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4. Ɋɟɠɢɦɵ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɫɢɫɬɟɦ

ɰɟɧɬɪɚɥɢɡɨɜɚɧɧɨɝɨ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ

4.1. ɍɫɥɨɜɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ

ȼ ɩɪɢɜɟɞɟɧɧɵɯ ɜ ɷɬɨɦ ɪɚɡɞɟɥɟ ɭɪɚɜɧɟɧɢɹɯ ɢɫɩɨɥɶɡɭɸɬɫɹ ɫɥɟɞɭɸ-

ɳɢɟ ɭɫɥɨɜɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ: t

ɧ.ɨ

– ɪɚɫɱɟɬɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɧɚɪɭɠɧɨɝɨ ɜɨɡ-

ɞɭɯɚ ɞɥɹ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɨɬɨɩɥɟɧɢɹ, °C, ɡɧɚɱɟɧɢɹ ɤɨɬɨɪɨɣ ɞɥɹ ɪɹɞɚ

ɪɚɣɨɧɨɜ ɛɵɜɲɟɝɨ ɋɋɋɊ ɩɪɢ ɜɟɞɟɧɵ ɜ ɩɪɢɥɨɠɟɧɢɢ 1; t

– ɬɟɤɭɳɟɟ ɡɧɚ-

ɱɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɧɚɪɭɠɧɨɝɨ ɜɨɡɞɭɯɚ, t

 t

ɧ.ɨ

; t

ɜ.ɪ

– ɪɚɫɱɟɬɧɚɹ ɬɟɦɩɟɪɚ-

ɬɭɪɚ ɜɨɡɞɭɯɚ ɨɬɚɩɥɢɜɚɟɦɵɯ ɩɨɦɟɳɟɧɢɣ, °C; t

– ɥɸɛɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɜɨɡ-

ɞɭɯɚ ɜ ɨɬɚɩɥɢɜɚɟɦɵɯ ɩɨɦɟɳɟɧɢɹɯ, °C; t

ɧ.ɜ

– ɪɚɫɱɟɬɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɧɚ-

ɪɭɠɧɨɝɨ ɜɨɡɞɭɯɚ ɞɥɹ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɜɟɧɬɢɥɹɰɢɢ, °C; t

ɧ.ɤ

– ɬɟɦɩɟɪɚɬɭɪɚ

ɧɚɪɭɠɧɨɝɨ ɜɨɡɞɭɯɚ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɧɚɱɚɥɭ ɢɥɢ ɤɨɧɰɭ ɨɬɨɩɢɬɟɥɶɧɨɝɨ

ɫɟɡɨɧɚ, °C; Q' – ɪɚɫɱɟɬɧɚɹ ɬɟɩɥɨɜɚɹ ɧɚɝɪɭɡɤɚ (ɞɥɹ ɨɬɨɩɥɟɧɢɹ ɫɨɨɬ-

ɜɟɬɫɬɜɭɟɬ ɧɚɪɭɠɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ t

ɧ.ɨ

)·

ɉɪɢ ɪɚɫɱɟɬɧɨɣ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɟ Q':

ɬɟɦɩɟɪɚɬɭɪɚ ɜɨɞɵ ɜ ɩɨ-

ɞɚɸɳɟɦ ɬɪɭɛɨɩɪɨɜɨɞɟ, °C;

– ɬɟɦɩɟɪɚɬɭɪɚ ɜɨɞɵ ɜ ɨɛɪɚɬɧɨɦ ɬɪɭɛɨ-

ɩɪɨɜɨɞɟ, °C;

– ɬɟɦɩɟɪɚɬɭɪɚ ɜɨɞɵ ɜ ɩɨɞɚɸɳɟɦ ɫɬɨɹɤɟ ɦɟɫɬɧɨɣ ɫɢɫɬɟ-

ɦɵ ɩɨɫɥɟ ɫɦɟɲɟɧɢɹ ɧɚ ɜɜɨɞɟ,

WW GW

– ɩɟɪɟɩɚɞ ɬɟɦɩɟɪɚɬɭɪ ɜɨ-

ɞɵ ɜ ɬɟɩɥɨɜɨɣ ɫɟɬɢ, °C;

WW T

– ɩɟɪɟɩɚɞ ɬɟɦɩɟɪɚɬɭɪ ɜɨɞɵ ɜ ɦɟɫɬ-

ɧɨɣ ɫɢɫɬɟɦɟ, °C;

ɩɪ

– ɫɪɟɞɧɹɹ ɬɟɦɩɟɪɚɬɭɪɚ ɧɚɝɪɟɜɚɬɟɥɶɧɨɝɨ ɩɪɢɛɨɪɚ ɜ

ɦɟɫɬɧɨɣ ɫɢɫɬɟɦɟ, °C;

ɫɪ

- ɫɪɟɞɧɹɹ ɬɟɦɩɟɪɚɬɭɪɚ ɧɚɝɪɟɜɚɟɦɨɣ ɫɪɟɞɵ, °C;

t' -ɬɟɦɩɟɪɚɬɭɪɧɵɣ ɧɚɩɨɪ ɧɚɝɪɟɜɚɬɟɥɶɧɨɝɨ ɩɪɢɛɨɪɚ ɦɟɫɬɧɨɣ ɫɢɫɬɟɦɵ,

ɜɪ

ɩɪ

tt W '

°C; k' – ɤɨɷɮɮɢɰɢɟɧɬ ɬɟɩɥɨɩɟɪɟɞɚɱɢ ɧɚɝɪɟɜɚɬɟɥɶɧɵɯ ɩɪɢ

ɛɨɪɨɜ ɦɟɫɬɧɨɣ ɫɢɫɬɟɦɵ, G' – ɪɚɫɯɨɞ ɜɨɞɵ ɜ ɬɟɩɥɨɜɨɣ ɫɟɬɢ; W'= G'c

- ɷɤ-

ɜɢɜɚɥɟɧɬ ɪɚɫɯɨɞɚ ɜɨɞɵ;

WGkt ,,,,,,,,,

ɩɪ321

'TGWWWWW

– ɬɟ ɠɟ ɜɟɥɢɱɢɧɵ

ɩɪɢ ɩɪɨɢɡɜɨɥɶɧɨɣ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɟ Q < Q'; u – ɤɨɷɮɮɢɰɢɟɧɬ ɫɦɟɲɟ-

ɧɢɹ, ɬ. ɟ. ɨɬɧɨɲɟɧɢɟ ɪɚɫɯɨɞɚ ɩɨɞɦɟɲɢɜɚɟɦɨɣ ɜɨɞɵ ɢɡ ɨɛɪɚɬɧɨɣ ɥɢɧɢɢ ɤ

ɪɚɫɯɨɞɭ ɜɨɞɵ ɢɡ ɩɨɞɚɸɳɟɣ ɥɢɧɢɢ ɬɟɩɥɨɜɨɣ ɫɟɬɢ; F – ɩɥɨɳɚɞɶ ɩɨɜɟɪɯ-

ɧɨɫɬɢ ɧɚɝɪɟɜɚɬɟɥɶɧɵɯ ɩɪɢɛɨɪɨɜ, ɦ

; ɋ

– ɬɟɩɥɨɟɦɤɨɫɬɶ ɜɨɞɵ, ɋ

= 4,19

ɤȾɠ/(ɤɝ· Ʉ) = 1 ɤɤɚɥ/(ɤɝ·

C);

__ _ __ _

,, , ,, ,QGW t k

GW T

' - ɨɬɧɨɫɢɬɟɥɶɧɵɟ ɜɟɥɢɱɢ-

ɧɵ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ, ɪɚɫɯɨɞɚ ɢ ɷɤɜɢɜɚɥɟɧɬɚ ɪɚɫɯɨɞɚ,

ɩɟɪɟɩɚɞɚ ɬɟɦɩɟɪɚɬɭɪ ɜ ɫɟɬɢ, ɩɟɪɟɩɚɞɚ ɬɟɦɩɟɪɚɬɭɪ ɜ ɦɟɫɬɧɨɣ ɫɢɫɬɟɦɟ,

ɬɟɦɩɟɪɚɬɭɪɧɨɝɨ ɧɚɩɨɪɚ ɜ ɧɚɝɪɟɜɚɬɟɥɶɧɵɯ ɩɪɢɛɨɪɚɯ, ɤɨɷɮɮɢɰɢɟɧɬɚ ɬɟɩ-

ɥɨɩɟɪɟɞɚɱɢ ɧɚɝɪɟɜɚɬɟɥɶɧɵɯ ɩɪɢɛɨɪɨɜ.

4.2. Ɇɟɬɨɞɵ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɨɬɩɭɫɤɚ ɬɟɩɥɚ

Ɍɟɩɥɨɜɚɹ ɧɚɝɪɭɡɤɚ ɚɛɨɧɟɧɬɨɜ ɧɟɩɨɫɬɨɹɧɧɚ. Ɉɧɚ ɢɡɦɟɧɹɟɬɫɹ ɜ ɡɚ-

ɜɢɫɢɦɨɫɬɢ ɨɬ ɦɟɬɟɨɪɨɥɨɝɢɱɟɫɤɢɯ ɭɫɥɨɜɢɣ (ɬɟɦɩɟɪɚɬɭɪɵ ɧɚɪɭɠɧɨɝɨ ɜɨɡ-

ɞɭɯɚ, ɫɤɨɪɨɫɬɢ ɜɟɬɪɚ, ɢɧɫɨɥɹɰɢɢ), ɪɟɠɢɦɚ ɪɚɫɯɨɞɚ ɜɨɞɵ ɧɚ ɝɨɪɹɱɟɟ ɜɨ-

ɞɨɫɧɚɛɠɟɧɢɟ, ɪɟɠɢɦɚ ɪɚɛɨɬɵ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɨɛɨɪɭɞɨɜɚɧɢɹ ɢ ɞɪɭɝɢɯ

ɮɚɤɬɨɪɨɜ. Ⱦɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɜɵɫɨɤɨɝɨ ɤɚɱɟɫɬɜɚ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ, ɚ ɬɚɤɠɟ

ɷɤɨɧɨɦɢɱɧɵɯ ɪɟɠɢɦɨɜ ɜɵɪɚɛɨɬɤɢ ɬɟɩɥɨɬɵ ɧɚ Ɍɗɐ ɢɥɢ ɜ ɤɨɬɟɥɶɧɵɯ ɢ

ɬɪɚɧɫɩɨɪɬɢɪɨɜɤɢ

ɟɟ ɩɨ ɬɟɩɥɨɜɵɦ ɫɟɬɹɦ ɜɵɛɢɪɚɟɬɫɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ

ɦɟɬɨɞ ɪɟɝɭɥɢɪɨɜɚɧɢɹ.

ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɩɭɧɤɬɚ ɨɫɭɳɟɫɬɜɥɟɧɢɹ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɪɚɡɥɢɱɚ-

ɸɬ ɰɟɧɬɪɚɥɶɧɨɟ, ɝɪɭɩɩɨɜɨɟ, ɦɟɫɬɧɨɟ ɢ ɢɧɞɢɜɢɞɭɚɥɶɧɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ.

ɐɟɧɬɪɚɥɶɧɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɜɵɩɨɥɧɹɟɬɫɹ ɧɚ Ɍɗɐ ɢɥɢ ɜ ɤɨɬɟɥɶ-

ɧɨɣ; ɝɪɭɩɩɨɜɨɟ – ɧɚ ɝɪɭɩɩɨɜɵɯ ɬɟɩɥɨɜɵɯ ɩɨɞɫɬɚɧɰɢɹɯ (ȽɌɉ); ɦɟɫɬɧɨɟ –

ɧɚ ɦɟɫɬɧɵɯ ɬɟɩɥɨɜɵɯ ɩɨɞɫɬɚɧɰɢɹɯ (ɆɌɉ), ɧɚɡɵɜɚɟɦɵɯ ɱɚɫɬɨ ɚɛɨɧɟɧɬ-

ɫɤɢɦɢ ɜɜɨɞɚɦɢ; ɢɧɞɢɜɢɞɭɚɥɶɧɨɟ – ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɧɚ ɬɟɩɥɨɩɨɬɪɟɛ-

ɥɹɸɳɢɯ ɩɪɢɛɨɪɚɯ. ȼ ɛɨɥɶɲɢɧɫɬɜɟ ɫɥɭɱɚɟɜ ɬɟɩɥɨɜɚɹ ɧɚɝɪɭɡɤɚ ɜ ɪɚɣɨɧɟ

ɪɚɡɧɨɪɨɞɧɚ. ȼ ɨɞɧɨɦ ɢ ɬɨɦ ɠɟ ɪɚɣɨɧɟ ɢ ɞɚɠɟ ɧɚ ɨɞɧɨɦ ɢ ɬɨɦ

ɠɟ ɚɛɨ-

ɧɟɧɬɫɤɨɦ ɜɜɨɞɟ ɤ ɬɟɩɥɨɜɨɣ ɫɟɬɢ ɩɪɢɫɨɟɞɢɧɹɟɬɫɹ ɪɚɡɧɨɪɨɞɧɚɹ ɬɟɩɥɨɜɚɹ

ɧɚɝɪɭɡɤɚ, ɧɚɩɪɢɦɟɪ: ɨɬɨɩɥɟɧɢɟ ɢ ɝɨɪɹɱɟɟ ɜɨɞɨɫɧɚɛɠɟɧɢɟ; ɨɬɨɩɥɟɧɢɟ,

ɜɟɧɬɢɥɹɰɢɹ ɢ ɝɨɪɹɱɟɟ ɜɨɞɨɫɧɚɛɠɟɧɢɟ ɢ ɬ. ɞ. Ʉɪɨɦɟ ɬɨɝɨ, ɜ ɤɪɭɩɧɵɯ ɝɨ-

ɪɨɞɚɯ ɫ ɩɪɨɬɹɠɟɧɧɵɦɢ ɬɟɩɥɨɜɵɦɢ ɫɟɬɹɦɢ ɚɛɨɧɟɧɬɵ, ɪɚɫɩɨɥɨɠɟɧɧɵɟ ɧɚ

ɪɚɡɧɨɦ ɪɚɫɫɬɨɹɧɢɢ ɨɬ Ɍɗɐ, ɢɡ-ɡɚ ɬɪɚɧɫɩɨɪɬɧɨɝɨ ɡɚɩɚɡɞɵɜɚɧɢɹ ɬɟɩɥɨɧɨ-

ɫɢɬɟɥɹ ɧɚɯɨɞɹɬɫɹ ɜ ɧɟɨɞɢɧɚɤɨɜɵɯ ɭɫɥɨɜɢɹɯ

Ⱦɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɜɵɫɨɤɨɣ ɷɤɨɧɨɦɢɱɧɨɫɬɢ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ ɫɥɟɞɭ-

ɟɬ ɩɪɢɦɟɧɹɬɶ ɤɨɦɛɢɧɢɪɨɜɚɧɧɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ, ɤɨɬɨɪɨɟ ɞɨɥɠɧɨ ɹɜɥɹɬɶ-

ɫɹ ɪɚɰɢɨɧɚɥɶɧɵɦ ɫɨɱɟɬɚɧɢɟɦ, ɩɨ ɤɪɚɣɧɟɣ ɦɟɪɟ, ɬɪɟɯ ɫɬɭɩɟɧɟɣ ɪɟɝɭɥɢ-

ɪɨɜɚɧɢɹ – ɰɟɧɬɪɚɥɶɧɨɝɨ, ɝɪɭɩɩɨɜɨɝɨ ɢɥɢ ɦɟɫɬɧɨɝɨ ɢ ɢɧɞɢɜɢɞɭɚɥɶɧɨɝɨ.

Ɉɞɧɚɤɨ

ɢɧɞɢɜɢɞɭɚɥɶɧɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɧɚ ɬɟ-

ɩɥɨɩɨɬɪɟɛɥɹɸɳɢɯ ɩɪɢɛɨɪɚɯ ɬɪɟɛɭɟɬ ɩɪɢɦɟɧɟɧɢɹ ɛɨɥɶɲɨɝɨ ɤɨɥɢɱɟɫɬɜɚ

ɢɧɞɢɜɢɞɭɚɥɶɧɵɯ ɪɟɝɭɥɹɬɨɪɨɜ. ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɷɬɨ ɧɟ ɜɫɟɝɞɚ ɜɵɩɨɥ-

ɧɢɦɨ, ɩɨɬɨɦɭ ɱɬɨ ɬɪɟɛɭɸɬɫɹ ɛɨɥɶɲɢɟ ɡɚɬɪɚɬɵ ɧɚ ɪɟɤɨɧɫɬɪɭɤɰɢɸ ɞɟɣɫɬ-

ɜɭɸɳɢɯ ɬɟɩɥɨɩɨɬɪɟɛɥɹɸɳɢɯ ɭɫɬɚɧɨɜɨɤ. Ɉɫɨɛɟɧɧɨ ɡɚɬɪɭɞɧɟɧɚ ɪɟɤɨɧɫɬ-

ɪɭɤɰɢɹ ɫɢɫɬɟɦ ɨɬɨɩɥɟɧɢɹ, ɤɨɬɨɪɵɟ ɜɵɩɨɥɧɟɧɵ ɩɨ ɨɞɧɨɬɪɭɛɧɨɣ ɫɯɟɦɟ,

ɤɨɝɞɚ ɪɚɛɨɬɚ ɨɞɧɢɯ ɧɚɝɪɟɜɚɬɟɥɶɧɵɯ ɩɪɢɛɨɪɨɜ ɠɟɫɬɤɨ ɫɜɹɡɚɧɚ ɫ ɪɚɛɨɬɨɣ

ɞɪɭɝɢɯ. ɉɨɷɬɨɦɭ ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɫɢɫɬɟɦ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ ɢ ɪɟɠɢɦɨɜ ɨɬ-

ɩɭɫɤɚ ɬɟɩɥɨɬɵ ɨɝɪɚɧɢɱɢɜɚɟɬɫɹ ɬɨɥɶɤɨ ɞɜɭɦɹ-ɬɪɟɦɹ ɫɬɭɩɟɧɹɦɢ – ɰɟɧ-

ɬɪɚɥɶɧɵɦ ɢ ɝɪɭɩɩɨɜɵɦ ɢ (ɢɥɢ) ɦɟɫɬɧɵɦ, ɚ ɜ ɫɢɫɬɟɦɚɯ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ

ɦɚɥɨɣ ɦɨɳɧɨɫɬɢ – ɨɞɧɨɣ ɫɬɭɩɟɧɶɸ ɧɚ ɢɫɬɨɱɧɢɤɟ ɬɟɩɥɨɬɵ.

ɗɮɮɟɤɬɢɜɧɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɦɨɠɟɬ ɛɵɬɶ ɞɨɫɬɢɝɧɭɬɨ ɬɨɥɶɤɨ ɫ ɩɨ-

ɦɨɳɶɸ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɫɢɫɬɟɦ ɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ

(ɋȺɊ), ɚ ɧɟ ɜɪɭɱɧɭɸ, ɤɚɤ ɷɬɨ ɢɦɟɥɨ ɦɟɫɬɨ ɜ ɧɚɱɚɥɶɧɵɣ ɩɟɪɢɨɞ ɪɚɡɜɢɬɢɹ

ɰɟɧɬɪɚɥɢɡɨɜɚɧɧɨɝɨ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ.

ɐɟɧɬɪɚɥɶɧɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɜɟɞɟɬɫɹ ɩɨ ɬɢɩɨɜɨɣ ɬɟɩɥɨɜɨɣ

ɧɚɝɪɭɡ-

ɤɟ, ɯɚɪɚɤɬɟɪɧɨɣ ɞɥɹ ɛɨɥɶɲɢɧɫɬɜɚ ɚɛɨɧɟɧɬɨɜ ɪɚɣɨɧɚ. Ɍɚɤɨɣ ɧɚɝɪɭɡɤɨɣ

ɦɨɠɟɬ ɛɵɬɶ ɤɚɤ ɨɞɢɧ ɜɢɞ ɧɚɝɪɭɡɤɢ, ɧɚɩɪɢɦɟɪ ɨɬɨɩɥɟɧɢɟ, ɬɚɤ ɢ ɞɜɚ ɪɚɡ-

ɧɵɯ ɜɢɞɚ ɩɪɢ ɨɩɪɟɞɟɥɟɧɧɨɦ ɤɨɥɢɱɟɫɬɜɟɧɧɨɦ ɫɨɨɬɧɨɲɟɧɢɢ, ɧɚɩɪɢɦɟɪ

ɨɬɨɩɥɟɧɢɟ ɢ ɝɨɪɹɱɟɟ ɜɨɞɨɫɧɚɛɠɟɧɢɟ ɩɪɢ ɡɚɞɚɧɧɨɦ ɫɨɨɬɧɨɲɟɧɢɢ ɪɚɫɱɟɬ-

ɧɵɯ ɡɧɚɱɟɧɢɣ ɷɬɢɯ ɧɚɝɪɭɡɨɤ.

ȼ 1970–1980 ɝɝ. ɧɚɲɥɨ ɲɢɪɨɤɨɟ ɩɪɢɦɟɧɟɧɢɟ ɰɟɧɬɪɚɥɶɧɨɟ ɪɟɝɭɥɢ-

ɪɨɜɚɧɢɟ ɩɨ ɫɨɜɦɟɳɟɧɧɨɣ

ɧɚɝɪɭɡɤɟ – ɨɬɨɩɥɟɧɢɹ ɢ ɝɨɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟ-

ɧɢɹ. ɗɬɢ ɧɚɝɪɭɡɤɢ ɹɜɥɹɸɬɫɹ ɨɫɧɨɜɧɵɦɢ ɜ ɫɨɜɪɟɦɟɧɧɵɯ ɝɨɪɨɞɚɯ ɢ ɩɪɢ

ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ ɦɟɬɨɞɟ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɦɨɠɧɨ ɭɞɨɜɥɟɬɜɨɪɹɬɶ ɧɚɝɪɭɡɤɭ

ɝɨɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ ɛɟɡ ɞɨɩɨɥɧɢɬɟɥɶɧɨɝɨ ɭɜɟɥɢɱɟɧɢɹ (ɢɥɢ ɫ ɧɟɡɧɚ-

ɱɢɬɟɥɶɧɵɦ ɭɜɟɥɢɱɟɧɢɟɦ) ɪɚɫɱɟɬɧɨɝɨ ɪɚɫɯɨɞɚ ɜɨɞɵ ɜ ɫɟɬɢ ɩɨ ɫɪɚɜɧɟɧɢɸ

ɫ ɪɚɫɱɟɬɧɵɦ ɪɚɫɯɨɞɨɦ ɜɨɞɵ ɧɚ ɨɬɨɩɥɟɧɢɟ. ɋɧɢɠɟɧɢɟ ɪɚɫɱɟɬɧɨɝɨ ɪɚɫɯɨ-

ɞɚ ɜɨɞɵ ɜ ɫɟɬɢ

ɩɪɢɜɨɞɢɬ ɤ ɭɦɟɧɶɲɟɧɢɸ ɞɢɚɦɟɬɪɨɜ ɬɪɭɛɨɩɪɨɜɨɞɨɜ ɬɟɩ-

ɥɨɜɵɯ ɫɟɬɟɣ, ɚ ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɢ ɤ ɫɧɢɠɟɧɢɸ ɧɚɱɚɥɶɧɵɯ ɡɚɬɪɚɬ ɧɚ ɢɯ ɫɨ-

ɨɪɭɠɟɧɢɟ.

Ʉɚɤ ɩɪɢ ɝɪɭɩɩɨɜɨɦ, ɬɚɤ ɢ ɩɪɢ ɦɟɫɬɧɨɦ ɪɟɝɭɥɢɪɨɜɚɧɢɢ ɢɫɩɨɥɶ-

ɡɭɸɬɫɹ ɋȺɊ, ɭɩɪɚɜɥɹɸɳɢɟ ɩɨɞɚɱɟɣ ɬɟɩɥɨɬɵ ɜ ɝɪɭɩɩɵ ɨɞɧɨɬɢɩɧɵɯ ɬɟɩ-

ɥɨɩɨɬɪɟɛɥɹɸɳɢɯ ɭɫɬɚɧɨɜɨɤ ɢɥɢ ɩɪɢɛɨɪɨɜ. ɉɪɢ ɬɚɤɨɦ ɪɟɲɟɧɢɢ ɡɧɚɱɢ-

ɬɟɥɶɧɨ ɫɨɤɪɚɳɚɟɬɫɹ ɤɨɥɢɱɟɫɬɜɨ ɭɫɬɚɧɚɜɥɢɜɚɟɦɵɯ ɚɜɬɨɪɟɝɭɥɹɬɨɪɨɜ, ɨɞ-

ɧɚɤɨ ɩɨɞɚɱɚ ɬɟɩɥɨɬɵ ɩɪɨɜɨɞɢɬɫɹ ɩɨ ɭɫɪɟɞɧɟɧɧɨɦɭ ɩɚɪɚɦɟɬɪɭ ɞɥɹ ɤɚɠ-

ɞɨɝɨ ɜɢɞɚ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ, ɢɡɦɟɪɹɟɦɨɦɭ ɜ ɨɞɧɨɣ ɢɥɢ ɧɟɫɤɨɥɶɤɢɯ

ɤɨɧɬɪɨɥɶɧɵɯ ɬɨɱɤɚɯ ɭɫɬɚɧɨɜɤɢ. ɉɪɢ ɧɚɥɢɱɢɢ ɜ ɦɟɫɬɧɨɣ

ɫɢɫɬɟɦɟ ɪɚɡɪɟ-

ɝɭɥɢɪɨɜɤɢ ɧɚɪɭɲɚɟɬɫɹ ɬɪɟɛɭɟɦɵɣ ɬɟɦɩɟɪɚɬɭɪɧɵɣ ɪɟɠɢɦ ɜ ɨɬɞɟɥɶɧɵɯ

ɬɨɱɤɚɯ, ɯɨɬɹ ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɪɟɝɭɥɢɪɭɟɦɨɝɨ ɩɚɪɚɦɟɬɪɚ ɜ ɤɨɧɬɪɨɥɶɧɨɣ

ɬɨɱɤɟ ɫɢɫɬɟɦɵ ɩɪɢ ɷɬɨɦ ɜɵɞɟɪɠɢɜɚɟɬɫɹ.

Ⱦɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɜɵɫɨɤɨɝɨ ɤɚɱɟɫɬɜɚ ɢ ɷɤɨɧɨɦɢɱɧɨɫɬɢ ɬɟɩɥɨɫɧɚɛ-

ɠɟɧɢɹ ɧɟɨɛɯɨɞɢɦɚ ɬɳɚɬɟɥɶɧɚɹ ɧɚɱɚɥɶɧɚɹ ɪɟɝɭɥɢɪɨɜɤɚ ɚɛɨɧɟɧɬɫɤɨɣ ɭɫ-

ɬɚɧɨɜɤɢ, ɨɛɟɫɩɟɱɢɜɚɸɳɚɹ ɩɪɚɜɢɥɶɧɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɬɟɩɥɨɧɨɫɢɬɟɥɹ ɩɨ

ɨɬɞɟɥɶɧɵɦ ɩɪɢɛɨɪɚɦ ɦɟɫɬɧɨɣ ɫɢɫɬɟɦɵ.

Ɉɫɧɨɜɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ ɜ ɚɛɨɧɟɧɬɫɤɢɯ

ɫɢɫɬɟɦɚɯ ɪɚɫɯɨɞɭɟɬ-

ɫɹ ɞɥɹ ɧɚɝɪɟɜɚɬɟɥɶɧɵɯ ɰɟɥɟɣ, ɩɨɷɬɨɦɭ ɬɟɩɥɨɜɚɹ ɧɚɝɪɭɡɤɚ ɡɚɜɢɫɢɬ ɜ ɩɟɪ-

ɜɭɸ ɨɱɟɪɟɞɶ ɨɬ ɪɟɠɢɦɚ ɬɟɩɥɨɨɬɞɚɱɢ ɧɚɝɪɟɜɚɬɟɥɶɧɵɯ ɩɪɢɛɨɪɨɜ. ɇɚɝɪɟ-

ɜɚɬɟɥɶɧɵɟ ɩɪɢɛɨɪɵ ɚɛɨɧɟɧɬɫɤɢɯ ɭɫɬɚɧɨɜɨɤ ɜɟɫɶɦɚ ɪɚɡɧɨɨɛɪɚɡɧɵ ɩɨ

ɫɜɨɟɦɭ ɯɚɪɚɤɬɟɪɭ, ɤɨɧɫɬɪɭɤɰɢɢ ɢ ɬɟɯɧɢɱɟɫɤɨɦɭ ɨɮɨɪɦɥɟɧɢɸ: ɷɬɨ ɨɬɨ-

ɩɢɬɟɥɶɧɵɟ ɩɪɢɛɨɪɵ, ɨɬɞɚɸɳɢɟ ɬɟɩɥɨɬɭ ɜɨɡɞɭɯɭ ɢɡɥɭɱɟɧɢɟɦ ɢ ɫɜɨɛɨɞ-

ɧɨɣ ɤɨɧɜɟɤɰɢɟɣ; ɜɟɧɬɢɥɹɰɢɨɧɧɵɟ ɤɚɥɨɪɢɮɟɪɵ, ɧɚɝɪɟɜɚɸɳɢɟ ɜɨɡɞɭɯ,

ɞɜɢɠɭɳɢɣɫɹ ɫ ɛɨɥɶɲɨɣ ɫɤɨɪɨɫɬɶɸ ɜɞɨɥɶ ɩɨɜɟɪɯɧɨɫɬɢ ɧɚɝɪɟɜɚ; ɪɚɡ-

ɥɢɱɧɵɟ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɟ ɚɩɩɚɪɚɬɵ, ɜ ɤɨɬɨɪɵɯ ɩɚɪ ɢɥɢ ɜɨɞɚ ɧɚɝɪɟɜɚɸɬ

ɜɬɨɪɢɱɧɵɣ ɚɝɟɧɬ. ɇɟɫɦɨɬɪɹ ɧɚ ɜɫɟ ɦɧɨɝɨɨɛɪɚɡɢɟ, ɬɟɩɥɨɨɬɞɚɱɚ ɜɫɟɯ ɜɢ-

ɞɨɜ ɧɚɝɪɟɜɚɬɟɥɶɧɵɯ ɩɪɢɛɨɪɨɜ ɦɨɠɟɬ ɛɵɬɶ ɨɩɢɫɚɧɚ ɨɛɳɢɦ ɭɪɚɜɧɟɧɢɟɦ

,)(

21ɩ

nWtnkFQ WW '

(4.1)

ɝɞɟ Q – ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ, ɨɬɞɚɧɧɨɟ ɡɚ ɜɪɟɦɹ ɩ; kF – ɩɪɨɢɡɜɟɞɟɧɢɟ ɤɨ-

ɷɮɮɢɰɢɟɧɬɚ ɬɟɩɥɨɩɟɪɟɞɚɱɢ ɧɚɝɪɟɜɚɬɟɥɶɧɵɯ ɩɪɢɛɨɪɨɜ ɧɚ ɢɯ ɩɨɜɟɪɯ-

ɧɨɫɬɶ ɧɚɝɪɟɜɚ; ¨t – ɫɪɟɞɧɹɹ ɪɚɡɧɨɫɬɶ ɬɟɦɩɟɪɚɬɭɪ ɦɟɠɞɭ ɝɪɟɸɳɟɣ ɢ ɧɚ-

ɝɪɟɜɚɟɦɨɣ ɫɪɟɞɨɣ; W

– ɷɤɜɢɜɚɥɟɧɬ ɪɚɫɯɨɞɚ ɩɟɪɜɢɱɧɨɣ (ɝɪɟɸɳɟɣ) ɫɪɟ-

ɞɵ;

, ɢ

ɬɟɦɩɟɪɚɬɭɪɵ ɩɟɪɜɢɱɧɨɣ (ɝɪɟɸɳɟɣ) ɫɪɟɞɵ ɧɚ ɜɯɨɞɟ ɜ ɧɚ-

ɝɪɟɜɚɬɟɥɶɧɵɣ ɩɪɢɛɨɪ ɢ ɧɚ ɜɵɯɨɞɟ ɢɡ ɧɟɝɨ.

ɋɪɟɞɧɹɹ ɪɚɡɧɨɫɬɶ ɬɟɦɩɟɪɚɬɭɪ ɦɨɠɟɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɚ ɜ ɩɟɪɜɨɦ

ɩɪɢɛɥɢɠɟɧɢɢ ɤɚɤ ɪɚɡɧɨɫɬɶ ɦɟɠɞɭ ɫɪɟɞɧɟɚɪɢɮɦɟɬɢɱɟɫɤɢɦɢ ɬɟɦɩɟɪɚɬɭ-

ɪɚɦɢ ɝɪɟɸɳɟɣ ɢ ɧɚɝɪɟɜɚɟɦɨɣ ɫɪɟɞɵ:

2121





WW

ɫɪ

t

WW

(4.2)

ɝɞɟ t

ɫɪ

– ɫɪɟɞɧɹɹ ɬɟɦɩɟɪɚɬɭɪɚ ɧɚɝɪɟɜɚɟɦɨɣ ɫɪɟɞɵ; t

ɢ t

– ɬɟɦɩɟɪɚɬɭɪɵ

ɜɬɨɪɢɱɧɨɣ (ɧɚɝɪɟɜɚɟɦɨɣ) ɫɪɟɞɵ ɧɚ ɜɯɨɞɟ ɜ ɧɚɝɪɟɜɚɬɟɥɶɧɵɣ ɩɪɢɛɨɪ ɢ ɧɚ

ɜɵɯɨɞɟ ɢɡ ɧɟɝɨ.

Ʉɚɤ ɫɥɟɞɭɟɬ ɢɡ ɭɪɚɜɧɟɧɢɣ (4.1) ɢ (4.2),

;

W W

ɫɪ

ntkFQ



WW

ɂɡ ɫɨɜɦɟɫɬɧɨɝɨ ɪɟɲɟɧɢɹ ɧɚɯɨɞɢɦ

5,01

)(

ɫɪ1

WkF



W

(4.3ɚ)

Ʉɚɤ ɜɢɞɧɨ ɢɡ (4.3 ɚ), ɬɟɩɥɨɜɚɹ ɧɚɝɪɭɡɤɚ ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɦɨɠɟɬ ɪɟ-

ɝɭɥɢɪɨɜɚɬɶɫɹ ɡɚ ɫɱɟɬ ɢɡɦɟɧɟɧɢɹ ɩɹɬɢ ɩɚɪɚɦɟɬɪɨɜ: ɤɨɷɮɮɢɰɢɟɧɬɚ ɬɟɩɥɨ-

ɩɟɪɟɞɚɱɢ ɧɚɝɪɟɜɚɬɟɥɶɧɵɯ ɩɪɢɛɨɪɨɜ k, ɩɥɨɳɚɞɢ ɜɤɥɸɱɟɧɧɨɣ ɩɨɜɟɪɯɧɨ-

ɫɬɢ ɧɚɝɪɟɜɚ F, ɬɟɦɩɟɪɚɬɭɪɵ ɝɪɟɸɳɟɝɨ ɬɟɩɥɨɧɨɫɢɬɟɥɹ ɧɚ ɜɯɨɞɟ ɜ ɩɪɢɛɨɪ

, ɷɤɜɢɜɚɥɟɧɬɚ ɪɚɫɯɨɞɚ ɝɪɟɸɳɟɝɨ ɬɟɩɥɨɧɨɫɢɬɟɥɹ W

, ɜɪɟɦɟɧɢ ɪɚɛɨɬɵ

ɩɪɢɛɨɪɚ ɩ. Ⱦɥɹ ɰɟɧɬɪɚɥɶɧɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɢɡ ɷɬɢɯ ɩɹɬɢ ɩɚɪɚɦɟɬɪɨɜ

ɩɪɚɤɬɢɱɟɫɤɢ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɬɨɥɶɤɨ Ĳ

ɢ W

. ɉɪɢ ɷɬɨɦ ɧɟɨɛɯɨɞɢɦɨ

ɭɱɢɬɵɜɚɬɶ, ɱɬɨ ɜɨɡɦɨɠɧɵɣ ɞɢɚɩɚɡɨɧ ɢɡɦɟɧɟɧɢɹ Ĳ

ɢ W

ɜ ɪɟɚɥɶɧɵɯ ɭɫ-

ɥɨɜɢɹɯ ɨɝɪɚɧɢɱɟɧ ɪɹɞɨɦ ɨɛɫɬɨɹɬɟɥɶɫɬɜ.

ɉɪɢ ɪɚɡɧɨɪɨɞɧɨɣ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɟ ɧɢɠɧɢɦ ɩɪɟɞɟɥɨɦ Ĳ

ɹɜɥɹɟɬɫɹ

ɨɛɵɱɧɨ ɬɟɦɩɟɪɚɬɭɪɚ, ɬɪɟɛɭɟɦɚɹ ɞɥɹ ɝɨɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ (ɨɛɵɱɧɨ

60 °ɋ). ȼɟɪɯɧɢɣ ɩɪɟɞɟɥ Ĳ

ɨɩɪɟɞɟɥɹɟɬɫɹ ɞɨɩɭɫɬɢɦɵɦ ɞɚɜɥɟɧɢɟɦ ɜ ɩɨ-

ɞɚɸɳɟɣ ɥɢɧɢɢ ɬɟɩɥɨɜɨɣ ɫɟɬɢ ɢɡ ɭɫɥɨɜɢɹ ɧɟɜɫɤɢɩɚɧɢɹ ɜɨɞɵ. ȼɟɪɯɧɢɣ

ɩɪɟɞɟɥ W

ɨɩɪɟɞɟɥɹɟɬɫɹ ɪɚɫɩɨɥɚɝɚɟɦɵɦ ɧɚɩɨɪɨɦ ɧɚ ȽɌɉ ɢɥɢ ɆɌɉ ɢ

ɝɢɞɪɚɜɥɢɱɟɫɤɢɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ ɚɛɨɧɟɧɬɫɤɢɯ ɭɫɬɚɧɨɜɨɤ. ɑɬɨ ɠɟ ɤɚɫɚ-

ɟɬɫɹ ɩɚɪɚɦɟɬɪɨɜ k, F ɢ ɩ, ɬɨ ɢɦɢ ɦɨɠɧɨ ɩɨɥɶɡɨɜɚɬɶɫɹ ɞɥɹ ɢɡɦɟɧɟɧɢɹ

ɪɚɫɯɨɞɚ ɬɟɩɥɨɬɵ, ɤɚɤ ɩɪɚɜɢɥɨ, ɬɨɥɶɤɨ ɩɪɢ ɦɟɫɬɧɨɦ ɪɟɝɭɥɢɪɨɜɚɧɢɢ.

ȿɫɥɢ ɬɟɩɥɨɧɨɫɢɬɟɥɟɦ ɫɥɭɠɢɬ ɧɚɫɵɳɟɧɧɵɣ ɩɚɪ, ɬɨ ɩɨɫɤɨɥɶɤɭ W

1/2, ɚ Ĳ

= Ĳ

= Ĳ, ɭɪɚɜɧɟɧɢɟ (4.3ɚ) ɩɪɢɧɢɦɚɟɬ ɜɢɞ





ɫɪ

ntkFQ W

(4.3ɛ)

ɝɞɟ Ĳ – ɬɟɦɩɟɪɚɬɭɪɚ ɤɨɧɞɟɧɫɚɰɢɢ ɩɚɪɚ, °ɋ.

Ɉɫɧɨɜɧɨɣ ɦɟɬɨɞ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ ɧɚɝɪɟɜɚɬɟɥɶ-

ɧɵɯ ɩɪɢɛɨɪɨɜ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɩɚɪɚ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɢɡɦɟɧɟɧɢɢ ɬɟɦɩɟ-

ɪɚɬɭɪɵ ɤɨɧɞɟɧɫɚɰɢɢ ɩɨɫɪɟɞɫɬɜɨɦ ɞɪɨɫɫɟɥɢɪɨɜɚɧɢɹ ɢɥɢ ɠɟ ɜ ɢɡɦɟɧɟɧɢɢ

ɜɪɟɦɟɧɢ ɩ ɪɚɛɨɬɵ ɩɪɢɛɨɪɚ, ɬ. ɟ. ɪɚɛɨɬɚ ɬɚɤ ɧɚɡɵɜɚɟɦɵɦɢ «ɩɪɨɩɭɫɤɚɦɢ».

Ɉɛɚ ɦɟɬɨɞɚ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɹɜɥɹɸɬɫɹ ɦɟɫɬɧɵɦɢ.

ȼ ɜɨɞɹɧɵɯ ɫɢɫɬɟɦɚɯ ɰɟɧɬɪɚɥɢɡɨɜɚɧɧɨɝɨ

ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ (ɋɐɌ)

ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɜɨɡɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɬɪɢ ɦɟɬɨɞɚ ɰɟɧɬɪɚɥɶɧɨɝɨ ɪɟɝɭ-

ɥɢɪɨɜɚɧɢɹ:

1) ɤɚɱɟɫɬɜɟɧɧɵɣ, ɡɚɤɥɸɱɚɸɳɢɣɫɹ ɜ ɪɟɝɭɥɢɪɨɜɚɧɢɢ ɨɬɩɭɫɤɚ ɬɟɩ-

ɥɨɬɵ ɩɭɬɟɦ ɢɡɦɟɧɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɬɟɩɥɨɧɨɫɢɬɟɥɹ ɧɚ ɜɯɨɞɟ ɜ ɩɪɢɛɨɪ

ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɪɚɫɯɨɞɟ ɬɟɩɥɨɧɨɫɢɬɟɥɹ, ɩɨɞɚɜɚɟɦɨɝɨ ɜ ɪɟɝɭɥɢɪɭɟɦɭɸ

ɭɫɬɚɧɨɜɤɭ;

2) ɤɨɥɢɱɟɫɬɜɟɧɧɵɣ, ɡɚɤɥɸɱɚɸɳɢɣɫɹ ɜ ɪɟɝɭɥɢɪɨɜɚɧɢɢ ɨɬɩɭɫɤɚ ɬɟ-

ɩɥɨɬɵ ɩɭɬɟɦ ɢɡɦɟɧɟɧɢɹ ɪɚɫɯɨɞɚ ɬɟɩɥɨɧɨɫɢɬɟɥɹ ɩɪɢ ɩɨɫɬɨɹɧɧɨɣ ɬɟɦɩɟ-

ɪɚɬɭɪɟ ɟɝɨ ɧɚ

ɜɯɨɞɟ ɜ ɪɟɝɭɥɢɪɭɟɦɭɸ ɭɫɬɚɧɨɜɤɭ;

3) ɤɚɱɟɫɬɜɟɧɧɨ-ɤɨɥɢɱɟɫɬɜɟɧɧɵɣ, ɡɚɤɥɸɱɚɸɳɢɣɫɹ ɜ ɪɟɝɭɥɢɪɨɜɚɧɢɢ

ɨɬɩɭɫɤɚ ɬɟɩɥɨɬɵ ɩɨɫɪɟɞɫɬɜɨɦ ɨɞɧɨɜɪɟɦɟɧɧɨɝɨ ɢɡɦɟɧɟɧɢɹ ɪɚɫɯɨɞɚ

) ɢ ɬɟɦɩɟɪɚɬɭɪɵ ɬɟɩɥɨɧɨɫɢɬɟɥɹ Ĳ

ɉɪɢ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɚɛɨɧɟɧɬɫɤɢɯ ɜɜɨɞɨɜ ɨɫɧɨɜɧɨɟ ɩɪɢɦɟɧɟɧɢɟ ɜ

ɝɨɪɨɞɚɯ ɩɨɥɭɱɢɥɨ ɰɟɧɬɪɚɥɶɧɨɟ ɤɚɱɟɫɬɜɟɧɧɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ, ɞɨɩɨɥɧɹɟ-

ɦɨɟ ɧɚ ȽɌɉ ɢɥɢ ɆɌɉ ɤɨɥɢɱɟɫɬɜɟɧɧɵɦ ɪɟɝɭɥɢɪɨɜɚɧɢɟɦ ɢɥɢ ɪɟɝɭɥɢɪɨɜɚ-

ɧɢɟ ɩɪɨɩɭɫɤɚɦɢ.

Ʉɚɱɟɫɬɜɟɧɧɚɹ ɪɚɛɨɬɚ ɨɬɨɩɢɬɟɥɶɧɵɯ ɭɫɬɚɧɨɜɨɤ ɠɢɥɵɯ ɢ ɨɛɳɟɫɬ-

ɜɟɧɧɵɯ ɡɞɚɧɢɣ ɩɪɢ ɩɪɢɦɟɧɟɧɢɢ ɤɨɥɢɱɟɫɬɜɟɧɧɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɢɥɢ ɪɟ-

ɝɭɥɢɪɨɜɚɧɢɹ ɩɪɨɩɭɫɤɚɦɢ ɜɨɡɦɨɠɧɚ ɬɨɥɶɤɨ ɩɪɢ ɩɪɢɫɨɟɞɢɧɟɧɢɢ ɷɬɢɯ ɭɫ-

ɬɚɧɨɜɨɤ ɤ ɬɟɩɥɨɜɨɣ ɫɟɬɢ ɩɨ ɧɟɡɚɜɢɫɢɦɨɣ ɫɯɟɦɟ ɢɥɢ ɩɨ ɡɚɜɢɫɢɦɨɣ ɫɯɟɦɟ

ɫɨ ɫɦɟɫɢɬɟɥɶɧɵɦ ɧɚɫɨɫɨɦ (ɫɦ. ɪɢɫ. 3.6, ɥ ɢ ɦ ɢ 3.10, ɤ ɢ ɥ). Ɍɨɥɶɤɨ ɩɪɢ

ɷɬɢɯ ɫɯɟɦɚɯ ɩɪɢɫɨɟɞɢɧɟɧɢɹ

ɜ ɦɟɫɬɧɵɯ ɨɬɨɩɢɬɟɥɶɧɵɯ ɭɫɬɚɧɨɜɤɚɯ ɦɨɠɟɬ

ɩɨɞɞɟɪɠɢɜɚɬɶɫɹ ɪɚɫɱɟɬɧɵɣ ɪɚɫɯɨɞ ɜɨɞɵ ɧɟɡɚɜɢɫɢɦɨ ɨɬ ɟɟ ɪɚɫɯɨɞɚ ɢɡ

ɬɟɩɥɨɜɨɣ ɫɟɬɢ.

ɉɪɢ ɩɪɢɫɨɟɞɢɧɟɧɢɢ ɨɬɨɩɢɬɟɥɶɧɵɯ ɭɫɬɚɧɨɜɨɤ ɤ ɬɟɩɥɨɜɨɣ ɫɟɬɢ ɩɨ

ɡɚɜɢɫɢɦɨɣ ɫɯɟɦɟ ɫ ɷɥɟɜɚɬɨɪɨɦ ɢ ɛɟɡ ɞɨɩɨɥɧɢɬɟɥɶɧɨɝɨ ɫɦɟɫɢɬɟɥɶɧɨɝɨ

ɧɚɫɨɫɚ ɫɧɢɠɟɧɢɟ ɪɚɫɯɨɞɚ ɫɟɬɟɜɨɣ ɜɨɞɵ ɜɵɡɵɜɚɟɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɟ ɢɡ-

ɦɟɧɟɧɢɟ ɟɟ ɪɚɫɯɨɞɚ ɜ ɦɟɫɬɧɨɣ ɫɢɫɬɟɦɟ. ɉɪɢ ɭɦɟɧɶɲɟɧɢɢ ɪɚɫɯɨɞɚ ɜɨɞɵ

ɨɬɨɩɢɬɟɥɶɧɨɣ ɭɫɬɚɧɨɜɤɟ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɩɟɪɟɩɚɞ ɬɟɦɩɟɪɚɬɭɪ ɜɨɞɵ ɜ ɨɬɨ-

ɩɢɬɟɥɶɧɵɯ ɩɪɢɛɨɪɚɯ ɢ ɜɨɡɪɚɫɬɚɟɬ ɝɪɚɜɢɬɚɰɢɨɧɧɵɣ ɩɟɪɟɩɚɞ, ɱɬɨ ɩɪɢ-

ɜɨɞɢɬ ɤ ɜɟɪɬɢɤɚɥɶɧɨɣ ɪɚɡɪɟɝɭɥɢɪɨɜɤɟ ɨɬɨɩɢɬɟɥɶɧɵɯ ɫɢɫɬɟɦ. ɗɬɨ ɨɛ-

ɫɬɨɹɬɟɥɶɫɬɜɨ ɨɝɪɚɧɢɱɢɜɚɟɬ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɤɨɥɢɱɟɫɬɜɟɧɧɨɝɨ ɪɟɝɭɥɢɪɨɜɚ-

ɧɢɹ ɜ ɞɜɭɯɬɪɭɛɧɵɯ ɨɬɨɩɢɬɟɥɶɧɵɯ ɭɫɬɚɧɨɜɤɚɯ ɠɢɥɵɯ ɡɞɚɧɢɣ, ɢɦɟɸɳɢɯ,

ɤɚɤ ɩɪɚɜɢɥɨ, ɡɧɚɱɢɬɟɥɶɧɭɸ ɜɵɫɨɬɭ ɢ ɧɟɛɨɥɶɲɭɸ ɩɨɬɟɪɸ ɧɚɩɨɪɚ ɩɪɢ

ɪɚɫɱɟɬɧɨɦ ɪɚɫɯɨɞɟ ɜɨɞɵ.

Ɋɚɡɪɟɝɭɥɢɪɨɜɤɚ

ɜ ɨɬɨɩɢɬɟɥɶɧɵɯ ɭɫɬɚɧɨɜɤɚɯ ɜɨɡɧɢɤɚɟɬ ɬɚɤɠɟ ɩɪɢ

ɪɟɝɭɥɢɪɨɜɚɧɢɢ ɩɪɨɩɭɫɤɚɦɢ, ɬɚɤ ɤɚɤ ɩɪɢ ɩɟɪɢɨɞɢɱɟɫɤɢɯ ɜɵɤɥɸɱɟɧɢɹɯ ɢ

ɜɤɥɸɱɟɧɢɹɯ ɰɢɪɤɭɥɹɰɢɢ ɨɬɨɩɢɬɟɥɶɧɵɟ ɩɪɢɛɨɪɵ, ɧɚɯɨɞɹɳɢɟɫɹ ɧɚ ɪɚɡ-

ɥɢɱɧɨɦ ɪɚɫɫɬɨɹɧɢɢ ɨɬ ɭɡɥɚ ɪɟɝɭɥɢɪɨɜɚɧɢɹ, ɧɚɯɨɞɹɬɫɹ ɜ ɧɟɨɞɢɧɚɤɨɜɵɯ

ɭɫɥɨɜɢɹɯ.

ɉɪɢ ɬɟɩɥɨɫɧɚɛɠɟɧɢɢ ɨɬ Ɍɗɐ ɤɨɦɛɢɧɢɪɨɜɚɧɧɚɹ ɜɵɪɚɛɨɬɤɚ ɷɥɟɤ-

ɬɪɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɩɪɢ ɰɟɧɬɪɚɥɶɧɨɦ ɤɚɱɟɫɬɜɟɧɧɨɦ ɪɟɝɭɥɢɪɨɜɚɧɢɢ

ɛɨɥɶɲɟ, ɱɟɦ ɩɪɢ ɞɪɭɝɢɯ ɦɟɬɨɞɚɯ ɰɟɧɬɪɚɥɶɧɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ.

ɐɟɧ-

ɬɪɚɥɶɧɨɟ ɤɨɥɢɱɟɫɬɜɟɧɧɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɭɫɬɭɩɚɟɬ ɤɚɱɟɫɬɜɟɧɧɨɦɭ ɪɟɝɭ-

ɥɢɪɨɜɚɧɢɸ ɜ ɨɬɧɨɲɟɧɢɢ ɫɬɚɛɢɥɶɧɨɫɬɢ ɬɟɩɥɨɜɨɝɨ ɪɟɠɢɦɚ ɨɬɨɩɢɬɟɥɶɧɵɯ

ɭɫɬɚɧɨɜɨɤ, ɩɪɢɫɨɟɞɢɧɟɧɧɵɯ ɤ ɬɟɩɥɨɜɨɣ ɫɟɬɢ ɩɨ ɡɚɜɢɫɢɦɨɣ ɫɯɟɦɟ ɫ ɷɥɟ-

ɜɚɬɨɪɧɵɦ ɫɦɟɲɟɧɢɟɦ ɛɟɡ ɭɫɬɚɧɨɜɤɢ ɞɨɩɨɥɧɢɬɟɥɶɧɨɝɨ ɫɦɟɫɢɬɟɥɶɧɨɝɨ

ɧɚɫɨɫɚ. ȼɫɥɟɞɫɬɜɢɟ ɩɟɪɟɦɟɧɧɨɝɨ ɪɚɫɯɨɞɚ ɜɨɞɵ ɜ ɫɟɬɢ ɪɚɫɯɨɞ ɷɥɟɤɬɪɨ-

ɷɧɟɪɝɢɢ ɧɚ ɩɟɪɟɤɚɱɤɭ ɜɨɞɵ ɩɪɢ ɤɨɥɢɱɟɫɬɜɟɧɧɨɦ ɪɟɝɭɥɢɪɨɜɚɧɢɢ ɦɟɧɶɲɟ,

ɱɟɦ ɩɪɢ ɤɚɱɟɫɬɜɟɧɧɨɦ.

ɉɪɢ

ɪɚɡɧɨɪɨɞɧɨɣ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɟ, ɤɨɝɞɚ ɩɪɢɦɟɧɟɧɢɟ ɰɟɧɬɪɚɥɶ-

ɧɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɜ ɬɟɱɟɧɢɟ ɜɫɟɝɨ ɨɬɨɩɢɬɟɥɶɧɨɝɨ ɫɟɡɨɧɚ ɧɟ ɞɚɟɬ ɜɨɡ-

ɦɨɠɧɨɫɬɢ ɫɨɱɟɬɚɬɶ ɬɪɟɛɨɜɚɧɢɹ ɪɚɡɥɢɱɧɵɯ ɚɛɨɧɟɧɬɨɜ, ɫɧɚɛɠɚɟɦɵɯ ɬɟɩ-

ɥɨɬɨɣ ɨɬ ɟɞɢɧɨɣ ɬɟɩɥɨɜɨɣ ɫɟɬɢ, ɩɪɢɯɨɞɢɬɫɹ ɦɟɧɹɬɶ ɦɟɬɨɞ ɰɟɧɬɪɚɥɶɧɨɝɨ

ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɧɚ ɪɚɡɥɢɱɧɵɯ ɞɢɚɩɚɡɨɧɚɯ ɨɬɨɩɢɬɟɥɶɧɨɝɨ ɩɟɪɢɨɞɚ.

ɐɟɧɬɪɚɥɶɧɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɨɬɩɭɫɤɚ ɬɟɩɥɨɬɵ ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɦɨ-

ɠɟɬ ɨɫɭɳɟɫɬɜɥɹɬɶɫɹ ɤɚɤ ɩɪɢ ɧɟɩɪɟɪɵɜɧɨɣ, ɬɚɤ

ɢ ɩɪɢ ɩɟɪɢɨɞɢɱɟɫɤɨɣ ɩɨ-

ɞɚɱɟ ɬɟɩɥɨɬɵ ɚɛɨɧɟɧɬɚɦ «ɩɪɨɩɭɫɤɚɦɢ». ȼ ɩɨɫɥɟɞɧɟɦ ɫɥɭɱɚɟ ɭɜɹɡɤɚ ɝɪɚ-

ɮɢɤɨɜ ɩɨɞɚɱɢ ɢ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɬɟɩɥɨɬɵ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɫ ɩɨɦɨɳɶɸ

ɪɚɡɥɢɱɧɵɯ ɬɟɩɥɨɚɤɤɭɦɭɥɢɪɭɸɳɢɯ ɭɫɬɚɧɨɜɨɤ.

Ⱦɥɹ ɜɫɟɯ ɫɢɫɬɟɦ ɧɟɩɪɟɪɵɜɧɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɞɟɣɫɬɜɢɬɟɥɶɧɵ ɫɥɟ-

ɞɭɸɳɢɟ ɡɚɜɢɫɢɦɨɫɬɢ, ɛɚɡɢɪɭɸɳɢɟɫɹ ɧɚ ɭɪɚɜɧɟɧɢɹɯ ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ

ɢ ɬɟɩɥɨɩɟɪɟɞɚɱɢ:

_____

tktWQ ' G

(4.4)

ȼ ɪɹɞɟ ɫɥɭɱɚɟɜ ɩɪɢ ɪɚɫɱɟɬɟ ɪɟɠɢɦɨɜ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɫ ɩɟɪɟɦɟɧɧɵɦ

ɪɚɫɯɨɞɨɦ ɜɨɞɵ ɩɪɢɯɨɞɢɬɫɹ ɡɚɞɚɜɚɬɶɫɹ ɡɚɜɢɫɢɦɨɫɬɶɸ ɪɚɫɯɨɞɚ ɢɥɢ ɷɤɜɢ-

ɜɚɥɟɧɬɚ ɪɚɫɯɨɞɚ ɜɨɞɵ ɜ ɫɟɬɢ ɨɬ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ. ɗɬɭ ɡɚɜɢɫɢɦɨɫɬɶ

ɭɞɨɛɧɨ ɨɩɢɫɵɜɚɬɶ ɷɦɩɢɪɢɱɟɫɤɢɦ ɭɪɚɜɧɟɧɢɟɦ

ɂɅɂ

(4.5)

ɉɪɢɧɰɢɩɢɚɥɶɧɨ ɭɪɚɜɧɟɧɢɟ (4.5) ɩɪɢɦɟɧɢɦɨ ɩɪɢ ɜɫɟɯ ɫɢɫɬɟɦɚɯ ɪɟɝɭɥɢ-

ɪɨɜɚɧɢɹ.

ɉɪɢ ɤɚɱɟɫɬɜɟɧɧɨɦ ɪɟɝɭɥɢɪɨɜɚɧɢɢ, ɬ. ɟ. ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɪɚɫɯɨɞɟ

ɫɟɬɟɜɨɣ ɜɨɞɵ, ɬ = 0, W = 1. Ʉɚɤ ɜɢɞɧɨ

ɢɡ (4.4), ɜ ɷɬɨɦ ɫɥɭɱɚɟ

GW Q

ɉɪɢ ɤɨɥɢɱɟɫɬɜɟɧɧɨɦ ɪɟɝɭɥɢɪɨ-

ɜɚɧɢɢ ɬ ~ 1. Ɍɨɝɞɚ ɤɚɤ ɜɢɞɧɨ ɢɡ

ɭɪɚɜɧɟɧɢɹ (4.5)

WQ t

ɉɪɢ ɤɚɱɟɫɬɜɟɧɧɨ-ɤɨɥɢɱɟɫɬɜɟɧɧɨɦ ɪɟ-

ɝɭɥɢɪɨɜɚɧɢɢ 0  m  1. Ʉɚɤ ɜɢɞɧɨ ɢɡ

ɜɵɪɚɠɟɧɢɹ (4.5), ɜ ɷɬɨɦ ɫɥɭɱɚɟ

WQ d

ɇɚ ɪɢɫ. 4.1 ɩɪɢɜɟɞɟɧɚ ɡɚɜɢɫɢɦɨɫɬɶ

)(WfQ d

ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɫɢɫɬɟɦɚɯ

ɪɟɝɭɥɢɪɨɜɚɧɢɹ.

Ɋɢɫ. 4.1 Ɂɚɜɢɫɢɦɨɫɬɶ

.)(

WfQ d

1–ɤɚɱɟɫɬɜɟɧɧɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ; 2 –

ɤɚɱɟɫɬɜɟɧɧɨ-ɤɨɥɢɱɟɫɬɜɟɧɧɨɟ ɪɟɝɭɥɢ-

ɪɨɜɚɧɢɟ; 3,4 – ɤɨɥɢɱɟɫɬɜɟɧɧɨɟ ɪɟɝɭ-

ɥɢɪɨɜɚɧɢɟ

4.3.

ɐɟɧɬɪɚɥɶɧɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ

ɨɞɧɨɪɨɞɧɨɣ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ

ȼ ɧɚɲɟɣ ɫɬɪɚɧɟ ɢ ɜɨ ɦɧɨɝɢɯ ɞɪɭɝɢɯ ɫɬɪɚɧɚɯ ɨɬɨɩɥɟɧɢɟ ɜ ɛɨɥɶ-

ɲɢɧɫɬɜɟ ɪɚɣɨɧɨɜ – ɨɫɧɨɜɧɨɣ ɜɢɞ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ, ɚ ɜ ɧɟɤɨɬɨɪɵɯ ɫɥɭ-

ɱɚɹɯ – ɟɞɢɧɫɬɜɟɧɧɚɹ ɬɟɩɥɨɜɚɹ ɧɚɝɪɭɡɤɚ. Ⱦɨɥɹ ɞɪɭɝɢɯ ɜɢɞɨɜ ɬɟɩɥɨɜɨɣ ɧɚ-

ɝɪɭɡɤɢ, ɧɚɩɪɢɦɟɪ ɝɨɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ ɢ ɜɟɧɬɢɥɹɰɢɢ, ɜ ɩɟɪɢɨɞ ɨɬɨ-

ɩɢɬɟɥɶɧɨɝɨ ɫɟɡɨɧɚ ɨɛɵɱɧɨ ɫɭɳɟɫɬɜɟɧɧɨ ɧɢɠɟ ɨɬɨɩɢɬɟɥɶɧɨɣ ɧɚɝɪɭɡɤɢ.

ɉɨɷɬɨɦɭ ɜ ɨɫɧɨɜɭ ɰɟɧɬɪɚɥɶɧɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ

ɱɚɫɬɨ ɡɚɤɥɚɞɵɜɚɟɬɫɹ ɡɚ-

ɤɨɧ ɢɡɦɟɧɟɧɢɹ ɨɬɨɩɢɬɟɥɶɧɨɣ ɧɚɝɪɭɡɤɢ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɧɚɪɭɠɧɨɝɨ ɜɨɡ-

ɞɭɯɚ.

ȼ ɪɚɣɨɧɚɯ ɫ ɩɪɟɨɛɥɚɞɚɸɳɟɣ ɨɬɨɩɢɬɟɥɶɧɨɣ ɧɚɝɪɭɡɤɨɣ ɰɟɧɬɪɚɥɶɧɨɟ

ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɨɬɩɭɫɤɚ ɬɟɩɥɨɬɵ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɨɫɭɳɟɫɬɜɥɹɬɶ ɩɨ ɷɤɜɢ-

ɜɚɥɟɧɬɧɨɣ ɧɚɪɭɠɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ.

ɉɨɞ ɷɤɜɢɜɚɥɟɧɬɧɨɣ ɧɚɪɭɠɧɨɣ ɬɟɦɩɟɪɚɬɭɪɨɣ t

ɩɨɧɢɦɚɟɬɫɹ ɧɚ-

ɪɭɠɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ, ɩɪɢ ɤɨɬɨɪɨɣ ɬɟɩɥɨɩɨɬɟɪɢ ɡɞɚɧɢɣ ɨɬ ɬɟɩɥɨɩɟɪɟɞɚɱɢ

ɱɟɪɟɡ ɧɚɪɭɠɧɵɟ ɨɝɪɚɠɞɟɧɢɹ ɪɚɜɧɵ ɮɚɤɬɢɱɟɫɤɢɦ ɬɟɩɥɨɩɨɬɟɪɹɦ ɷɬɢɯ ɡɞɚ-

ɧɢɣ ɫ ɭɱɟɬɨɦ ɢɧɮɢɥɶɬɪɚɰɢɢ ɯɨɥɨɞɧɨɝɨ ɜɨɡɞɭɯɚ ɢ ɫɨɥɧɟɱɧɨɣ ɪɚɞɢɚɰɢɢ.

ɐɟɧɬɪɚɥɶɧɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɨɬɨɩɢɬɟɥɶɧɨɣ ɧɚɝɪɭɡɤɢ. Ɂɚɞɚɱɚ

ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɫɨɫɬɨɢɬ ɜ ɩɨɞɞɟɪɠɚɧɢɢ ɪɚɫɱɟɬɧɨɣ ɜɧɭɬɪɟɧɧɟɣ ɬɟɦɩɟɪɚ-

ɬɭɪɵ

ɜ ɨɬɚɩɥɢɜɚɟɦɵɯ ɩɨɦɟɳɟɧɢɹɯ. Ɋɚɫɫɦɨɬɪɢɦ ɬɪɢ ɬɟɨɪɟɬɢɱɟɫɤɢ

ɜɨɡɦɨɠɧɵɯ ɦɟɬɨɞɚ ɰɟɧɬɪɚɥɶɧɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɨɬɨɩɢɬɟɥɶɧɨɣ ɧɚɝɪɭɡ-

ɤɢ: ɤɚɱɟɫɬɜɟɧɧɵɣ, ɤɨɥɢɱɟɫɬɜɟɧɧɵɣ ɢ ɤɚɱɟɫɬɜɟɧɧɨ-ɤɨɥɢɱɟɫɬɜɟɧɧɵɣ.

Ʉɚɱɟɫɬɜɟɧɧɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ. Ɋɚɫɱɟɬ ɤɚɱɟɫɬɜɟɧɧɨɝɨ ɪɟɝɭɥɢɪɨ-

ɜɚɧɢɹ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɨɩɪɟɞɟɥɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ ɜɨɞɵ ɜ ɬɟɩɥɨɜɨɣ ɫɟɬɢ ɜ

ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɷɤɜɢɜɚɥɟɧɬɟ ɪɚɫɯɨɞɚ

ɬɟɩɥɨɧɨɫɢɬɟɥɹ ɜ ɬɟɩɥɨɜɨɣ ɫɟɬɢ, ɬ. ɟ. ɩɪɢ W

ɉɪɢ ɡɚɜɢɫɢɦɨɣ ɫɯɟɦɟ ɩɪɢɫɨɟɞɢɧɟɧɢɹ ɨɬɨɩɢɬɟɥɶɧɵɯ ɭɫɬɚɧɨɜɨɤ ɤ

ɬɟɩɥɨɜɨɣ ɫɟɬɢ (ɫɦ. ɪɢɫ. 3.5,

ɚ-ɜ

ɢ 3.9,

ɚ-ɜ)

ɭɪɚɜɧɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɧɵɯ

ɝɪɚɮɢɤɨɜ ɹɜɥɹɸɬɫɹ ɱɚɫɬɧɵɦɢ ɫɥɭɱɚɹɦɢ ɭɪɚɜɧɟɧɢɣ (4.33ɚ) ɢ (4.34ɚ) ɩɪɢ

= 1.

ɉɪɢ ɩɪɢɧɭɞɢɬɟɥɶɧɨɣ ɰɢɪɤɭɥɹɰɢɢ ɜɨɡɞɭɯɚ ɜɞɨɥɶ ɩɨɜɟɪɯɧɨɫɬɢ ɧɚ-

ɝɪɟɜɚ ɨɬɨɩɢɬɟɥɶɧɵɯ ɩɪɢɛɨɪɨɜ (ɧɚɩɪɢɦɟɪ, ɜ ɨɬɨɩɢɬɟɥɶɧɵɯ ɚɝɪɟɝɚɬɚɯ

ɜɨɡɞɭɲɧɨɝɨ ɨɬɨɩɥɟɧɢɹ) ɤɨɷɮɮɢɰɢɟɧɬ ɬɟɩɥɨɩɟɪɟɞɚɱɢ ɨɫɬɚɟɬɫɹ ɩɪɚɤɬɢɱɟ-

ɫɤɢ ɩɨɫɬɨɹɧɧɵɦ ɧɟɡɚɜɢɫɢɦɨ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɜɨɞɵ ɜ ɩɪɢɛɨɪɟ. Ⱦɥɹ ɷɬɢɯ

ɭɫɥɨɜɢɣ ɬɟɦɩɟɪɚɬɭɪɧɵɟ ɝɪɚɮɢɤɢ ɩɪɢɧɢɦɚɸɬ ɜɢɞ ɩɪɹɦɵɯ ɥɢɧɢɣ.

,)(

ɨɜ.ɪ

ɨ1ɜ.ɪɨ1

Qtt W W

(4.6)

,)(

ɨɜ.ɪ

ɨ2ɜ.ɪɨ2

Qtt W W

(4.7)

Ɍɚɛɥɢɰɚ 4.1

Ɍɟɦɩɟɪɚɬɭɪɚ ɜɨɞɵ ɜ ɬɟɩɥɨɜɨɣ ɫɟɬɢ ɩɪɢ ɤɚɱɟɫɬɜɟɧɧɨɦ ɪɟɝɭɥɢɪɨɜɚ-

ɧɢɢ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ ɢ ɡɚɜɢɫɢɦɨɣ ɫɯɟɦɟ ɩɪɢɫɨɟɞɢɧɟɧɢɹ ɨɬɨɩɢɬɟɥɶɧɵɯ

ɭɫɬɚɧɨɜɨɤ

Ɍɟɦɩɟɪɚɬɭɪɚ ɜɨɞɵ ɜ ɩɨɞɚɸɳɟɣ ɥɢɧɢɢ Ĳ

ɨ1

, °ɋ, ɩɪɢ įĲ'

ɨ ,

°ɋ

Ɍɟɦɩɟɪɚɬɭɪɚ ɜɨɞɵ ɩɨɫɥɟ ɨɬɨ-

ɩɢɬɟɥɶɧɨɣ ɭɫɬɚɧɨɜɤɢ Ĳ

ɨ2

, °ɋ

25 40 50 60 70 80

0,2 38,3 ~1,3 43,3 45,3 47,3 49,3 33,3

0,4 54,0 60,0 64,0 68,0 72,0 76,0 44,0

0,6 68,5 77,5 83,5 89,5 95,6 101,5 53,5

0,8 82,0 9~,0 102,0 110,0 118,0 126,0 62,0

1,0 95,0 110,0 120,0 130,0 140,0 150,0 70,0

4.4. ɐɟɧɬɪɚɥɢɡɨɜɚɧɧɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɪɚɡɧɨɪɨɞɧɨɣ ɬɟɩɥɨɜɨɣ

ɧɚɝɪɭɡɤɢ

ɉɪɟɠɞɟ ɜɫɟɝɨ, ɧɟɨɛɯɨɞɢɦɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɩɪɢɦɟɧɟɧɢɟ ɬɨɥɶɤɨ

ɰɟɧɬɪɚɥɶɧɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɫɢɫɬɟɦ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ ɧɟ ɦɨɠɟɬ ɨɛɟɫɩɟ-

ɱɢɬɶ ɤɚɱɟɫɬɜɟɧɧɨɟ ɢ ɷɤɨɧɨɦɢɱɧɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɪɚɡɧɨɪɨɞɧɵɯ ɬɟɩɥɨ-

ɜɵɯ ɧɚɝɪɭɡɨɤ. ɐɟɧɬɪɚɥɶɧɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ, ɜɵɩɨɥɧɹɹ ɝɪɭɛɭɸ ɪɟɝɭɥɢ-

ɪɨɜɤɭ ɫɢɫɬɟɦɵ ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ, ɩɨɡɜɨɥɹɟɬ ɫɧɢɡɢɬɶ ɧɚɝɪɭɡɤɭ ɧɚ ɫɢɫɬɟɦɵ

ɝɪɭɩɩɨɜɨɝɨ ɢ ɦɟɫɬɧɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ. Ɉɞɧɚɤɨ ɧɚɢɛɨɥɟɟ ɷɮɮɟɤɬɢɜɧɵɦ

ɦɟɬɨɞɨɦ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɪɚɡɧɨɪɨɞɧɵɯ ɬɟɩɥɨɜɵɯ ɧɚɝɪɭɡɨɤ ɹɜɥɹɟɬɫɹ ɢɧɞɢ-

ɜɢɞɭɚɥɶɧɨɟ

ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɬɟɩɥɨɩɨɬɪɟɛɥɹɸɳɢɯ ɭɫɬɚɧɨɜɨɤ, ɬɚɤ ɤɚɤ

ɬɨɥɶɤɨ ɩɪɢ ɢɧɞɢɜɢɞɭɚɥɶɧɨɦ ɪɟɝɭɥɢɪɨɜɚɧɢɢ ɦɨɠɧɨ ɭɱɟɫɬɶ ɜɫɟ ɮɚɤɬɨɪɵ,

ɜɥɢɹɸɳɢɟ ɧɚ ɬɟɩɥɨɜɵɟ ɧɚɝɪɭɡɤɢ.

Ɉɛɵɱɧɨ ɜ ɝɨɪɨɞɚɯ ɨɫɧɨɜɧɨɣ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɨɣ ɹɜɥɹɟɬɫɹ ɨɬɨɩɥɟ-

ɧɢɟ. ɋɭɳɟɫɬɜɟɧɧɨɟ ɪɚɡɜɢɬɢɟ, ɨɫɨɛɟɧɧɨ ɜ ɧɨɜɵɯ ɝɨɪɨɞɫɤɢɯ ɪɚɣɨɧɚɯ,

ɩɪɢɨɛɪɟɥɨ ɜ ɩɨɫɥɟɞɧɢɟ ɝɨɞɵ ɝɨɪɹɱɟɟ ɜɨɞɨɫɧɚɛɠɟɧɢɟ. Ɂɧɚɱɢɬɟɥɶɧɨ

ɦɟɧɶɲɟ ɜɟɧɬɢɥɹɰɢɨɧɧɚɹ ɧɚɝɪɭɡɤɚ ɝɨɪɨɞɫɤɢɯ ɪɚɣɨɧɨɜ. ɉɨɷɬɨɦɭ ɰɟɧ-

ɬɪɚɥɶɧɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɝɨɪɨɞɫɤɢɯ

ɪɚɣɨɧɨɜ ɨɪɢɟɧɬɢɪɭɸɬ ɨɛɵɱɧɨ ɧɚ

ɨɬɨɩɢɬɟɥɶɧɭɸ ɧɚɝɪɭɡɤɭ ɢɥɢ ɠɟ ɧɚ ɫɨɜɦɟɳɟɧɧɭɸ ɧɚɝɪɭɡɤɭ ɨɬɨɩɥɟɧɢɹ ɢ

ɝɨɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ.

ȼ ɬɨɦ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɭ ɛɨɥɶɲɢɧɫɬɜɚ ɚɛɨɧɟɧɬɨɜ ɪɚɣɨɧɚ ɨɬɫɭɬɫɬɜɭɟɬ

ɧɚɝɪɭɡɤɚ ɝɨɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ, ɰɟɧɬɪɚɥɶɧɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɜ ɝɨɪɨ-

ɞɚɯ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɨ ɡɚɤɨɧɭ, ɢɡɦɟɧɟɧɢɹ ɨɬɨɩɢɬɟɥɶɧɨɣ ɧɚɝɪɭɡɤɢ. ȿɫɥɢ

ɭ ɛɨɥɶɲɢɧɫɬɜɚ ɚɛɨɧɟɧɬɨɜ ɜ ɪɚɣɨɧɟ ɧɚɪɹɞɭ ɫ ɨɬɨɩɥɟɧɢɟɦ ɢɦɟɸɬɫɹ ɭɫɬɚ-

ɧɨɜɤɢ ɝɨɪɹɱɟɝɨ

ɜɨɞɨɫɧɚɛɠɟɧɢɹ, ɰɟɧɬɪɚɥɶɧɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɱɚɫɬɨ ɨɫɭ-

ɳɟɫɬɜɥɹɟɬɫɹ ɩɨ ɡɚɤɨɧɭ ɢɡɦɟɧɟɧɢɹ ɫɨɜɦɟɳɟɧɧɨɣ ɧɚɝɪɭɡɤɢ ɨɬɨɩɥɟɧɢɹ ɢ

ɝɨɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ. ɇɟɪɚɜɧɨɦɟɪɧɨɫɬɢ ɫɭɬɨɱɧɨɝɨ ɝɪɚɮɢɤɚ ɫɭɦɦɚɪ-

ɧɨɣ ɧɚɝɪɭɡɤɢ ɜɵɪɚɜɧɢɜɚɸɬɫɹ ɡɚ ɫɱɟɬ ɬɟɩɥɨɚɤɤɭɦɭɥɢɪɭɸɳɟɣ ɫɩɨɫɨɛɧɨ-

ɫɬɢ ɫɬɪɨɢɬɟɥɶɧɵɯ ɤɨɧɫɬɪɭɤɰɢɣ ɨɬɚɩɥɢɜɚɟɦɵɯ ɡɞɚɧɢɣ ɢɥɢ ɠɟ ɩɭɬɟɦ ɭɫ-

ɬɚɧɨɜɤɢ ɫɩɟɰɢɚɥɶɧɵɯ ɚɤɤɭɦɭɥɹɬɨɪɨɜ ɝɨɪɹɱɟɣ ɜɨɞɵ. ɉɪɢ ɪɚɡɧɨɪɨɞɧɨɣ

ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɟ ɪɚɣɨɧɚ ɧɟɡɚɜɢɫɢɦɨ ɨɬ ɰɟɧɬɪɚɥɶɧɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ

ɞɨɥɠɧɨ ɩɪɨɜɨɞɢɬɶɫɹ ɝɪɭɩɩɨɜɨɟ ɢ (ɢɥɢ) ɦɟɫɬɧɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ, ɤɚɤ ɩɪɚ-

ɜɢɥɨ, ɜɫɟɯ ɜɢɞɨɜ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ.

ɉɪɢ ɷɬɨɦ ɬɟɦɩɟɪɚɬɭɪɚ ɜɨɞɵ ɜ ɩɨɞɚɸɳɟɦ ɬɪɭɛɨɩɪɨɜɨɞɟ ɬɟɩɥɨɜɨɣ

ɫɟɬɢ ɧɟ ɞɨɥɠɧɚ ɫɧɢɠɚɬɶɫɹ ɧɢɠɟ ɭɪɨɜɧɹ

, ɨɩɪɟɞɟɥɹɟɦɨɝɨ ɭɫɥɨɜɢɹɦɢ ɝɨ-

ɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟɧɢɹ.

ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫɨ ɋɇɢɉ 2.04.01-85 ɬɟɦɩɟɪɚɬɭɪɚ ɝɨɪɹɱɟɣ ɜɨɞɵ ɜ

ɦɟɫɬɚɯ ɜɨɞɨɪɚɡɛɨɪɚ ɞɨɥɠɧɚ ɛɵɬɶ ɧɟ ɧɢɠɟ 60 °ɋ ɩɪɢ ɨɬɤɪɵɬɨɣ ɫɢɫɬɟɦɟ

ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ ɢ 50 °ɋ ɩɪɢ ɡɚɤɪɵɬɨɣ.

ɋ ɭɱɟɬɨɦ ɫɧɢɠɟɧɢɹ ɬɟɦɩɟ-

ɪɚɬɭɪɵ ɜɨɞɵ ɜ ɦɟɫɬɧɵɯ ɤɨɦɦɭ-

ɧɢɤɚɰɢɹɯ ɝɨɪɹɱɟɝɨ ɜɨɞɨɫɧɚɛɠɟ-

ɧɢɹ ɢ ɩɟɪɟɩɚɞɚ ɬɟɦɩɟɪɚɬɭɪ ɦɟɠɞɭ

ɝɪɟɸɳɟɣ ɢ ɧɚɝɪɟɜɚɟɦɨɣ ɜɨɞɨɣ ɜ

ɩɨɞɨɝɪɟɜɚɬɟɥɟ ɝɨɪɹɱɟɝɨ ɜɨɞɨ-

ɫɧɚɛɠɟɧɢɹ ɦɢɧɢɦɚɥɶɧɚɹ ɬɟɦɩɟ-

ɪɚɬɭɪɚ ɜɨɞɵ ɜ ɩɨɞɚɸɳɟɦ ɬɪɭɛɨ-

ɩɪɨɜɨɞɟ ɬɟɩɥɨɜɨɣ ɫɟɬɢ ɩɪɢ ɨɬ-

ɤɪɵɬɨɣ ɢ ɩɪɢ ɡɚɤɪɵɬɨɣ ɫɢɫɬɟɦɟ

ɬɟɩɥɨɫɧɚɛɠɟɧɢɹ ɩɪɢɧɢɦɚɟɬɫɹ

ɨɛɵɱɧɨ ɪɚɜɧɨɣ ɢɥɢ ɜɵɲɟ 65 °ɋ,

ɬ. ɟ.

ɨ1

ccc

= 65 °ɋ.

ɇɚ ɪɢɫ. 4.2 ɩɪɢɜɟɞɟɧɵ ɝɪɚ-

ɮɢɤɢ ɬɟɦɩɟɪɚɬɭɪ ɢ ɪɚɫɯɨɞɨɜ ɫɟ-

ɬɟɜɨɣ ɜɨɞɵ ɩɪɢ ɤɨɦɛɢɧɢɪɨɜɚɧ-

ɧɨɦ ɪɟɝɭɥɢɪɨɜɚɧɢɢ ɨɬɨɩɢɬɟɥɶɧɨɣ

ɧɚɝɪɭɡɤɢ, ɬ. ɟ. ɩɪɢ ɩɪɢɦɟɧɟɧɢɢ

ɪɚɡɧɵɯ ɦɟɬɨɞɨɜ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɜ

ɪɚɡɥɢɱɧɵɯ ɞɢɚɩɚɡɨɧɚɯ ɧɚɪɭɠɧɵɯ

ɬɟɦɩɟɪɚɬɭɪ.

Ƚɪɚɮɢɤ ɬɟɦɩɟɪɚɬɭɪ ɜ ɩɨ-

ɞɚɸɳɟɦ ɬɪɭɛɨɩɪɨɜɨɞɟ ɬɟɩɥɨɜɨɣ

ɫɟɬɢ ɢɦɟɟɬ ɜɢɞ ɥɨɦɚɧɨɣ ɥɢɧɢɢ

(ɪɢɫ. 4.2, ɛ). ɉɪɢ ɧɚɪɭɠɧɵɯ ɬɟɦ-

ɩɟɪɚɬɭɪɚɯ

ɧ.ɢɧ

tt 

ɝɞɟ

ɧ.ɢ

–

ɧɚɪɭɠɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ, ɫɨɨɬɜɟɬ-

ɫɬɜɭɸɳɚɹ, ɢɡɥɨɦɭ ɬɟɦɩɟɪɚɬɭɪɧɨ-

ɝɨ ɝɪɚɮɢɤɚ, ɝɪɚɮɢɤ ɬɟɦɩɟɪɚɬɭɪ

Ɋɢɫ. 4.2. Ƚɪɚɮɢɤɢ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ

(ɚ), ɬɟɦɩɟɪɚɬɭɪ (ɛ) ɢ ɪɚɫɯɨɞɨɜ ɫɟɬɟɜɨɣ

ɜɨɞɵ (ɜ) ɩɪɢ ɤɨɦɛɢɧɢɪɨɜɚɧɧɨɦ ɪɟɝɭ-

ɥɢɪɨɜɚɧɢɢ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ

1– ɤɨɥɢɱɟɫɬɜɟɧɧɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ; 2 –

ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɦɟɫɬɧɵɦɢ ɩɪɨɩɭɫɤɚɦɢ