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101325 ɉɚ, ɢɧɨɝɞɚ ɢɫɩɨɥɶɡɭɟɬɫɹ ɟɞɢɧɢɰɚ ɛɚɪ (1ɛɚɪ = 10

ɉɚ). Ɋɚɡɥɢɱɚɸɬ

ɞɚɜɥɟɧɢɟ ɚɛɫɨɥɸɬɧɨɟ (ɢɧɨɝɞɚ ɭɩɨɬɪɟɛɥɹɸɬ ɬɟɪɦɢɧ «ɩɨɥɧɨɟ») ɢ ɢɡɛɵ-

ɬɨɱɧɨɟ. Ⱥɛɫɨɥɸɬɧɵɦ ɧɚɡɵɜɚɟɬɫɹ ɞɚɜɥɟɧɢɟ, ɨɩɪɟɞɟɥɺɧɧɨɟ ɫ ɭɱɟɬɨɦ ɚɬ-

ɦɨɫɮɟɪɧɨɝɨ ɞɚɜɥɟɧɢɹ. ɂɡɛɵɬɨɱɧɨɟ ɞɚɜɥɟɧɢɟ ɷɬɨ ɞɚɜɥɟɧɢɟ ɫɜɟɪɯ ɚɬɦɨ-

ɫɮɟɪɧɨɝɨ, ɨɩɪɟɞɟɥɟɧɧɨɟ ɛɟɡ ɭɱɟɬɚ ɚɬɦɨɫɮɟɪɧɨɝɨ

ɚɛɫ ɚɬɦ ɢɡɛ

ɢɡɛ ɚɛɫ ɚɬɦ

;

P ɊɊ

ɊɊɊ



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ɉɨɜɟɪɯɧɨɫɬɢ ɪɚɜɧɨɝɨ ɞɚɜɥɟɧɢɹ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɫɟɦɟɣɫɬɜɨ ɝɨ-

ɪɢɡɨɧɬɚɥɶɧɵɯ ɩɥɨɫɤɨɫɬɟɣ, ɜɨ ɜɫɟɯ ɬɨɱɤɚɯ ɤɨɬɨɪɵɯ ɞɚɜɥɟɧɢɟ ɨɞɢɧɚɤɨɜɨ.

ɋɜɨɛɨɞɧɚɹ ɩɨɜɟɪɯɧɨɫɬɶ ɠɢɞɤɨɫɬɢ ɞɥɹ ɨɝɪɚɧɢɱɟɧɧɨɝɨ ɨɛɴɟɦɚ, ɬ. ɟ. ɩɨ-

ɜɟɪɯɧɨɫɬɶ ɧɚ ɝɪɚɧɢɰɟ ɠɢɞɤɨɣ ɢ ɝɚɡɨɨɛɪɚɡɧɨɣ ɫɪɟɞ, ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ –

ɨɞɧɚ ɢɡ ɩɥɨɫɤɨɫɬɟɣ ɪɚɜɧɨɝɨ ɞɚɜɥɟɧɢɹ, ɧɚ ɤɨɬɨɪɭɸ ɩɪɢɥɨɠɟɧɨ ɩɨɫɬɨɹɧ-

ɧɨɟ ɞɚɜɥɟɧɢɟ, ɪɚɜɧɨɟ ɚɬɦɨɫɮɟɪɧɨɦɭ.

1.5.1. ɉɬɨɩɝɨɩɠ ɮɫɛɝɨɠɨɣɠ ɞɣɟɫɩɬɭɛɭɣɥɣ

Ƚɢɞɪɨɫɬɚɬɢɱɟɫɤɨɟ ɞɚɜɥɟɧɢɟ ɜ ɥɸɛɨɣ ɬɨɱɤɟ ɠɢɞɤɨɫɬɢ ɪ ɫɤɥɚɞɵɜɚɟɬ-

ɫɹ ɢɡ ɞɚɜɥɟɧɢɹ ɧɚ ɟɟ ɫɜɨɛɨɞɧɭɸ ɩɨɜɟɪɯɧɨɫɬɶ ɪ

ɢ ɞɚɜɥɟɧɢɹ ɫɬɨɥɛɚ ɠɢɞ-

ɤɨɫɬɢ, ɜɵɫɨɬɚ ɤɨɬɨɪɨɝɨ ɪɚɜɧɚ ɪɚɫɫɬɨɹɧɢɸ h ɨɬ ɷɬɨɣ ɬɨɱɤɢ ɞɨ ɫɜɨɛɨɞɧɨɣ

ɩɨɜɟɪɯɧɨɫɬɢ:

pgh

 ,

ɝɞɟ ɪ – ɝɢɞɪɨɫɬɚɬɢɱɟɫɤɨɟ ɞɚɜɥɟɧɢɟ, ɉɚ; ɪ

– ɞɚɜɥɟɧɢɟ ɧɚ ɫɜɨɛɨɞɧɭɸ ɩɨ-

ɜɟɪɯɧɨɫɬɶ ɠɢɞɤɨɫɬɢ, ɉɚ; h – ɜɵɫɨɬɚ ɫɬɨɥɛɚ ɠɢɞɤɨɫɬɢ ɧɚɞ ɞɚɧɧɨɣ ɬɨɱ-

ɤɨɣ, ɦ.

ɉɨɫɥɟɞɧɟɟ ɜɵɪɚɠɟɧɢɟ ɧɚɡɵɜɚɟɬɫɹ ɨɫɧɨɜɧɵɦ ɭɪɚɜɧɟɧɢɟɦ ɝɢɞɪɨɫɬɚ-

ɬɢɤɢ. ɂɡ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ ɫɥɟɞɭɟɬ, ɱɬɨ ɜɧɟɲɧɟɟ ɞɚɜɥɟɧɢɟ ɪ

ɧɚ ɫɜɨɛɨɞɧɭɸ

ɩɨɜɟɪɯɧɨɫɬɶ ɠɢɞɤɨɫɬɢ ɩɟɪɟɞɚɸɬɫɹ ɜ ɥɸɛɭɸ ɬɨɱɤɭ ɠɢɞɤɨɫɬɢ ɪɚɜɧɨɦɟɪɧɨ

(ɡɚɤɨɧ ɉɚɫɤɚɥɹ) ɢ ɩɨɡɜɨɥɹɟɬ ɨɩɪɟɞɟɥɢɬɶ ɞɚɜɥɟɧɢɟ ɜ ɥɸɛɨɣ ɬɨɱɤɟ.

ɉɨɥɧɚɹ ɫɢɥɚ, ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɩɥɨɫɤɭɸ ɫɬɟɧɤɭ, ɪɚɜɧɚ ɩɪɨɢɡɜɟɞɟ-

ɧɢɸ ɜɟɥɢɱɢɧɵ ɫɦɨɱɟɧɧɨɣ ɩɥɨɳɚɞɢ ɫɬɟɧɤɢ F

ɫɦ

ɧɚ ɝɢɞɪɨɫɬɚɬɢɱɟɫɤɨɟ ɞɚɜ-

ɥɟɧɢɟ ɜ ɟɟ ɰɟɧɬɪɟ ɬɹɠɟɫɬɢ:

0 ɫɦ

()



ȼ ɨɬɤɪɵɬɨɦ ɫɨɫɭɞɟ ɩɪɢ ɪ

= 0 ɩɨɥɧɚɹ ɫɢɥɚ ɞɚɜɥɟɧɢɹ

ɰ.ɬ. ɫɦ

ɝɞɟ h

ɰ.ɬ.

– ɝɥɭɛɢɧɚ ɩɨɝɪɭɠɟɧɢɹ ɰɟɧɬɪɚ ɬɹɠɟɫɬɢ ɩɥɨɳɚɞɢ, ɦ.

Ɍɨɱɤɚ ɩɪɢɥɨɠɟɧɢɹ ɫɢɥɵ Ɋ ɧɚɡɵɜɚɟɬɫɹ ɰɟɧɬɪɨɦ ɞɚɜɥɟɧɢɹ. ɐɟɧɬɪ

ɞɚɜɥɟɧɢɹ ɨɛɵɱɧɨ ɥɟɠɢɬ ɧɢɠɟ ɰɟɧɬɪɚ ɬɹɠɟɫɬɢ ɫɬɟɧɤɢ. Ⱦɥɹ ɩɪɹɦɨɭɝɨɥɶ-

ɧɨɣ ɫɬɟɧɤɢ, ɧɚɩɪɢɦɟɪ, ɰɟɧɬɪ ɬɹɠɟɫɬɢ ɧɚɯɨɞɢɬɫɹ ɧɚ ɪɚɫɫɬɨɹɧɢɢ ɩɨɥɨɜɢ-

ɧɵ ɜɵɫɨɬɵ ɨɬ ɨɫɧɨɜɚɧɢɹ, ɚ ɰɟɧɬɪ ɞɚɜɥɟɧɢɹ – ɧɚ ɪɚɫɫɬɨɹɧɢɢ ɨɞɧɨɣ ɬɪɟɬɢ

ɜɵɫɨɬɵ.

1.5.2. Ɍɣɦɛ ɟɛɝɦɠɨɣɺ ɡɣɟɥɩɬɭɣ ɨɛ ɥɫɣɝɩɦɣɨɠɤɨɮɹ ɪɩɝɠɫɰɨɩɬɭɷ

ɇɚ ɪɢɫ. 1.5.2.1 ɩɪɟɞɫɬɚɜɥɟɧɚ ɤɪɢɜɨɥɢɧɟɣɧɚɹ ɩɨɜɟɪɯɧɨɫɬɶ ɜ ɜɢɞɟ ɨɞ-

ɧɨɣ ɱɟɬɜɟɪɬɨɣ ɱɚɫɬɢ ɩɨɜɟɪɯɧɨɫɬɢ ɰɢɥɢɧɞɪɚ, ɨɤɪɭɠɟɧɧɨɣ ɠɢɞɤɨɫɬɶɸ

ɬɨɥɶɤɨ ɫ ɨɞɧɨɣ ɫɬɨɪɨɧɵ. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɪɟɡɭɥɶɬɢɪɭɸɳɟɣ ɫɢɥɵ ɞɚɜɥɟ-

ɧɢɹ ɧɚ ɷɬɭ ɩɨɜɟɪɯɧɨɫɬɶ. ɧɚɱɚɥɟ ɪɚɫɫɱɢɬɵɜɚɸɬ ɝɨɪɢɡɨɧɬɚɥɶɧɭɸ ɫɨɫɬɚɜ-

ɥɹɸɳɭɸ Ɋ

, ɡɚɬɟɦ ɜɟɪɬɢɤɚɥɶɧɭɸ ɫɨɫɬɚɜɥɹɸɳɭɸ Ɋ

ɢ ɜɵɱɢɫɥɹɸɬ ɢɯ ɝɟɨ-

ɦɟɬɪɢɱɟɫɤɭɸ ɫɭɦɦɭ Ɋ:

PPP 

Ɋɢɫ. 1.5.2.1

Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɨɩɪɟɞɟɥɢɬɶ ɝɨɪɢɡɨɧɬɚɥɶɧɭɸ ɫɨɫɬɚɜɥɹɸɳɭɸ ɫɢɥɵ

ɞɚɜɥɟɧɢɹ, ɧɟɨɛɯɨɞɢɦɨ ɫɩɪɨɟɰɢɪɨɜɚɬɶ ɤɪɢɜɨɥɢɧɟɣɧɭɸ ɩɨɜɟɪɯɧɨɫɬɶ ɧɚ

ɜɟɪɬɢɤɚɥɶɧɭɸ ɩɥɨɫɤɨɫɬɶ ɢ ɨɩɪɟɞɟɥɢɬɶ ɟɟ ɤɚɤ ɫɢɥɭ, ɞɟɣɫɬɜɭɸɳɭɸ ɧɚ

ɩɥɨɫɤɭɸ ɫɬɟɧɤɭ:

0 ɰɩɪ

()

Pp ghF

 ,

ɝɞɟ ɪ

– ɞɚɜɥɟɧɢɟ ɜɨɡɞɭɯɚ ɧɚ ɫɜɨɛɨɞɧɭɸ ɩɨɜɟɪɯɧɨɫɬɶ ɠɢɞɤɨɫɬɢ, h

– ɪɚɫ-

ɫɬɨɹɧɢɟ ɨɬ ɫɜɨɛɨɞɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɞɨ ɰɟɧɬɪɚ ɬɹɠɟɫɬɢ ɜɟɪɬɢɤɚɥɶɧɨɣ

ɩɥɨɫɤɨɫɬɢ, F

ɩɪ

– ɩɥɨɳɚɞɶ ɩɪɨɟɤɰɢɢ ɤɪɢɜɨɥɢɧɟɣɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɧɚ ɜɟɪ-

ɬɢɤɚɥɶɧɭɸ ɩɥɨɫɤɨɫɬɶ. ȼɟɪɬɢɤɚɥɶɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ

ɮɨɪɦɭɥɟ:

ɬ.ɞ.z

PgW

ɝɞɟ W

ɬ.ɞ.

– ɨɛɴɟɦ ɬɟɥɚ ɞɚɜɥɟɧɢɹ (ɧɚ ɪɢɫ. 1.5.2.1 ɬɟɥɨ ɞɚɜɥɟɧɢɹ ɜɵɞɟɥɟɧɨ

ɛɨɥɟɟ ɬɟɦɧɵɦ ɰɜɟɬɨɦ). Ɍɟɥɨ ɞɚɜɥɟɧɢɹ ɫɬɪɨɢɬɫɹ ɩɪɨɟɰɢɪɨɜɚɧɢɟɦ ɤɪɢɜɨ-

ɥɢɧɟɣɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɧɚ ɫɜɨɛɨɞɧɭɸ ɩɨɜɟɪɯɧɨɫɬɶ ɢɥɢ ɟɟ ɩɪɨɞɨɥɠɟɧɢɟ,

ɚ ɡɚɬɟɦ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɟɝɨ ɨɛɴɟɦ.

ɉɪɢ ɪɟɲɟɧɢɢ ɡɚɞɚɱ ɜ ɝɢɞɪɚɜɥɢɤɟ ɩɪɢɦɟɧɹɸɬ ɨɫɧɨɜɧɵɟ ɡɚɤɨɧɵ ɢ

ɦɟɬɨɞɵ ɦɟɯɚɧɢɤɢ ɢ, ɭɱɢɬɵɜɚɹ ɨɛɳɢɟ ɫɜɨɣɫɬɜɚ ɠɢɞɤɨɫɬɟɣ, ɩɨɥɭɱɚɸɬ

ɪɟɲɟɧɢɟ, ɩɨɡɜɨɥɹɸɳɟɟ ɨɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ ɢ ɞɚɜɥɟɧɢɟ ɜ ɥɸɛɨɣ ɬɨɱɤɟ

ɡɚɧɹɬɨɝɨ ɠɢɞɤɨɫɬɶɸ ɩɪɨɫɬɪɚɧɫɬɜɚ. ɗɬɨ ɞɚɺɬ ɜɨɡɦɨɠɧɨɫɬɶ ɪɚɫɫɱɢɬɚɬɶ, ɜ

ɱɚɫɬɧɨɫɬɢ, ɢ ɫɢɥɵ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ

ɦɟɠɞɭ ɠɢɞɤɨɫɬɶɸ ɢ ɬɜɺɪɞɵɦ ɬɟɥɨɦ.

Ɉɫɧɨɜɧɵɦ ɨɛɴɟɤɬɨɦ ɝɢɞɪɚɜɥɢɤɢ ɹɜɥɹɟɬɫɹ ɩɨɬɨɤ ɠɢɞɤɨɫɬɢ, ɬ. ɟ. ɞɜɢɠɟ-

ɧɢɟ ɦɚɫɫɵ ɠɢɞɤɨɫɬɢ ɦɟɠɞɭ ɨɝɪɚɧɢɱɢɜɚɸɳɢɦɢ ɩɨɜɟɪɯɧɨɫɬɹɦɢ (ɫɬɟɧɤɢ

ɬɪɭɛ, ɤɚɧɚɥɨɜ).

ɉɨɬɨɤ ɠɢɞɤɨɫɬɢ ɢɦɟɟɬ ɫɥɟɞɭɸɳɢɟ ɨɫɧɨɜɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ:

ɠ.ɫ.

– ɩɥɨɳɚɞɶ ɠɢɜɨɝɨ ɫɟɱɟɧɢɹ, ɦ

;

– ɫɦɨɱɟɧɧɵɣ ɩɟɪɢɦɟɬɪ ɢɥɢ ɩɟɪɢɦɟɬɪ ɠɢɜɨɝɨ ɫɟɱɟɧɢɹ, ɫɨɩɪɢɤɚ-

ɫɚɸɳɢɣɫɹ ɫɨ ɫɬɟɧɤɚɦɢ, ɨɝɪɚɧɢɱɢɜɚɸɳɢɦɢ ɩɨɬɨɤ, ɦ;

– ɝɢɞɪɚɜɥɢɱɟɫɤɢɣ ɪɚɞɢɭɫ, ɦ, ɨɩɪɟɞɟɥɹɟɦɵɣ ɜ ɜɢɞɟ

ɠ.ɫ.

, ɜɯɨɞɹɳɢɟ ɜ ɪɚɫɱɺɬɧɵɟ ɡɚɜɢɫɢɦɨɫɬɢ, ɤɨɬɨɪɵɟ ɩɪɢɦɟɧɹɸɬɫɹ ɜ ɩɪɚɤ-

ɬɢɤɟ ɝɢɞɪɚɜɥɢɱɟɫɤɢɯ ɪɚɫɱɺɬɨɜ.

1.6. ɋɛɬɲɠɭ ɭɫɮɜɩɪɫɩɝɩɟɩɝ

ɍɪɚɜɧɟɧɢɟ Ȼɟɪɧɭɥɥɢ ɞɥɹ ɷɥɟɦɟɧɬɚɪɧɨɣ ɫɬɪɭɣɤɢ (ɪɢɫ. 1.6.1.) ɪɟɚɥɶ-

ɧɨɣ ɠɢɞɤɨɫɬɢ

11 2 2

Pu Pu

gz gz

  +A , Ⱦɠ/ɤɝ,

ɝɞɟ

+A – ɩɨɬɟɪɢ ɭɞɟɥɶɧɨɣ ɷɧɟɪɝɢɢ

11 22

Pu Pu

zz h

gg gg

 + , ɦ,

ɝɞɟ

– ɩɨɬɟɪɢ ɧɚɩɨɪɚ.

ɍɪɚɜɧɟɧɢɟ Ȼɟɪɧɭɥɥɢ ɞɥɹ ɩɨɬɨɤɚ:

11 2 2

PV PV

gz gz

  A , Ⱦɠ/ɤɝ

11 22

PV PV

zzh

gg gg

  , ɦ

ɝɞɟ

– ɩɨɩɪɚɜɨɱɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ, ɤɨɬɨɪɵɣ ɦɟɧɹɟɬɫɹ ɨɬ 1,03 ɞɨ 2. Ⱦɥɹ

ɪɚɡɜɢɬɨɝɨ ɬɭɪɛɭɥɟɧɬɧɨɝɨ ɬɟɱɟɧɢɹ 1

, ɞɥɹ ɥɚɦɢɧɚɪɧɨɝɨ ɬɟɱɟɧɢɹ 2

Ɋɢɫ. 1.6.1

ȼ ɭɪɚɜɧɟɧɢɢ Ȼɟɪɧɭɥɥɢ ɩɨɫɥɟɞɧɟɟ ɫɥɚɝɚɟɦɨɟ ɜ ɩɪɚɜɨɣ ɱɚɫɬɢ ɩɪɟɞ-

ɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ:

A – ɩɨɬɟɪɢ ɭɞɟɥɶɧɨɣ ɷɧɟɪɝɢɢ;

h – ɩɨ-

ɬɟɪɢ ɧɚɩɨɪɚ.

ɉɨɬɟɪɢ ɧɚɩɨɪɚ ɜ ɬɪɭɛɨɩɪɨɜɨɞɚɯ ɪɚɡɞɟɥɹɸɬ ɧɚ ɞɜɚ ɜɢɞɚ: ɩɨɬɟɪɢ ɧɚ

ɬɪɟɧɢɟ ɩɨ ɞɥɢɧɟ ɢ ɩɨɬɟɪɢ ɧɚ ɦɟɫɬɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ, ɤɨɬɨɪɵɟ ɜɨɡɧɢɤɚ-

ɸɬ ɧɚ ɧɟɛɨɥɶɲɨɦ ɩɨ ɩɪɨɬɹɠɟɧɧɨɫɬɢ ɭɱɚɫɬɤɟ ɜ ɪɟɡɭɥɶɬɚɬɟ ɢɡɦɟɧɟɧɢɹ ɧɚ-

ɩɪɚɜɥɟɧɢɹ ɬɟɱɟɧɢɹ ɢɥɢ ɜ ɪɟɡɭɥɶɬɚɬɟ ɢɡɦɟɧɟɧɢɹ ɩɥɨɳɚɞɢ ɩɨɩɟɪɟɱɧɨɝɨ

ɫɟɱɟɧɢɹ, ɬ. ɟ. ɫɭɦɦɚɪɧɵɟ ɩɨɬɟɪɢ

h ɩɪɟɞɫɬɚɜɥɹɸɬ ɤɚɤ

w ɬɪ ɦ

hh h 

¦¦

Ʉɚɤ ɛɵɥɨ ɨɬɦɟɱɟɧɨ ɪɚɧɟɟ, ɩɨɬɟɪɢ ɧɚ ɬɪɟɧɢɟ, ɧɟɡɚɜɢɫɢɦɨ ɨɬ ɪɟɠɢɦɚ

ɬɟɱɟɧɢɹ, ɦɨɝɭɬ ɛɵɬɶ ɪɚɫɫɱɢɬɚɧɵ ɩɨ ɮɨɪɦɭɥɟ Ⱦɚɪɫɢ

ɬɪ





Ɉɞɧɚɤɨ ɤɨɷɮɮɢɰɢɟɧɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɧɚ ɬɪɟɧɢɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ-

ɪɚɡɧɨɦɭ. Ⱦɥɹ ɥɚɦɢɧɚɪɧɨɝɨ ɬɟɱɟɧɢɹ ɜ ɤɪɭɝɥɵɯ ɬɪɭɛɚɯ ɨɧ ɪɚɜɟɧ

ȿɫɥɢ ɠɟ ɪɟɠɢɦ ɬɟɱɟɧɢɹ ɬɭɪɛɭɥɟɧɬɧɵɣ, ɬɨ

, ɤɪɨɦɟ ɱɢɫɥɚ Ɋɟɣɧɨɥɶɞɫɚ,

ɡɚɜɢɫɢɬ ɨɬ ɬɚɤ ɧɚɡɵɜɚɟɦɨɣ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɲɟɪɨɯɨɜɚɬɨɫɬɢ

' , ɝɞɟ ' –

ɫɪɟɞɧɹɹ ɜɵɫɨɬɚ ɜɵɫɬɭɩɨɜ ɲɟɪɨɯɨɜɚɬɨɫɬɢ ɜɧɭɬɪɟɧɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɬɪɭɛ,

ɨɩɪɟɞɟɥɹɟɦɚɹ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɦɚɬɟɪɢɚɥɚ ɬɪɭɛ ɩɨ ɫɩɪɚɜɨɱɧɢɤɚɦ.

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɞɥɹ ɧɚɯɨɠɞɟɧɢɹ

ɜ ɫɥɭɱɚɟ ɬɭɪɛɭɥɟɧɬɧɨɝɨ ɬɟɱɟɧɢɹ

ɧɟɨɛɯɨɞɢɦɨ ɜɵɱɢɫɥɢɬɶ ɱɢɫɥɨ Ɋɟɣɧɨɥɶɞɫɚ ɢ ɨɬɧɨɫɢɬɟɥɶɧɭɸ ɲɟɪɨɯɨɜɚ-

ɬɨɫɬɶ, ɚ ɡɚɬɟɦ, ɩɨɥɶɡɭɹɫɶ ɫɩɪɚɜɨɱɧɢɤɨɦ, ɧɚɣɬɢ ɡɧɚɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ

ɧɚ ɬɪɟɧɢɟ (ɪɢɫ. 1.6.2).

Ɋɢɫ. 1.6.2

Ⱦɥɹ ɪɚɫɱɟɬɚ ɩɨɬɟɪɶ ɧɚ ɦɟɫɬɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜɫɟɯ ɪɚɡɧɨɜɢɞɧɨɫɬɟɣ

ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɮɨɪɦɭɥɭ ȼɟɣɫɛɚɯɚ

w ɦ

[

ɝɞɟ

[

– ɤɨɷɮɮɢɰɢɟɧɬ ɦɟɫɬɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ, ɨɩɪɟɞɟɥɹɟɦɵɣ ɩɨ ɫɩɪɚ-

ɜɨɱɧɢɤɚɦ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɜɢɞɚ ɦɟɫɬɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ.

1.6.1. Ʌɦɛɬɬɣɯɣɥɛɱɣɺ ɭɫɮɜɩɪɫɩɝɩɟɩɝ

ɋ ɝɢɞɪɚɜɥɢɱɟɫɤɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ ɜɟɫ ɬɪɭɛɨɩɪɨɜɨɞɚ ɩɪɢɧɹɬɨ ɞɟɥɢɬɶ

ɧɚ ɤɨɪɨɬɤɢɟ ɢ ɞɥɢɧɧɵɟ, ɩɪɨɫɬɵɟ ɢ ɫɥɨɠɧɵɟ. Ʉ ɤɨɪɨɬɤɢɦ ɨɬɧɨɫɹɬ ɬɪɭɛɨ-

ɩɪɨɜɨɞɵ, ɞɥɹ ɤɨɬɨɪɵɯ ɩɨɬɟɪɢ ɩɨ ɞɥɢɧɟ ɧɚ ɬɪɟɧɢɟ ɨɞɧɨɝɨ ɩɨɪɹɞɤɚ ɫ ɩɨ-

ɬɟɪɹɦɢ ɧɚ ɦɟɫɬɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ, ɬ. ɟ.

ɬɪ ɦ

hh|

. ɋ ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ

ɞɥɢɧɧɵɦɢ ɧɚɡɵɜɚɸɬ ɬɪɭɛɨɩɪɨɜɨɞɵ, ɞɥɹ ɤɨɬɨɪɵɯ

ɬɪ ɦ

hh!!

. ɉɪɨɫɬɵɦɢ

ɹɜɥɹɸɬɫɹ ɬɪɭɛɨɩɪɨɜɨɞɵ ɛɟɡ ɤɚɤɢɯ-ɥɢɛɨ ɨɬɜɟɬɜɥɟɧɧɵɣ, ɫɨɫɬɚɜɥɟɧɧɵɟ ɢɡ

ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɫɨɟɞɢɧɟɧɧɵɯ ɬɪɭɛ. ɉɪɢ ɪɚɫɱɟɬɟ ɥɸɛɵɯ ɬɪɭɛɨɩɪɨɜɨɞɨɜ

ɢɫɩɨɥɶɡɭɸɬɫɹ ɫɥɟɞɭɸɳɢɟ ɭɪɚɜɧɟɧɢɹ:

ɭɪɚɜɧɟɧɢɟ Ȼɟɪɧɭɥɥɢ;

ɭɪɚɜɧɟɧɢɟ ɩɨɫɬɨɹɧɧɨɝɨ ɪɚɫɯɨɞɚ (ɭɪɚɜɧɟɧɢɟ ɧɟɪɚɡɪɵɜɧɨɫɬɢ).

1.6.2. ɋɛɬɲɠɭ ɪɫɩɬɭɩɞɩ ɥɩɫɩɭɥɩɞɩ ɭɫɮɜɩɪɫɩɝɩɟɛ

Ɋɚɫɱɟɬ ɤɨɪɨɬɤɨɝɨ ɬɪɭɛɨɩɪɨɜɨɞɚ (ɪɢɫ. 1.6.2.1) ɫ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɦ

ɫɨɟɞɢɧɟɧɢɟɦ ɬɪɭɛ ɪɚɫɫɦɨɬɪɢɦ ɧɚ ɩɪɢɦɟɪɟ ɫɥɟɞɭɸɳɟɣ ɡɚɞɚɱɢ.

Ɋɢɫ. 1.6.2.1

ɉɪɢ ɪɚɫɱɟɬɚɯ ɬɪɭɛɨɩɪɨɜɨɞɨɜ ɫɬɚɜɹɬɫɹ, ɤɚɤ ɩɪɚɜɢɥɨ, ɫɥɟɞɭɸɳɢɟ ɡɚ-

ɞɚɱɢ:

ɨɩɪɟɞɟɥɢɬɶ ɧɚɩɨɪ

, ɟɫɥɢ ɢɡɜɟɫɬɟɧ ɪɚɫɯɨɞ Q ;

ɨɩɪɟɞɟɥɢɬɶ ɪɚɫɯɨɞ

Q ɩɪɢ ɢɡɜɟɫɬɧɨɦ ɧɚɩɨɪɟ, ɩɪɢ ɷɬɨɦ ɞɨɥɠɧɵ

ɛɵɬɶ ɢɡɜɟɫɬɧɵ ɪɚɡɦɟɪɵ ɬɪɭɛɨɩɪɨɜɨɞɚ ɢ ɤɨɷɮɮɢɰɢɟɧɬɵ ɫɨɩɪɨɬɢɜɥɟɧɢɹ.

ȼ ɧɚɲɟɦ ɫɥɭɱɚɟ ɷɬɨ:

,, , ,,

ɜɯ ɡɚɞ ɜɪ ɜɵɯ

[

O[ [ O[

Ɂɚɩɢɲɟɦ ɭɪɚɜɧɟɧɢɟ Ȼɟɪɧɭɥɥɢ ɞɥɹ ɫɟɱɟɧɢɣ aa ɢ ɛɛ ɨɬɧɨɫɢ-

ɬɟɥɶɧɨ ɩɥɨɫɤɨɫɬɢ ɫɪɚɜɧɟɧɢɹ, ɩɪɨɜɟɞɟɧɧɨɣ ɩɨ ɨɫɢ ɬɪɭɛɵ.

a ɛ

aa ɛɛ

a ɛ w

PV PV

zzh

gg gg



   .

Ɉɩɪɟɞɟɥɢɦ ɡɧɚɱɟɧɢɟ ɫɥɚɝɚɟɦɵɯ ɭɪɚɜɧɟɧɢɹ ɢɡ ɭɫɥɨɜɢɣ ɡɚɞɚɱɢ.

12 12

,, , 0

a ɛ a ɛɚɬ

ZHZHPPPVV

Ɉɬɫɸɞɚ ɭɪɚɜɧɟɧɢɟ Ȼɟɪɧɭɥɥɢ ɩɪɢɦɟɬ ɜɢɞ:

a ɛ w

a ɛ





ɢɥɢ

a ɛ



2222 22

111 1 1 22 2

2222 22

a ɛ

ɜɯ ɬɪ ɡɚɞ ɜɪ ɬɪ ɜɵɯ

ɜɯ ɡɚɞ ɜɪ ɜɵɯ

hhhhhhh

VVVV VV

gdg g gdg g

[O [ [O [



   

Ⱦɚɥɟɟ, ɪɚɫɱɟɬ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɫɜɨɞɢɦ ɤ ɨɞɧɨɣ ɫɤɨɪɨɫɬɢ. Ⱦɥɹ ɷɬɨɝɨ

ɢɡ ɭɪɚɜɧɟɧɢɹ ɪɚɫɯɨɞɚ ɜɵɪɚɠɚɟɦ

11 2 2 1 2

VF VF V V

ɉɨɫɥɟ ɩɨɞɫɬɚɧɨɜɤɢ ɜ ɩɪɟɞɵɞɭɳɟɟ ɪɚɜɟɧɫɬɜɨ ɜɦɟɫɬɨ

V ɡɧɚɱɟɧɢɟ

ɫɤɨɪɨɫɬɢ

V , ɩɨɥɭɱɢɦ

ɫɭɦ

[

ɝɞɟ

244

212 2 2

444

111 1 2

ɫɭɦ ɜɯ ɡɚɞ ɜɪ ɜɵɯ

ddd

ddd d d

[[ O [ [O[

§·

 

¨¸

©¹

ɉɨɫɥɟɞɧɢɣ ɜɢɞ ɭɪɚɜɧɟɧɢɹ Ȼɟɪɧɭɥɥɢ ɢ ɹɜɥɹɟɬɫɹ ɪɚɫɱɟɬɧɨɣ ɡɚɜɢɫɢ-

ɦɨɫɬɶɸ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɧɟɢɡɜɟɫɬɧɵɯ ɜ ɩɪɢɜɟɞɟɧɧɵɯ ɡɚɞɚɱɚɯ.

1.6.3. ɋɛɬɲɠɭ ɟɦɣɨɨɶɰ ɭɫɮɜɩɪɫɩɝɩɟɩɝ

Ɇɟɬɨɞɢɤɚ ɪɚɫɱɟɬɚ ɞɥɢɧɧɵɯ ɬɪɭɛ (ɪɢɫ. 1.6.3.1.) ɧɢ ɱɟɦ ɧɟ ɨɬɥɢɱɚɟɬ-

ɫɹ ɨɬ ɦɟɬɨɞɢɤɢ ɪɚɫɱɟɬɚ ɤɨɪɨɬɤɢɯ ɬɪɭɛɨɩɪɨɜɨɞɨɜ ɡɚ ɢɫɤɥɸɱɟɧɢɟ ɬɨɝɨ,

ɱɬɨ ɩɨɬɟɪɹɦɢ ɧɚ ɦɟɫɬɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ, ɚ ɩɨɬɟɪɢ ɧɚ

ɬɪɟɧɢɟ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨ ɜɢɞɨɢɡɦɟɧɟɧɧɨɣ ɮɨɪɦɭɥɟ Ⱦɚɪɫɢ, ɤɨɬɨɪɚɹ ɧɚ-

ɡɵɜɚɟɬɫɹ ɜɨɞɨɩɪɨɜɨɞɧɨɣ:

ɬɪ

Ɋɢɫ. 1.6.3.1

ɂɡ ɭɪɚɜɧɟɧɢɹ Ȼɟɪɧɭɥɥɢ, ɡɚɩɢɫɚɧɧɨɝɨ ɞɥɹ ɫɟɱɟɧɢɣ aa ɢ ɛɛ ,

ɫɥɟɞɭɟɬ

ɬɪ

ɢɥɢ

222

123

222

123

QQQ



AA A

123

QQ Q Q .

ɉɚɪɚɦɟɬɪ

ɜ ɜɨɞɨɩɪɨɜɨɞɧɨɣ ɮɨɪɦɭɥɟ ɧɚɡɵɜɚɟɬɫɹ ɦɨɞɭɥɶ ɪɚɫ-

ɯɨɞɚ, ɤɨɬɨɪɵɣ ɨɩɪɟɞɟɥɹɟɬ ɩɪɨɩɭɫɤɧɭɸ ɫɩɨɫɨɛɧɨɫɬɶ ɬɪɭɛɨɩɪɨɜɨɞɚ ɢ ɨɩ-

ɪɟɞɟɥɹɟɬɫɹ ɩɨ ɫɩɪɚɜɨɱɧɢɤɚɦ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɞɢɚɦɟɬɪɚ ɬɪɭɛ.

1.7. Ⱦɣɟɫɛɝɦɣɲɠɬɥɣɤ ɫɛɬɲɠɭ ɣɬɭɠɲɠɨɣɺ ɡɣɟɥɩɬɭɠɤ

ɂɫɬɟɱɟɧɢɟ ɠɢɞɤɨɫɬɟɣ ɢɡ ɨɬɜɟɪɫɬɢɣ ɢ ɧɚɫɚɞɤɨɜ ɢɦɟɟɬ ɛɨɥɶɲɨɟ

ɩɪɚɤɬɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ, ɩɨɫɤɨɥɶɤɭ ɨɧɢ ɩɪɢɦɟɧɹɸɬɫɹ ɩɪɢ ɪɟɲɟɧɢɢ ɦɧɨ-

ɝɢɯ ɬɟɯɧɢɱɟɫɤɢɯ ɡɚɞɚɱ. ɇɚɩɪɢɦɟɪ, ɜ ɪɚɡɥɢɱɧɵɯ ɞɜɢɝɚɬɟɥɹɯ ɜɧɭɬɪɟɧɧɟɝɨ

ɫɝɨɪɚɧɢɹ ɩɪɢ ɩɨɞɚɱɟ ɬɨɩɥɢɜɚ, ɩɪɢ ɤɨɧɫɬɪɭɢɪɨɜɚɧɢɢ ɫɨɩɟɥ ɢ ɮɨɪɫɭɧɨɤ,

ɝɞɟ ɧɟɨɛɯɨɞɢɦɚ ɫɬɪɨɝɚɹ ɞɨɡɢɪɨɜɤɚ ɢ ɪɚɫɯɨɞ ɠɢɞɤɨɫɬɢ, ɚ ɬɚɤɠɟ ɜ ɝɢɞɪɨ-

ɦɨɧɢɬɨɪɧɵɯ ɢ ɜ ɷɠɟɤɬɨɪɧɵɯ ɭɫɬɚɧɨɜɤɚɯ, ɪɚɡɪɚɛɚɬɵɜɚɸɳɢɯ ɝɪɭɧɬɵ

ɝɢɞɪɨɬɟɯɧɢɱɟɫɤɢɯ ɫɨɨɪɭɠɟɧɢɹɯ, ɫɨɞɟɪɠɚɳɢɯ ɡɚɬɜɨɪɵ ɢɥɢ ɨɬɜɟɪɫɬɢɹ

ɞɥɹ ɫɛɪɨɫɚ ɜɨɞɵ.

ɂɫɬɟɱɟɧɢɟ ɠɢɞɤɨɫɬɢ ɦɨɠɟɬ ɩɪɨɢɫɯɨɞɢɬɶ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɢ ɩɟɪɟ-

ɦɟɧɧɨɦ ɧɚɩɨɪɚɯ, ɱɟɪɟɡ ɦɚɥɨɟ ɢɥɢ ɛɨɥɶɲɨɟ ɨɬɜɟɪɫɬɢɟ, ɱɟɪɟɡ ɧɚɫɚɞɤɢ

ɪɚɡɥɢɱɧɨɣ ɤɨɧɫɬɪɭɤɰɢɢ. Ʉɪɨɦɟ ɬɨɝɨ, ɢɫɬɟɱɟɧɢɟ ɦɨɠɟɬ ɛɵɬɶ ɫɜɨɛɨɞɧɵɦ

ɜ ɚɬɦɨɫɮɟɪɭ ɢɥɢ ɜɚɤɭɭɦ ɢ ɩɨɞ ɭɪɨɜɟɧɶ (ɡɚɬɨɩɥɟɧɧɨɟ ɢɫɬɟɱɟɧɢɟ).

ɉɪɢ ɜɵɯɨɞɟ ɫɬɪɭɢ ɢɡ ɨɬɜɟɪɫɬɢɹ ɫɬɪɭɹ ɩɪɟɬɟɪɩɟɜɚɟɬ

ɫɠɚɬɢɟ. ɋɠɚɬɨɟ

ɫɟɱɟɧɢɟ ɫɬɪɭɢ ɧɚɯɨɞɢɬɫɹ ɩɪɢɦɟɪɧɨ ɧɚ ɪɚɫɫɬɨɹɧɢɢ 0,5

d ɨɬ ɫɬɟɧɤɢ ɪɟɡɟɪ-

ɜɭɚɪɚ.

Ɉɬɧɨɲɟɧɢɟ ɩɥɨɳɚɞɢ ɫɬɪɭɢ ɜ ɫɠɚɬɨɦ ɫɟɱɟɧɢɢ ɤ ɩɥɨɳɚɞɢ ɜɫɟɝɨ ɨɬ-

ɜɟɪɫɬɢɹ ɧɚɡɵɜɚɟɬɫɹ

ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɫɠɚɬɢɹ ɫɬɪɭɢ:

Ɂɧɚɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ ɫɠɚɬɢɹ ɫɬɪɭɢ ɡɚɜɢɫɢɬ ɨɬ ɯɚɪɚɤɬɟɪɚ ɞɟɮɨɪ-

ɦɚɰɢɢ ɩɨɬɨɤɚ.

ɉɪɢɦɟɪ ɢɫɬɟɱɟɧɢɹ ɠɢɞɤɨɫɬɢ ɢɡ ɤɪɭɝɥɨɝɨ ɨɬɜɟɪɫɬɢɹ ɞɢɚɦɟɬɪɨɦ

ɜɟɪɬɢɤɚɥɶɧɨɣ ɬɨɧɤɨɣ ɫɬɟɧɤɟ ɫɨɫɭɞɚ ɩɪɟɞɫɬɚɜɥɟɧ ɧɚ ɪɢɫ. 1.7.1.

ɋɬɟɧɤɚ ɫɱɢɬɚɟɬɫɹ ɬɨɧɤɨɣ, ɟɫɥɢ ɟɺ ɬɨɥɳɢɧɚ

< 0,2d

ɢ ɧɟ ɜɥɢɹɟɬ ɧɚ

ɭɫɥɨɜɢɹ ɢɫɬɟɱɟɧɢɹ. Ɉɫɧɨɜɧɨɣ ɡɚɞɚɱɟɣ ɪɚɫɱɟɬɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɢɫɬɟɱɟɧɢɹ

ɹɜɥɹɟɬɫɹ ɨɩɪɟɞɟɥɟɧɢɟ ɫɤɨɪɨɫɬɢ ɢɫɬɟɱɟɧɢɹ ɢ ɪɚɫɯɨɞɚ ɠɢɞɤɨɫɬɢ.

Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɫɤɨɪɨɫɬɢ ɢɫɬɟɱɟɧɢɹ ɢɫɩɨɥɶɡɭɟɬɫɹ ɭɪɚɜɧɟɧɢɟ Ȼɟɪ-

ɧɭɥɥɢ ɞɥɹ ɫɟɱɟɧɢɣ 1–1 ɢ 2–2, ɭɱɢɬɵɜɚɹ, ɱɬɨ ɩɥɨɫɤɨɫɬɶ ɫɪɚɜɧɟɧɢɹ ɩɪɨ-

ɯɨɞɢɬ ɱɟɪɟɡ ɰɟɧɬɪ ɬɹɠɟɫɬɢ ɨɬɜɟɪɫɬɢɹ, ɬ. ɟ.

1 =

2 =

11 0c

ɜɯ

pV pV

gggg

 '

Ɋɢɫ. 1.7.1.

ɉɨɬɟɪɢ ɧɚɩɨɪɚ ɦɟɠɞɭ ɫɟɱɟɧɢɹɦɢ 1–1 ɢ 2–2 ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨ ɮɨɪ-

ɦɭɥɟ ȼɟɣɫɛɚɯɚ:

ɜɯ ɜɯ

[

ɝɞɟ

ɜɯ

[

– ɤɨɷɮɮɢɰɢɟɧɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɨɬɜɟɪɫɬɢɹ.

ȼɜɟɞɺɦ ɨɛɨɡɧɚɱɟɧɢɟ ɞɥɹ ɤɨɷɮɮɢɰɢɟɧɬɚ ɫɤɨɪɨɫɬɢ ɢɫɬɟɱɟɧɢɹ, ɭɱɢ-

ɬɵɜɚɸɳɟɝɨ ɩɨɬɟɪɢ ɫɤɨɪɨɫɬɢ ɧɚ ɦɟɫɬɧɨɦ ɫɨɩɪɨɬɢɜɥɟɧɢɢ (ɧɚ ɨɫɬɪɨɣ

ɤɪɨɦɤɟ ɜɯɨɞɧɨɝɨ ɨɬɜɟɪɫɬɢɹ);

ɜɯ

1 İn

[



ɝɞɟ

– ɤɨɷɮɮɢɰɢɟɧɬ ɫɠɚɬɢɹ ɫɬɪɭɢ ɞɥɹ ɤɪɭɝɥɵɯ ɨɬɜɟɪɫɬɢɣ, ɪɚɜ-

ɧɵɣ 0,64;

/nFF

– ɤɨɷɮɮɢɰɢɟɧɬ, ɭɱɢɬɵɜɚɸɳɢɣ ɜɥɢɹɧɢɟ ɫɤɨɪɨɫɬɢ

ɩɨɬɨɤɚ ɩɟɪɟɞ ɜɯɨɞɧɵɦ ɨɬɜɟɪɫɬɢɟɦ ɧɚ ɤɨɷɮɮɢɰɢɟɧɬ ɫɤɨɪɨɫɬɢ (ɩɪɢ ɢɫɬɟ-

ɱɟɧɢɢ ɢɡ ɦɚɥɵɯ ɨɬɜɟɪɫɬɢɣ n o 0).

ɉɪɢ ɢɫɬɟɱɟɧɢɢ ɯɨɥɨɞɧɨɣ ɜɨɞɵ ɱɟɪɟɡ ɦɚɥɨɟ ɨɬɜɟɪɫɬɢɟ ɨɛɵɱɧɨ ɩɪɢ-

ɧɢɦɚɸɬ

| 0,97 – 0,98;

[

ɜɯ

| 0,06.

ɉɨ ɤɨɷɮɮɢɰɢɟɧɬɭ ɫɤɨɪɨɫɬɢ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɤɨɷɮɮɢɰɢɟɧɬ ɫɨɩɪɨ-

ɬɢɜɥɟɧɢɹ

[

ɜɯ

1/ 1

.

ɗɬɢ ɤɨɷɮɮɢɰɢɟɧɬɵ ɡɚɜɢɫɹɬ ɨɬ ɧɚɩɨɪɚ ɇ ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɨɬ ɫɤɨɪɨ-

ɫɬɢ ɢɫɬɟɱɟɧɢɹ, ɜɹɡɤɨɫɬɢ ɠɢɞɤɨɫɬɢ, ɮɨɪɦɵ ɢ ɪɚɡɦɟɪɨɜ ɨɬɜɟɪɫɬɢɹ, ɚ ɩɨ-

ɷɬɨɦɭ ɢ ɨɬ ɱɢɫɥɚ Ɋɟɣɧɨɥɶɞɫɚ. Ɉɛɵɱɧɨ ɩɪɢɧɢɦɚɸɬ

= f(Re).

Ʉɨɷɮɮɢɰɢɟɧɬ ɫɤɨɪɨɫɬɢ ɜɵɱɢɫɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ:

ȼɜɟɞɺɦ ɨɛɨɡɧɚɱɟɧɢɟ

ɜɯ

1-n



ɝɞɟ

ȝ – ɤɨɷɮɮɢɰɢɟɧɬ ɪɚɫɯɨɞɚ.

Ɍɚɤ ɤɚɤ ɞɥɹ ɦɚɥɵɯ ɨɬɜɟɪɫɬɢɣ ɤɨɷɮɮɢɰɢɟɧɬ ɫɠɚɬɢɹ

= 0,64, ɚ ɤɨɷɮ-

ɮɢɰɢɟɧɬ ɫɤɨɪɨɫɬɢ

= 0,97, ɬɨ,

= 0,640,97 = 0,62.

ɍɱɢɬɵɜɚɹ ɡɚɜɢɫɢɦɨɫɬɶ

ɨɬ

/nFF , ɦɨɠɧɨ ɧɚɣɬɢ ɬɚɤɠɟ ɡɚɜɢɫɢ-

ɦɨɫɬɶ

= f(n,

[

ɜɯ

ɉɪɢ ɢɫɬɟɱɟɧɢɢ ɢɡ ɦɚɥɵɯ ɨɬɜɟɪɫɬɢɣ

n o 0

ɜɯ

[



ȼ ɫɥɭɱɚɟ ɢɫɬɟɱɟɧɢɹ ɢɡ ɫɨɫɭɞɨɜ ɫɨ ɫɜɨɛɨɞɧɨɣ ɩɨɜɟɪɯɧɨɫɬɶɸ:

2VgH

;

2QFgH

ɝɞɟ

()Hpp g



– ɜɵɫɨɬɚ ɭɪɨɜɧɹ ɠɢɞɤɨɫɬɢ ɧɚɞ ɰɟɧɬɪɚɥɶɧɵɦ ɨɬ-

ɜɟɪɫɬɢɟɦ (ɩɪɢ ɞɢɚɦɟɬɪɟ ɨɬɜɟɪɫɬɢɹ

ddH )

Ɉɩɵɬɚɦɢ ɭɫɬɚɧɨɜɥɟɧɨ, ɱɬɨ ɤɨɷɮɮɢɰɢɟɧɬ

P ɫɭɳɟɫɬɜɟɧɧɵɦ ɨɛɪɚɡɨɦ

ɢɡɦɟɧɹɟɬɫɹ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɮɨɪɦɵ, ɪɚɡɦɟɪɨɜ ɨɬɜɟɪɫɬɢɹ ɢ ɨɬ ɧɚɩɨɪɚ.

ɉɪɢɱɺɦ, ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɪɚɡɦɟɪɨɜ ɨɬɜɟɪɫɬɢɹ ɤɨɷɮɮɢɰɢɟɧɬ ɪɚɫɯɨɞɚ

ɭɦɟɧɶɲɚɟɬɫɹ, ɚ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɧɚɩɨɪɚ ɭɦɟɧɶɲɚɟɬɫɹ ɜɥɢɹɧɢɟ ɪɚɡɦɟɪɨɜ

ɨɬɜɟɪɫɬɢɹ ɧɚ ɤɨɷɮɮɢɰɢɟɧɬ

ɉɪɢ ɧɟɩɨɥɧɨɦ ɫɠɚɬɢɢ ɤɨɷɮɮɢɰɢɟɧɬ ɪɚɫɯɨɞɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪ-

ɦɭɥɚɦ:

10,152

§·



¨¸

©¹

– ɞɥɹ ɤɪɭɝɥɵɯ ɨɬɜɟɪɫɬɢɣ;

10,128

§·



¨¸

©¹

– ɞɥɹ ɩɪɹɦɨɭɝɨɥɶɧɵɯ ɨɬɜɟɪɫɬɢɣ.

Ɂɞɟɫɶ

– ɤɨɷɮɮɢɰɢɟɧɬ ɪɚɫɯɨɞɚ ɞɥɹ ɚɧɚɥɨɝɢɱɧɨɝɨ ɨɬɜɟɪɫɬɢɹ ɩɪɢ

ɩɨɥɧɨɦ ɫɠɚɬɢɢ;

n – ɱɚɫɬɶ ɩɟɪɢɦɟɬɪɚ ɨɬɜɟɪɫɬɢɹ, ɝɞɟ ɨɬɫɭɬɫɬɜɭɟɬ ɫɠɚɬɢɟ;

p – ɱɚɫɬɶ ɩɟɪɢɦɟɬɪɚ ɨɬɜɟɪɫɬɢɹ, ɝɞɟ ɨɬɫɭɬɫɬɜɭɟɬ ɫɠɚɬɢɟ.