Беспалов В.И. Системы и источники энергоснабжения

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ɧɨɱɧɨɣ ɷɤɨɧɨɦɢɤɢ ɭɤɚɡɚɧɧɚɹ ɜɵɲɟ ɪɟɝɥɚɦɟɧɬɚɰɢɹ ɞɢɚɦɟɬɪɨɜ ɢ ɫɯɟɦ ɬɟ-

ɩɥɨɜɵɯ ɫɟɬɟɣ ɧɟ ɦɨɠɟɬ ɫɱɢɬɚɬɶɫɹ ɟɞɢɧɫɬɜɟɧɧɨ ɩɪɚɜɢɥɶɧɵɦ ɪɟɲɟɧɢɟɦ.

5.3. Ɉɫɧɨɜɧɵɟ ɪɚɫɱɟɬɧɵɟ ɡɚɜɢɫɢɦɨɫɬɢ

ɍɪɚɜɧɟɧɢɟ Ȼɟɪɧɭɥɥɢ ɞɥɹ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɞɜɢɠɟɧɢɹ ɩɨ ɬɪɭɛɨ-

ɩɪɨɜɨɞɭ ɧɟɫɠɢɦɚɟɦɨɣ ɠɢɞɤɨɫɬɢ, ɜɵɪɚɠɚɸɳɟɟ ɷɧɟɪɝɟɬɢɱɟɫɤɢɣ ɛɚɥɚɧɫ

ɷɬɨɣ ɠɢɞɤɨɫɬɢ, ɨɬɧɟɫɟɧɧɵɣ ɤ ɟɞɢɧɢɰɟ ɦɚɫɫɵ, ɛɟɡ ɭɱɟɬɚ ɟɟ ɷɧɬɚɥɶɩɢɢ,

ɦɨɠɟɬ ɛɵɬɶ ɡɚɩɢɫɚɧɨ ɜ ɜɢɞɟ





(5.1)

ɝɞɟ

– ɝɟɨɦɟɬɪɢɱɟɫɤɚɹ ɜɵɫɨɬɚ ɨɫɢ ɬɪɭɛɨɩɪɨɜɨɞɚ ɜ ɫɟɱɟɧɢɹɯ 1 ɢ 2

ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ ɨɬɫɱɟɬɚ, ɦ;

– ɫɤɨɪɨɫɬɢ ɞɜɢɠɟɧɢɹ ɠɢɞɤɨɫɬɢ ɜ ɫɟɱɟɧɢɹɯ 1 ɢ 2, ɦ/ɫ;

– ɞɚɜɥɟɧɢɹ ɠɢɞɤɨɫɬɢ, ɢɡɦɟɪɟɧɧɵɟ ɧɚ ɭɪɨɜɧɟ ɨɫɢ ɬɪɭɛɨɩɪɨɜɨɞɚ ɜ

ɫɟɱɟɧɢɹɯ 1 ɢ 2, ɉɚ;

– ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɧɚ ɭɱɚɫɬɤɟ 1 – 2;

– ɩɥɨɬɧɨɫɬɶ ɠɢɞɤɨɫɬɢ, ɤɝ/ɦ

;

– ɭɫɤɨɪɟɧɢɟ ɫɜɨɛɨɞɧɨɝɨ ɩɚɞɟɧɢɹ,

= 9,81 ɦ/ɫ

ɉɟɪɜɵɣ ɱɥɟɧ ɜ (5.1)

– ɭɞɟɥɶɧɚɹ ɷɧɟɪɝɢɹ ɜɵɫɨɬɵ ɜ ɞɚɧɧɨɦ ɫɟ-

ɱɟɧɢɢ, (ɨɬɧɟɫɟɧɧɚɹ ɤ ɟɞɢɧɢɰɟ ɦɚɫɫɵ ɠɢɞɤɨɫɬɢ), Ⱦɠ/ɤɝ;

– ɭɞɟɥɶ-

ɧɚɹ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɠɢɞɤɨɫɬɢ ɜ ɞɚɧɧɨɦ ɫɟɱɟɧɢɢ, Ⱦɠ/ɤɝ;

–

ɭɞɟɥɶɧɚɹ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɢ ɠɢɞɤɨɫɬɢ ɜ ɞɚɧɧɨɦ ɫɟɱɟɧɢɢ, Ⱦɠ/ɤɝ;

UGp

– ɭɞɟɥɶɧɚɹ ɩɨɬɟɪɹ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ ɠɢɞɤɨɫɬɢ ɢɡ-ɡɚ ɬɪɟɧɢɹ

ɢ ɦɟɫɬɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɧɚ ɭɱɚɫɬɤɟ ɬɪɭɛɨɩɪɨɜɨɞɚ 1 – 2, Ⱦɠ/ɤɝ, ɤɨɬɨ-

ɪɚɹ ɩɟɪɟɯɨɞɢɬ ɜ ɬɟɩɥɨɬɭ, ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɭɜɟɥɢɱɟɧɢɸ ɭɞɟɥɶɧɨɣ ɷɧɬɚɥɶ-

ɩɢɢ ɠɢɞɤɨɫɬɢ ɜ ɩɪɨɰɟɫɫɟ ɟɟ ɞɜɢɠɟɧɢɹ ɩɨ ɬɪɭɛɨɩɪɨɜɨɞɭ.

ɇɚɪɹɞɭ ɫ ɭɞɟɥɶɧɨɣ ɷɧɟɪɝɢɟɣ ɜ ɝɢɞɪɚɜɥɢɱɟɫɤɨɦ ɪɚɫɱɟɬɟ ɬɟɩɥɨɜɵɯ

ɫɟɬɟɣ ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɪɭɝɨɣ ɩɚɪɚɦɟɬɪ – ɧɚɩɨɪ, ɦ

ZH 



(5.1ɚ)

ɝɞɟ

– ɞɚɜɥɟɧɢɟ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ, ɉɚ;

= ɇ – ɩɶɟɡɨɦɟɬɪɢɱɟɫɤɢɣ ɧɚ-

ɩɨɪ, ɦ;

– ɭɞɟɥɶɧɵɣ ɜɟɫ ɠɢɞɤɨɫɬɢ, ɇ/ɦ

ɉɪɢ ɝɢɞɪɚɜɥɢɱɟɫɤɨɦ ɪɚɫɱɟɬɟ ɬɟɩɥɨɜɵɯ ɫɟɬɟɣ, ɤɚɤ ɩɪɚɜɢɥɨ, ɧɟ

ɭɱɢɬɵɜɚɸɬ ɨɬɧɨɲɟɧɢɟ

gw 2/

, ɩɪɟɞɫɬɚɜɥɹɸɳɟɟ ɫɨɛɨɣ ɫɤɨɪɨɫɬɧɨɣ ɧɚɩɨɪ

ɩɨɬɨɤɚ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ, ɬɚɤ ɤɚɤ ɨɧ ɫɨɫɬɚɜɥɹɟɬ ɫɪɚɜɧɢɬɟɥɶɧɨ ɧɟɛɨɥɶɲɭɸ

ɞɨɥɸ ɩɨɥɧɨɝɨ ɧɚɩɨɪɚ ɢ ɢɡɦɟɧɹɟɬɫɹ ɩɨ ɞɥɢɧɟ ɫɟɬɢ ɧɟɡɧɚɱɢɬɟɥɶɧɨ.

Ɉɛɵɱɧɨ ɩɪɢɧɢɦɚɸɬ

ZH 



(5.2)

ɬ. ɟ. ɫɱɢɬɚɸɬ ɩɨɥɧɵɣ ɧɚɩɨɪ ɪɚɜɧɵɦ ɫɭɦɦɟ ɩɶɟɡɨɦɟɬɪɢɱɟɫɤɨɝɨ ɧɚɩɨɪɚ ɢ

ɜɵɫɨɬɵ ɪɚɫɩɨɥɨɠɟɧɢɹ ɨɫɢ ɬɪɭɛɨɩɪɨɜɨɞɚ ɧɚɞ ɩɥɨɫɤɨɫɬɶɸ ɨɬɫɱɟɬɚ. ɉɨɞ

ɩɶɟɡɨɦɟɬɪɢɱɟɫɤɢɦ ɧɚɩɨɪɨɦ ɩɨɧɢɦɚɟɬɫɹ ɞɚɜɥɟɧɢɟ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ, ɜɵ-

ɪɚɠɟɧɧɨɟ ɜ ɥɢɧɟɣɧɵɯ ɟɞɢɧɢɰɚɯ (ɨɛɵɱɧɨ ɜ ɦɟɬɪɚɯ) ɫɬɨɥɛɚ ɬɨɣ ɠɢɞɤɨɫɬɢ,

ɤɨɬɨɪɚɹ ɩɟɪɟɞɚɟɬɫɹ ɩɨ ɬɪɭɛɨɩɪɨɜɨɞɭ.

ɂɡ (5.2) ɫɥɟɞɭɟɬ, ɱɬɨ

ZHH 

. ɉɶɟɡɨɦɟɬɪɢɱɟɫɤɢɣ ɧɚɩɨɪ ɪɚɜɟɧ

ɪɚɡɧɨɫɬɢ ɦɟɠɞɭ ɩɨɥɧɵɦ ɧɚɩɨɪɨɦ ɢ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɜɵɫɨɬɨɣ ɨɫɢ ɬɪɭ-

ɛɨɩɪɨɜɨɞɚ ɧɚɞ ɩɥɨɫɤɨɫɬɶɸ ɨɬɫɱɟɬɚ. ɉɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɢ ɩɨɬɟɪɹ ɧɚɩɨɪɚ

ɜ ɫɟɬɢ, ɢɥɢ ɪɚɫɩɨɥɚɝɚɟɦɵɣ ɩɟɪɟɩɚɞ (ɪɚɡɧɨɫɬɶ ɧɚɩɨɪɨɜ), ɜ ɫɟɬɢ ɫɜɹɡɚɧɵ

ɫɥɟɞɭɸɳɢɦɢ ɡɚɜɢɫɢɦɨɫɬɹɦɢ:

ɝɞɟ

– ɩɨɬɟɪɹ ɧɚɩɨɪɚ

ɢɥɢ ɪɚɫɩɨɥɚɝɚɟɦɵɣ ɧɚɩɨɪ, ɦ;

– ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ, ɢɥɢ

ɪɚɫɩɨɥɚɝɚɟɦɵɣ ɩɟɪɟɩɚɞ ɞɚɜ-

ɥɟɧɢɹ, ɉɚ;

Rh,

– ɭɞɟɥɶɧɚɹ ɩɨ-

ɬɟɪɹ ɧɚɩɨɪɚ (ɛɟɡɪɚɡɦɟɪɧɚɹ ɜɟ-

ɥɢɱɢɧɚ) ɢ ɭɞɟɥɶɧɨɟ ɩɚɞɟɧɢɟ

ɞɚɜɥɟɧɢɹ, ɉɚ/ɦ.

ɉɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɜ

ɬɪɭɛɨɩɪɨɜɨɞɟ ɦɨɠɟɬ ɛɵɬɶ

ɩɪɟɞɫɬɚɜɥɟɧɨ ɤɚɤ ɫɭɦɦɚ ɞɜɭɯ

ɫɥɚɝɚɟɦɵɯ: ɥɢɧɟɣɧɨɝɨ ɩɚɞɟɧɢɹ

ɢ ɩɚɞɟɧɢɹ ɜ ɦɟɫɬɧɵɯ ɫɨɩɪɨ-

ɬɢɜɥɟɧɢɹɯ

ɦɥ

ppp GG G

(5.5)

ɝɞɟ

– ɥɢɧɟɣɧɨɟ ɩɚɞɟɧɢɟ ɞɚɜ-

ɥɟɧɢɹ;

– ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɜ ɦɟɫɬɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ.

;gppH UG

G G

(5.3)

),( U

gRRh

(5.4)

Ɋɢɫ. 5.2. ɋɯɟɦɚ ɞɜɢɠɟɧɢɹ ɠɢɞɤɨɫɬɢ

ɩɨ ɬɪɭɛɨɩɪɨɜɨɞɭ.

ɉɥɨɫɤɨɫɬɶ

ɨɬɫɱɟɬɚ

Ʌɢɧɟɣɧɨɟ ɩɚɞɟɧɢɟ

ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɧɚ

ɩɪɹɦɨɥɢɧɟɣɧɵɯ ɭɱɚɫɬɤɚɯ ɬɪɭɛɨɩɪɨɜɨɞɚ. ɉɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɜ ɦɟɫɬɧɵɯ

ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ

– ɷɬɨ ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɜ ɚɪɦɚɬɭɪɟ (ɜɟɧɬɢɥɹɯ, ɡɚ-

ɞɜɢɠɤɚɯ, ɤɪɚɧɚɯ ɢ ɬ. ɞ.) ɢ ɞɪɭɝɢɯ ɷɥɟɦɟɧɬɚɯ ɨɛɨɪɭɞɨɜɚɧɢɹ, ɪɚɡɦɟɳɟɧ-

ɧɵɯ ɧɟɪɚɜɧɨɦɟɪɧɨ ɩɨ ɞɥɢɧɟ ɬɪɭɛɨɩɪɨɜɨɞɚ (ɤɨɥɟɧɹɯ, ɲɚɣɛɚɯ, ɩɟɪɟɯɨɞɚɯ

ɢ ɬ. ɩ.).

0,01

0,02

0,03

0,04

0,05

0,06

0,08

1 - Re); 2 - Reɥɚɦɢɧɚɪɧɨɟ ( = 64/ ɝɥɚɞɤɚɹ (Ȼɥɚɡɢɭɫ, = 0,3164/

0,250

)

Ƚɥɚɞɤɚɹ (ɇɢɤɭɪɚɞɡɟ, = 0,0032+0,221/ )Re

0,237

;

Ɋɢɫ. 5.3. Ɂɚɜɢɫɢɦɨɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬɚ ɬɪɟɧɢɹ ɝɥɚɞɤɢɯ ɬɪɭɛ ɨɬ ɱɢɫɥɚ Ɋɟɣɧɨɥɶɞɫɚ

Ʌɢɧɟɣɧɨɟ ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɜ ɬɪɭɛɨɩɪɨɜɨɞɚɯ, ɬɪɚɧɫɩɨɪɬɢɪɭɸ-

ɳɢɯ ɠɢɞɤɨɫɬɶ ɢɥɢ ɝɚɡɵ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ

ɥɥ

(

5.6

)

ɝɞɟ

– ɥɢɧɟɣɧɨɟ ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɧɚ ɭɱɚɫɬɤɟ, ɉɚ;

– ɭɞɟɥɶɧɨɟ ɩɚ-

ɞɟɧɢɟ ɞɚɜɥɟɧɢɹ, ɬ. ɟ. ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ, ɨɬɧɟɫɟɧɧɨɟ ɤ ɟɞɢɧɢɰɟ ɞɥɢɧɵ

ɬɪɭɛɨɩɪɨɜɨɞɚ, ɉɚ/ɦ;

– ɞɥɢɧɚ ɬɪɭɛɨɩɪɨɜɨɞɚ, ɦ.

ɂɫɯɨɞɧɨɣ ɡɚɜɢɫɢɦɨɫɬɶɸ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɭɞɟɥɶɧɨɝɨ ɥɢɧɟɣɧɨɝɨ

ɩɚɞɟɧɢɹ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ ɹɜɥɹɟɬɫɹ ɭɪɚɜɧɟɧɢɟ Ⱦɚɪɫɢ

,812.0

(5.6)

ɝɞɟ

– ɤɨɷɮɮɢɰɢɟɧɬ ɝɢɞɪɚɜɥɢɱɟɫɤɨɝɨ ɬɪɟɧɢɹ (ɛɟɡɪɚɡɦɟɪɧɚɹ ɜɟɥɢɱɢɧɚ);

– ɫɤɨɪɨɫɬɶ ɫɪɟɞɵ, ɦ/ɫ;

– ɩɥɨɬɧɨɫɬɶ ɫɪɟɞɵ, ɤɝ/ɦ

;

– ɜɧɭɬɪɟɧɧɢɣ

ɞɢɚɦɟɬɪ ɬɪɭɛɨɩɪɨɜɨɞɚ, ɦ;

– ɦɚɫɫɨɜɵɣ ɪɚɫɯɨɞ, ɤɝ/ɫ.

Ʉɨɷɮɮɢɰɢɟɧɬ ɝɢɞɪɚɜɥɢɱɟɫɤɨɝɨ ɬɪɟɧɢɹ

ɡɚɜɢɫɢɬ ɨɬ ɫɨɫɬɨɹɧɢɹ

ɫɬɟɧɤɢ ɬɪɭɛɵ (ɝɥɚɞɤɚɹ ɢɥɢ ɲɟɪɨɯɨɜɚɬɚɹ) ɢ ɪɟɠɢɦɚ ɞɜɢɠɟɧɢɹ ɠɢɞɤɨɫɬɢ

(ɥɚɦɢɧɚɪɧɨɟ ɢɥɢ ɬɭɪɛɭɥɟɧɬɧɨɟ).

Ƚɥɚɞɤɢɟ ɬɪɭɛɵ ɜ ɬɟɯɧɢɤɟ ɬɪɚɧɫɩɨɪɬɢɪɨɜɤɢ ɬɟɩɥɨɬɵ ɢɦɟɸɬ ɨɝɪɚ-

ɧɢɱɟɧɧɨɟ ɩɪɢɦɟɧɟɧɢɟ (ɜ ɨɫɧɨɜɧɨɦ ɜ ɬɟɩɥɨɨɛɦɟɧɧɵɯ ɚɩɩɚɪɚɬɚɯ). Ɉɫ-

ɧɨɜɧɨɟ ɩɪɢɦɟɧɟɧɢɟ ɞɥɹ ɬɪɚɧɫɩɨɪɬɢɪɨɜɤɢ ɬɟɩɥɨɬɵ ɢɦɟɸɬ ɲɟɪɨɯɨɜɚɬɵɟ

ɫɬɚɥɶɧɵɟ ɬɪɭɛɵ.

ɒɟɪɨɯɨɜɚɬɭɸ ɩɨɜɟɪɯɧɨɫɬɶ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɫɨɫɬɨɹɳɟɣ ɢɡ ɪɹɞɚ

ɷɥɟɦɟɧɬɚɪɧɵɯ ɜɵɫɬɭɩɨɜ

ȼ ɤɚɱɟɫɬɜɟ ɩɟɪɜɨɝɨ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɩɚɪɚɦɟɬɪɚ ɲɟɪɨɯɨɜɚɬɨ-

ɫɬɢ ɩɪɢɧɢɦɚɸɬ ɜɵɫɨɬɭ ɜɵɫɬɭɩɚ ɲɟɪɨɯɨɜɚɬɨɫɬɢ, ɧɚɡɵɜɚɟɦɭɸ ɚɛɫɨɥɸɬ-

ɧɨɣ ɲɟɪɨɯɨɜɚɬɨɫɬɶɸ ɫɬɟɧɤɢ. ɍ ɛɨɥɶɲɢɧɫɬɜɚ ɪɚɛɨɬɚɸɳɢɯ ɫɬɚɥɶɧɵɯ

ɬɪɭɛɨɩɪɨɜɨɞɨɜ ɨɧɚ ɫɨɫɬɚɜɥɹɟɬ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɬɟɯɧɨɥɨɝɢɢ ɢɡɝɨɬɨɜɥɟ-

ɧɢɹ ɬɪɭɛ ɢ ɭɫɥɨɜɢɣ ɷɤɫɩɥɭɚɬɚɰɢɢ ɨɬ 0,05 ɞɨ 2 ɦɦ. ȼ ɤɚɱɟɫɬɜɟ ɜɬɨɪɨɝɨ

ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɝɨ ɩɚɪɚɦɟɬɪɚ ɩɪɢɧɢɦɚɸɬ ɨɬɧɨɲɟɧɢɟ ɚɛɫɨɥɸɬɧɨɣ ɲɟ-

ɪɨɯɨɜɚɬɨɫɬɢ ɤ ɪɚɞɢɭɫɭ ɬɪɭɛɨɩɪɨɜɨɞɚ

, ɧɚɡɵɜɚɟɦɨɟ ɨɬɧɨɫɢɬɟɥɶɧɨɣ

ɲɟɪɨɯɨɜɚɬɨɫɬɶɸ.

Ʉɚɤ ɩɨɤɚɡɵɜɚɸɬ ɢɫɫɥɟɞɨɜɚɧɢɹ ɫɬɚɥɶɧɵɯ ɬɪɭɛ, ɩɪɨɜɟɞɟɧɧɵɟ

Ƚ.Ⱥ. Ɇɭɪɢɧɵɦ ɜ ɥɚɛɨɪɚɬɨɪɢɢ ɬɟɩɥɨɮɢɤɚɰɢɢ ȼɌɂ, ɩɪɢ ɦɚɥɵɯ ɱɢɫɥɚɯ Re

ɤɨɷɮɮɢɰɢɟɧɬ ɝɢɞɪɚɜɥɢɱɟɫɤɨɝɨ ɬɪɟɧɢɹ

ɢɦɟɟɬ ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ.

ɋ ɭɜɟɥɢɱɟɧɢɟɦ ɱɢɫɥɚ Re ɤɨɷɮɮɢɰɢɟɧɬ ɝɢɞɪɚɜɥɢɱɟɫɤɨɝɨ ɬɪɟɧɢɹ ɦɨɧɨ-

ɬɨɧɧɨ ɭɦɟɧɶɲɚɟɬɫɹ ɢ ɩɪɢ ɧɟɤɨɬɨɪɨɦ ɡɧɚɱɟɧɢɢ Re

ɩɪ

ɩɪɚɤɬɢɱɟɫɤɢ ɞɨɫɬɢ-

ɝɚɟɬ ɦɢɧɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ. ɉɪɢ ɞɚɥɶɧɟɣɲɟɦ ɭɜɟɥɢɱɟɧɢɢ ɱɢɫɥɚ Re ɤɨ-

ɷɮɮɢɰɢɟɧɬ ɝɢɞɪɚɜɥɢɱɟɫɤɨɝɨ ɬɪɟɧɢɹ ɨɫɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɵɦ.

ɋ ɞɨɫɬɚɬɨɱɧɨɣ ɞɥɹ ɩɪɚɤɬɢɱɟɫɤɢɯ ɪɚɫɱɟɬɨɜ ɬɨɱɧɨɫɬɶɸ ɩɪɢɧɢɦɚɸɬ,

ɱɬɨ ɜ ɬɚɤ ɧɚɡɵɜɚɟɦɨɣ ɩɟɪɟɯɨɞɧɨɣ ɨɛɥɚɫɬɢ, ɬ. ɟ. ɩɪɢ 2300 < Re < Re

ɩɪ

ɤɨ-

ɷɮɮɢɰɢɟɧɬ ɝɢɞɪɚɜɥɢɱɟɫɤɨɝɨ ɬɪɟɧɢɹ ɡɚɜɢɫɢɬ ɤɚɤ ɨɬ ɷɤɜɢɜɚɥɟɧɬɧɨɣ ɨɬɧɨ-

ɫɢɬɟɥɶɧɨɣ ɲɟɪɨɯɨɜɚɬɨɫɬɢ k

/r, ɬɚɤ ɢ ɨɬ ɱɢɫɥɚ Re, ɚ ɩɪɢ Re > Re

ɩɪ

ɤɨɷɮ-

ɮɢɰɢɟɧɬ ɝɢɞɪɚɜɥɢɱɟɫɤɨɝɨ ɬɪɟɧɢɹ ɡɚɜɢɫɢɬ ɬɨɥɶɤɨ ɨɬ k /r ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ

ɱɢɫɥɚ Re.

ɉɨɞ ɷɤɜɢɜɚɥɟɧɬɧɨɣ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɲɟɪɨɯɨɜɚɬɨɫɬɶɸ ɪɟɚɥɶɧɨɝɨ

ɬɪɭɛɨɩɪɨɜɨɞɚ ɩɨɧɢɦɚɟɬɫɹ ɢɫɤɭɫɫɬɜɟɧɧɚɹ ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɪɚɜɧɨɦɟɪɧɚɹ

ɲɟɪɨɯɨɜɚɬɨɫɬɶ ɰɢɥɢɧɞɪɢɱɟɫɤɨɣ ɫɬɟɧɤɢ, ɤɨɷɮɮɢɰɢɟɧɬ ɝɢɞɪɚɜɥɢɱɟɫɤɨɝɨ

ɬɪɟɧɢɹ ɤɨɬɨɪɨɣ ɜ ɨɛɥɚɫɬɢ Re > Re

ɩɪ

, ɬɚɤɨɣ ɠɟ, ɤɚɤ ɢ ɜ ɞɚɧɧɨɦ ɪɟɚɥɶ-

ɧɨɦ ɬɪɭɛɨɩɪɨɜɨɞɟ.

ɉɨɥɭɱɟɧɧɚɹ ɨɩɵɬɧɵɦ ɩɭɬɟɦ ɡɚɜɢɫɢɦɨɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬɚ ɝɢɞɪɚɜ-

ɥɢɱɟɫɤɨɝɨ ɬɪɟɧɢɹ ɫɬɚɥɶɧɵɯ ɬɪɭɛ ɨɬ ɱɢɫɥɚ Re ɢ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɲɟɪɨɯɨ-

ɜɚɬɨɫɬɢ ɯɨɪɨɲɨ ɨɩɢɫɵɜɚɟɬɫɹ ɭɧɢɜɟɪɫɚɥɶɧɵɦ ɭɪɚɜɧɟɧɢɟɦ, ɩɪɟɞɥɨɠɟɧ-

ɧɵɦ Ⱥ.Ⱦ. Ⱥɥɶɬɲɭɥɟɦ [1],

25,0

)Re68d(11,0  O k

(5.7)

ɇɚ ɨɫɧɨɜɟ ɢɦɟɸɳɢɯɫɹ ɦɚɬɟɪɢɚɥɨɜ ɝɢɞɪɚɜɥɢɱɟɫɤɢɯ ɢɫɩɵɬɚɧɢɣ ɬɟ-

ɩɥɨɜɵɯ ɫɟɬɟɣ ɢ ɜɨɞɨɩɪɨɜɨɞɨɜ ɜ ɋɇɢɉ 2.04.07-86 ɪɟɤɨɦɟɧɞɭɸɬɫɹ ɫɥɟ-

ɞɭɸɳɢɟ ɡɧɚɱɟɧɢɹ ɚɛɫɨɥɸɬɧɨɣ ɷɤɜɢɜɚɥɟɧɬɧɨɣ ɲɟɪɨɯɨɜɚɬɨɫɬɢ, ɦ, ɞɥɹ

ɝɢɞɪɚɜɥɢɱɟɫɤɨɝɨ ɪɚɫɱɟɬɚ ɬɟɩɥɨɜɵɯ ɫɟɬɟɣ [130]:

ɩɚɪɨɩɪɨɜɨɞɵ .......................…………………… …………….0,2· 10

–3

ɜɨɞɹɧɵɟ ɫɟɬɢ ɜ ɭɫɥɨɜɢɹɯ ɧɨɪɦɚɥɶɧɨɣ ɷɤɫɩɥɭɚɬɚɰɢɢ ………0,5 ·10

–3

ɤɨɧɞɟɧɫɚɬɨɩɪɨɜɨɞɵ ɢ ɫɟɬɢ ɝɨɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ ......... .1·10

–3

ȼ ɬɟɩɥɨɜɵɯ ɫɟɬɹɯ ɨɛɵɱɧɨ Re > Re

ɩɪ

ɩɨɷɬɨɦɭ ɬɟɩɥɨɜɵɟ ɫɟɬɢ, ɤɚɤ

ɩɪɚɜɢɥɨ, ɪɚɛɨɬɚɸɬ ɜ ɤɜɚɞɪɚɬɢɱɧɨɣ ɨɛɥɚɫɬɢ.

Ⱦɢɚɦɟɬɪɵ ɬɪɭɛɨɩɪɨɜɨɞɨɜ ɩɪɢ ɬɪɚɧɫɩɨɪɬɢɪɨɜɤɟ ɠɢɞɤɨɫɬɟɣ ɨɩɪɟ-

ɞɟɥɹɸɬɫɹ ɩɨ ɮɨɪɦɭɥɟ

0,19

38,0ɜ

/ RGAd

(5.8)

Ɂɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɚ Ⱥ

ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥ. 5.1.

Ɏɨɪɦɭɥɭ (5.8) ɞɥɹ ɥɢɧɟɣɧɨɝɨ ɩɚɞɟɧɢɹ ɞɚɜɥɟɧɢɹ ɜ ɤɜɚɞɪɚɬɢɱɧɨɣ

ɨɛɥɚɫɬɢ ɦɨɠɧɨ ɩɪɢɜɟɫɬɢ ɤ ɜɢɞɭ, ɛɨɥɟɟ ɭɞɨɛɧɨɦɭ ɞɥɹ ɩɪɚɤɬɢɱɟɫɤɢɯ ɪɚɫ-

ɱɟɬɨɜ. Ⱦɥɹ ɜɨɞɵ, ɝɞɟ ȡ = const ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ

;

25.5

GAR

0,19

38,0ɜ

/ RGAd

625.2

dRAG

0,5

(5.8ɚ)

Ⱦɥɹ ɩɪɚɤɬɢɱɟɫɤɢɯ ɪɚɫɱɟɬɨɜ ɜ ɩɟɪɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɭɞɨɛɧɨ ɩɨɥɶ-

ɡɨɜɚɬɶɫɹ ɧɨɦɨɝɪɚɦɦɚɦɢ, ɩɨɫɬɪɨɟɧɧɵɦɢ ɩɨ ɩɪɢɜɟɞɟɧɧɵɦ ɜɵɲɟ ɭɪɚɜɧɟ-

ɧɢɹɦ. ɇɚ ɪɢɫɭɧɤɟ 5.4 ɩɪɢɜɟɞɟɧɚ ɧɨɦɨɝɪɚɦɦɚ ɞɥɹ ɝɢɞɪɚɜɥɢɱɟɫɤɨɝɨ ɪɚɫ-

ɱɟɬɚ ɬɪɭɛɨɩɪɨɜɨɞɨɜ ɞɢɚɦɟɬɪɨɦ d = 0,007 – 1,392 ɦ, ɫ ɚɛɫɨɥɸɬɧɨɣ ɲɟɪɨ-

ɯɨɜɚɬɨɫɬɶɸ k

= 0,0005 ɦ, ɩɪɢ ɩɥɨɬɧɨɫɬɢ ɜɨɞɵ = 975 ɤɝ/ɦ

, ɚ ɞɥɹ ɩɚɪɚ

= 2,45 ɤɝ/ɦ

Ɇɟɫɬɧɨɟ ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ. ȿɫɥɢ ɧɚ ɭɱɚɫɬɤɟ ɬɪɭɛɨɩɪɨɜɨɞɚ ɢɦɟ-

ɟɬɫɹ ɪɹɞ ɦɟɫɬɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ, ɬɨ ɫɭɦɦɚɪɧɨɟ ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɜɨ

ɜɫɟɯ ɦɟɫɬɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ, ɉɚ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ

(5.9)

ɝɞɟ

– ɫɭɦɦɚ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɦɟɫɬɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ, ɭɫɬɚɧɨɜɥɟɧɧɵɯ

ɧɚ ɭɱɚɫɬɤɟ;

ȟ– ɛɟɡɪɚɡɦɟɪɧɚɹ ɜɟɥɢɱɢɧɚ, ɡɚɜɢɫɹɳɚɹ ɨɬ ɯɚɪɚɤɬɟɪɚ ɫɨɩɪɨ-

ɬɢɜɥɟɧɢɹ.

Ɋɢɫ. 5.4. ɇɨɦɨɝɪɚɦɦɚ ɞɥɹ ɝɢɞɪɚɜɥɢɱɟɫɤɨɝɨ ɪɚɫɱɟɬɚ ɬɪɭɛɨɩɪɨɜɨɞɨɜ.

ȿɫɥɢ ɩɪɟɞɫɬɚɜɢɬɶ ɩɪɹɦɨɥɢɧɟɣɧɵɣ ɬɪɭɛɨɩɪɨɜɨɞ ɞɢɚɦɟɬɪɨɦ d,

ɥɢɧɟɣɧɨɟ ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɧɚ ɤɨɬɨɪɨɦ ɪɚɜɧɨ ɩɚɞɟɧɢɸ ɞɚɜɥɟɧɢɹ ɜ

ɦɟɫɬɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ, ɬɨ ɞɥɢɧɚ ɬɚɤɨɝɨ ɭɱɚɫɬɤɚ ɬɪɭɛɨɩɪɨɜɨɞɚ

ɧɚɡɵɜɚɟɬɫɹ ɷɤɜɢɜɚɥɟɧɬɧɨɣ ɞɥɢɧɨɣ ɦɟɫɬɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ.

Ɉɧɚ

ɦɨɠɟɬ ɛɵɬɶ ɧɚɣɞɟɧɚ ɢɡ ɪɚɜɟɧɫɬɜɚ

, ɬɨ ɟɫɬɶ , ɨɬɤɭɞɚ ɩɨɥɭɱɚɟɦ

ɢɥɢ

1,25

ȟ .

ɷ l

lA d

Ɉɬɧɨɲɟɧɢɟ ɩɚɞɟɧɢɹ ɞɚɜɥɟɧɢɹ ɜ ɦɟɫɬɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ ɬɪɭɛɨ-

ɩɪɨɜɨɞɚ ɤ ɥɢɧɟɣɧɨɦɭ ɩɚɞɟɧɢɸ ɜ ɷɬɨɦ ɬɪɭɛɨɩɪɨɜɨɞɟ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ

ɞɨɥɸ ɦɟɫɬɧɵɯ ɩɨɬɟɪɶ. ɇɟɬɪɭɞɧɨ ɜɢɞɟɬɶ, ɱɬɨ ɞɨɥɹ ɦɟɫɬɧɵɯ ɩɨɬɟɪɶ ɪɚɜ-

ɧɚ ɨɬɧɨɲɟɧɢɸ ɷɤɜɢɜɚɥɟɧɬɧɨɣ ɞɥɢɧɵ ɦɟɫɬɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɤ ɞɥɢɧɟ

ɬɪɭɛɨɩɪɨɜɨɞɚ:

(5.9ɚ)

ɂɡ ɫɨɜɦɟɫɬɧɨɝɨ ɪɟɲɟɧɢɹ ɷɬɢɯ ɭɪɚɜɧɟɧɢɣ ɩɨ ɫɭɦɦɟ ɤɨɷɮɮɢɰɢɟɧ-

ɬɨɜ ɦɟɫɬɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɢ ɪɚɫɩɨɥɚɝɚɟɦɨɦɭ ɩɟɪɟɩɚɞɭ ɞɚɜɥɟɧɢɣ

ɦɨɠɧɨ ɧɚɣɬɢ ɞɨɥɸ ɦɟɫɬɧɵɯ ɩɨɬɟɪɶ

24,0

48,0

24,0

)/()1( lp

[

D

(5.10)

ɝɞɟ

19,0

/1,5 kA

Ⱦɥɹ ɭɞɨɛɫɬɜɚ ɭɪɚɜɧɟɧɢɟ (5.9) ɡɚɩɢɫɵɜɚɟɬɫɹ ɜ ɫɥɟɞɭɸɳɟɦ ɩɪɢ-

ɛɥɢɠɟɧɧɨɦ ɜɢɞɟ:

/)1(

[

D

(5.10 ɚ)

ȼ ɩɪɟɞɟɥɚɯ ɢɡɦɟɧɟɧɢɹ

ɨɬ 0 ɞɨ 1 ɫ ɩɨɝɪɟɲɧɨɫɬɶɸ ± 6 % ɦɨɠɧɨ

ɩɪɢɧɹɬɶ

15,1

[

(5.10 ɛ)

ɉɪɢ ɬɪɚɧɫɩɨɪɬɢɪɨɜɤɟ ɠɢɞɤɨɫɬɢ, ɜ ɱɚɫɬɧɨɫɬɢ ɜɨɞɵ,

15,1

[

(5.10 ɜ)

ɝɞɟ

– ɪɚɫɩɨɥɚɝɚɟɦɵɣ ɩɟɪɟɩɚɞ ɞɚɜɥɟɧɢɣ, ɉɚ.

ȼ ɬɚɛɥ. 5.1 ɩɪɢɜɟɞɟɧɵ ɤɨɷɮɮɢɰɢɟɧɬɵ

, ɜɯɨɞɹɳɢɟ ɜ ɮɨɪɦɭɥɵ (5.8) –

(5.10).

Ʉɚɤ ɜɢɞɧɨ ɢɡ (5.10 ɚ) – (5.10 ɜ), ɞɨɥɹ ɦɟɫɬɧɵɯ ɩɨɬɟɪɶ ɜɨɡɪɚɫɬɚɟɬ

ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɫɭɦɦɵ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɦɟɫɬɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɧɚ

ɟɞɢɧɢɰɭ ɞɥɢɧɵ ɬɪɭɛɨɩɪɨɜɨɞɚ

[ l/

, ɚ ɬɚɤɠɟ ɩɪɢ ɫɧɢɠɟɧɢɢ ɪɚɫɩɨɥɚ-

ɝɚɟɦɨɝɨ ɭɞɟɥɶɧɨɝɨ ɩɟɪɟɩɚɞɚ ɞɚɜɥɟɧɢɣ ɧɚ ɟɞɢɧɢɰɭ ɞɥɢɧɵ ɬɪɭɛɨɩɪɨɜɨɞɚ

lp /G

ɋɭɦɦɚɪɧɨɟ ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ. ɋɭɦɦɚ ɩɚɞɟɧɢɣ ɞɚɜɥɟɧɢɹ – ɥɢ-

ɧɟɣɧɨɝɨ ɢ ɜ ɦɟɫɬɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ – ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ

Ɍɚɛɥɢɰɚ 5.1

Ɂɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ

ɜ ɮɨɪɦɭɥɚɯ (5.8) –(5.10)

Ʉɨɷɮɮɢɰɢɟɧɬ ȼɵɪɚɠɟɧɢɟ

Ⱥɛɫɨɥɸɬɧɚɹ ɷɤɜɢɜɚɥɟɧɬɧɚɹ ɲɟɪɨɯɨɜɚ-

ɬɨɫɬɶ

, ɦ

0,0002 0,0005 0,001

0,25

ɦ,

25,0

0894,0

10,6·10

-3

13,3·10

-3

15,92·10

-3

ɤɝA



3,25ɜ

ɦ,

U/0894,0

25,0

10,92·10

-6

13,62·10

-6

16,3·10

-6

0,0475

ɦ,

0475,0

63,0

0,414 0,435 0,488

19,00,62ɜ

/ɦ, ɤɝA

19,00475,0

/63,0 U

111,5·10

-3

117·10

-3

121·10

-3

0,125-

ɦ,

125,0

35,3

9,65 8.62 7,89

625,10,5ɜ

/ɦ, ɤɝA

5,0125,0

/35,3 U

302 269 246

0,19-

ɦ,

19,0

1,5

25,2 21,4 18,6

4,00,53ɜ

/ɦ, ɤɝA

)/(1,5

24,019,0

4,54 3,82 3,34

0,25-

ɦ,

25,0

1,9

76,4 60,7 51,1

),()1/(

)1(

ɷɥɥ

ɥɦɥ

llRR

pppp

 D

G GG G

(5.11)

ɨɬɤɭɞɚ

)1(/

DG lpR

(5.12)

5.4. ɉɨɪɹɞɨɤ ɝɢɞɪɚɜɥɢɱɟɫɤɨɝɨ ɪɚɫɱɟɬɚ

ɉɪɢ ɝɢɞɪɚɜɥɢɱɟɫɤɨɦ ɪɚɫɱɟɬɟ ɬɪɭɛɨɩɪɨɜɨɞɨɜ ɨɛɵɱɧɨ ɡɚɞɚɧɵ ɪɚɫ-

ɯɨɞ ɬɟɩɥɨɧɨɫɢɬɟɥɹ ɢ ɫɭɦɦɚɪɧɨɟ ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɧɚ ɭɱɚɫɬɤɟ. Ɍɪɟɛɭɟɬɫɹ

ɨɩɪɟɞɟɥɢɬɶ ɞɢɚɦɟɬɪ ɬɪɭɛɨɩɪɨɜɨɞɚ. Ɋɚɫɱɟɬ ɫɨɫɬɨɢɬ ɢɡ ɞɜɭɯ ɷɬɚɩɨɜ: ɩɪɟɞ-

ɜɚɪɢɬɟɥɶɧɨɝɨ ɢ ɩɪɨɜɟɪɨɱɧɨɝɨ.

Ƚɢɞɪɚɜɥɢɱɟɫɤɢɣ ɪɚɫɱɟɬ ɭɩɪɨɳɚɟɬɫɹ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɧɨɦɨ-

ɝɪɚɦɦ (ɪɢɫ. 5.4).

ɉɪɟɞɜɚɪɢɬɟɥɶɧɵɣ ɪɚɫɱɟɬ

1. Ɂɚɞɚɸɬɫɹ ɞɨɥɟɣ ɦɟɫɬɧɵɯ ɩɨɬɟɪɶ ɢɥɢ ɜɵɱɢɫɥɹɸɬ ɟɟ ɩɨ ɮɨɪɦɭɥɟ

(5.10).

2. ɇɚɯɨɞɹɬ ɭɞɟɥɶɧɨɟ ɥɢɧɟɣɧɨɟ ɩɚɞɟɧɢɟ ɞɚɜɥɟɧɢɹ ɩɨ (5.12).

3. Ɉɩɪɟɞɟɥɹɸɬ ɫɪɟɞɧɸɸ ɩɥɨɬɧɨɫɬɶ ɬɟɩɥɨɧɨɫɢɬɟɥɹ ɧɚ ɭɱɚɫɬɤɟ ɩɨ ɮɨɪ-

ɦɭɥɟ

2/)

ɤɨɧɧɚɱ(ɫɪ

UUU

(5.13)

ɂɧɞɟɤɫɵ «ɧɚɱ» ɢ «ɤɨɧ» ɨɬɧɨɫɹɬɫɹ ɤ ɧɚɱɚɥɭ ɢ ɤɨɧɰɭ ɭɱɚɫɬɤɚ. ȿɫɥɢ

ɬɟɩɥɨɧɨɫɢɬɟɥɶ – ɠɢɞɤɨɫɬɶ, ɬɨ ɩɪɢɧɢɦɚɸɬ

ɫɪɤɨɧɧɚɱ

U U U

4. Ɉɩɪɟɞɟɥɹɸɬ ɞɢɚɦɟɬɪ ɬɪɭɛɨɩɪɨɜɨɞɚ ɢɡ ɩɪɟɞɩɨɥɨɠɟɧɢɹ ɟɝɨ ɪɚɛɨ-

ɬɵ ɜ ɤɜɚɞɪɚɬɢɱɧɨɣ ɨɛɥɚɫɬɢ ɩɨ (5.8).

ɉɪɨɜɟɪɨɱɧɵɣ ɪɚɫɱɟɬ

1. ɉɪɟɞɜɚɪɢɬɟɥɶɧɨ ɪɚɫɫɱɢɬɚɧɧɵɣ ɞɢɚɦɟɬɪ ɨɤɪɭɝɥɹɸɬ ɞɨ ɛɥɢɠɚɣɲɟɝɨ

ɩɨ ɫɬɚɧɞɚɪɬɭ. Ɍɚɛɥɢɰɚ ɫɬɚɧɞɚɪɬɧɵɯ ɞɢɚɦɟɬɪɨɜ ɬɪɭɛ, ɩɪɢɦɟɧɹɟɦɵɯ ɩɪɢ

ɬɪɚɧɫɩɨɪɬɢɪɨɜɤɟ ɜɨɞɵ ɢ ɜɨɞɹɧɨɝɨ ɩɚɪɚ, ɩɪɢɜɟɞɟɧɚ ɜ ɩɪɢɥɨɠɟɧɢɢ 9.

2. Ɉɩɪɟɞɟɥɹɸɬ ɱɢɫɥɨ

, ɫɪɚɜɧɢɜɚɸɬ ɟɝɨ ɫ ɩɪɟɞɟɥɶɧɵɦ ɡɧɚɱɟɧɢ-

ɟɦ

ɩɪ

. ɍɫɬɚɧɚɜɥɢɜɚɸɬ ɪɚɫɱɟɬɧɭɸ ɨɛɥɚɫɬɶ, ɜ ɤɨɬɨɪɨɣ ɪɚɛɨɬɚɟɬ ɬɪɭɛɨ-

ɩɪɨɜɨɞ,

Ɉɩɪɟɞɟɥɟɧɢɟ ɨɛɥɚɫɬɢ, ɜ ɤɨɬɨɪɨɣ ɪɚɛɨɬɚɟɬ ɬɪɭɛɨɩɪɨɜɨɞ, ɫɥɟɞɭɟɬ

ɩɪɨɜɨɞɢɬɶ ɬɨɥɶɤɨ ɩɪɢ ɪɚɫɱɟɬɟ ɭɱɚɫɬɤɨɜ ɫ ɦɚɥɨɣ ɧɚɝɪɭɡɤɨɣ (ɚɛɨɧɟɧɬɫɤɢɟ

ɨɬɜɟɬɜɥɟɧɢɹ ɫ ɦɚɥɵɦ ɪɚɫɯɨɞɨɦ ɬɟɩɥɨɧɨɫɢɬɟɥɹ). ɉɪɢ ɪɚɫɱɟɬɟ ɦɚɝɢɫɬ-

ɪɚɥɶɧɵɯ ɥɢɧɢɣ ɢ ɨɫɧɨɜɧɵɯ ɨɬɜɟɬɜɥɟɧɢɣ ɩɪɨɜɟɪɤɭ ɪɚɫɱɟɬɧɨɣ ɨɛɥɚɫɬɢ

ɦɨɠɧɨ ɧɟ

ɜɵɩɨɥɧɹɬɶ, ɫɱɢɬɚɹ, ɱɬɨ ɷɬɢ ɫɟɬɢ ɪɚɛɨɬɚɸɬ ɜ ɤɜɚɞɪɚɬɢɱɧɨɣ ɨɛ-

ɥɚɫɬɢ.

ɉɪɢ ɪɚɫɱɟɬɟ ɩɚɪɨɩɪɨɜɨɞɨɜ ɫɨɩɨɫɬɚɜɥɹɸɬ ɩɨɥɭɱɟɧɧɨɟ ɡɧɚɱɟɧɢɟ

ɫɪ

ɫ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɩɪɢɧɹɬɵɦ. ɉɪɢ ɛɨɥɶɲɨɦ ɪɚɫɯɨɠɞɟɧɢɢ ɡɚɞɚɸɬɫɹ

ɛɨɥɟɟ ɛɥɢɡɤɢɦɢ ɡɧɚɱɟɧɢɹɦɢ ɷɬɢɯ

ɜɟɥɢɱɢɧ ɢ ɜɧɨɜɶ ɨɫɭɳɟɫɬɜɥɹɸɬ

ɩɪɨɜɟɪɨɱɧɵɣ ɪɚɫɱɟɬ.

5.5. ɉɶɟɡɨɦɟɬɪɢɱɟɫɤɢɣ ɝɪɚɮɢɤ

ɉɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɢ ɷɤɫɩɥɭɚɬɚɰɢɢ ɪɚɡɜɟɬɜɥɟɧɧɵɯ ɬɟɩɥɨɜɵɯ ɫɟ-

ɬɟɣ ɲɢɪɨɤɨ ɢɫɩɨɥɶɡɭɟɬɫɹ

ɩɶɟɡɨɦɟɬɪɢɱɟɫɤɢɣ ɝɪɚɮɢɤ, ɧɚ ɤɨɬɨɪɨɦ ɜ ɤɨɧ-

ɤɪɟɬɧɨɦ ɦɚɫɲɬɚɛɟ ɧɚɧɟɫɟɧɵ ɪɟɥɶɟɮ ɦɟɫɬɧɨɫɬɢ, ɜɵɫɨɬɚ ɩɪɢɫɨɟɞɢɧɟɧ-

ɧɵɯ ɡɞɚɧɢɣ, ɧɚɩɨɪ ɜ ɫɟɬɢ; ɩɨ ɧɟɦɭ ɥɟɝɤɨ ɨɩɪɟɞɟɥɢɬɶ ɧɚɩɨɪ (ɞɚɜɥɟɧɢɟ) ɢ

ɪɚɫɩɨɥɚɝɚɟɦɵɣ ɧɚɩɨɪ (ɩɟɪɟɩɚɞ ɞɚɜɥɟɧɢɣ) ɜ ɥɸɛɨɣ ɬɨɱɤɟ ɫɟɬɢ ɢ ɚɛɨ-

ɧɟɧɬɫɤɢɯ ɫɢɫɬɟɦɚɯ.

ɇɚ ɪɢɫ. 5.5 ɩɪɢɜɟɞɟɧɵ ɩɶɟɡɨɦɟɬɪɢɱɟɫɤɢɣ ɝɪɚɮɢɤ ɞɜɭɯɬɪɭɛɧɨɣ ɜɨ-

ɞɹɧɨɣ ɫɢɫɬɟɦɵ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ ɢ ɩɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ ɫɢɫɬɟɦɵ. Ɂɚ

ɝɨɪɢɡɨɧɬɚɥɶɧɭɸ ɩɥɨɫɤɨɫɬɶ ɨɬɫɱɟɬɚ ɧɚɩɨɪɨɜ ɩɪɢɧɹɬ ɭɪɨɜɟɧɶ I-I, ɢɦɟɸ-

ɳɢɣ ɝɨɪɢɡɨɧɬɚɥɶɧɭɸ ɨɬɦɟɬɤɭ 0;

– ɝɪɚɮɢɤ ɧɚɩɨɪɨɜ ɩɨɞɚɸɳɟɣ

ɥɢɧɢɢ ɫɟɬɢ;

1ɨ

4ɨ

– ɝɪɚɮɢɤ ɧɚɩɨɪɨɜ ɨɛɪɚɬɧɨɣ ɥɢɧɢɢ ɫɟɬɢ;

1ɨ

–

ɩɨɥɧɵɣ ɧɚɩɨɪ ɜ ɨɛɪɚɬɧɨɦ ɤɨɥɥɟɤɬɨɪɟ ɢɫɬɨɱɧɢɤɚ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ

–

ɧɚɩɨɪ, ɪɚɡɜɢɜɚɟɦɵɣ ɫɟɬɟɜɵɦ ɧɚɫɨɫɨɦ 1;ɇ

ɫɬ

– ɩɨɥɧɵɣ ɧɚɩɨɪ, ɪɚɡɜɢɜɚɟ-

ɦɵɣ ɩɨɞɩɢɬɨɱɧɵɦ ɧɚɫɨɫɨɦ, ɢɥɢ, ɱɬɨ ɬɨ ɠɟ, ɩɨɥɧɵɣ ɫɬɚɬɢɱɟɫɤɢɣ ɧɚɩɨɪ

ɬɟɩɥɨɜɨɣ ɫɟɬɢ; ɇ

– ɩɨɥɧɵɣ ɧɚɩɨɪ ɜ ɬɨɱɤɟ Ʉ ɧɚ ɧɚɝɧɟɬɚɬɟɥɶɧɨɦ ɩɚɬɪɭɛɤɟ

ɧɚɫɨɫɚ 1;

– ɩɨɬɟɪɹ ɧɚɩɨɪɚ ɫɟɬɟɜɨɣ ɜɨɞɵ ɜ ɬɟɩɥɨɩɨɞɝɨɬɨɜɢɬɟɥɶ-

ɧɨɣ ɭɫɬɚɧɨɜɤɟ III;

– ɩɨɥɧɵɣ ɧɚɩɨɪ ɜ ɩɨɞɚɸɳɟɦ ɤɨɥɥɟɤɬɨɪɟ ɢɫɬɨɱɧɢɤɚ ɬɟɩɥɨɫɧɚɛɠɟ-

ɧɢɹ:

ɤɤ1

HHH

G

. Ɋɚɫɩɨɥɚɝɚɟɦɵɣ ɧɚɩɨɪ ɫɟɬɟɜɨɣ ɜɨɞɵ ɧɚ ɤɨɥɥɟɤɬɨ-

ɪɚɯ Ɍɗɐ

ɨ111

HHH



. ɇɚɩɨɪ ɜ ɥɸɛɨɣ ɬɨɱɤɟ ɬɟɩɥɨɜɨɣ ɫɟɬɢ, ɧɚɩɪɢ-

ɦɟɪ ɜ ɬɨɱɤɟ 3, ɨɛɨɡɧɚɱɚɟɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:

– ɩɨɥɧɵɣ ɧɚɩɨɪ ɜ

ɬɨɱɤɟ 3 ɩɨɞɚɸɳɟɣ ɥɢɧɢɢ ɫɟɬɢ;

3ɨ

– ɩɨɥɧɵɣ ɧɚɩɨɪ ɜ ɬɨɱɤɟ 3 ɨɛɪɚɬɧɨɣ

ɥɢɧɢɢ ɫɟɬɢ.

ȿɫɥɢ ɝɟɨɞɟɡɢɱɟɫɤɚɹ ɜɵɫɨɬɚ ɨɫɢ ɬɪɭɛɨɩɪɨɜɨɞɚ ɧɚɞ ɩɥɨɫɤɨɫɬɶɸ ɨɬ-

ɫɱɟɬɚ ɜ ɷɬɨɣ ɬɨɱɤɟ ɫɟɬɢ ɪɚɜɧɚ Z

, ɬɨ ɩɶɟɡɨɦɟɬɪɢɱɟɫɤɢɣ ɧɚɩɨɪ ɜ ɬɨɱɤɟ 3

ɩɨɞɚɸɳɟɣ ɥɢɧɢɢ



, ɚ ɩɶɟɡɨɦɟɬɪɢɱɟɫɤɢɣ ɧɚɩɨɪ ɜ ɨɛɪɚɬɧɨɣ ɥɢ-

ɧɢɢ

3ɨ3

ZH 

. Ɋɚɫɩɨɥɚɝɚɟɦɵɣ ɧɚɩɨɪ ɜ ɬɨɱɤɟ 3 ɬɟɩɥɨɜɨɣ ɫɟɬɢ ɪɚɜɟɧ ɪɚɡ-

ɧɨɫɬɢ ɩɶɟɡɨɦɟɬɪɢɱɟɫɤɢɯ ɧɚɩɨɪɨɜ ɩɨɞɚɸɳɟɣ ɢ ɨɛɪɚɬɧɨɣ ɥɢɧɢɣ ɬɟɩɥɨ-

ɜɨɣ ɫɟɬɢ ɢɥɢ, ɱɬɨ ɨɞɧɨ ɢ ɬɨ ɠɟ, ɪɚɡɧɨɫɬɢ

ɩɨɥɧɵɯ ɧɚɩɨɪɨɜ

ɨ3n33

HHH 

Ɋɚɫɩɨɥɚɝɚɟɦɵɣ ɧɚɩɨɪ ɜ ɬɟɩɥɨɜɨɣ ɫɟɬɢ ɜ ɭɡɥɟ ɩɪɢɫɨɟɞɢɧɟɧɢɹ ɚɛɨɧɟɧɬɚ Ⱦ:

ɨ444

HHH



(5.13)

ɝɞɟ

ɨ4

– ɩɨɥɧɵɟ ɧɚɩɨɪɵ ɜ ɩɨɞɚɸɳɟɣ ɢ ɨɛɪɚɬɧɨɣ ɥɢɧɢɹɯ ɬɟ-

ɩɥɨɜɨɣ ɫɟɬɢ ɜ ɬɨɱɤɟ 4. ɉɨɬɟɪɹ ɧɚɩɨɪɚ ɜ ɩɨɞɚɸɳɟɣ ɥɢɧɢɢ ɬɟɩɥɨɜɨɣ ɫɟɬɢ

ɧɚ ɭɱɚɫɬɤɟ ɦɟɠɞɭ ɢɫɬɨɱɧɢɤɨɦ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ ɢ ɚɛɨɧɟɧɬɨɦ Ⱦ:

HHH  G



(5.14)

ɉɨɬɟɪɹ ɧɚɩɨɪɚ ɜ ɨɛɪɚɬɧɨɣ ɥɢɧɢɢ ɧɚ ɷɬɨɦ ɭɱɚɫɬɤɟ ɬɟɩɥɨɜɨɣ ɫɟɬɢ

4ɨ1ɨ

HHH  G

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(5.15)

ɉɪɢ ɪɚɛɨɬɟ ɫɟɬɟɜɨɝɨ ɧɚɫɨɫɚ 1 (ɫɦ. ɪɢɫ. 5.4, ɚ) ɧɚɩɨɪ ɇ

ɫɬ

, ɪɚɡɜɢɜɚɟ-

ɦɵɣ ɩɨɞɩɢɬɨɱɧɵɦ ɧɚɫɨɫɨɦ II, ɞɪɨɫɫɟɥɢɪɭɟɬɫɹ ɪɟɝɭɥɹɬɨɪɨɦ ɞɚɜɥɟɧɢɹ IV

ɞɨ ɇ

ɨ1