɧɚɝɧɟɬɚɬɟɥɶ; ɉɏ – ɩɪɨɦɟɠɭɬɨɱɧɵɣ ɯɨɥɨɞɢɥɶɧɢɤ; Ʉ – ɤɨɦɩɪɟɫɫɨɪ;
Ʉɋ – ɤɚɦɟɪɚ ɫɝɨɪɚɧɢɹ; ȽɌ – ɝɚɡɨɜɚɹ ɬɭɪɛɢɧɚ; ɗ – ɷɤɨɧɨɦɚɣɡɟɪ;
ȼɈ – ɜɥɚɝɨɨɬɞɟɥɢɬɟɥɶ; Ɋ ɪɟɝɟɧɟɪɚɬɢɜɧɵɣ ɬɟɩɥɨɨɛɦɟɧɧɢɤ;
ɌȾ – ɬɭɪɛɨɞɟɬɚɧɞɟɪ;
ɋ – ɫɟɩɚɪɚɬɨɪ ɋɈ
; ɗȾ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɶ
2
94
Ɂɚɫɚɫɵɜɚɟɦɵɣ ɢɡ ɚɬɦɨɫɮɟɪɵ ɜɨɡɞɭɯ ɫɠɢɦɚɟɬɫɹ ɬɭɪɛɨɧɚɝɧɟɬɚɬɟɥɟɦ ɇ
ɢ ɱɟɪɟɡ ɜɨɞɹɧɨɣ ɩɪɨɦɟɠɭɬɨɱɧɵɣ ɯɨɥɨɞɢɥɶɧɢɤ ɉɏ (ɩɪɨɰɟɫɫ 1–2–3) ɩɨɞɚɟɬɫɹ ɜ ɤɨɦɩɪɟɫɫɨɪ Ʉ, ɝɞɟ ɫɠɢɦɚɟɬɫɹ (ɩɪɨɰɟɫɫ 3–4). ɋɠɚɬɵɣ ɜɨɡɞɭɯ ɧɚɝɧɟɬɚɟɬɫɹ ɜ ɤɚɦɟɪɭ ɫɝɨɪɚɧɢɹ Ʉɋ ɢ ɩɨɞɨɝɪɟɜɚɟɬɫɹ (ɩɪɨɰɟɫɫ 4–5) ɞɨ ɬɟɦɩɟɪɚɬɭɪɵ 1000–1200 Ʉ ɩɪɢ ɫɠɢɝɚɧɢɢ ɠɢɞɤɨɝɨ ɢɥɢ ɝɚɡɨɨɛɪɚɡɧɨɝɨ ɬɨɩɥɢɜɚ. ȼɵɫɨɤɨɬɟɦɩɟɪɚɬɭɪɧɚɹ ɝɚɡɨɜɨɡɞɭɲɧɚɹ ɫɦɟɫɶ ɩɨɫɬɭɩɚɟɬ ɧɚ ɱɚɫɬɢɱɧɨɟ ɪɚɫɲɢɪɟ
-
ɧɢɟ ɜ ɝɚɡɨɜɭɸ ɬɭɪɛɢɧɭ ȽɌ (ɩɪɨɰɟɫɫ 5–6), ɦɨɳɧɨɫɬɶ ɤɨɬɨɪɨɣ ɢɫɩɨɥɶɡɭɟɬɫɹ
ɞɥɹ ɩɪɢɜɨɞɚ ɤɨɦɩɪɟɫɫɨɪɚ, ɢ ɡɚɬɟɦ ɜ ɷɤɨɧɨɦɚɣɡɟɪ ɗ, ɝɞɟ ɛɥɚɝɨɞɚɪɹ ɬɟɩɥɨɨɛɦɟɧɭ ɫ ɩɢɬɚɬɟɥɶɧɨɣ ɜɨɞɨɣ (ɩɪɨɰɟɫɫ 6–7) ɜɵɪɚɛɚɬɵɜɚɟɬɫɹ ɩɚɪ ɢɥɢ ɝɨɪɹɱɚɹ ɜɨɞɚ. Ⱦɚɥɟɟ ɝɚɡɨɜɵɣ ɩɨɬɨɤ, ɩɪɨɣɞɹ ɜɥɚɝɨɨɬɞɟɥɢɬɟɥɶ ȼɈ, ɧɚɩɪɚɜɥɹɟɬɫɹ
ɜ ɯɨɥɨɞɢɥɶɧɭɸ ɱɚɫɬɶ, ɝɞɟ ɨɯɥɚɠɞɚɟɬɫɹ (ɩɪɨɰɟɫɫ 7–8) ɨɛɪɚɬɧɵɦ ɩɨɬɨɤɨɦ
ɜ ɪɟɝɟɧɟɪɚɬɨɪɟ Ɋ.
ɉɪɢ
ɪɚɫɲɢɪɟɧɢɢ ɩɪɨɞɭɤɬɨɜ ɫɝɨɪɚɧɢɹ ɬɨɩɥɢɜɚ (ɉɋɌ) ɜ ɬɭɪɛɨɞɟɬɚɧɞɟɪɟ (ɩɪɨɰɟɫɫ 89) ɬɟɦɩɟɪɚɬɭɪɚ ɩɨɬɨɤɚ ɫɧɢɠɚɟɬɫɹ ɧɢɠɟ ɬɟɦɩɟɪɚɬɭɪɵ ɧɚɫɵ-
ɳɟɧɢɹ ɬɜɟɪɞɨɝɨ ɞɢɨɤɫɢɞɚ ɭɝɥɟɪɨɞɚ (ɋɈ
ɞɨɣ ɮɚɡɵ ɋɈ
, ɤɨɬɨɪɚɹ ɡɚɬɟɦ ɨɬɞɟɥɹɟɬɫɹ ɜ ɫɟɩɚɪɚɬɨɪɟ ɋ. Ɉɛɪɚɬɧɵɣ ɩɨɬɨɤ
2
) ɢ ɩɪɨɢɫɯɨɞɢɬ ɜɵɩɚɞɟɧɢɟ ɬɜɟɪ-
2
ɝɚɡɨɜ ɧɚɩɪɚɜɥɹɟɬɫɹ ɜ ɛɥɨɤ ɪɟɝɟɧɟɪɚɬɨɪɨɜ, ɨɯɥɚɠɞɚɟɬ ɩɪɹɦɨɣ ɩɨɬɨɤ
(ɩɪɨɰɟɫɫ 10–11) ɢ ɡɚɬɟɦ ɜɵɛɪɚɫɵɜɚɟɬɫɹ ɜ ɚɬɦɨɫɮɟɪɭ. Ɋɚɛɨɬɚ ɪɚɫɲɢɪɟɧɢɹ
ɩɚɪɨɝɚɡɨɜɨɣ ɫɦɟɫɢ ɜ ɬɭɪɛɨɞɟɬɚɧɞɟɪɟ ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɥɹ ɱɚɫɬɢɱɧɨɣ ɤɨɦɩɟɧɫɚɰɢɢ ɷɧɟɪɝɢɢ, ɩɨɬɪɟɛɥɹɟɦɨɣ ɧɚɝɧɟɬɚɬɟɥɟɦ ɨɬ ɚɫɢɧɯɪɨɧɧɨɝɨ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɹ ɗȾ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɭɳɧɨɫɬɶ ɪɚɛɨɬɵ ɭɫɬɚɧɨɜɤɢ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɩɨɷɬɚɩɧɨɦ
ɨɯɥɚɠɞɟɧɢɢ
ɉɋɌ, ɜɵɪɚɛɚɬɵɜɚɟɦɵɯ ɝɚɡɨɬɭɪɛɨɝɟɧɟɪɚɬɨɪɨɦ ɩɪɢ ɩɨɜɵɲɟɧɧɨɦ ɞɚɜɥɟɧɢɢ ɢ ɬɟɦɩɟɪɚɬɭɪɟ ɜ ɷɤɨɧɨɦɚɣɡɟɪɟ, ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɩɚɪɚ ɢɥɢ ɝɨɪɹɱɟɣ ɜɨɞɵ, ɢ ɞɚɥɶɧɟɣɲɟɦ ɨɯɥɚɠɞɟɧɢɢ ɜ ɪɟɝɟɧɟɪɚɬɢɜɧɨɦ ɬɟɩɥɨɨɛɦɟɧɧɢɤɟ
ɢ ɬɭɪɛɨɞɟɬɚɧɞɟɪɟ.
ȼ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɫɯɟɦɟ ɉɋɌ ɧɟ ɬɨɥɶɤɨ ɫɨɜɟɪɲɚɸɬ ɪɚɛɨɬɭ ɜ ɝɚɡɨɜɨɣ
ɬɭɪɛɢɧɟ ɢ ɬɭɪɛɨɞɟɬɚɧɞɟɪɟ, ɧɨ ɢ ɹɜɥɹɸɬɫɹ ɯɨɥɨɞɢɥɶɧɵɦ ɚɝɟɧɬɨɦ. ɗɬɨ ɩɪɢɜɨɞɢɬ ɤ ɫɧɢɠɟɧɢɸ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ
ɩɨɬɟɪɶ, ɫɜɹɡɚɧɧɵɯ ɫ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟɦ
ɷɧɟɪɝɢɢ, ɢɦɟɸɳɢɦ ɦɟɫɬɨ ɜ ɨɛɵɱɧɵɯ ɬɟɩɥɨɫɢɥɨɜɵɯ ɢ ɯɨɥɨɞɢɥɶɧɵɯ ɭɫɬɚɧɨɜɤɚɯ. ɉɨɜɵɲɟɧɢɟ ɞɚɜɥɟɧɢɹ ɝɚɡɚ ɜ ɬɟɩɥɨɭɬɢɥɢɡɚɰɢɨɧɧɨɣ ɱɚɫɬɢ ɢ ɤɨɧɞɟɧɫɚɰɢɹ ɜɨɞɹɧɵɯ ɩɚɪɨɜ, ɩɪɢɫɭɬɫɬɜɭɸɳɢɯ ɜ ɉɋɌ, ɭɜɟɥɢɱɢɜɚɟɬ ɤɨɷɮɮɢɰɢɟɧɬ ɬɟɩɥɨɩɟɪɟɞɚɱɢ ɢ ɩɨɡɜɨɥɹɟɬ ɭɦɟɧɶɲɢɬɶ ɩɨɜɟɪɯɧɨɫɬɶ ɬɟɩɥɨɨɛɦɟɧɧɵɯ
ɚɩɩɚɪɚɬɨɜ ɢ ɢɯ ɦɟɬɚɥɥɨɟɦɤɨɫɬɶ.
ȼɚɠɧɨɣ ɨɫɨɛɟɧɧɨɫɬɶɸ ɩɪɨɰɟɫɫɚ ɨɯɥɚɠɞɟɧɢɹ ɜ ɷɤɨɧɨɦɚɣɡɟɪɟ ɹɜɥɹɟɬɫɹ
ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɬɟɩɥɨɬɵ ɤɨɧɞɟɧɫɚɰɢɢ
ɜɨɞɹɧɵɯ ɩɚɪɨɜ ɩɪɨɞɭɤɬɨɜ ɝɨɪɟɧɢɹ.
95
ȼ ɪɚɛɨɱɟɦ ɩɪɨɰɟɫɫɟ ɰɢɤɥɚ ɢɫɩɨɥɶɡɭɟɬɫɹ ɜɵɫɲɚɹ ɬɟɩɥɨɬɜɨɪɧɚɹ ɫɩɨɫɨɛɧɨɫɬɶ ɬɨɩɥɢɜɚ. ɂɡɜɟɫɬɧɨ, ɱɬɨ ɪɚɡɧɨɫɬɶ ɦɟɠɞɭ ɜɵɫɲɟɣ ɢ ɧɢɡɲɟɣ ɬɟɩɥɨɬɜɨɪɧɨɣ ɫɩɨɫɨɛɧɨɫɬɶɸ, ɧɚɩɪɢɦɟɪ, ɞɥɹ ɩɪɢɪɨɞɧɨɝɨ ɝɚɡɚ, ɫɨɫɬɚɜɥɹɟɬ 12 %,
ɜɫɥɟɞɫɬɜɢɟ ɱɟɝɨ ɭɬɢɥɢɡɚɰɢɹ ɷɬɨɣ ɧɢɡɤɨɩɨɬɟɧɰɢɚɥɶɧɨɣ ɬɟɩɥɨɬɵ ɜ ɰɢɤɥɟ
ɨɛɟɫɩɟɱɢɜɚɟɬ ɡɧɚɱɢɬɟɥɶɧɨɟ ɩɨɜɵɲɟɧɢɟ ɬɟɩɥɨɜɨɝɨ ɷɮɮɟɤɬɚ.
ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɜɵɫɨɤɢɣ ɷɤɨɥɨɝɢɱɟɫɤɢɣ ɷɮɮɟɤɬ ɭɫɬɚɧɨɜɤɢ ɫɜɹ-
ɡɚɧ ɫ ɭɦɟɧɶɲɟɧɢɟɦ ɡɚɝɪɹɡɧɟɧɢɣ ɨɤɪɭɠɚɸɳɟɣ
ɫɪɟɞɵ ɜɫɥɟɞɫɬɜɢɟ ɫɧɢɠɟɧɢɹ
ɬɟɩɥɨɩɨɬɟɪɶ ɢ ɜɵɛɪɨɫɨɜ ɋɈ2 ɢ ɬɨɤɫɢɱɧɵɯ ɨɤɢɫɥɨɜ ɚɡɨɬɚ ɢ ɫɟɪɵ ɜ ɚɬɦɨɫɮɟɪɭ ɫ ɨɬɪɚɛɨɬɚɜɲɢɦɢ ɉɋɌ. ɋɨɜɦɟɫɬɧɚɹ ɤɨɧɞɟɧɫɚɰɢɹ ɨɤɢɫɥɨɜ ɚɡɨɬɚ ɢ
ɫɟɪɵ ɫ ɜɨɞɹɧɵɦɢ ɩɚɪɚɦɢ ɩɪɨɢɫɯɨɞɢɬ ɜ ɬɟɩɥɨɭɬɢɥɢɡɚɰɢɨɧɧɨɣ ɱɚɫɬɢ ɭɫɬɚɧɨɜɤɢ.
8.2. ȼɢɯɪɟɜɵɟ ɨɯɥɚɞɢɬɟɥɢ
ȼ 1933 ɝ. Ɋɚɧɤ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɭɫɬɚɧɨɜɢɥ ɪɚɡɥɢɱɢɟ ɜ ɬɟɦɩɟɪɚɬɭɪɚɯ
ɩɨɬɨɤɨɜ ɜɨɡɞɭɯɚ, ɞɜɢɠɭɳɢɯɫɹ ɭ ɨɫɢ ɢ ɧɚ ɩɟɪɢɮɟɪɢɢ ɰɢɤɥɨɧɧɨɝɨ ɩɵɥɟɭɥɨɜɢɬɟɥɹ. ɗɬɨ ɨɬɤɪɵɬɢɟ ɨɩɪɨɜɟɪɝɚɥɨɫɶ ɞɨ ɨɩɭɛɥɢɤɨɜɚɧɢɹ ɪɚɛɨɬɵ ɏɢɥɶɲɚ
ɜ 1946 ɝ. ɉɪɨɰɟɫɫ ɬɟɦɩɟɪɚɬɭɪɧɨɝɨ ɪɚɡɞɟɥɟɧɢɹ ɝɚɡɚ, ɨɫɭɳɟɫɬɜɥɹɟɦɵɣ ɜ
ɜɢɯɪɟɜɨɣ ɬɪɭɛɟ, ɜɵɡɜɚɥ ɡɧɚɱɢɬɟɥɶɧɵɣ ɢɧɬɟɪɟɫ ɜɫɥɟɞɫɬɜɢɟ ɩɪɨɫɬɨɬɵ ɟɟ
ɤɨɧɫɬɪɭɤɰɢɢ (ɪɢɫ. 8.6).
ɋɠɚɬɵɣ ɝɚɡ ɩɨɞɜɨɞɢɬɫɹ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ
ɜ ɰɢɥɢɧɞɪɢɱɟɫɤɭɸ ɬɪɭɛɭ 3 ɱɟɪɟɡ ɫɨɩɥɨ 1 ɩɨ ɤɚɫɚɬɟɥɶɧɨɣ ɤ ɜɧɭɬɪɟɧɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ
ɬɪɭɛɵ. Ƚɚɡ ɫɨɜɟɪɲɚɟɬ ɜɪɚɳɚɬɟɥɶɧɨɟ ɞɜɢɠɟɧɢɢ, ɨɞɧɨɜɪɟɦɟɧɧɨ ɩɟɪɟɦɟɳɚɹɫɶ
ɨɬ ɫɨɩɥɚ 1 ɤ ɞɪɨɫɫɟɥɸ 2, ɩɪɢɱɟɦ ɱɟɪɟɡ ɞɢɚɮɪɚɝɦɭ 4 (ɢɥɢ ɱɟɪɟɡ ɬɪɭɛɭ ɦɟɧɶɲɟɝɨ ɞɢɚɦɟɬɪɚ) ɜɵɯɨɞɢɬ ɯɨɥɨɞɧɵɣ ɩɨɬɨɤ ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ Ɍ
ɞɪɨɫɫɟɥɶ 2 ɩɨ ɩɟɪɢɮɟɪɢɢ ɬɪɭɛɵ – ɝɨɪɹɱɢɣ ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ Ɍ
(Ɍ2), ɚ ɱɟɪɟɡ
ɏ
(Ɍ3). ɉɪɢ ɞɚɜ-
Ƚ
ɥɟɧɢɢ 0,30,5 Ɇɉɚ ɬɟɦɩɟɪɚɬɭɪɚ ɨɯɥɚɠɞɟɧɧɨɝɨ ɝɚɡɚ ɧɚ 3070 °ɋ ɧɢɠɟ
ɧɚɱɚɥɶɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɝɚɡɚ.
ɉɪɨɰɟɫɫ ɬɟɦɩɟɪɚɬɭɪɧɨɝɨ ɪɚɡɞɟɥɟɧɢɹ ɜɨɡɞɭɯɚ ɜ ɜɢɯɪɟɜɨɣ ɬɪɭɛɟ (ɪɢɫ. 8.7)
ɦɨɠɟɬ ɛɵɬɶ ɭɩɪɨɳɟɧɧɨ ɩɪɟɞɫɬɚɜɥɟɧ ɜ Ɍs-ɞɢɚɝɪɚɦɦɟ:
ɬɨɱɤɚ 1 ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɧɚɱɚɥɶɧɨɟ ɫɨɫɬɨɹɧɢɟ ɜɨɡɞɭɯɚ ɩɟɪɟɞ ɫɨɩɥɨɦ
ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ Ɍ
= ɌɈɋ ɢ ɞɚɜɥɟɧɢɢ ɪ1;
1
ɬɨɱɤɢ 2 ɢ 3 ɯɚɪɚɤɬɟɪɢɡɭɸɬ ɫɨɫɬɨɹɧɢɟ ɯɨɥɨɞɧɨɝɨ ɢ ɝɨɪɹɱɟɝɨ ɜɨɡɞɭɯɚ
ɩɨɫɥɟ ɩɪɨɰɟɫɫɚ ɪɚɡɞɟɥɟɧɢɹ ɜ ɜɢɯɪɟɜɨɣ ɬɪɭɛɟ;
ɬɨɱɤɚ 4 ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɫɨɫɬɨɹɧɢɟ ɜɨɡɞɭɯɚ, ɡɚɫɚɫɵɜɚɟɦɨɝɨ ɜ ɤɨɦɩɪɟɫɫɨɪ.
96
ɐɢɤɥ ɫɨɫɬɨɢɬ: ɢɡ ɩɨɥɢɬɪɨɩɧɵɯ ɩɪɨɰɟɫɫɨɜ 12 ɢ 13, ɫɨɜɟɪɲɚɸɳɢɯɫɹ
ɨɞɧɨɜɪɟɦɟɧɧɨ ɩɪɢ ɪɚɫɲɢɪɟɧɢɢ ɜɨɡɞɭɯɚ ɜ ɜɢɯɪɟɜɨɣ ɬɪɭɛɟ; ɢɡ ɩɪɨɰɟɫɫɚ 24,
ɯɚɪɚɤɬɟɪɢɡɭɸɳɟɝɨ ɩɨɞɜɨɞ ɬɟɩɥɨɬɵ ɤ ɪɚɛɨɱɟɦɭ ɜɟɳɟɫɬɜɭ ɨɬ ɢɫɬɨɱɧɢɤɚ
ɧɢɡɤɨɣ ɬɟɦɩɟɪɚɬɭɪɵ; ɢɡ ɩɪɨɰɟɫɫɚ 34 ɨɬɜɨɞɚ ɬɟɩɥɨɬɵ; ɢɡ ɩɪɨɰɟɫɫɚ 41 –
ɫɠɚɬɢɹ ɜ ɢɡɨɬɟɪɦɢɱɟɫɤɨɦ ɩɪɨɰɟɫɫɟ. ɉɪɢ ɚɞɢɚɛɚɬɧɨɦ ɫɠɚɬɢɢ ɜ ɤɨɦɩɪɟɫɫɨɪɟ ɜɦɟɫɬɨ ɩɪɨɰɟɫɫɚ 41 ɫɥɟɞɭɟɬ
ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɩɪɨɰɟɫɫɵ 45 ɢ 51 –
ɨɯɥɚɠɞɟɧɢɹ ɜ ɯɨɥɨɞɢɥɶɧɢɤɟ.
A
1
L
2
D
4
A-A
A
3
A
1
2
A
4
3
ɚ
A-A
ɛ
ɜ ɝ ɞ ɟ
Ɋɢɫ. 8.6. ɋɯɟɦɚ ɜɢɯɪɟɜɨɣ ɬɪɭɛɵ:
ɚ – ɩɪɹɦɨɬɨɱɧɨɣ ɬɢɩ; ɛ – ɩɪɨɬɢɜɨɬɨɱɧɵɣ ɬɢɩ;
ɜ – ɩɪɹɦɨɬɨɱɧɵɣ ɫɨɩɥɨɜɨɣ ɜɜɨɞ; ɝ – ɜɜɨɞ ɫ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɣ
ɡɚɤɪɭɬɤɨɣ ɩɨɬɨɤɚ; ɞ – ɞɜɭɯɫɨɩɥɨɜɵɣ ɜɜɨɞ; ɟ – ɦɧɨɝɨɫɨɩɥɨɜɵɣ ɜɜɨɞ
97
ɗɧɟɪɝɨɨɛɦɟɧ ɦɟɠɞɭ ɰɟɧɬɪɚɥɶɧɨɣ ɢ ɩɟɪɢɮɟɪɢɣɧɨɣ ɱɚɫɬɹɦɢ ɩɨɬɨɤɚ ɯɚ-
'
Ɍ
'
Ɍ
Ƚ
'
Ɍ
ɪɚɤɬɟɪɢɡɭɟɬɫɹ ɫɭɳɟɫɬɜɟɧɧɨɣ ɧɟɨɛɪɚɬɢɦɨɫɬɶɸ, ɩɨɷɬɨɦɭ ɩɪɨɰɟɫɫ ɪɚɫɲɢɪɟɧɢɹ ɯɨɥɨɞɧɨɝɨ ɩɨɬɨɤɚ ɜɨɡɞɭɯɚ ɢɡɨɛɪɚɠɚɟɬɫɹ ɧɟ ɢɡɨɷɧɬɪɨɩɨɣ (12'), ɚ ɧɟɨɛɪɚɬɢɦɵɦ ɩɨɥɢɬɪɨɩɧɵɦ 12.
Ɍ
p
=const
1
5
p2=const
ȼɢɯɪɟɜɵɟ ɬɪɭɛɵ, ɪɚɛɨɬɚɸɳɢɟ ɩɪɢ
ɨɞɢɧɚɤɨɜɨɦ ɨɬɧɨɲɟɧɢɢ ɞɚɜɥɟɧɢɣ
S
= ɪ1 / ɪ2, ɧɨ ɩɪɢ ɪɚɡɧɵɯ ɬɟɦɩɟɪɚɬɭ-
ɪɚɯ Ɍ1 ɜɨɡɞɭɯɚ ɩɟɪɟɞ ɜɢɯɪɟɜɨɣ ɬɪɭ-
3
1
4
2
2'
Ɋɢɫ. 8.7. ɉɪɨɰɟɫɫ ɬɟɦɩɟɪɚɬɭɪɧɨɝɨ
ɪɚɡɞɟɥɟɧɢɹ ɜɨɡɞɭɯɚ ɜ ɜɢɯɪɟɜɨɣ
ɬɪɭɛɟ ɜ Ɍs-ɞɢɚɝɪɚɦɦɟ
Ɍ
Ɍ
ɏ
Ɍ
S
Ɍ
ɛɨɣ, ɨɛɵɱɧɨ ɫɪɚɜɧɢɜɚɸɬ ɧɟ ɩɨ ɬɟɦɩɟ-
Ƚ
ɪɚɬɭɪɧɵɦ ɷɮɮɟɤɬɚɦ ɨɯɥɚɠɞɟɧɢɹ
'Ɍ
= Ɍ1 – Ɍɏ ɢ ɧɚɝɪɟɜɚ 'ɌȽ = ɌȽ – Ɍ1
ɏ
ɏ
(ɫɦ. ɪɢɫ. 8.7), ɚ ɩɨ ɨɬɧɨɫɢɬɟɥɶɧɵɦ
ɬɟɦɩɟɪɚɬɭɪɚɦ ɯɨɥɨɞɧɨɝɨ ɢ ɝɨɪɹɱɟɝɨ
S
ɩɨɬɨɤɨɜ 4
s
ɬɟɦɩɟɪɚɬɭɪɧɨɣ ɷɮɮɟɤɬɢɜɧɨɫɬɢ
= 'Ɍ
= Ɍɏ / Ɍ1 ɢ 4Ƚ = ɌȽ / Ɍ1 ɢ
ɏ
/ 'ɌS, ɝɞɟ 'ɌS – ɷɮɮɟɤɬ ɨɯɥɚ-
ɏ
K
=
ɠɞɟɧɢɹ ɩɪɢ ɢɡɨɷɧɬɪɨɩɧɨɦ ɪɚɫɲɢɪɟɧɢɢ.
ɗɮɮɟɤɬ ɨɯɥɚɠɞɟɧɢɹ:
TT
S
'
S
/1 kk
.1
Ⱥɞɢɚɛɚɬɧɵɟ ɜɢɯɪɟɜɵɟ ɬɪɭɛɵ ɧɟ ɢɦɟɸɬ ɫɢɫɬɟɦɵ ɨɯɥɚɠɞɟɧɢɹ ɝɨɪɹɱɟɝɨ
ɤɨɧɰɚ. Ⱦɥɢɧɚ ɟɝɨ ɫɨɫɬɚɜɥɹɟɬ ɨɬ 3 ɞɨ 20 ɞɢɚɦɟɬɪɨɜ D ɜɢɯɪɟɜɨɣ ɬɪɭɛɵ:
L = (320) D.
ȼ ɧɟɚɞɢɚɛɚɬɧɵɯ ɬɪɭɛɚɯ ɜɵɫɨɤɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɩɟɪɢɮɟɪɢɣɧɵɯ ɫɥɨɟɜ
ɜɢɯɪɹ ɩɨɡɜɨɥɹɟɬ ɨɬɜɨɞɢɬɶ ɨɬ ɧɢɯ ɬɟɩɥɨɬɭ ɜ ɨɤɪɭɠɚɸɳɭɸ ɫɪɟɞɭ. ȼɵɫɨɤɚɹ
ɬɭɪɛɭɥɟɧɬɧɨɫɬɶ ɢ ɡɧɚɱɢɬɟɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɩɟɪɢɮɟɪɢɣɧɵɯ ɫɥɨɟɜ ɨɛɟɫɩɟɱɢɜɚɟɬ
ɛɨɥɶɲɢɟ ɡɧɚɱɟɧɢɹ ɬɟɩɥɨɨɬɞɚɱɢ ɤ ɫɬɟɧɤɟ ɝɨɪɹɱɟɝɨ ɤɨɧɰɚ. ɇɚ ɪɢɫɭɧɤɟ 8.8
ɩɨɤɚɡɚɧɵ ɧɟɤɨɬɨɪɵɟ ɫɩɨɫɨɛɵ ɨɯɥɚɠɞɟɧɢɹ ɝɨɪɹɱɟɝɨ ɩɨɬɨɤɚ.
ȼ ɤɚɱɟɫɬɜɟ ɪɚɛɨɱɢɯ ɜɟɳɟɫɬɜ ɦɨɝɭɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɵ ɜɨɡɞɭɯ, ɩɪɢɪɨɞɧɵɣ ɝɚɡ, ɝɟɥɢɣ
ɢ ɞɪ. ɇɚɢɛɨɥɶɲɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɩɨɥɭɱɢɥɢ ɜɢɯɪɟɜɵɟ
ɬɪɭɛɵ, ɪɚɛɨɬɚɸɳɢɟ ɧɚ ɜɨɡɞɭɯɟ.
98
G
G
Ƚ
P
)
G
G
P
G
T1
=(1
=
ɏ
T
ɏ
T
1W
T
2W
T
Ƚ
T
1
T
T
ɏ
T
1W
Ƚ
T
Ƚ
T
2W
ɚ ɛ
T
1
T
ɏ
T
Ƚ
T
Ɉɋ
T
T
Ƚ
1
T
ɏ
T
1W
T
2W
ɜ ɝ
T
T
ɏ
1
T
T
ɏ
T
ɏ
1
T
T
Ƚ
1W
T
1
T
2W
ɞ ɟ ɠ
Ɋɢɫ. 8.8. ɋɩɨɫɨɛɵ ɨɯɥɚɠɞɟɧɢɹ ɝɨɪɹɱɟɝɨ ɩɨɬɨɤɚ
ɜ ɧɟɚɞɢɚɛɚɬɧɵɯ ɜɢɯɪɟɜɵɯ ɬɪɭɛɚɯ:
ɚ – ɠɢɞɤɨɫɬɶɸ, ɩɪɨɤɚɱɢɜɚɟɦɨɣ ɱɟɪɟɡ ɪɭɛɚɲɤɭ; ɛ – ɠɢɞɤɨɫɬɶɸ,
ɩɨɞɚɜɚɟɦɨɣ ɜ ɩɨɥɨɫɬɶ ɝɨɪɹɱɟɝɨ ɤɨɧɰɚ ɢ ɤɨɧɬɚɤɬɢɪɭɸɳɟɣ
ɫ ɩɟɪɢɮɟɪɢɟɣ ɜɢɯɪɹ; ɜ – ɡɦɟɟɜɢɤɨɦ ɜ ɩɨɥɨɫɬɢ ɝɨɪɹɱɟɝɨ ɤɨɧɰɚ;
ɝ – ɜɨɡɞɭɯɨɦ, ɷɠɟɤɬɢɪɭɟɦɵɦ ɝɨɪɹɱɢɦ ɩɨɬɨɤɨɦ; ɞ – ɩɪɢ ɛɚɪɛɨɬɚɠɟ
ɝɨɪɹɱɟɝɨ ɩɨɬɨɤɚ ɱɟɪɟɡ ɢɫɩɚɪɹɸɳɭɸɫɹ ɠɢɞɤɨɫɬɶ; ɟ – ɨɯɥɚɠɞɟɧɢɟ
ɜ ɢɫɩɚɪɢɬɟɥɶɧɨ-ɤɨɧɞɟɧɫɚɬɨɪɧɨɦ
ɤɨɧɬɭɪɟ; ɠ – ɨɯɥɚɠɞɟɧɢɟ
ɧɚ ɜɧɭɬɪɟɧɧɟɦ ɨɪɟɛɪɟɧɢɢ ɝɨɪɹɱɟɝɨ ɤɨɧɰɚ
Ⱦɨɫɬɨɢɧɫɬɜɚɦɢ ɜɢɯɪɟɜɵɯ ɬɪɭɛ ɹɜɥɹɸɬɫɹ ɩɪɨɫɬɨɬɚ ɢɡɝɨɬɨɜɥɟɧɢɹ ɢ
ɷɤɫɩɥɭɚɬɚɰɢɢ, ɤɨɦɩɚɤɬɧɨɫɬɶ, ɜɵɫɨɤɚɹ ɧɚɞɟɠɧɨɫɬɶ ɪɚɛɨɬɵ, ɦɚɥɚɹ ɢɧɟɪɰɢɨɧɧɨɫɬɶ ɩɪɢ ɜɵɯɨɞɟ ɧɚ ɪɚɛɨɱɢɣ ɪɟɠɢɦ. Ɉɫɧɨɜɧɨɣ ɧɟɞɨɫɬɚɬɨɤ – ɧɢɡɤɚɹ
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ɷɧɟɪɝɟɬɢɱɟɫɤɚɹ ɷɮɮɟɤɬɢɜɧɨɫɬɶ. ɋɬɟɩɟɧɶ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɫɨɜɟɪɲɟɧɫɬɜɚ ɫɨɫɬɚɜɥɹɟɬ ɧɟɫɤɨɥɶɤɨ ɩɪɨɰɟɧɬɨɜ.
ȼɢɯɪɟɜɵɟ ɬɪɭɛɵ, ɢɫɩɨɥɶɡɭɟɦɵɟ ɜ ɯɨɥɨɞɢɥɶɧɨɣ ɬɟɯɧɢɤɟ, ɦɨɠɧɨ ɪɚɡɞɟɥɢɬɶ ɧɚ ɬɪɢ ɝɪɭɩɩɵ:
1. Ɍɪɭɛɵ, ɩɪɟɞɧɚɡɧɚɱɟɧɧɵɟ ɞɥɹ ɨɯɥɚɠɞɟɧɢɹ ɱɚɫɬɢ ɩɨɞɚɜɚɟɦɨɝɨ ɜɨɡɞɭɯɚ ɞɨ ɜɨɡɦɨɠɧɨ ɛɨɥɟɟ ɧɢɡɤɨɣ ɬɟɦɩɟɪɚɬɭɪɵ. ɗɬɨ ɚɞɢɚɛɚɬɧɵɟ ɜɢɯɪɟɜɵɟ
ɬɪɭɛɵ ɫ ɞɨɥɟɣ ɯɨɥɨɞɧɨɝɨ ɩɨɬɨɤɚ
P
= Gɏ / G = 0,20,4.
2. Ɍɪɭɛɵ, ɢɫɩɨɥɶɡɭɟɦɵɟ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɦɢɧɢɦɚɥɶɧɵɯ ɬɟɦɩɟɪɚɬɭɪ
ɜɧɭɬɪɢ ɫɚɦɨɣ ɬɪɭɛɵ, ɪɚɛɨɬɚɸɳɟɣ, ɤɚɤ ɩɪɚɜɢɥɨ, ɛɟɡ ɨɬɜɨɞɚ ɯɨɥɨɞɧɨɝɨ ɩɨɬɨɤɚ (ɫɚɦɨɜɚɤɭɭɦɢɪɭɸɳɢɟɫɹ ɜɢɯɪɟɜɵɟ ɬɪɭɛɵ, ɝɞɟ
P
= 0).
3. Ɍɪɭɛɵ, ɩɪɢɦɟɧɹɟɦɵɟ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɦɚɤɫɢɦɚɥɶɧɨɣ ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢ-
ɬɟɥɶɧɨɫɬɢ, ɧɟɚɞɢɚɛɚɬɧɵɟ (ɫ ɢɧɬɟɧɫɢɜɧɵɦ ɨɯɥɚɠɞɟɧɢɟɦ ɝɨɪɹɱɟɝɨ ɤɨɧɰɚ)
ɜɢɯɪɟɜɵɟ ɬɪɭɛɵ, ɝɞɟ P > 0,6.
ȼɢɯɪɟɜɵɟ ɬɪɭɛɵ ɦɨɝɭɬ ɪɚɛɨɬɚɬɶ ɜ ɫɨɱɟɬɚɧɢɢ ɫ ɪɚɡɥɢɱɧɵɦɢ ɚɩɩɚɪɚɬɚɦɢ (ɬɟɩɥɨɨɛɦɟɧɧɢɤɢ, ɷɠɟɤɬɨɪɵ ɢ ɞɪ.), ɨɛɪɚɡɭɹ ɩɪɢ ɷɬɨɦ ɜɢɯɪɟɜɵɟ ɯɨɥɨɞɢɥɶɧɵɟ ɚɝɪɟɝɚɬɵ ɪɚɡɥɢɱɧɵɯ ɬɢɩɨɜ, ɝɥɚɜɧɵɟ ɢɡ ɤɨɬɨɪɵɯ – ɪɟɝɟɧɟɪɚɬɢɜɧɵɟ, ɤɚɫɤɚɞɧɵɟ ɢ ɫɬɭɩɟɧɱɚɬɵɟ (ɪɢɫ. 8.9).
Ɍ
ɏ
1
Ɍ
1
2
Ɍ
ɋɠɚɬɵɣ ɜɨɡɞɭɯ
Ɉɋ
1
ɋɠɚɬɵɣ
ɜɨɡɞɭɯ
Ɉɯɥɚɠɞɚɸɳɚɹ
ɠɢɞɤɨɫɬɶ
Ɍ
1W
Ɍ
ɏ
Ɍ
1
4
3
Ɍ
2W
ɋɠɚɬɵɣ ɜɨɡɞɭɯ
Ɍ
Ɍ'
ɏ
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ɏ
1
Ɉɋ
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Ƚ
ɚ ɛ ɜ
Ɋɢɫ. 8.9 (ɧɚɱɚɥɨ). ɋɯɟɦɵ ɜɢɯɪɟɜɵɯ ɯɨɥɨɞɢɥɶɧɵɯ ɚɝɪɟɝɚɬɨɜ:
ɚ – ɪɟɝɟɧɟɪɚɬɢɜɧɚɹ ɫ ɬɟɩɥɨɨɛɦɟɧɧɢɤɨɦ-ɪɟɤɭɩɟɪɚɬɨɪɨɦ; ɛ
– ɪɟɝɟɧɟɪɚɬɢɜɧɚɹ
ɫ ɞɜɭɯɫɟɤɰɢɨɧɧɵɦ ɪɟɝɟɧɟɪɚɬɨɪɨɦ ɢ ɩɟɪɟɤɥɸɱɚɬɟɥɹɦɢ ɩɨɬɨɤɨɜ;
ɜ – ɞɜɭɯɫɬɭɩɟɧɱɚɬɚɹ ɫ ɷɠɟɤɬɢɪɨɜɚɧɢɟɦ ɚɬɦɨɫɮɟɪɧɨɝɨ ɜɨɡɞɭɯɚ ɝɨɪɹɱɢɦ
ɩɨɬɨɤɨɦ ɢɡ ɜɢɯɪɟɜɨɣ ɬɪɭɛɵ ɜɬɨɪɨɣ ɫɬɭɩɟɧɢ:
1 – ɯɨɥɨɞɢɥɶɧɚɹ ɤɚɦɟɪɚ; 2 – ɬɟɩɥɨɨɛɦɟɧɧɢɤ; 3 – ɪɟɝɟɧɟɪɚɬɨɪ;
4 – ɩɟɪɟɤɥɸɱɚɬɟɥɶ ɩɨɬɨɤɚ
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