Заканчивание / Книга_заканчивание скважин
.pdfɉɨɞ ɩɪɨɧɢɰɚɟɦɨɫɬɶɸ ɩɨɪɢɫɬɨɣ ɫɪɟɞɵ ɩɨɧɢɦɚɟɬɫɹ ɫɜɨɣɫɬɜɨ ɩɪɨɩɭɫɤɚɬɶ ɱɟɪɟɡ ɫɟɛɹ ɠɢɞɤɨɫɬɶ ɢɥɢ ɝɚɡ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɩɪɢɥɨɠɟɧɧɨɝɨ ɝɪɚɞɢɟɧɬɚ ɞɚɜɥɟɧɢɹ, ɬ.ɟ. ɷɬɨ ɩɪɨɜɨɞɢɦɨɫɬɶ ɩɨɪɢɫɬɨɣ ɫɪɟɞɵ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɠɢɞɤɨɫɬɢ ɢɥɢ ɝɚɡɭ.
Ⱦɥɹ ɝɚɡɚ ɩɪɢ ɢɡɨɬɟɪɦɢɱɟɫɤɨɦ ɬɟɱɟɧɢɢ ɢ ɩɪɟɧɟɛɪɟɠɟɧɢɢ ɟɝɨ ɦɚɫɫɨɣ ɜ ɨɞɧɨɦɟɪɧɨɦ ɫɥɭɱɚɟ ɡɚɤɨɧ Ⱦɚɪɫɢ ɢɦɟɟɬ ɜɢɞ:
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Q k |
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ɝɞɟ |
ɤɨɧɫɬɚɧɬɚ, |
ɹɜɥɹɸɳɚɹɫɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɝɚɡɚ ɜ ɩɨɪɢɫɬɨɣ |
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ɫɪɟɞɟ. |
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ɋɨɦɧɨɠɢɬɟɥɶ |
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¸, ɜɜɟɞɟɧɧɵɣ Ʉɥɢɧɤɟɧɛɟɪɝɨɦ, ɭɱɢɬɵɜɚɟɬ ɷɮɮɟɤɬ |
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ɫɤɨɥɶɠɟɧɢɹ ɝɚɡɚ ɜɞɨɥɶ ɫɬɟɧɨɤ ɩɨɪ (ɷɮɮɟɤɬ Ʉɥɢɧɤɟɧɛɟɪɝɚ, ɤɨɬɨɪɵɣ ɩɪɨɹɜɥɹɟɬɫɹ ɩɪɢ ɧɟɛɨɥɶɲɢɯ ɞɚɜɥɟɧɢɹɯ), ɢ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɧɢɰɚɟɦɨɫɬɢ
kɝ |
k (1 |
b), |
(2.19) |
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ɝɞɟ ɪ = (ɪ1+ɪ2)/2 – ɫɪɟɞɧɟɟ ɞɚɜɥɟɧɢɟ ɝɚɡɚ ɜ ɮɢɥɶɬɪɚɰɢɨɧɧɨɦ ɩɨɬɨɤɟ, ɉɚ.
ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɢɡɦɟɪɹɸɬ ɨɛɵɱɧɨ ɫ ɩɨɦɨɳɶɸ ɝɚɡɚ. ɉɪɢ ɷɬɨɦ ɧɟɨɛɯɨɞɢɦɨ ɩɪɨɜɨɞɢɬɶ ɢɡɦɟɪɟɧɢɹ ɩɪɢ ɧɟɫɤɨɥɶɤɢɯ ɡɧɚɱɟɧɢɹɯ ɫɪɟɞɧɟɝɨ ɞɚɜɥɟɧɢɹ, ɱɬɨ ɩɨɡɜɨɥɹɟɬ ɭɫɬɚɧɨɜɢɬɶ ɤɨɧɫɬɚɧɬɭ b ɜ ɷɤɫɩɟɪɢɦɟɧɬɚɯ ɫɨɝɥɚɫɧɨ ɡɚɤɨɧɭ Ⱦɚɪɫɢ. ȼ ɤɨɨɪɞɢɧɚɬɚɯ 2·Q·Ș·p2·l/S·(p12-p22) ɢ 2·(ɪ1+ɪ2) ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɞɚɧɧɵɟ ɞɨɥɠɧɵ ɥɨɠɢɬɶɫɹ ɧɚ ɩɪɹɦɭɸ, ɨɬɫɟɤɚɸɳɭɸ ɨɬ ɨɫɢ ɨɪɞɢɧɚɬ ɨɬɪɟɡɨɤ k ɢ ɢɦɟɸɳɭɸ ɬɚɧɝɟɧɫ ɭɝɥɚ ɧɚɤɥɨɧɚ k·b.
ɋɥɟɞɭɟɬ ɬɚɤɠɟ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɩɪɢ ɬɟɱɟɧɢɢ ɠɢɞɤɨɫɬɢ ɱɟɪɟɡ ɩɨɪɢɫɬɭɸ ɫɪɟɞɭ, ɤɨɬɨɪɚɹ ɧɚɫɵɳɟɧɚ ɩɥɚɫɬɨɜɵɦ ɮɥɸɢɞɨɦ, ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɡɚɜɢɫɢɬ ɨɬ
31
ɧɚɫɵɳɟɧɧɨɫɬɢ ɢɦ ɩɨɪɢɫɬɨɣ ɫɪɟɞɵ. Ɍɚɤ, ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɢɥɢ ɮɚɡɨɜɚɹ, ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɞɥɹ ɜɨɞɵ ɢ ɧɟɮɬɢ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ Ɋɢɫɭɧɨɤ 2.1. ɉɪɢ ɬɚɤɨɦ ɬɟɱɟɧɢɢ ɞɥɹ ɤɚɠɞɨɣ ɢɡ ɮɚɡ ɫɩɪɚɜɟɞɥɢɜ ɡɚɤɨɧ Ⱦɚɪɫɢ, ɧɨ ɟɝɨ ɫɥɟɞɭɟɬ ɡɚɩɢɫɵɜɚɬɶ ɜ ɜɢɞɟ:
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kɮ k dp |
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(2.20) |
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P dl |
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ɝɞɟ ɨɬɧɨɫɢɬɟɥɶɧɚɹ (ɮɚɡɨɜɚɹ) ɩɪɨɧɢɰɚɟɦɨɫɬɶ, ɞ.ɟ..
ɮ
Ɂɧɚɱɟɧɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɧɟ ɦɨɝɭɬ ɛɵɬɶ ɛɨɥɶɲɟ ɟɞɢɧɢɰɵ, ɧɨ ɢ ɫɭɦɦɚ ɢɯ ɞɥɹ ɞɜɭɯɮɚɡɧɵɯ ɫɢɫɬɟɦ ɧɟ ɩɪɢ ɥɸɛɨɦ ɡɧɚɱɟɧɢɢ ɧɚɫɵɳɟɧɧɨɫɬɢ ɪɚɜɧɚ ɟɞɢɧɢɰɟ. Ɂɧɚɱɟɧɢɹ ɮɚɡɨɜɵɯ ɩɪɨɧɢɰɚɟɦɨɫɬɟɣ ɡɚɜɢɫɹɬ ɨɬ ɬɢɩɚ ɩɨɪɢɫɬɨɣ ɫɪɟɞɵ, ɧɚɫɵɳɚɸɳɢɯ ɮɥɸɢɞɨɜ ɢ ɱɢɫɥɚ ɮɚɡ.
Ɍɟɱɟɧɢɟ ɠɢɞɤɨɫɬɟɣ ɫɤɜɨɡɶ ɩɨɪɢɫɬɭɸ ɫɪɟɞɭ ɩɨɞɱɢɧɹɟɬɫɹ ɡɚɤɨɧɭ Ⱦɚɪɫɢ ɥɢɲɶ ɩɪɢ ɦɚɥɵɯ ɫɤɨɪɨɫɬɹɯ ɬɟɱɟɧɢɹ. ɉɪɢ ɛɨɥɶɲɢɯ ɫɤɨɪɨɫɬɹɯ ɬɟɱɟɧɢɹ ɥɢɧɟɣɧɵɣ ɡɚɤɨɧ ɮɢɥɶɬɪɚɰɢɢ (Ⱦɚɪɫɢ) ɧɚɪɭɲɚɟɬɫɹ, ɩɨɷɬɨɦɭ ɢɫɩɨɥɶɡɭɸɬ ɡɚɤɨɧɵ ɜɢɞɚ:
p1 - p2 |
a Qn |
(2.21) |
L |
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ɢɥɢ
p1 - p2 |
a Q b Q2 . |
(2.22) |
L |
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Ɋɢɫɭɧɨɤ 2.1 – ɂɡɦɟɪɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨɣ (ɮɚɡɨɜɨɣ) ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɞɥɹ ɜɨɞɵ (ɤɪɢɜɚɹ 1) ɢ ɧɟɮɬɢ (ɤɪɢɜɚɹ 2) ɜ ɩɟɫɱɚɧɨɦ ɤɨɥɥɟɤɬɨɪɟ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɜɨɞɨɧɚɫɵɳɟɧɧɨɫɬɢ
Ⱦɜɭɱɥɟɧɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ, ɩɪɟɞɫɬɚɜɥɹɸɳɚɹ ɫɨɛɨɣ ɡɚɤɨɧ Ɏɨɪɯɝɟɣɦɟɪɚ, ɜ ɩɨɫɥɟɞɧɟɟ ɜɪɟɦɹ ɧɚɯɨɞɢɬ ɛɨɥɶɲɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ, ɱɟɦ ɫɬɟɩɟɧɧɚɹ. Ʉɨɷɮɮɢɰɢɟɧɬɵ ɤɚɤ ɜ ɫɬɟɩɟɧɧɨɣ, ɬɚɤ ɢ ɜ ɞɜɭɱɥɟɧɧɨɣ ɡɚɜɢɫɢɦɨɫɬɹɯ, ɧɟ ɹɜɥɹɸɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ ɩɪɨɧɢɰɚɟɦɨɫɬɢ – ɷɬɨ ɧɟɤɨɬɨɪɵɟ ɪɚɡɦɟɪɧɵɟ ɩɚɪɚɦɟɬɪɵ ɬɟɱɟɧɢɹ, ɡɚɜɢɫɹɳɢɟ ɨɬ ɫɜɨɣɫɬɜ ɮɥɸɢɞɨɜ ɢ ɩɨɪɢɫɬɨɣ ɫɪɟɞɵ.
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Ⱦɥɹ ɨɩɢɫɚɧɢɹ ɬɟɱɟɧɢɹ ɠɢɞɤɨɫɬɢ ɜ ɩɨɝɥɨɳɚɸɳɢɯ ɩɥɚɫɬɚɯ ȼ.ɂ. Ɇɢɯɚɳɟɜɢɱɟɦ ɛɵɥɚ ɩɪɟɞɥɨɠɟɧɚ ɮɨɪɦɭɥɚ:
Q k1 'p k2 'p k3 ('p)2 , |
(2.23) |
ɨɯɜɚɬɵɜɚɸɳɚɹ ɬɟɱɟɧɢɟ ɜ ɬɪɟɳɢɧɧɨɣ ɢɥɢ ɤɚɜɟɪɧɨɡɧɨɣ (ɩɟɪɜɵɣ ɱɥɟɧ), ɫɪɟɞɧɟɩɨɪɢɫɬɨɣ (ɜɬɨɪɨɣ ɱɥɟɧ) ɢ ɦɟɥɤɨɩɨɪɢɫɬɨɣ (ɬɪɟɬɢɣ ɱɥɟɧ) ɫɪɟɞɚɯ.
Ʉɨɷɮɮɢɰɢɟɧɬɵ ɩɪɨɧɢɰɚɟɦɨɫɬɢ k1, k2 ɢ k3 ɧɚɯɨɞɹɬɫɹ ɩɨ ɪɟɡɭɥɶɬɚɬɚɦ ɢɫɫɥɟɞɨɜɚɧɢɹ ɫɤɜɚɠɢɧ, ɩɨ ɢɧɞɢɤɚɬɨɪɧɵɦ ɤɪɢɜɵɦ ǻɪ-Q.
Ⱦɥɹ ɩɪɚɤɬɢɤɢ ɛɭɪɟɧɢɹ ɩɪɟɞɫɬɚɜɥɹɟɬ ɢɧɬɟɪɟɫ ɨɛɨɛɳɟɧɧɵɣ ɡɚɤɨɧ Ⱦɚɪɫɢ, ɤɨɬɨɪɵɣ ɨɯɜɚɬɵɜɚɟɬ ɬɟɱɟɧɢɟ ɜɹɡɤɨɩɥɚɫɬɢɱɧɵɯ ɠɢɞɤɨɫɬɟɣ ɜ ɩɨɪɢɫɬɨɣ ɫɪɟɞɟ ɢ ɡɚɩɢɫɵɜɚɟɬɫɹ (Ⱥ.ɏ. Ɇɢɪɡɚɞɠɚɧɡɚɞɟ) ɜ ɜɢɞɟ:
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k |
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k |
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¨1 |
grad p |
¸ |
grad p, |
(2.24) |
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¹ |
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ɝɞɟ |
ɧɚɱɚɥɶɧɵɣ ɝɪɚɞɢɟɧɬ ɞɚɜɥɟɧɢɹ ɞɥɹ ɩɨɪɢɫɬɨɣ ɫɪɟɞɵ, ɩɪɢ |
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ɤɨɬɨɪɨɦ ɧɚɱɢɧɚɟɬɫɹ ɞɜɢɠɟɧɢɟ ɠɢɞɤɨɫɬɟɣ ɜ ɧɟɣ. |
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Ⱦɥɹ ɨɛɨɛɳɟɧɧɨɝɨ ɡɚɤɨɧɚ Ⱦɚɪɫɢ ȣ = 0 ɩɪɢ |grad p| G ɢ ȣ > 0 ɩɪɢ |grad p| > G. Ⱦɥɹ ɨɞɧɨɦɟɪɧɨɣ ɮɢɥɶɬɪɚɰɢɢ ɨɛɨɛɳɟɧɧɵɣ ɡɚɤɨɧ Ⱦɚɪɫɢ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ:
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k |
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'p 'p0 |
, |
(2.25) |
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L |
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ɝɞɟ ǻɪ |
ɬɟɤɭɳɢɣ ɩɟɪɟɩɚɞ ɞɚɜɥɟɧɢɹ, ɉɚ; |
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ǻɪ0 |
ɩɟɪɟɩɚɞ |
ɞɚɜɥɟɧɢɹ, |
ɧɟɨɛɯɨɞɢɦɵɣ |
ɞɥɹ ɩɪɟɨɞɨɥɟɧɢɹ |
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ɩɪɟɞɟɥɶɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɫɞɜɢɝɚ ɜ ɩɨɪɢɫɬɨɦ ɨɛɪɚɡɰɟ ɞɥɢɧɨɣ
L, ɉɚ.
Ɂɧɚɱɟɧɢɟ ǻɪ0 ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ:
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'p0 |
d |
W0 L |
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(2.26) |
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k |
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ɝɞɟ IJ0 |
– ɩɪɟɞɟɥɶɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɫɞɜɢɝɚ ɞɥɹ ɜɹɡɤɨɩɥɚɫɬɢɱɧɨɣ |
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ɠɢɞɤɨɫɬɢ, ɉɚ; |
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– ɩɨɫɬɨɹɧɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ, d = (155y180)·10-4; |
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k– ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɧɢɰɚɟɦɨɫɬɢ, ɦ2.
ȼɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɭɤɚɡɚɧɧɵɦ ɜɵɲɟ ɞɥɹ ɜɹɡɤɨɩɥɚɫɬɢɱɧɨɣ ɠɢɞɤɨɫɬɢ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɨɞɧɨɦɟɪɧɨɦ ɫɥɭɱɚɟ
X |
k 'p |
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a k W0 |
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(2.27) |
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P L |
P |
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ɬ.ɟ. ɩɪɢ ǻɪ > ǻɪ0 ɠɢɞɤɨɫɬɶ ɛɭɞɟɬ ɬɟɱɶ ɜ ɩɨɪɢɫɬɨɣ ɫɪɟɞɟ. ɍɤɚɡɚɧɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɩɨɡɜɨɥɹɟɬ ɧɚɣɬɢ ɝɥɭɛɢɧɭ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɜɹɡɤɨɩɥɚɫɬɢɱɧɨɣ ɠɢɞɤɨɫɬɢ ɜ ɩɨɪɢɫɬɭɸ ɫɪɟɞɭ ɩɪɢ ɩɟɪɟɩɚɞɟ ǻɪ. ɀɢɞɤɨɫɬɶ ɨɫɬɚɧɨɜɢɬɫɹ ɩɨɫɥɟ
ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɧɚ ɪɚɫɫɬɨɹɧɢɟ L0, ɨɩɪɟɞɟɥɹɟɦɨɟ ɢɡ ɭɫɥɨɜɢɹ: |
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X |
k 'p |
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a |
k W0 |
0, |
(2.28) |
P L |
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P |
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ɬ.ɟ. |
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L0 |
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'p |
k . |
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(2.29) |
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W0 d |
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Ɋɚɫɫɦɚɬɪɢɜɚɟɦɵɟ ɡɚɤɨɧɵ ɮɢɥɶɬɪɚɰɢɢ ɩɨɡɜɨɥɹɸɬ ɩɨɥɭɱɚɬɶ ɤɨɥɢɱɟɫɬɜɟɧɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɠɟɧɢɹ ɠɢɞɤɨɫɬɟɣ ɢ ɝɚɡɨɜ ɜ ɩɥɚɫɬɚɯ ɜ ɩɪɨɰɟɫɫɟ ɛɭɪɟɧɢɹ ɧɟɮɬɹɧɵɯ ɢ ɝɚɡɨɜɵɯ ɫɤɜɚɠɢɧ.
35
2.1.2. Ⱦɜɢɠɟɧɢɟ ɠɢɞɤɨɫɬɟɣ ɢ ɝɚɡɨɜ ɜ ɩɥɚɫɬɚɯ
ɉɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɞɜɢɠɟɧɢɹ ɠɢɞɤɨɫɬɟɣ ɢ ɝɚɡɨɜ ɜ ɩɥɚɫɬɚɯ, ɩɪɟɞɫɬɚɜɥɹɸɳɢɯ ɫɨɛɨɣ ɩɪɨɧɢɰɚɟɦɭɸ ɫɪɟɞɭ, ɧɟɨɛɯɨɞɢɦɨ ɡɧɚɬɶ ɯɚɪɚɤɬɟɪ ɢɡɦɟɧɟɧɢɹ ɞɚɜɥɟɧɢɹ ɜ ɬɨɱɤɚɯ ɩɥɚɫɬɚ ɢ ɧɚ ɟɝɨ ɝɪɚɧɢɰɚɯ, ɚ ɨɫɨɛɟɧɧɨ ɧɚ ɫɬɟɧɤɚɯ ɫɤɜɚɠɢɧɵ, ɚ ɬɚɤɠɟ ɪɚɫɯɨɞ ɩɥɚɫɬɨɜɵɯ ɮɥɸɢɞɨɜ ɱɟɪɟɡ ɤɚɤɢɟ-ɥɢɛɨ ɨɝɪɚɧɢɱɢɜɚɸɳɢɟ ɩɨɜɟɪɯɧɨɫɬɢ. ɉɪɢ ɛɭɪɟɧɢɢ ɷɬɨ ɩɪɟɞɫɬɚɜɥɹɟɬ ɢɧɬɟɪɟɫ ɫ ɩɨɡɢɰɢɢ ɨɰɟɧɤɢ ɩɪɨɰɟɫɫɨɜ ɝɚɡɨɧɟɮɬɟɜɨɞɨɩɪɨɹɜɥɟɧɢɣ, ɩɨɝɥɨɳɟɧɢɣ, ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɛɭɪɨɜɨɝɨ ɪɚɫɬɜɨɪɚ ɜ ɩɪɨɞɭɤɬɢɜɧɵɟ ɩɥɚɫɬɵ, ɭɯɭɞɲɟɧɢɹ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɩɪɢɡɚɛɨɣɧɨɣ ɡɨɧɵ ɢ ɞɪ.
Ɋɚɫɫɦɨɬɪɢɦ ɧɟɫɤɨɥɶɤɨ ɱɚɫɬɧɵɯ ɫɥɭɱɚɟɜ, ɩɪɟɞɫɬɚɜɥɹɸɳɢɯ ɢɧɬɟɪɟɫ ɫ ɩɨɡɢɰɢɣ ɩɪɨɜɨɞɤɢ ɧɟɮɬɹɧɵɯ ɢ ɝɚɡɨɜɵɯ ɫɤɜɚɠɢɧ ɢ ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɪɚɡɥɢɱɧɵɯ ɪɚɫɱɟɬɚɯ ɩɪɢ ɛɭɪɟɧɢɢ.
ɉɭɫɬɶ ɩɪɢ ɛɭɪɟɧɢɢ ɫɤɜɚɠɢɧɵ ɪɚɞɢɭɫɨɦ rɫ, ɦ ɱɚɫɬɢɱɧɨ (Ɋɢɫɭɧɨɤ 2, ɛ) ɢɥɢ ɩɨɥɧɨɫɬɶɸ (Ɋɢɫɭɧɨɤ 2, ɜ) ɜɫɤɪɵɬ ɩɪɨɧɢɰɚɟɦɵɣ ɩɥɚɫɬ ɤɪɭɝɨɜɨɝɨ ɤɨɧɬɭɪɚ ɪɚɞɢɭɫɨɦ Rɤ, ɦ, ɢɦɟɸɳɢɣ ɧɟɩɪɨɧɢɰɚɟɦɵɟ ɤɪɨɜɥɸ ɢ ɩɨɞɨɲɜɭ ɢ ɬɨɥɳɢɧɭ h, ɦ (Ɋɢɫɭɧɨɤ 2).
Ɋɢɫɭɧɨɤ 2.2 – ɋɯɟɦɵ ɜɫɤɪɵɬɢɹ ɩɪɨɧɢɰɚɟɦɨɝɨ ɩɥɚɫɬɚ ɫɤɜɚɠɢɧɨɣ
36
ȼ ɫɥɭɱɚɟ ɩɪɢɦɟɧɢɦɨɫɬɢ ɡɚɤɨɧɚ Ⱦɚɪɫɢ ɞɥɹ ɧɟɫɠɢɦɚɟɦɨɣ ɠɢɞɤɨɫɬɢ ɫɩɪɚɜɟɞɥɢɜɵ ɫɥɟɞɭɸɳɢɟ ɮɨɪɦɭɥɵ ɞɥɹ ɪɚɫɱɟɬɚ ɪɚɫɯɨɞɚ ɩɪɢ ɫɬɚɰɢɨɧɚɪɧɨɣ ɮɢɥɶɬɪɚɰɢɢ.
ɉɪɢ ɛɨɥɶɲɨɣ ɦɨɳɧɨɫɬɢ ɩɥɚɫɬɚ (Ɋɢɫɭɧɨɤ 2, ɚ) ɢɦɟɟɦ ɮɨɪɦɭɥɭ ɞɥɹ ɪɚɫɱɟɬɚ ɪɚɫɯɨɞɚ ɧɚ ɫɬɟɧɤɚɯ ɫɤɜɚɠɢɧɵ:
Q |
2 S k pɤ pɫ |
, |
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§ |
1 |
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· |
(2.30) |
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P ¨ |
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¸ |
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¨r |
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R |
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¸ |
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© |
ɫ |
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ɤ ¹ |
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ɝɞɟ pɤ – ɞɚɜɥɟɧɢɟ ɧɚ ɤɨɧɬɭɪɟ ɩɢɬɚɧɢɹ ɫɤɜɚɠɢɧɵ, ɉɚ. pɫ – ɞɚɜɥɟɧɢɟ ɫɬɟɧɤɚɯ ɫɤɜɚɠɢɧɵ, ɉɚ.
ɢɥɢ
Q |
2 S k rɫ pɤ pɫ , |
ɬɚɤ ɤɚɤ |
1 |
o0. |
(2.31) |
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P |
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R c |
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ɉɪɢ ɷɬɨɦ ɞɥɹ ɪɤ > ɪɫ ɫɤɜɚɠɢɧɚ ɩɪɨɹɜɥɹɟɬ ɫ ɞɟɛɢɬɨɦ Q, ɚ ɜ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɩɨɝɥɨɳɚɟɬ.
ɉɪɢ ɭɫɥɨɜɢɢ rc << h ɢ ɧɟɡɧɚɱɢɬɟɥɶɧɨɦ ɡɚɝɥɭɛɥɟɧɢɢ (Ɋɢɫɭɧɨɤ 2, ɛ) ɮɨɪɦɭɥɚ ɞɥɹ ɪɚɫɱɟɬɚ ɫ ɭɞɨɜɥɟɬɜɨɪɢɬɟɥɶɧɨɣ ɞɥɹ ɢɧɠɟɧɟɪɧɵɯ ɪɚɫɱɟɬɨɜ ɬɨɱɧɨɫɬɶɸ ɢɦɟɟɬ ɜɢɞ:
Q |
2 S h k pɤ pɫ . |
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§ h |
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R ɤ |
· |
(2.32) |
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¨ |
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ln |
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¸ |
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P ¨ r |
1,5 h ¸ |
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© ɫ |
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¹ |
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Ⱥɧɚɥɨɝɢɱɧɨ ɩɪɢ ɪɤ > ɪɫ ɢɦɟɟɬ ɦɟɫɬɨ ɩɪɨɹɜɥɟɧɢɟ ɫ ɞɟɛɢɬɨɦ Q, ɚ ɜ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ – ɩɨɝɥɨɳɟɧɢɟ.
ɇɚɤɨɧɟɰ, ɩɪɢ ɜɫɤɪɵɬɢɢ ɩɥɚɫɬɚ ɧɚ ɜɫɸ ɟɝɨ ɦɨɳɧɨɫɬɶ (Ɋɢɫɭɧɨɤ 2, ɜ) ɪɚɫɯɨɞ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ Ⱦɸɩɸɢ
37
Q |
2 S h k pɤ pɫ |
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P ln |
R ɤ |
(2.33) |
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rc
ɩɪɢ ɬɟɯ ɠɟ ɭɫɥɨɜɢɹɯ.
Ɉɛɵɱɧɨ ɤɪɚɣɧɟ ɫɥɨɠɧɨ ɡɚɞɚɜɚɬɶɫɹ ɪɚɞɢɭɫɨɦ ɤɨɧɬɭɪɚ ɩɢɬɚɧɢɹ. ȿɫɥɢ ɩɪɢ ɟɝɨ ɡɚɞɚɧɢɢ ɨɲɢɛɢɬɶɫɹ ɜ m ɪɚɡ, ɬɨ:
ln m R ɤ |
ln |
R ɤ |
ln m, |
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1,5 h |
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1,5 h |
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(2.34) |
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ln m R ɤ |
ln Rɤ ln m. |
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rc |
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rc |
(2.35) |
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ɉɪɢ ɭɫɥɨɜɢɢ, ɱɬɨ ɪɚɞɢɭɫ ɤɨɧɬɭɪɚ ɩɢɬɚɧɢɹ ɨɛɵɱɧɨ ɜ ɫɨɬɧɢ ɢɥɢ ɬɵɫɹɱɢ ɪɚɡ ɛɨɥɶɲɟ ɦɨɳɧɨɫɬɢ ɩɥɚɫɬɚ ɢɥɢ ɪɚɞɢɭɫɚ ɫɤɜɚɠɢɧɵ, ɩɟɪɜɵɟ ɱɥɟɧɵ ɜɫɟɝɞɚ ɛɭɞɭɬ ɧɚ ɩɨɪɹɞɨɤ ɛɨɥɶɲɟ ɜɬɨɪɵɯ ɱɥɟɧɨɜ ɩɪɢ m = 2-3. ɉɨɷɬɨɦɭ ɩɨɝɪɟɲɧɨɫɬɢ ɨɬ ɨɲɢɛɨɱɧɨɝɨ ɡɚɞɚɧɢɹ ɪɚɞɢɭɫɨɦ ɤɨɧɬɭɪɚ ɩɢɬɚɧɢɹ ɜ 2-3 ɪɚɡɚ ɩɪɢɜɨɞɹɬ ɤ ɨɲɢɛɤɚɦ ɩɨɪɹɞɤɚ 10 %, ɬ.ɟ. ɞɜɭ-, ɬɪɟɯɤɪɚɬɧɵɟ ɨɲɢɛɤɢ ɩɪɢ ɡɚɞɚɧɢɢ ɪɚɞɢɭɫɨɦ ɤɨɧɬɭɪɚ ɩɢɬɚɧɢɹ ɜɩɨɥɧɟ ɞɨɩɭɫɬɢɦɵ.
ȼɫɟ ɩɪɢɜɟɞɟɧɧɵɟ ɮɨɪɦɭɥɵ ɦɨɝɭɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɵ ɢ ɞɥɹ ɬɟɱɟɧɢɹ ɝɚɡɨɜ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɜɦɟɫɬɨ ɪɚɡɧɨɫɬɢ ɞɚɜɥɟɧɢɣ ɧɟɨɛɯɨɞɢɦɨ ɩɪɢɦɟɧɹɬɶ ɪɚɡɧɨɫɬɶ ɤɜɚɞɪɚɬɨɜ ɞɚɜɥɟɧɢɣ, ɬ.ɟ.
'ɪ2 ɪɤ2 - ɪɫ2 ,
(2.36)
ɚ ɜɦɟɫɬɨ ɨɛɴɟɦɧɨɝɨ ɪɚɫɯɨɞɚ Q ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɪɢɜɟɞɟɧɧɵɣ ɤ ɫɬɚɧɞɚɪɬɧɵɦ ɭɫɥɨɜɢɹɦ (ɧɚɩɪɢɦɟɪ, ɤ ɚɬɦɨɫɮɟɪɧɵɦ ɞɚɜɥɟɧɢɸ ɢ ɬɟɦɩɟɪɚɬɭɪɟ) ɨɛɴɟɦɧɵɣ ɪɚɫɯɨɞ Qɩɪɢɜ. Ɍɚɤ, ɮɨɪɦɭɥɚ Ⱦɸɩɸɢ ɩɪɢ ɬɟɱɟɧɢɢ ɝɚɡɨɜ ɢɦɟɟɬ ɜɢɞ:
Qɩɪɢɜ |
S h k pɤ2 pɫ2 , |
(2.37) |
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pɚɬ P ln |
Rɤ |
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rc |
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38
ɚ ɞɥɹ ɫɥɭɱɚɹ ɨɞɧɨɦɟɪɧɨɝɨ ɬɟɱɟɧɢɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɮɨɪɦɭɥɚ ɛɵɥɚ ɩɪɢɜɟɞɟɧɚ ɜɵɲɟ, ɝɞɟ ɜ ɨɬɥɢɱɢɟ ɨɬ ɮɨɪɦɭɥɵ ɞɥɹ ɠɢɞɤɨɫɬɢ ɩɨɹɜɢɥɫɹ ɦɧɨɠɢɬɟɥɶ 1/ɪɚɬ (ɝɞɟ ɪɚɬ – ɚɬɦɨɫɮɟɪɧɨɟ ɞɚɜɥɟɧɢɟ, ɉɚ).
ȼɨ ɜɫɟɯ ɪɚɫɫɦɨɬɪɟɧɧɵɯ ɡɚɜɢɫɢɦɨɫɬɹɯ ɫɜɹɡɶ ɦɟɠɞɭ ɪɚɫɯɨɞɨɦ ɢ ɩɟɪɟɩɚɞɨɦ ɞɚɜɥɟɧɢɹ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ ɫɥɟɞɭɸɳɢɯ ɦɨɞɟɥɟɣ
Ⱦɥɹ ɠɢɞɤɨɫɬɢ |
Ⱦɥɹ ɝɚɡɚ |
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ǻɪ = A·Q |
ǻɪ2 |
= A·Q |
ǻɪ = A·Qn |
ǻɪ2 |
= A·Qn |
ǻɪ = A·Q + B·Q2 |
ǻɪ2 |
= A·Q + B·Q2 |
Ɂɞɟɫɶ ɤɨɧɫɬɚɧɬɵ A ɢ B ɜ ɤɚɠɞɨɦ ɫɥɭɱɚɟ ɢɦɟɸɬ ɫɜɨɣ ɫɦɵɫɥ, ɧɨ ɤɨɧɫɬɚɧɬɵ Ⱥ ɜɫɟɝɞɚ ɫɨɞɟɪɠɚɬ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɫɪɟɞɵ ɢ ɜɹɡɤɨɫɬɶ ɮɥɸɢɞɚ, ɚ ɤɨɧɫɬɚɧɬɚ ȼ ɡɚɜɢɫɢɬ ɨɬ ɝɟɨɦɟɬɪɢɢ ɩɨɪɢɫɬɨɣ ɫɪɟɞɵ, ɢɧɟɪɰɢɨɧɧɵɯ ɷɮɮɟɤɬɨɜ ɢ ɞɪ. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɭɤɚɡɚɧɧɵɯ ɤɨɧɫɬɚɧɬ ɢɫɩɨɥɶɡɭɸɬ ɪɚɡɥɢɱɧɵɟ ɦɟɬɨɞɵ ɢɫɫɥɟɞɨɜɚɧɢɹ ɩɥɚɫɬɨɜ, ɩɨɡɜɨɥɹɸɳɢɟ ɩɨɥɭɱɚɬɶ ɤɪɢɜɵɟ ǻɪ = f(Q), ɨɛɪɚɛɨɬɤɚ ɤɨɬɨɪɵɯ ɞɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɢɞɟɧɬɢɮɢɰɢɪɨɜɚɬɶ ɤɨɧɫɬɚɧɬɵ Ⱥ ɢ ȼ. Ɉɫɧɨɜɧɨɣ ɩɪɢɟɦ ɨɛɪɚɛɨɬɤɢ ɩɨɥɭɱɚɟɦɵɯ ɤɪɢɜɵɯ – ɨɛɪɚɛɨɬɤɚ ɩɨ ɦɟɬɨɞɭ ɧɚɢɦɟɧɶɲɢɯ ɤɜɚɞɪɚɬɨɜ ɢɥɢ ɟɝɨ ɪɚɡɥɢɱɧɵɟ ɦɨɞɢɮɢɤɚɰɢɢ.
2.1.3. Ƚɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɟ ɫɨɜɟɪɲɟɧɫɬɜɨ ɫɤɜɚɠɢɧɵ
Ʉɚɤ ɭɠɟ ɝɨɜɨɪɢɥɨɫɶ, ɩɪɢɬɨɤ ɠɢɞɤɨɫɬɢ ɤ ɡɚɛɨɸ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɢ ɫɨɜɟɪɲɟɧɧɨɣ ɫɤɜɚɠɢɧɵ ɨɩɢɫɵɜɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ Ⱦɸɩɸɢ, ɩɪɟɞɫɬɚɜɥɟɧɧɨɦ ɜ ɮɨɪɦɭɥɟ (2.33).
Ƚɢɞɪɨɞɢɧɚɦɢɱɟɫɤɢ ɫɨɜɟɪɲɟɧɧɨɣ ɫɱɢɬɚɟɬɫɹ ɫɤɜɚɠɢɧɚ, ɪɚɡɦɟɳɟɧɧɚɹ ɜ ɰɟɧɬɪɟ ɤɪɭɝɨɜɨɝɨ ɩɥɚɫɬɚ ɪɚɞɢɭɫɨɦ Rɤ, ɫɜɨɣɫɬɜɚ ɤɨɬɨɪɨɝɨ ɢɡɨɬɪɨɩɧɵ ɜɨ ɜɫɟɯ
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ɧɚɩɪɚɜɥɟɧɢɹɯ. ɉɪɢ ɷɬɨɦ ɠɢɞɤɨɫɬɶ ɩɨɫɬɭɩɚɟɬ ɤ ɨɬɤɪɵɬɨɦɭ ɡɚɛɨɸ ɢ ɹɜɥɹɟɬɫɹ ɨɞɧɨɮɚɡɧɨɣ ɢ ɧɟɫɠɢɦɚɟɦɨɣ. Ɍ.ɤ. ɩɪɢɬɨɤ ɠɢɞɤɨɫɬɢ ɤ ɫɤɜɚɠɢɧɟ ɧɨɫɢɬ ɪɚɞɢɚɥɶɧɵɣ ɯɚɪɚɤɬɟɪ, ɦɨɠɧɨ ɭɬɜɟɪɠɞɚɬɶ, ɱɬɨ ɜ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɢ ɫɨɜɟɪɲɟɧɧɨɣ ɫɤɜɚɠɢɧɟ ɨɫɧɨɜɧɚɹ ɞɨɥɹ ɩɟɪɟɩɚɞɚ ɞɚɜɥɟɧɢɹ ɫɨɫɪɟɞɨɬɨɱɟɧɚ ɜ ɡɨɧɟ ɩɥɚɫɬɚ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɜɨɤɪɭɝ ɫɬɟɧɨɤ ɫɤɜɚɠɢɧɵ. Ɍɚɤ, ɟɫɥɢ ɩɪɢɬɨɤ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɨɬ ɤɨɧɬɭɪɚ ɩɢɬɚɧɢɹ, ɧɚɯɨɞɹɳɟɝɨɫɹ ɧɚ ɪɚɫɫɬɨɹɧɢɢ 300 ɦ ɨɬ ɫɬɟɧɤɢ ɫɤɜɚɠɢɧɵ ɪɚɞɢɭɫɨɦ 0,1 ɦ, ɬɨ ɩɨɥɨɜɢɧɚ ɜɫɟɝɨ ɩɟɪɟɩɚɞɚ ɞɚɜɥɟɧɢɹ ɪɚɫɯɨɞɭɟɬɫɹ ɧɚ ɩɪɨɞɜɢɠɟɧɢɟ ɠɢɞɤɨɫɬɢ ɜ ɩɨɪɢɫɬɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ ɬɨɥɶɤɨ ɜ ɡɨɧɟ 5,5 ɦ ɜɨɤɪɭɝ ɫɤɜɚɠɢɧɵ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɪɢɫɤɜɚɠɢɧɧɚɹ ɡɨɧɚ ɩɥɚɫɬɚ ɢɝɪɚɟɬ ɪɟɲɚɸɳɭɸ ɪɨɥɶ ɜ ɩɪɢɬɨɤɟ ɠɢɞɤɨɫɬɢ ɤ ɫɤɜɚɠɢɧɟ.
ɉɪɢɬɨɤ ɠɢɞɤɨɫɬɢ ɜ ɪɟɚɥɶɧɭɸ ɫɤɜɚɠɢɧɭ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɩɪɢɬɨɤɚ ɜ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɢ ɫɨɜɟɪɲɟɧɧɭɸ ɫɤɜɚɠɢɧɭ ɬɟɦ, ɱɬɨ ɜ ɩɪɢɫɤɜɚɠɢɧɧɨɣ ɡɨɧɟ ɩɥɚɫɬɚ ɢ ɜ ɫɚɦɨɣ ɫɤɜɚɠɢɧɟ ɩɪɨɬɢɜ ɩɪɨɞɭɤɬɢɜɧɨɝɨ ɝɨɪɢɡɨɧɬɚ ɜɨɡɧɢɤɚɸɬ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɮɢɥɶɬɪɚɰɢɨɧɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɢɡ-ɡɚ ɢɫɤɪɢɜɥɟɧɢɹ ɢ ɡɚɝɭɫɬɟɧɢɹ ɥɢɧɢɣ ɬɨɤɚ ɩɥɚɫɬɨɜɵɯ ɮɥɸɢɞɨɜ. ɍɱɢɬɵɜɚɹ ɫɨɜɪɟɦɟɧɧɵɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɨ ɮɢɥɶɬɪɚɰɢɢ ɠɢɞɤɨɫɬɟɣ ɢ ɝɚɡɨɜ ɜ ɩɨɪɢɫɬɵɯ ɫɪɟɞɚɯ ɢ ɨ ɬɟɯɧɨɥɨɝɢɹɯ ɡɚɤɚɧɱɢɜɚɧɢɹ ɫɤɜɚɠɢɧ, ɜɵɞɟɥɹɸɬ ɬɪɢ ɬɢɩɚ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɧɟɫɨɜɟɪɲɟɧɫɬɜɚ ɫɤɜɚɠɢɧ (Ɋɢɫɭɧɨɤ 2.3):
Ɋɢɫɭɧɨɤ 2.3 – ɋɯɟɦɵ ɩɪɢɬɨɤɚ ɜ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɢ ɫɨɜɟɪɲɟɧɧɭɸ (ɚ) ɢ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɢ ɧɟɫɨɜɟɪɲɟɧɧɵɟ ɫɤɜɚɠɢɧɵ ɩɨ ɤɚɱɟɫɬɜɭ (ɛ), ɫɬɟɩɟɧɢ (ɜ) ɢ ɯɚɪɚɤɬɟɪɭ (ɝ) ɜɫɤɪɵɬɢɹ
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