LR_TE_SEUt_1

ɉɪɚɤɬɢɱɟɫɤɨɟ ɡɚɧɹɬɢɟ ʋ2 (6 ɱɚɫɨɜ)

ɊȺɋɑȿɌ ɏɈȾɄɈɋɌɂ ɋɍȾɇȺ ɋ ȼɂɇɌɈɆ ɊȿȽɍɅɂɊɍȿɆɈȽɈ ɒȺȽȺ

ɐɟɥɶ ɡɚɧɹɬɢɹ. Ɉɩɪɟɞɟɥɟɧɢɟ ɜɥɢɹɧɢɹ ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɵɯ ɮɚɤɬɨɪɨɜ ɧɚ ɩɚɪɚɦɟɬɪɵ ɯɨɞɤɨɫɬɢ ɞɥɹ ɫɭɞɨɜ ɫ ɜɢɧɬɨɦ ɪɟɝɭɥɢɪɭɟɦɨɝɨ ɲɚɝɚ (ȼɊɒ).

Ɂɚɞɚɧɢɹ ɞɥɹ ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɵɯ ɪɚɫɱɟɬɨɜ ɯɨɞɤɨɫɬɢ ɫɭɞɧɚ ɫ ȼɊɒ

1.Ɉɩɪɟɞɟɥɢɬɶ ɧɨɦɢɧɚɥɶɧɭɸ ɪɚɫɱɟɬɧɭɸ ɫɤɨɪɨɫɬɶ ɩɪɢ ɩɥɚɜɚɧɢɢ ɫɭɞɧɚ ɜ ɪɚɡɥɢɱɧɵɯ ɩɨɝɨɞɧɵɯ ɭɫɥɨɜɢɹɯ (ɫɦ. ɪɢɫ. 2.1).

2.Ɉɩɪɟɞɟɥɢɬɶ ɧɚɢɛɨɥɶɲɭɸ ɞɨɫɬɢɠɢɦɭɸ ɫɤɨɪɨɫɬɶ ɫɭɞɧɚ ɢ ɲɚɝɨɜɨɟ

ɨɬɧɨɲɟɧɢɟ ɝɪɟɛɧɨɝɨ ɜɢɧɬɚ ɩɪɢ ɪɚɛɨɬɟ ɞɜɢɝɚɬɟɥɹ ɧɚ ɩɪɨɦɟɠɭɬɨɱɧɨɦ ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɨɦ ɪɟɠɢɦɟ ɫ ɱɚɫɬɨɬɨɣ ɜɪɚɳɟɧɢɹ ɩ = ɦɢɧ-1 (ɪɢɫ. 2.1).

3.ɍɫɬɚɧɨɜɢɬɶ ɡɚɜɢɫɢɦɨɫɬɶ ɦɟɠɞɭ ɱɚɫɬɨɬɨɣ ɜɪɚɳɟɧɢɹ ɢ ɲɚɝɨɜɵɦ ɨɬɧɨɲɟɧɢɟɦ ɝɪɟɛɧɨɝɨ ɜɢɧɬɚ, ɪɟɚɥɢɡɚɰɢɹ ɤɨɬɨɪɨɣ ɧɟɨɛɯɨɞɢɦɚ ɞɥɹ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ ɧɚ ɲɜɚɪɬɨɜɧɨɦ ɪɟɠɢɦɟ ɩɨ ɜɟɪɯɧɟɣ ɨɝɪɚɧɢɱɢɬɟɥɶɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ (ɪɢɫ. 2.1).

4.ȼɨɫɩɪɨɢɡɜɟɫɬɢ ɧɚ ɲɜɚɪɬɨɜɚɯ ɧɨɦɢɧɚɥɶɧɵɣ ɪɚɫɱɟɬɧɵɣ ɪɟɠɢɦ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ ɩɨ ɜɟɪɯɧɟɣ ɨɝɪɚɧɢɱɢɬɟɥɶɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ, ɨɩɪɟɞɟɥɢɬɶ ɧɚɢɛɨɥɶɲɭɸ ɬɹɝɭ ɜɢɧɬɚ ɧɚ ɲɜɚɪɬɨɜɧɨɦ ɪɟɠɢɦɟ (ɪɢɫ. 2.1).

5.Ɉɩɪɟɞɟɥɢɬɶ ɧɚɢɛɨɥɶɲɭɸ ɞɨɫɬɢɠɢɦɭɸ ɫɤɨɪɨɫɬɶ ɫɭɞɧɚ ɩɪɢ ɜɫɟɯ ɜɚɪɢɚɧɬɚɯ ɜɤɥɸɱɟɧɢɹ ɷɧɟɪɝɟɬɢɱɟɫɤɨɣ ɭɫɬɚɧɨɜɤɢ, ɧɚɣɬɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɡɧɚɱɟɧɢɹ ɲɚɝɨɜɨɝɨ ɨɬɧɨɲɟɧɢɹ ȼɊɒ (ɪɢɫ. 2.2). Ɋɟɝɭɥɢɪɨɜɚɧɢɟ ɫɤɨɪɨɫɬɢ ɫɭɞɧɚ ɜɵɩɨɥɧɹɟɬɫɹ ɬɨɥɶɤɨ ɢɡɦɟɧɟɧɢɟɦ ɲɚɝɨɜɨɝɨ ɨɬɧɨɲɟɧɢɹ ɩɪɢ ɧɟɢɡɦɟɧɧɨɣ ɧɨɦɢɧɚɥɶɧɨɣ ɱɚɫɬɨɬɟ ɜɪɚɳɟɧɢɹ ɜɢɧɬɚ.

6.Ɉɩɪɟɞɟɥɢɬɶ ɩɨɥɟɡɧɭɸ ɬɹɝɭ ɝɪɟɛɧɨɝɨ ɜɢɧɬɚ ɫɭɞɧɚ ɧɚ ɲɜɚɪɬɨɜɧɨɦ ɪɟɠɢɦɟ ɩɪɢ ɪɚɛɨɬɟ ɧɚ ɜɢɧɬ ɨɞɧɨɝɨ ɢ ɞɜɭɯ ɝɥɚɜɧɵɯ ɞɜɢɝɚɬɟɥɟɣ (ɪɢɫ. 2.2).

7.ɉɨɥɶɡɭɹɫɶ ɬɹɝɨɜɵɦɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ ɫɭɞɧɚ (ɪɢɫ. 2.3), ɨɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ ɫɜɨɛɨɞɧɨɝɨ ɯɨɞɚ ɫɭɞɧɚ ɩɪɢ ɪɚɛɨɬɟ ɞɜɢɝɚɬɟɥɹ ɧɚ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ.

8.Ɉɩɪɟɞɟɥɢɬɶ ɲɚɝɨɜɨɟ ɨɬɧɨɲɟɧɢɟ ȼɊɒ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɪɚɛɨɬɭ ɞɜɢɝɚɬɟɥɹ ɩɨ ɜɟɪɯɧɟɣ ɨɝɪɚɧɢɱɢɬɟɥɶɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɧɚ ɲɜɚɪɬɨɜɧɨɦ ɪɟɠɢɦɟ ɩɪɢ ɱɚɫɬɨɬɟ ɜɪɚɳɟɧɢɹ ɩ = ɨɛ/ɦɢɧ (ɫɦ. ɪɢɫ. 2.3).

9.ɉɨɥɶɡɭɹɫɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ ɫɜɨɛɨɞɧɨɝɨ ɯɨɞɚ ɫɭɞɧɚ ɜ ɤɨɨɪɞɢɧɚɬɚɯ

Ne - ɩ (ɪɢɫ. 2.5), ɨɩɪɟɞɟɥɢɬɶ ɧɚɢɛɨɥɶɲɭɸ ɞɨɫɬɢɠɢɦɭɸ ɫɤɨɪɨɫɬɶ ɫɭɞɧɚ ɩɪɢ ɪɚɛɨɬɟ ɞɜɢɝɚɬɟɥɹ ɧɚ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ.

10.ȼ ɪɟɡɭɥɶɬɚɬɟ ɧɟɢɫɩɪɚɜɧɨɫɬɢ ɦɟɯɚɧɢɡɦɚ ɢɡɦɟɧɟɧɢɹ ɲɚɝɚ ȼɊɒ ɟɝɨ

ɥɨɩɚɫɬɢ ɨɫɬɚɥɢɫɶ ɡɚɮɢɤɫɢɪɨɜɚɧɧɵɦɢ ɜ ɩɨɥɨɠɟɧɢɢ, ɩɪɢ ɤɨɬɨɪɨɦ ɇ/D = . Ɉɩɪɟɞɟɥɢɬɶ ɧɚɢɛɨɥɶɲɭɸ ɞɨɫɬɢɠɢɦɭɸ ɫɤɨɪɨɫɬɶ ɫɭɞɧɚ ɛɟɡ ɩɟɪɟɝɪɭɡɤɢ ɝɥɚɜɧɨɝɨ ɞɜɢɝɚɬɟɥɹ (ɪɢɫ. 2.5).

11. Ʌɨɩɚɫɬɢ ȼɊɒ ɡɚɮɢɤɫɢɪɨɜɚɧɵ ɜ ɩɨɥɨɠɟɧɢɢ, ɩɪɢ ɤɨɬɨɪɨɦ ɇ/D = . Ɉɩɪɟɞɟɥɢɬɶ ɧɚɢɛɨɥɶɲɭɸ ɞɨɫɬɢɠɢɦɭɸ ɫɤɨɪɨɫɬɶ ɫɭɞɧɚ ɢ ɩɚɪɚɦɟɬɪɵ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ (ɪɢɫ. 2.5).

12. ɋɤɨɪɨɫɬɶ ɫɭɞɧɚ vs =ɭɡ.	ɍɫɬɚɧɨɜɢɬɶ	ɧɟɨɛɯɨɞɢɦɨɟ	ɲɚɝɨɜɨɟ
ɨɬɧɨɲɟɧɢɟ ȼɊɒ ɢ ɩɚɪɚɦɟɬɪɵ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ		(ɪɢɫ. 2.5).

13.ɇɟɢɫɩɪɚɜɟɧ ɜɵɧɨɫɧɨɣ ɭɤɚɡɚɬɟɥɶ ɲɚɝɚ (ȼɍɒ). ɉɨ ɬɚɯɨɦɟɬɪɭ ɭɫɬɚɧɨɜɥɟɧɚ ɱɚɫɬɨɬɚ ɜɪɚɳɟɧɢɹ ɞɜɢɝɚɬɟɥɹ ɩ = ɦɢɧ-1, ɩɨ ɥɚɝɭ – ɫɤɨɪɨɫɬɶ ɫɭɞɧɚ vs = ɭɡ. ɇɚɣɬɢ ɲɚɝɨɜɨɟ ɨɬɧɨɲɟɧɢɟ ȼɊɒ ɢ ɡɚɝɪɭɡɤɭ ɞɜɢɝɚɬɟɥɹ (ɪɢɫ. 2.5.).

14.ɉɨ ɬɚɯɨɦɟɬɪɭ ɭɫɬɚɧɨɜɥɟɧɚ ɱɚɫɬɨɬɚ ɜɪɚɳɟɧɢɹ ɞɜɢɝɚɬɟɥɹ ɩ = ɦɢɧ-1, ɩɨ ɭɤɚɡɚɬɟɥɸ ɲɚɝɚ – ɲɚɝɨɜɨɟ ɨɬɧɨɲɟɧɢɟ ɇ/D = . Ɉɩɪɟɞɟɥɢɬɶ ɩɨɬɪɟɛɥɹɟɦɭɸ ɦɨɳɧɨɫɬɶ ɢ ɫɤɨɪɨɫɬɶ ɫɭɞɧɚ (ɪɢɫ. 2.5).

15.ɇɚ ɫɭɞɧɟ ɩɪɢɦɟɧɟɧɚ ɫɢɫɬɟɦɚ ɫɨɜɦɟɫɬɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɝɥɚɜɧɵɦ ɞɜɢɝɚɬɟɥɟɦ ɢ ȼɊɒ. ɉɨɥɶɡɭɹɫɶ ɩɪɨɝɪɚɦɦɧɵɦɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ (ɪɢɫ. 2.8), ɨɩɢɫɚɬɶ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɜɵɜɟɞɟɧɢɹ ȼɊɒ ɢ ɝɥɚɜɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɜ ɨɛɥɚɫɬɶ ɨɩɬɢɦɚɥɶɧɵɯ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ɭɫɬɚɧɨɜɤɢ ɧɚ ɫɜɨɛɨɞɧɨɦ ɯɨɞɭ.

16.Ɉɩɪɟɞɟɥɢɬɶ ɪɚɫɯɨɞ ɬɨɩɥɢɜɚ ɝɥɚɜɧɵɦ ɞɜɢɝɚɬɟɥɟɦ ɩɪɢ ɜɪɚɳɟɧɢɢ ɝɪɟɛɧɨɝɨ ɜɢɧɬɚ ɧɚ «ɯɨɥɨɫɬɨɦ» ɯɨɞɭ (ɪɢɫ. 2.9).

17.Ɉɩɪɟɞɟɥɢɬɶ ɪɚɫɯɨɞ ɬɨɩɥɢɜɚ ɝɥɚɜɧɵɦ ɞɜɢɝɚɬɟɥɟɦ ɩɪɢ ɞɜɢɠɟɧɢɢ ɩɨɥɧɵɦ ɯɨɞɨɦ (ɪɢɫ. 2.9).

18.ɉɨɥɶɡɭɹɫɶ ɞɢɚɝɪɚɦɦɨɣ ɯɨɞɤɨɫɬɢ ɫɭɞɧɚ ɩɪɢ ɩɨɫɬɨɹɧɧɨɣ ɧɨɦɢɧɚɥɶɧɨɣ ɱɚɫɬɨɬɟ ɜɪɚɳɟɧɢɹ ɜɢɧɬɚ (ɪɢɫ. 2.11), ɨɩɪɟɞɟɥɢɬɶ ɧɚɢɛɨɥɶɲɭɸ ɫɤɨɪɨɫɬɶ ɫɜɨɛɨɞɧɨɝɨ ɯɨɞɚ ɜ ɫɥɭɱɚɟ ɪɚɛɨɬɵ ɧɚ ɜɢɧɬ ɞɜɭɯ ɝɥɚɜɧɵɯ ɞɜɢɝɚɬɟɥɟɣ

ɢɜɚɥɨɦɨɬɨɪɚ ɫɭɦɦɚɪɧɨɣ ɦɨɳɧɨɫɬɶɸ __ ɤȼɬ.

19.ɉɨɥɶɡɭɹɫɶ ɪɢɫ. 2.11, ɜɵɛɪɚɬɶ ɜɚɪɢɚɧɬ ɜɤɥɸɱɟɧɢɹ ɷɧɟɪɝɟɬɢɱɟɫɤɨɣ ɭɫɬɚɧɨɜɤɢ ɞɥɹ ɞɜɢɠɟɧɢɹ ɫɭɞɧɚ ɫɨ ɫɤɨɪɨɫɬɶɸ vs = __ ɭɡ.

20.Ɉɩɪɟɞɟɥɢɬɶ ɦɨɳɧɨɫɬɶ, ɧɟɨɛɯɨɞɢɦɭɸ ɞɥɹ ɜɪɚɳɟɧɢɹ ɝɪɟɛɧɨɝɨ ɜɢɧɬɚ ɧɚ ɪɟɠɢɦɟ «ɋɬɨɩ» (ɪɢɫ. 2.11).

21.ɉɨɥɶɡɭɹɫɶ ɞɢɚɝɪɚɦɦɨɣ ɯɨɞɤɨɫɬɢ ɫɭɞɧɚ ɩɪɢ ɩɨɫɬɨɹɧɧɨɣ ɧɨɦɢɧɚɥɶɧɨɣ ɱɚɫɬɨɬɟ ɜɪɚɳɟɧɢɹ ɜɢɧɬɚ (ɫɦ. ɪɢɫ. 2.12), ɨɩɪɟɞɟɥɢɬɶ ɩɨɥɨɠɟɧɢɟ ɪɭɤɨɹɬɤɢ ɜɵɧɨɫɧɨɝɨ ɭɤɚɡɚɬɟɥɹ ɲɚɝɚ ȼɊɒ, ɧɟɨɛɯɨɞɢɦɨɟ ɞɥɹ ɞɜɢɠɟɧɢɹ ɫɨ ɫɤɨɪɨɫɬɶɸ

vs = ɭɡ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɡɚɝɪɭɡɤɭ ɞɜɢɝɚɬɟɥɟɣ ɢ ɱɚɫɨɜɨɣ ɪɚɫɯɨɞ ɬɨɩɥɢɜɚ.

22.ɉɨɥɶɡɭɹɫɶ ɪɢɫ 2.12, ɨɩɪɟɞɟɥɢɬɶ ɩɨɬɪɟɛɥɹɟɦɭɸ ɜɪɚɳɚɸɳɢɦɫɹ ɜɢɧɬɨɦ ɦɨɳɧɨɫɬɶ ɢ ɪɚɫɯɨɞ ɬɨɩɥɢɜɚ ɜ ɪɟɠɢɦɟ «ɋɬɨɩ».

1. Ɉɛɳɢɟ ɫɜɟɞɟɧɢɹ

ɉɪɢ ɪɚɛɨɬɟ ɧɚ ɝɪɟɛɧɨɣ ɜɢɧɬ (Ƚȼ) ɪɟɠɢɦ ɝɥɚɜɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɩɨɞɱɢɧɹɟɬɫɹ ɩɪɹɦɨɦɭ ɫɢɥɨɜɨɦɭ ɞɟɣɫɬɜɢɸ Ƚȼ, ɬ.ɟ. ɪɚɡɜɢɜɚɟɦɚɹ ɦɨɳɧɨɫɬɶ ȽȾ ɧɚ ɪɚɡɥɢɱɧɵɯ ɪɟɠɢɦɚɯ ɪɚɛɨɬɵ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɦɨɳɧɨɫɬɢ, ɩɨɬɪɟɛɥɹɟɦɨɣ Ƚȼ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɞɜɢɝɚɬɟɥɶ ɪɚɛɨɬɚɟɬ ɩɨ ɬɚɤ ɧɚɡɵɜɚɟɦɨɣ ɜɢɧɬɨɜɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ.

ȼ ɭɫɬɚɧɨɜɤɚɯ ɫ ɝɪɟɛɧɵɦ ɜɢɧɬɨɦ ɮɢɤɫɢɪɨɜɚɧɧɨɝɨ ɲɚɝɚ (ȼɎɒ) ɢɡɦɟɧɟɧɢɟ ɪɟɠɢɦɚ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ ɜ ɨɛɵɱɧɵɯ ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɵɯ ɭɫɥɨɜɢɹɯ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɩɭɬɟɦ ɭɩɪɚɜɥɟɧɢɹ ɢ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɞɜɢɝɚɬɟɥɹ ɡɚ ɫɱɟɬ ɢɡɦɟɧɟɧɢɹ ɩɨɞɚɱɢ ɬɨɩɥɢɜɚ. ɉɪɢ ɷɬɨɦ ɠɟɫɬɤɚɹ ɫɜɹɡɶ ɪɚɛɨɬɵ ȽȾ ɢ Ƚȼ ɢɯ ɫɨɜɦɟɫɬɧɚɹ ɫɨɝɥɚɫɨɜɚɧɧɨɫɬɶ, ɨɩɪɟɞɟɥɹɟɬ ɪɟɠɢɦ ɪɚɛɨɬɵ ȽȾ ɢ ɨɝɪɚɧɢɱɢɜɚɟɬ ɟɝɨ ɜɨɡɦɨɠɧɨɫɬɢ ɩɨɥɧɨɝɨ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɧɨɦɢɧɚɥɶɧɨɣ ɦɨɳɧɨɫɬɢ ɜ ɪɚɡɥɢɱɧɵɯ ɢɡɦɟɧɹɸɳɢɯɫɹ ɭɫɥɨɜɢɹɯ ɩɥɚɜɚɧɢɹ ɫɭɞɧɚ. Ɍɚɤɚɹ ɫɜɹɡɶ

ȽȾ ɫ ȼɎɒ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɵɯ ɭɫɥɨɜɢɣ ɫɭɞɧɚ, ɤɨɝɞɚ ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɹɟɬɫɹ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɟɝɨ ɞɜɢɠɟɧɢɸ (ɢɡɦɟɧɟɧɢɟ ɨɫɚɞɤɢ, ɦɟɥɤɨɜɨɞɶɟ, ɲɬɨɪɦɨɜɵɟ ɭɫɥɨɜɢɹ, ɨɛɪɚɫɬɚɧɢɟ ɤɨɪɩɭɫɚ ɢ Ƚȼ ɢ ɞɪ.), ɩɪɢɜɨɞɢɬ ɤ ɪɟɠɢɦɚɦ ɪɚɛɨɬɵ ȽȾ ɧɚ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɢ «ɬɹɠɟɥɵɣ» ɢɥɢ «ɥɟɝɤɢɣ» ɜɢɧɬ, ɚ ɬɚɤɠɟ ɡɧɚɱɢɬɟɥɶɧɨ ɫɭɠɚɟɬ ɦɚɧɟɜɪɟɧɧɵɟ ɤɚɱɟɫɬɜɚ ɫɭɞɧɚ.

ɉɪɢɦɟɧɟɧɢɟ ȼɊɒ ɜɨ ɦɧɨɝɨɦ ɫɧɢɦɚɟɬ ɜɵɲɟɭɤɚɡɚɧɧɵɟ ɧɟɞɨɫɬɚɬɤɢ ȼɎɒ ɡɚ ɫɱɟɬ ɬɨɝɨ, ɱɬɨ ɢɡɦɟɧɟɧɢɟ ɧɚɝɪɭɡɤɢ ɞɜɢɝɚɬɟɥɹ ɜ ɭɫɬɚɧɨɜɤɚɯ ɫ ȼɊɒ ɦɨɠɟɬ ɨɫɭɳɟɫɬɜɥɹɬɶɫɹ ɧɟ ɬɨɥɶɤɨ ɡɚ ɫɱɟɬ ɢɡɦɟɧɟɧɢɹ ɩɨɞɚɱɢ ɬɨɩɥɢɜɚ, ɚ ɬɚɤɠɟ ɩɭɬɟɦ ɜɨɡɞɟɣɫɬɜɢɹ ɧɚ ɲɚɝ ɜɢɧɬɚ. ɗɬɨ ɡɧɚɱɢɬɟɥɶɧɨ ɪɚɫɲɢɪɹɟɬ ɨɛɥɚɫɬɶ ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɵɯ ɪɟɠɢɦɨɜ ɷɧɟɪɝɟɬɢɱɟɫɤɨɣ ɭɫɬɚɧɨɜɤɢ, ɭɜɟɥɢɱɢɜɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɩɨɥɧɨɝɨ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɧɨɦɢɧɚɥɶɧɨɣ ɦɨɳɧɨɫɬɢ ȽȾ, ɭɥɭɱɲɚɟɬ ɦɚɧɟɜɪɟɧɧɨɟ ɤɚɱɟɫɬɜɚ ɫɭɞɧɚ, ɤɨɦɩɟɧɫɢɪɭɟɬ ɜɥɢɹɧɢɟ ɜɧɟɲɧɢɯ ɮɚɤɬɨɪɨɜ ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭɜɢɧɬɚɢɢɫɤɥɸɱɚɟɬɪɟɠɢɦɵɪɚɛɨɬɵɜɨɛɥɚɫɬɢ«ɬɹɠɟɥɨɝɨ» ɜɢɧɬɚ.

ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɭɫɬɚɧɨɜɤɢ ɫ ȼɊɒ ɦɨɠɧɨ ɜɵɞɟɥɢɬɶ ɬɪɢ ɨɫɧɨɜɧɵɟ ɜɨɡɦɨɠɧɵɟ ɫɨɱɟɬɚɧɢɹ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ȽȾ ɢ Ƚȼ:

1.Ɋɟɠɢɦ ɪɚɛɨɬɵ ȽȾ ɩɪɢ ɩɨɫɬɨɹɧɧɨɣ ɱɚɫɬɨɬɟ ɜɪɚɳɟɧɢɹ ɜɚɥɚ (n = const) ɢ ɩɟɪɟɦɟɧɧɨɦ ɲɚɝɨɜɨɦ ɨɬɧɨɲɟɧɢɢ Ƚȼ (H/D = var) ɝɞɟ ɇ – ɲɚɝ ɜɢɧɬɚ, D – ɟɝɨ ɞɢɚɦɟɬɪ.

2.ɉɪɢ ɪɚɛɨɬɟ ɞɜɢɝɚɬɟɥɹ ɫ ɩɟɪɟɦɟɧɧɨɣ ɱɚɫɬɨɬɨɣ ɜɪɚɳɟɧɢɹ ɜɚɥɚ (n = var) ɢ ɢɡɦɟɧɹɟɦɵɦ ɲɚɝɨɜɵɦ ɨɬɧɨɲɟɧɢɟɦ (H/D = var).

3.Ɋɟɠɢɦ ɪɚɛɨɬɵ ɭɫɬɚɧɨɜɤɢ ɜ ɭɫɥɨɜɢɹɯ ɮɢɤɫɢɪɨɜɚɧɧɨɝɨ ɲɚɝɚ, ɬ.ɟ. ɤɨɝɞɚ ɧɟ ɦɟɧɹɟɬɫɹ ɲɚɝɨɜɨɟ ɨɬɧɨɲɟɧɢɟ (H/D = const), ɚ ɦɨɳɧɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɢ

ɱɚɫɬɨɬɚ ɜɪɚɳɟɧɢɹ ɢɡɦɟɧɹɸɬɫɹ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɡɚɤɨɧɨɦ ɜɢɧɬɨɜɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ (n = var, Ne = cn3, ɝɞɟ ɫ – ɩɨɫɬɨɹɧɧɚɹ ɜɢɧɬɨɜɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ).

ɉɟɪɜɵɣ ɜɚɪɢɚɧɬ – ɭɩɪɚɜɥɟɧɢɟ ȼɊɒ ɩɪɢ ɩɨɫɬɨɹɧɧɨɣ ɱɚɫɬɨɬɟ ɜɪɚɳɟɧɢɹ, ɩɪɢɦɟɧɹɟɬɫɹ ɞɥɹ ɬɪɚɧɫɩɨɪɬɧɵɯ ɫɭɞɨɜ, ɬɪɚɭɥɟɪɨɜ ɢ ɞɪɭɝɢɯ ɬɢɩɨɜ ɫɭɞɨɜ, ɝɞɟ ɟɫɬɶ ɜɨɡɦɨɠɧɨɫɬɶ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɜɚɥɨɝɟɧɟɪɚɬɨɪɚ ɧɚ ɪɚɡɥɢɱɧɵɯ ɧɚɝɪɭɡɨɱɧɵɯ ɪɟɠɢɦɚɯ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ.

ȼɬɨɪɨɣ ɫɩɨɫɨɛ – ɭɩɪɚɜɥɟɧɢɟ ɩɭɬɟɦ ɢɡɦɟɧɟɧɢɹ ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ ɢ ɲɚɝɚ ɜɢɧɬɚ, ɬɚɤ ɧɚɡɵɜɚɟɦɨɟ ɤɨɦɛɢɧɚɬɨɪɧɨɟ ɭɩɪɚɜɥɟɧɢɟ, ɩɪɢɦɟɧɹɟɬɫɹ ɜ ɨɫɧɨɜɧɨɦ ɞɥɹ ɱɚɫɬɢɱɧɵɯ ɧɚɝɪɭɡɨɤ ɞɜɢɝɚɬɟɥɹ ɢ ɦɚɧɟɜɪɟɧɧɵɯ ɪɟɠɢɦɨɜ. ɗɬɨɬ ɜɚɪɢɚɧɬ, ɤɚɤ ɩɨɤɚɡɵɜɚɟɬ ɩɪɚɤɬɢɤɚ, ɩɨɡɜɨɥɹɟɬ ɫɧɢɡɢɬɶ ɪɚɫɯɨɞ ɬɨɩɥɢɜɚ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɞɪɭɝɢɦɢ ɫɩɨɫɨɛɚɦɢ ɭɩɪɚɜɥɟɧɢɹ.

Ɍɪɟɬɢɣ ɫɩɨɫɨɛ – ɪɚɛɨɬɚ ȼɊɒ ɩɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɮɢɤɫɢɪɨɜɚɧɧɨɝɨ ɲɚɝɚ ɢɫɩɨɥɶɡɭɟɬɫɹ, ɤɚɤ ɩɪɚɜɢɥɨ, ɧɚ ɪɟɠɢɦɚɯ ɩɨɥɧɨɝɨ ɯɨɞɚ.

ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɩɪɢ ɪɚɛɨɬɟ ɧɚ ȼɊɒ ɭɫɥɨɜɢɹ ɞɥɹ ɩɟɪɟɝɪɭɡɤɢ ȽȾ ɫɬɚɧɨɜɹɬɫɹ ɛɨɥɟɟ ɜɟɪɨɹɬɧɵɦɢ, ɱɟɦ ɩɪɢ ɪɚɛɨɬɟ ɧɚ ȼɎɒ, ɬɚɤ ɤɚɤ ɭɩɪɚɜɥɟɧɢɟ ɦɨɠɟɬ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɨɞɧɨɜɪɟɦɟɧɧɨ ɢɡɦɟɧɟɧɢɟɦ ɩɨɞɚɱɢ ɬɨɩɥɢɜɚ ɧɚ ȽȾ ɢ ɢɡɦɟɧɟɧɢɟɦ ɲɚɝɚ Ƚȼ. Ɍ.ɟ. ɜ ɨɬɥɢɱɢɟ ɨɬ ɪɚɛɨɬɵ ȽȾ ɧɚ ȼɎɒ ɜ ɩɪɨɩɭɥɴɫɢɜɧɨɣ ɭɫɬɚɧɨɜɤɟ ɫ ȼɊɒ ɜɦɟɫɬɨ ɨɞɧɨɝɨ ɭɩɪɚɜɥɹɟɦɨɝɨ ɜɨɡɞɟɣɫɬɜɢɹ ɜɜɨɞɹɬɫɹ ɞɜɚ (ɬɨɩɥɢɜɨ ɢ ɲɚɝ Ƚȼ).

ɗɬɢ ɨɛɫɬɨɹɬɟɥɶɫɬɜɚ ɜɵɞɜɢɝɚɸɬ ɫɩɟɰɢɮɢɱɟɫɤɢɟ ɬɪɟɛɨɜɚɧɢɹ ɤ ɧɚɡɧɚɱɟɧɢɸ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ȽȾ, ɤ ɫɢɫɬɟɦɚɦ ɭɩɪɚɜɥɟɧɢɹ ɢ ɡɚɲɢɬɵ. ȼ ɩɪɨɝɪɚɦɦɚɯ ɞɢɫɬɚɧɰɢɨɧɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɝɥɚɜɧɵɦ ɞɜɢɝɚɬɟɥɟɦ ɫ ȼɊɒ ɨɛɵɱɧɨ

ɩɪɟɞɭɫɦɚɬɪɢɜɚɟɬɫɹ ɪɟɝɭɥɹɬɨɪ ɧɚɝɪɭɡɤɢ, ɤɨɬɨɪɵɣ ɫɜɹɡɵɜɚɟɬ ɩɨɥɨɠɟɧɢɟ ɪɟɣɤɢ ɬɨɩɥɢɜɧɨɝɨ ɧɚɫɨɫɚ ɢ ɪɚɡɜɨɪɨɬ ɥɨɩɚɫɬɟɣ ɜɢɧɬɚ, ɧɟ ɞɨɩɭɫɤɚɹ ɜɨɡɦɨɠɧɨɫɬɢ ɩɟɪɟɝɪɭɡɤɢ ɞɜɢɝɚɬɟɥɹ ɩɭɬɟɦ ɜɨɡɞɟɣɫɬɜɢɹ ɧɚ ɢɡɦɟɧɟɧɢɟ ɲɚɝɚ ɜɢɧɬɚ [5].

Ⱦɥɹ ɭɫɬɚɧɨɜɨɤ ɫ ȼɎɒ ɪɚɡɪɚɛɚɬɵɜɚɸɬɫɹ ɩɚɫɩɨɪɬɧɵɟ ɞɢɚɝɪɚɦɦɵ ɩɪɨɩɭɥɶɫɢɜɧɨɣ ɭɫɬɚɧɨɜɤɢ, ɧɚ ɤɨɬɨɪɵɯ ɫɬɪɨɹɬɫɹ ɝɪɚɮɢɤɢ ɢɡɦɟɧɟɧɢɹ ɦɨɳɧɨɫɬɢ ȽȾ, ɩɨɥɟɡɧɨɣ ɬɹɝɢ ɜɢɧɬɚ ɢ ɞɪɭɝɢɯ ɩɨɤɚɡɚɬɟɥɟɣ ɪɚɛɨɬɵ ɋɗɍ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɫɤɨɪɨɫɬɢ ɞɜɢɠɟɧɢɹ ɫɭɞɧɚ ɢ ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ Ƚȼ. Ɍɚɤɢɟ ɝɪɚɮɢɤɢ, ɩɨɤɚɡɵɜɚɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ȽȾ ɢ Ƚȼ, ɩɨɡɜɨɥɹɸɬ ɧɚɡɧɚɱɚɬɶ ɢ ɤɨɧɬɪɨɥɢɪɨɜɚɬɶ ɪɟɠɢɦɵ ɪɚɛɨɬɵ ɩɪɨɩɭɥɶɫɢɜɧɨɣ ɭɫɬɚɧɨɜɤɢ ɜ ɪɚɡɥɢɱɧɵɯ ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɵɯ ɭɫɥɨɜɢɹɯ ɩɥɚɜɚɧɢɹ ɫɭɞɧɚ.

ȼ ɨɬɥɢɱɢɟ ɨɬ ɭɫɬɚɧɨɜɨɤ ɫ ȼɎɒ ɬɚɤɭɸ ɩɚɫɩɨɪɬɧɭɸ ɞɢɚɝɪɚɦɦɭ ɞɥɹ ɭɫɬɚɧɨɜɨɤ ɫ ȼɊɒ ɩɪɚɤɬɢɱɟɫɤɢ ɪɚɫɫɱɢɬɚɬɶ ɢ ɩɨɫɬɪɨɢɬɶ ɨɱɟɧɶ ɫɥɨɠɧɨ, ɬ.ɤ. ɬɪɟɛɭɟɬɫɹ ɭɜɹɡɚɬɶ (ɫɨɝɥɚɫɨɜɚɬɶ) ɦɟɠɞɭ ɫɨɛɨɣ ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɶɲɟɟ ɱɢɫɥɨ ɢɡɦɟɧɹɸɳɢɯɫɹ ɩɨɤɚɡɚɬɟɥɟɣ (Ne, H/D, n, v) ɪɚɛɨɬɵ ɩɪɨɩɭɥɶɫɢɜɧɨɣ ɭɫɬɚɧɨɜɤɢ (ɉɍ). ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɞɥɹ ɷɬɨɣ ɰɟɥɢ ɧɭɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɢ ɩɨɫɬɪɨɢɬɶ ɦɧɨɠɟɫɬɜɨ ɱɚɫɬɧɵɯ ɩɚɫɩɨɪɬɧɵɯ ɞɢɚɝɪɚɦɦ ɞɥɹ ɪɚɡɥɢɱɧɵɯ ɭɫɥɨɜɢɣ ɩɥɚɜɚɧɢɹ ɫɭɞɧɚ ɫ ȼɊɒ.

2. Ɇɟɬɨɞɢɤɚ ɜɵɩɨɥɧɟɧɢɹ ɢ ɫɨɞɟɪɠɚɧɢɟ ɨɬɱɟɬɚ

ɉɪɢɦɟɪ ɡɚɞɚɱɢ 1.

Ɉɩɪɟɞɟɥɢɬɶ ɧɨɦɢɧɚɥɶɧɭɸ ɪɚɫɱɟɬɧɭɸ ɫɤɨɪɨɫɬɶ ɩɪɢ ɩɥɚɜɚɧɢɢ ɫɭɞɧɚ ɜ ɪɚɡɥɢɱɧɵɯ ɩɨɝɨɞɧɵɯ ɭɫɥɨɜɢɹɯ (ɫɦ. ɪɢɫ. 2.1).

Ɋɟɲɟɧɢɟ.

Ⱥɛɫɰɢɫɫɚ ɬɨɱɤɢ ɩɟɪɟɫɟɱɟɧɢɹ ɤɪɢɜɵɯ 1 ɢ 4 ɭɤɚɡɵɜɚɟɬ ɢɫɤɨɦɭɸ ɫɤɨɪɨɫɬɶ ɫɭɞɧɚ ɧɚ ɬɢɯɨɣ ɜɨɞɟ (vsmɚɯ = __ ɭɡ). ɇɟɨɛɯɨɞɢɦɨɟ ɲɚɝɨɜɨɟ ɨɬɧɨɲɟɧɢɟ ɝɪɟɛɧɨɝɨ ɜɢɧɬɚ (ɇ/D = ) ɧɚɣɞɟɧɨ ɩɨ ɤɪɢɜɨɣ 9. ɇɚɢɛɨɥɶɲɚɹ ɞɨɫɬɢɠɢɦɚɹ ɫɤɨɪɨɫɬɶ ɫɭɞɧɚ ɩɪɢ ɪɚɛɨɬɟ ɞɜɢɝɚɬɟɥɹ ɧɚ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ ɜ ɭɫɥɨɜɢɹɯ ɜɫɬɪɟɱɧɨɝɨ ɜɟɬɪɚ ɫɢɥɨɣ 3 ɢ 6 ɛɚɥɥɨɜ ɫɨɫɬɚɜɥɹɟɬ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ vs1 = ɭɡ ɢ vs2 = ɭɡ (ɧɚɣɞɟɧɚ ɧɚ ɩɟɪɟɫɟɱɟɧɢɢ ɤɪɢɜɵɯ 2 ɢ 3 ɫ ɤɪɢɜɨɣ 4). ȼɨ ɢɡɛɟɠɚɧɢɟ ɩɟɪɟɝɪɭɡɤɢ ɞɜɢɝɚɬɟɥɹ ɲɚɝɨɜɨɟ ɨɬɧɨɲɟɧɢɟ ɜɢɧɬɚ ɩɪɢ ɜɫɬɪɟɱɧɨɦ ɜɟɬɪɟ ɞɨɥɠɧɨ ɛɵɬɶ ɧɟɫɤɨɥɶɤɨ ɭɦɟɧɶɲɟɧɨ. ɇɚɩɪɢɦɟɪ, ɩɪɢ ɜɟɬɪɟ 6 ɛɚɥɥɨɜ ɜ ɬɨɱɤɟ ɩɟɪɟɫɟɱɟɧɢɹ ɨɪɞɢɧɚɬɵ vs2 = ɭɡ ɫ ɤɪɢɜɨɣ 9 ɩɨɥɭɱɢɦ ɇ/D = __ .

ɉɪɢɦɟɪ ɡɚɞɚɱɢ 2.

Ɉɩɪɟɞɟɥɢɬɶ ɧɚɢɛɨɥɶɲɭɸ ɞɨɫɬɢɠɢɦɭɸ ɫɤɨɪɨɫɬɶ ɫɭɞɧɚ ɢ ɲɚɝɨɜɨɟ ɨɬɧɨɲɟɧɢɟ ɝɪɟɛɧɨɝɨ ɜɢɧɬɚ ɩɪɢ ɪɚɛɨɬɟ ɞɜɢɝɚɬɟɥɹ ɧɚ ɩɪɨɦɟɠɭɬɨɱɧɨɦ ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɨɦ ɪɟɠɢɦɟ ɫ ɱɚɫɬɨɬɨɣ ɜɪɚɳɟɧɢɹ ɩ = 200 ɦɢɧ-1 (ɪɢɫ. 2.1).

Ɋɟɲɟɧɢɟ.

Ɂɚɞɚɱɚ ɪɟɲɚɟɬɫɹ ɚɧɚɥɨɝɢɱɧɨ ɩɪɟɞɵɞɭɳɟɣ: ɬɨɱɤɚ ɩɟɪɟɫɟɱɟɧɢɹ ɤɪɢɜɵɯ 1 ɢ 7 ɭɤɚɡɵɜɚɟɬ ɫɤɨɪɨɫɬɶ vs = 10,6 ɭɡ, ɤɨɬɨɪɨɣ ɧɚ ɤɪɢɜɨɣ 12 ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɲɚɝɨɜɨɟ ɨɬɧɨɲɟɧɢɟ ɇ/D = 0,97 .

ɉɪɢɦɟɪ ɡɚɞɚɱɢ 3.

ɍɫɬɚɧɨɜɢɬɶ ɡɚɜɢɫɢɦɨɫɬɶ ɦɟɠɞɭ ɱɚɫɬɨɬɨɣ ɜɪɚɳɟɧɢɹ ɢ ɲɚɝɨɜɵɦ

ɨɬɧɨɲɟɧɢɟɦ ɝɪɟɛɧɨɝɨ ɜɢɧɬɚ, ɪɟɚɥɢɡɚɰɢɹ ɤɨɬɨɪɨɣ ɧɟɨɛɯɨɞɢɦɚ ɞɥɹ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ ɧɚ ɲɜɚɪɬɨɜɧɨɦ ɪɟɠɢɦɟ ɩɨ ɜɟɪɯɧɟɣ ɨɝɪɚɧɢɱɢɬɟɥɶɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ (ɪɢɫ. 2.1).

Ɋɟɲɟɧɢɟ.

Ɍɨɱɤɢ ɩɟɪɟɫɟɱɟɧɢɹ ɤɪɢɜɵɯ 9, 10, 11, 12, 13 ɫ ɨɫɶɸ ɨɪɞɢɧɚɬ (vs = 0)

ɭɤɚɡɵɜɚɸɬ ɡɧɚɱɟɧɢɹ: (ɇ/D)1 = __; (ɇ/D)2 =__ ; (ɇ/D)3 = __; (ɇ/D)4 = __; (ɇ/D)5 = __ ɞɥɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɡɧɚɱɟɧɢɣ ɩ1 = ; ɩ2 = ; ɩ3 = ; ɩ4 = ; ɩ5 = ɦɢɧ-1.

ɉɪɢɦɟɪ ɡɚɞɚɱɢ 4.

ȼɨɫɩɪɨɢɡɜɟɫɬɢ ɧɚ ɲɜɚɪɬɨɜɚɯ ɧɨɦɢɧɚɥɶɧɵɣ ɪɚɫɱɟɬɧɵɣ ɪɟɠɢɦ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ ɩɨ ɜɟɪɯɧɟɣ ɨɝɪɚɧɢɱɢɬɟɥɶɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ, ɨɩɪɟɞɟɥɢɬɶ ɧɚɢɛɨɥɶɲɭɸ ɬɹɝɭ ɜɢɧɬɚ ɧɚ ɲɜɚɪɬɨɜɧɨɦ ɪɟɠɢɦɟ (ɪɢɫ. 2.1).

Ɋɟɲɟɧɢɟ.

ȼ ɩɪɢɦɟɪɟ 3 ɞɥɹ ɩ = 300 ɦɢɧ-1 ɭɤɚɡɚɧɨ ɡɧɚɱɟɧɢɟ ɇ/D = 0,50 (ɤɪɢɜɚɹ 9). ɇɚɝɪɭɡɤɚ ɧɚ ɞɜɢɝɚɬɟɥɶ ɫɨɫɬɚɜɢɬ 590 ɤȼɬ, ɝɪɟɛɧɨɣ ɜɢɧɬ ɪɚɡɨɜɶɟɬ ɬɹɝɭ Ɋɟɲɜ = 99 ɤɇ (ɬɨɱɤɚ ɩɟɪɟɫɟɱɟɧɢɹ ɤɪɢɜɨɣ 4 ɫ ɨɫɶɸ ɨɪɞɢɧɚɬ).

ɉɪɢɦɟɪ ɡɚɞɚɱɢ 5.

Ɉɩɪɟɞɟɥɢɬɶ ɧɚɢɛɨɥɶɲɭɸ ɞɨɫɬɢɠɢɦɭɸ ɫɤɨɪɨɫɬɶ ɫɭɞɧɚ ɩɪɢ ɜɫɟɯ ɜɚɪɢɚɧɬɚɯ ɜɤɥɸɱɟɧɢɹ ɷɧɟɪɝɟɬɢɱɟɫɤɨɣ ɭɫɬɚɧɨɜɤɢ, ɧɚɣɬɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɡɧɚɱɟɧɢɹ ɲɚɝɨɜɨɝɨ ɨɬɧɨɲɟɧɢɹ ȼɊɒ (ɫɦ. ɪɢɫ. 2,2). Ɋɟɝɭɥɢɪɨɜɚɧɢɟ ɫɤɨɪɨɫɬɢ ɫɭɞɧɚ ɜɵɩɨɥɧɹɟɬɫɹ ɬɨɥɶɤɨ ɢɡɦɟɧɟɧɢɟɦ ɲɚɝɨɜɨɝɨ ɨɬɧɨɲɟɧɢɹ ɩɪɢ ɧɟɢɡɦɟɧɧɨɣ ɧɨɦɢɧɚɥɶɧɨɣ ɱɚɫɬɨɬɟ ɜɪɚɳɟɧɢɹ ɜɢɧɬɚ.

Ɋɟɲɟɧɢɟ.

Ⱥɛɫɰɢɫɫɵ ɬɨɱɟɤ ɩɟɪɟɫɟɱɟɧɢɹ ɤɪɢɜɨɣ 6 ɫ ɤɪɢɜɵɦɢ 1, 3, 4, 5 ɭɤɚɡɵɜɚɸɬ ɢɫɤɨɦɭɸ ɫɤɨɪɨɫɬɶ vs1 = ; vs2 = ; vs3 = ; vs4 = ɭɡ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɩɪɢ ɪɚɛɨɬɟ ɨɞɧɨɝɨ ɝɥɚɜɧɨɝɨ ɞɜɢɝɚɬɟɥɹ, ɞɜɭɯ ɝɥɚɜɧɵɯ ɞɜɢɝɚɬɟɥɟɣ ɫ ɨɬɛɨɪɨɦ ɦɨɳɧɨɫɬɢ ɧɚ ɜɚɥɨɝɟɧɟɪɚɬɨɪ, ɞɜɭɯ ɝɥɚɜɧɵɯ ɞɜɢɝɚɬɟɥɟɣ, ɞɜɭɯ ɝɥɚɜɧɵɯ ɞɜɢɝɚɬɟɥɟɣ ɢ ɜɚɥɨɦɨɬɨɪɚ. Ʌɨɩɚɫɬɢ ȼɊɒ ɞɨɥɠɧɵ ɭɫɬɚɧɚɜɥɢɜɚɬɶɫɹ ɫ ɲɚɝɨɜɵɦ ɨɬɧɨɲɟɧɢɟɦ

(ɇ/D) = ; (ɇ/D)2 = ; (ɇ/D)3 = ; (ɇ/D)4 = (ɤɪɢɜɵɟ 2, 7, 8, 9).

ɉɪɢɦɟɪ ɡɚɞɚɱɢ 6.

Ɉɩɪɟɞɟɥɢɬɶ ɩɨɥɟɡɧɭɸ ɬɹɝɭ ɝɪɟɛɧɨɝɨ ɜɢɧɬɚ ɫɭɞɧɚ ɧɚ ɲɜɚɪɬɨɜɧɨɦ ɪɟɠɢɦɟ ɩɪɢ ɪɚɛɨɬɟ ɧɚ ɜɢɧɬ ɨɞɧɨɝɨ ɢ ɞɜɭɯ ɝɥɚɜɧɵɯ ɞɜɢɝɚɬɟɥɟɣ (ɪɢɫ. 2.2).

Ɋɟɲɟɧɢɟ.

Ɍɨɱɤɢ ɩɟɪɟɫɟɱɟɧɢɹ ɤɪɢɜɵɯ 1 ɢ 4 ɫ ɨɫɶɸ ɨɪɞɢɧɚɬ ɞɚɸɬ Ɋɟɲɜ1 = ɢ Ɋɟɲɜ2 = ɤɇ ɩɪɢ (ɇ/D) = ; (ɇ/D)2 = (ɤɪɢɜɵɟ 2 ɢ 8).

ɉɪɢɦɟɪ ɡɚɞɚɱɢ 7.

ɉɨɥɶɡɭɹɫɶ ɬɹɝɨɜɵɦɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ ɫɭɞɧɚ (ɫɦ. ɪɢɫ. 2.3), ɨɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ ɫɜɨɛɨɞɧɨɝɨ ɯɨɞɚ ɫɭɞɧɚ ɩɪɢ ɪɚɛɨɬɟ ɞɜɢɝɚɬɟɥɹ ɧɚ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ.

Ɋɟɲɟɧɢɟ.

ɂɡ ɭɫɥɨɜɢɹ Ɋɟɢɡɛ 0 ɫɤɨɪɨɫɬɶ vsmɚɯ = _ɭɡ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜ ɬɨɱɤɟ

ɩɟɪɟɫɟɱɟɧɢɹ ɤɪɢɜɨɣ 5 ɫ ɨɫɶɸ ɚɛɫɰɢɫɫ. ȼɨɫɫɬɚɜɥɹɹ ɩɟɪɩɟɧɞɢɤɭɥɹɪ ɢɡ ɧɚɣɞɟɧɧɨɣ ɬɨɱɤɢ ɞɨ ɩɟɪɟɫɟɱɟɧɢɹ ɫ ɧɢɠɧɟɣ ɤɪɢɜɨɣ ɫɟɦɟɣɫɬɜɚ 4, ɩɨɥɭɱɢɦ ɇ/D = (ɫɦ. ɩɪɢɦɟɪ 1).

ɉɪɢɦɟɪ ɡɚɞɚɱɢ 8.

Ɉɩɪɟɞɟɥɢɬɶ ɲɚɝɨɜɨɟ ɨɬɧɨɲɟɧɢɟ ȼɊɒ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɪɚɛɨɬɭ ɞɜɢɝɚɬɟɥɹ ɩɨ ɜɟɪɯɧɟɣ ɨɝɪɚɧɢɱɢɬɟɥɶɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɧɚ ɲɜɚɪɬɨɜɧɨɦ ɪɟɠɢɦɟ ɩɪɢ ɱɚɫɬɨɬɟ ɜɪɚɳɟɧɢɹ ɩ = 150 ɦɢɧ-1 (ɪɢɫ. 2.3).

Ɋɟɲɟɧɢɟ.

ȼ ɬɨɱɤɟ ɩɟɪɟɫɟɱɟɧɢɹ ɤɪɢɜɨɣ 4 ɫ ɨɫɶɸ ɨɪɞɢɧɚɬ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ

ɇ/D = 0,915 (ɫɦ. ɩɪɢɦɟɪ 3). ɉɨɥɟɡɧɚɹ ɬɹɝɚ ɜɢɧɬɚ ɩɪɢ ɷɬɨɦ ɫɨɫɬɚɜɥɹɟɬ 51,4 ɤɇ.

ɉɪɢɦɟɪ ɡɚɞɚɱɢ 9.

ɉɨɥɶɡɭɹɫɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ ɫɜɨɛɨɞɧɨɝɨ ɯɨɞɚ cɭɞɧɚ ɜ ɤɨɨɪɞɢɧɚɬɚɯ Nɟ - ɩ (ɪɢɫ. 2.5), ɨɩɪɟɞɟɥɢɬɶ ɧɚɢɛɨɥɶɲɭɸ ɞɨɫɬɢɠɢɦɭɸ ɫɤɨɪɨɫɬɶ ɫɭɞɧɚ ɩɪɢ ɪɚɛɨɬɟ ɞɜɢɝɚɬɟɥɹ ɧɚ ɧɨɦɢɧɚɥɶɧɨɦ ɪɟɠɢɦɟ.

Ɋɟɲɟɧɢɟ.

ɇɚɯɨɞɢɦ ɧɚ ɜɟɪɯɧɟɣ ɨɝɪɚɧɢɱɢɬɟɥɶɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɞɜɢɝɚɬɟɥɹ ɬɨɱɤɭ ɫ ɩɚɪɚɦɟɬɪɚɦɢ ɧɨɦɢɧɚɥɶɧɨɝɨ ɪɟɠɢɦɚ (Nɟ = 1765 ɤȼɬ, ɩ = 225 ɦɢɧ-1). ɍɫɬɚɧɚɜɥɢɜɚɟɦ ɫɤɨɪɨɫɬɶ ɫɭɞɧɚ (vs ɭɡ) ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɲɚɝɨɜɨɟ ɨɬɧɨɲɟɧɢɟ ȼɊɒ ɇ/D = ___ .

ɉɪɢɦɟɪ ɡɚɞɚɱɢ 10.

ȼɪɟɡɭɥɶɬɚɬɟ ɧɟɢɫɩɪɚɜɧɨɫɬɢ ɦɟɯɚɧɢɡɦɚ ɢɡɦɟɧɟɧɢɹ ɲɚɝɚ ȼɊɒ ɟɝɨ ɥɨɩɚɫɬɢ ɨɫɬɚɥɢɫɶ ɡɚɮɢɤɫɢɪɨɜɚɧɧɵɦɢ ɜ ɩɨɥɨɠɟɧɢɢ, ɩɪɢ ɤɨɬɨɪɨɦ ɇ/D = 0,98. Ɉɩɪɟɞɟɥɢɬɶ ɧɚɢɛɨɥɶɲɭɸ ɞɨɫɬɢɠɢɦɭɸ ɫɤɨɪɨɫɬɶ ɫɭɞɧɚ ɛɟɡ ɩɟɪɟɝɪɭɡɤɢ ɝɥɚɜɧɨɝɨ ɞɜɢɝɚɬɟɥɹ (ɪɢɫ. 2.5).

Ɋɟɲɟɧɢɟ.

ȼɬɨɱɤɟ ɩɟɪɟɫɟɱɟɧɢɹ ɜɢɧɬɨɜɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɇ/D = 0,98 ɫ ɜɟɪɯɧɟɣ

ɨɝɪɚɧɢɱɢɬɟɥɶɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɞɜɢɝɚɬɟɥɹ ɨɩɪɟɞɟɥɹɟɦ vs = 12 ɭɡ. Ⱦɨɩɭɫɬɢɦɚɹ ɱɚɫɬɨɬɚ ɜɪɚɳɟɧɢɹ ɞɜɢɝɚɬɟɥɹ ɫɨɫɬɚɜɥɹɟɬ ɩ = 150 ɦɢɧ-1, ɡɚɝɪɭɡɤɚ

—1165 ɤȼɬ.

ɉɪɢɦɟɪ ɡɚɞɚɱɢ 11.

Ʌɨɩɚɫɬɢ ȼɊɒ ɡɚɮɢɤɫɢɪɨɜɚɧɵ ɜ ɩɨɥɨɠɟɧɢɢ, ɩɪɢ ɤɨɬɨɪɨɦ ɇ/D = 0,3. Ɉɩɪɟɞɟɥɢɬɶ ɧɚɢɛɨɥɶɲɭɸ ɞɨɫɬɢɠɢɦɭɸ ɫɤɨɪɨɫɬɶ ɫɭɞɧɚ ɢ ɩɚɪɚɦɟɬɪɵ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ (ɪɢɫ. 2.5).

Ɋɟɲɟɧɢɟ.

ȼ ɬɨɱɤɟ ɩɟɪɟɫɟɱɟɧɢɹ ɜɢɧɬɨɜɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɇ/D = 0,3 ɫ ɨɪɞɢɧɚɬɨɣ ɧɨɦɢɧɚɥɶɧɨɣ ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ ɞɜɢɝɚɬɟɥɹ ɩ = 225 ɦɢɧ-1 ɨɩɪɟɞɟɥɹɟɦ vs = 9 ɭɡ,

Nɟ = 920 ɤȼɬ.

ɉɪɢɦɟɪ ɡɚɞɚɱɢ 12

ɋɤɨɪɨɫɬɶ ɫɭɞɧɚ vs = 9 ɭɡ. ɍɫɬɚɧɨɜɢɬɶ ɧɟɨɛɯɨɞɢɦɨɟ ɲɚɝɨɜɨɟ ɨɬɧɨɲɟɧɢɟ ȼɊɒ ɢ ɩɚɪɚɦɟɬɪɵ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ (ɪɢɫ. 2.5).

Ɋɟɲɟɧɢɟ.

ɇɚ ɤɪɢɜɨɣ vs = 9 ɭɡ ɧɚɯɨɞɢɦ ɧɢɡɲɭɸ ɬɨɱɤɭ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɦɢɧɢɦɭɦɭ ɩɨɬɪɟɛɥɹɟɦɨɣ ɦɨɳɧɨɫɬɢ (Ne = 440 ɤȼɬ). ɑɟɪɟɡ ɷɬɭ ɬɨɱɤɭ ɩɪɨɯɨɞɢɬ ɨɪɞɢɧɚɬɚ

n= 125 ɦɢɧ-1 ɢ ɤɪɢɜɚɹ ɇ/D = 0,8.

ɉɪɢɦɟɪ ɡɚɞɚɱɢ 13.

ɇɟɢɫɩɪɚɜɟɧ ȼɍɒ. ɉɨ ɬɚɯɨɦɟɬɪɭ ɭɫɬɚɧɨɜɥɟɧɚ ɱɚɫɬɨɬɚ ɜɪɚɳɟɧɢɹ ɞɜɢɝɚɬɟɥɹ n = 170 ɦɢɧ-1, ɩɨ ɥɚɝɭ — ɫɤɨɪɨɫɬɶ ɫɭɞɧɚ vs = 11 ɭɡ. ɇɚɣɬɢ ɲɚɝɨɜɨɟ ɨɬɧɨɲɟɧɢɟ ȼɊɒ ɢ ɡɚɝɪɭɡɤɭ ɞɜɢɝɚɬɟɥɹ (ɪɢɫ. 2.5).

Ɋɟɲɟɧɢɟ.

ȼ ɩɟɪɟɫɟɱɟɧɢɢ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɪɹɦɨɣ n = 170 ɦɢɧ-1 ɢ ɤɪɢɜɨɣ vs = 11 ɭɡ ɨɩɪɟɞɟɥɹɟɦ ɬɨɱɤɭ, ɤɨɬɨɪɨɣ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɇ/D = 0,68 ɢ Ne = 860 ɤȼɬ.

ɉɪɢɦɟɪ ɡɚɞɚɱɢ 14.

ɉɨ ɬɚɯɨɦɟɬɪɭ ɭɫɬɚɧɨɜɥɟɧɚ ɱɚɫɬɨɬɚ ɜɪɚɳɟɧɢɹ ɞɜɢɝɚɬɟɥɹ n = 170 ɦɢɧ-1, ɩɨ ɭɤɚɡɚɬɟɥɸ ɲɚɝɚ — ɲɚɝɨɜɨɟ ɨɬɧɨɲɟɧɢɟ ɇ/D = 0,5 . Ɉɩɪɟɞɟɥɢɬɶ ɩɨɬɪɟɛɥɹɟɦɭɸ ɦɨɳɧɨɫɬɶ ɢ ɫɤɨɪɨɫɬɶ ɫɭɞɧɚ (ɪɢɫ. 2.5).

Ɋɟɲɟɧɢɟ.

ȼ ɩɟɪɟɫɟɱɟɧɢɢ ɨɪɞɢɧɚɬɵ n = 170 ɦɢɧ-1 ɢ ɤɪɢɜɨɣ ɇ/D = 0,5 ɧɚɯɨɞɢɦ ɫɤɨɪɨɫɬɶ ɫɭɞɧɚ vs = 9 ɭɡ ɢ ɦɨɳɧɨɫɬɶ ɞɜɢɝɚɬɟɥɹ Ne = 600 ɤȼɬ.

ɉɪɢɦɟɪ ɡɚɞɚɱɢ 15.

ɇɚ ɫɭɞɧɟ ɩɪɢɦɟɧɟɧɚ ɫɢɫɬɟɦɚ ɫɨɜɦɟɫɬɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɝɥɚɜɧɵɦ ɞɜɢɝɚɬɟɥɟɦ ɢ ȼɊɒ. ɉɨɥɶɡɭɹɫɶ ɩɪɨɝɪɚɦɦɧɵɦɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ (ɪɢɫ. 2.8), ɨɩɢɫɚɬɶ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɜɵɜɟɞɟɧɢɹ ȼɊɒ ɢ ɝɥɚɜɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɜ ɨɛɥɚɫɬɶ ɨɩɬɢɦɚɥɶɧɵɯ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ɭɫɬɚɧɨɜɤɢ ɧɚ ɫɜɨɛɨɞɧɨɦ ɯɨɞɭ.

Ɋɟɲɟɧɢɟ.

Ɋɟɠɢɦɭ «ɋɬɨɩ» ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɧɭɥɟɜɨɟ ɩɨɥɨɠɟɧɢɟ ɪɭɤɨɹɬɤɢ ɭɩɪɚɜɥɟɧɢɹ (H/D = -0,04, ɪɢɫ. 2.8). ɍɜɟɥɢɱɟɧɢɟ ɫɤɨɪɨɫɬɢ ɫɭɞɧɚ ɞɨ vs § 4,5 ɭɡ ɩɪɨɢɡɜɨɞɢɬɫɹ ɩɟɪɟɜɨɞɨɦ ɪɭɤɨɹɬɤɢ ɜ ɩɨɥɨɠɟɧɢɟ 3,5 ɩɪɢ ɧɟɢɡɦɟɧɧɨɣ ɱɚɫɬɨɬɟ ɜɪɚɳɟɧɢɹ

(n § 105 ɦɢɧ-1). Ⱦɚɥɶɧɟɣɲɟɟ ɭɜɟɥɢɱɟɧɢɟ ɫɤɨɪɨɫɬɢ ɫɭɞɧɚ ɞɨ vs § 7 ɭɡ ɫɨɩɪɨɜɨɠɞɚɟɬɫɹ ɨɞɧɨɜɪɟɦɟɧɧɵɦ ɭɜɟɥɢɱɟɧɢɟɦ ɲɚɝɚ ɜɢɧɬɚ (ɪɭɤɨɹɬɤɚ ɭɩɪɚɜɥɟɧɢɹ ɩɟɪɟɜɨɞɢɬɫɹ ɜ ɩɨɥɨɠɟɧɢɟ 5, H/D ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɨɬ 0,6 ɞɨ 0,8) ɢ ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ ɞɜɢɝɚɬɟɥɹ (ɞɨ 127 ɦɢɧ-1). ɉɟɪɟɜɨɞ ɩɪɨɩɭɥɶɫɢɜɧɨɝɨ ɤɨɦɩɥɟɤɫɚ ɧɚ ɩɨɥɧɵɣ ɯɨɞ ɜ ɨɛɥɚɫɬɢ ɧɚɢɛɨɥɟɟ ɷɤɨɧɨɦɢɱɧɵɯ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ɜɵɩɨɥɧɹɟɬɫɹ ɩɪɢ ɧɟɢɡɦɟɧɧɨɦ ɲɚɝɨɜɨɦ ɨɬɧɨɲɟɧɢɢ ȼɊɒ ( H/D = 0,79) ɡɚ ɫɱɟɬ ɭɜɟɥɢɱɟɧɢɹ ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ ɞɜɢɝɚɬɟɥɹ ɞɨ ɧɨɦɢɧɚɥɶɧɨɣ ( n = 200 ɦɢɧ-1). ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɟɪɟɜɨɞ ɪɭɤɨɹɬɤɢ ɭɩɪɚɜɥɟɧɢɹ ɢɡ ɩɨɥɨɠɟɧɢɹ 5 ɜ ɩɨɥɨɠɟɧɢɟ 7,75 ɫɨɩɪɨɜɨɠɞɚɟɬɫɹ ɬɨɥɶɤɨ ɢɡɦɟɧɟɧɢɟɦ ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ ɞɜɢɝɚɬɟɥɹ.

ɉɪɢɦɟɪ ɡɚɞɚɱɢ 16.

Ɉɩɪɟɞɟɥɢɬɶ ɪɚɫɯɨɞ ɬɨɩɥɢɜɚ ɝɥɚɜɧɵɦ ɞɜɢɝɚɬɟɥɟɦ ɩɪɢ ɜɪɚɳɟɧɢɢ ɝɪɟɛɧɨɝɨ ɜɢɧɬɚ ɧɚ «ɯɨɥɨɫɬɨɦ» ɯɨɞɭ (ɫɦ. ɪɢɫ. 2.9).

Ɋɟɲɟɧɢɟ.

ȼ ɩɨɥɨɠɟɧɢɢ ɧɭɥɟɜɨɝɨ ɭɩɨɪɚ ȼɊɒ (vs = 0, ɇ/D = -0,04) ɱɚɫɨɜɨɣ ɪɚɫ ɯɨɞ ɬɨɩɥɢɜɚ ɢɡɦɟɧɹɟɬɫɹ ɨɬ Gɱɬ 1 = ɤɝ/ɱ ɩɪɢ ɦɢɧɢɦɚɥɶɧɨ ɭɫɬɨɣɱɢɜɨɣ ɱɚɫɬɨɬɟ

ɜɪɚɳɟɧɢɹ 80 ɨɛ/ɦɢɧ ɞɨ Gɱɬ 2 = ɤɝ/ɱ ɩɪɢ ɧɨɦɢɧɚɥɶɧɨɣ ɱɚɫɬɨɬɟ ɜɪɚɳɟɧɢɹ

200 ɦɢɧ-1.

ɉɪɢɦɟɪ ɡɚɞɚɱɢ 17.

Ɉɩɪɟɞɟɥɢɬɶ ɪɚɫɯɨɞ ɬɨɩɥɢɜɚ ɝɥɚɜɧɵɦ ɞɜɢɝɚɬɟɥɟɦ ɩɪɢ ɞɜɢɠɟɧɢɢ ɩɨɥɧɵɦ ɯɨɞɨɦ (ɪɢɫ. 2.9).

Ɋɟɲɟɧɢɟ.

ȼ ɬɨɱɤɟ ɩɟɪɟɫɟɱɟɧɢɹ ɨɪɞɢɧɚɬɵ ɩ = 200 ɦɢɧ-1 ɫ ɜɢɧɬɨɜɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɩɪɢ ɇ/D = 0,79 ɨɩɪɟɞɟɥɹɟɦ ɫɤɨɪɨɫɬɶ ɫɭɞɧɚ vs §13 ɭɡ ɢ ɱɚɫɨɜɨɣ ɪɚɫɯɨɞ ɬɨɩɥɢɜɚ Gɱɬ = ɤɝ/ɱ.

ɉɪɢɦɟɪ ɡɚɞɚɱɢ 18.

ɉɨɥɶɡɭɹɫɶ ɞɢɚɝɪɚɦɦɨɣ ɯɨɞɤɨɫɬɢ ɫɭɞɧɚ ɩɪɢ ɩɨɫɬɨɹɧɧɨɣ ɧɨɦɢɧɚɥɶɧɨɣ ɱɚɫɬɨɬɟ ɜɪɚɳɟɧɢɹ ɜɢɧɬɚ (ɪɢɫ. 2.11), ɨɩɪɟɞɟɥɢɬɶ ɧɚɢɛɨɥɶɲɭɸ ɫɤɨɪɨɫɬɶ ɫɜɨɛɨɞɧɨɝɨ ɯɨɞɚ ɜ ɫɥɭɱɚɟ ɪɚɛɨɬɵ ɧɚ ɜɢɧɬ ɞɜɭɯ ɝɥɚɜɧɵɯ ɞɜɢɝɚɬɟɥɟɣ ɢ ɜɚɥɨɦɨɬɨɪɚ ɫɭɦɦɚɪɧɨɣ ɦɨɳɧɨɫɬɶɸ Nɟ = 1215 ɤȼɬ.

Ɋɟɲɟɧɢɟ.

Ɂɚɞɚɧɧɨɣ ɦɨɳɧɨɫɬɢ ɧɚ ɤɪɢɜɨɣ 1 ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɤɨɪɨɫɬɶ vs mɚɯ = 12,5 ɭɡ, ɞɥɹ ɞɨɫɬɢɠɟɧɢɹɤɨɬɨɪɨɣɥɨɩɚɫɬɢȼɊɒɞɨɥɠɧɵɛɵɬɶɪɚɡɜɟɪɧɭɬɵɩɨɞɭɝɥɨɦij= 210.

ɉɪɢɦɟɪ ɡɚɞɚɱɢ 19.

ɉɨɥɶɡɭɹɫɶ ɪɢɫ. 2.11, ɜɵɛɪɚɬɶ ɜɚɪɢɚɧɬ ɜɤɥɸɱɟɧɢɹ ɷɧɟɪɝɟɬɢɱɟɫɤɨɣ ɭɫɬɚɧɨɜɤɢ ɞɥɹ ɞɜɢɠɟɧɢɹ ɫɭɞɧɚ ɫɨ ɫɤɨɪɨɫɬɶɸ vs = 10 ɭɡ.

Ɋɟɲɟɧɢɟ.

Ɂɚɞɚɧɧɨɣ ɫɤɨɪɨɫɬɢ ɧɚ ɤɪɢɜɨɣ 1 ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɦɨɳɧɨɫɬɶ ɭɫɬɚɧɨɜɤɢ

Ne = 500 ɤȼɬ ɤɨɬɨɪɚɹ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɜɤɥɸɱɟɧɢɟɦ ɨɞɧɨɝɨ ɝɥɚɜɧɨɝɨ ɞɜɢɝɚɬɟɥɹ

(Ne = 493 ɤȼɬ.). ɋɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɭɝɨɥ ɪɚɡɜɨɪɨɬɚ ɥɨɩɚɫɬɟɣ ȼɊɒ ɫɨɫɬɚɜɥɹɟɬ ij = 130.

ɉɪɢɦɟɪ ɡɚɞɚɱɢ 20.

Ɉɩɪɟɞɟɥɢɬɶ ɦɨɳɧɨɫɬɶ, ɧɟɨɛɯɨɞɢɦɭɸ ɞɥɹ ɜɪɚɳɟɧɢɹ ɝɪɟɛɧɨɝɨ ɜɢɧɬɚ ɧɚ ɪɟɠɢɦɟ «ɋɬɨɩ» (ɪɢɫ. 2.11).

Ɋɟɲɟɧɢɟ.

Ɇɵɫɥɟɧɧɨ ɩɪɨɞɨɥɠɢɜ ɨɫɶ ɚɛɰɢɫɫ, ɚ ɬɚɤɠɟ ɤɪɢɜɵɟ 1 ɢ 2 ɜɥɟɜɨ ɢ ɩɪɨɜɟɞɹ ɨɪɞɢɧɚɬɭ vs = 0, ɭɫɬɚɧɚɜɥɢɜɚɟɦ Ne = 200 ɤȼɬ, ij = 00.

ɉɪɢɦɟɪ ɡɚɞɚɱɢ 21.

ɉɨɥɶɡɭɹɫɶ ɞɢɚɝɪɚɦɦɨɣ ɯɨɞɤɨɫɬɢ ɫɭɞɧɚ ɩɪɢ ɩɨɫɬɨɹɧɧɨɣ ɧɨɦɢɧɚɥɶɧɨɣ ɱɚɫɬɨɬɟ ɜɪɚɳɟɧɢɹ ɜɢɧɬɚ (ɪɢɫ. 2.12), ɨɩɪɟɞɟɥɢɬɶ ɩɨɥɨɠɟɧɢɟ ɪɭɤɨɹɬɤɢ ɜɵɧɨɫɧɨɝɨ ɭɤɚɡɚɬɟɥɹ ɲɚɝɚ ȼɊɒ, ɧɟɨɛɯɨɞɢɦɨɟ ɞɥɹ ɞɜɢɠɟɧɢɹ ɫɨ ɫɤɨɪɨɫɬɶɸ vs = 14 ɭɡ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɡɚɝɪɭɡɤɭ ɞɜɢɝɚɬɟɥɟɣ ɢ ɱɚɫɨɜɨɣ ɪɚɫɯɨɞ ɬɨɩɥɢɜɚ.

Ɋɟɲɟɧɢɟ.

ȼ ɩɟɪɟɫɟɱɟɧɢɢ ɝɨɪɢɡɨɧɬɚɥɢ ɧɚ ɭɪɨɜɧɟ 14 ɭɡ ɫ ɤɪɢɜɨɣ vs, ɨɩɪɟɞɟɥɹɟɦ ɩɨɥɨɠɟɧɢɟ ɪɭɤɨɹɬɤɢ ȼɍɒ ɉ = 7,6 . ɗɬɨɦɭ ɩɨɥɨɠɟɧɢɸ ɧɚ ɤɪɢɜɨɣ Nɟ

ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɦɨɳɧɨɫɬɶ 3500 ɤȼɬ, ɚ ɧɚ ɤɪɢɜɨɣ Gɱɬ — ɱɚɫɨɜɨɣ ɪɚɫɯɨɞ ɬɨɩɥɢɜɚ 620 ɤɝ/ɱ.

ɉɪɢɦɟɪ ɡɚɞɚɱɢ 22.

ɉɨɥɶɡɭɹɫɶ ɪɢɫ 2.12, ɨɩɪɟɞɟɥɢɬɶ ɩɨɬɪɟɛɥɹɟɦɭɸ ɜɪɚɳɚɸɳɢɦɫɹ ɜɢɧɬɨɦ ɦɨɳɧɨɫɬɶ ɢ ɪɚɫɯɨɞ ɬɨɩɥɢɜɚ ɜ ɪɟɠɢɦɟ «ɋɬɨɩ».

Ɋɟɲɟɧɢɟ.

ȼ ɩɨɥɨɠɟɧɢɢ ɪɭɤɨɹɬɤɢ ȼɍɒ ɉ § ___ (vs = 0 ) ɧɚ ɥɟɜɨɣ ɲɤɚɥɟ ɨɩɪɟɞɟɥɹɟɦ Nɟ = ɤȼɬ, ɚ ɧɚ ɜɵɧɨɫɧɨɣ ɲɤɚɥɟ — Gɱɬ= ___ ɤɝ/ɱ.

Ʉɨɧɬɪɨɥɶɧɵɟ ɜɨɩɪɨɫɵ

1.ȼ ɤɚɤɨɦ ɫɥɭɱɚɟ ȽȾ ɪɚɛɨɬɚɟɬ ɩɨ ɜɢɧɬɨɜɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ?

2.ɑɟɦ ɨɬɥɢɱɚɸɬɫɹ ɭɩɪɚɜɥɟɧɢɹ ɝɥɚɜɧɵɦ ɞɜɢɝɚɬɟɥɟɦ ɫɭɞɧɚ ɫ ȼɊɒ ɢ ɫ ȼɎɒ?

3.Ʉɚɤɢɟ ɨɫɧɨɜɧɵɟ ɜɨɡɦɨɠɧɵɟ ɪɟɠɢɦɵ ɪɚɛɨɬɚ ȽȾ ɢ Ƚȼ ɦɨɠɧɨ ɨɫɭɳɟɫɬɜɢɬɶ ɜ ɭɫɬɚɧɨɜɤɟ ɫ ȼɊɒ?

4.ɉɨɱɟɦɭ ɩɪɢ ɪɚɛɨɬɟ ɧɚ ȼɊɒ ɭɫɥɨɜɢɹ ɪɚɛɨɬɵ ɞɥɹ ɩɟɪɟɝɪɭɡɤɢ ȽȾ ɫɬɚɧɨɜɹɬɫɹ ɛɨɥɟɟ ɜɟɪɨɹɬɧɵɦɢ?

5.ɑɬɨ ɬɚɤɨɟ ɪɟɝɭɥɹɬɨɪ ɧɚɝɪɭɡɤɢ ɢ ɞɥɹ ɤɚɤɢɯ ɰɟɥɟɣ ɨɧ ɩɪɟɞɧɚɡɧɚɱɟɧ?

6.Ʉɚɤɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɫɭɳɟɫɬɜɭɟɬ ɦɟɠɞɭ ɫɤɨɪɨɫɬɶɸ ɫɭɞɧɚ ɢ ɲɚɝɨɦ ȼɊɒ?

7.Ʉɚɤɢɟ ɨɝɪɚɧɢɱɢɬɟɥɶɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ȽȾ ɫɭɳɟɫɬɜɭɸɬ ɩɪɢ ɪɚɛɨɬɟ ɧɚ ȼɊɒ?

ɉɪɚɤɬɢɱɟɫɤɨɟ ɡɚɧɹɬɢɟ ʋ3 (4 ɱɚɫɚ)

ɂɋɋɅȿȾɈȼȺɇɂȿ ȻȿɁɈɉȺɋɇɕɏ ɊȿɀɂɆɈȼ ɊȺȻɈɌɕ ȽɅȺȼɇɈȽɈ ɋɍȾɈȼɈȽɈ ȾɂɁȿɅə ɋ ȽȺɁɈɌɍɊȻɂɇɇɕɆ ɇȺȾȾɍȼɈɆ

ɐɟɥɶ ɡɚɧɹɬɢɹ. ɇɚɭɱɢɬɶɫɹ ɩɪɨɢɡɜɨɞɢɬɶ ɜɵɛɨɪ ɢ ɚɧɚɥɢɡ ɛɟɡɨɩɚɫɧɵɯ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ɝɥɚɜɧɨɝɨ ɫɭɞɨɜɨɝɨ ɞɢɡɟɥɹ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɨɝɪɚɧɢɱɢɬɟɥɶɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɨ ɫɪɟɞɧɟɦɭ ɢɧɞɢɤɚɬɨɪɧɨɦɭ ɞɚɜɥɟɧɢɸ ɜ ɭɫɥɨɜɢɹɯ ɷɤɫɩɥɭɚɬɚɰɢɢ.

Ɂɚɞɚɧɢɟ.

1.ɉɨ ɢɫɯɨɞɧɵɦ ɬɚɤɬɢɤɨ-ɬɟɯɧɢɱɟɫɤɢɦ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦ ɝɥɚɜɧɨɝɨ ɫɭɞɨɜɨɝɨ ɞɢɡɟɥɹ ɩɪɨɢɡɜɟɫɬɢ ɪɚɫɱɟɬ ɢ ɩɨɫɬɪɨɟɧɢɟ ɨɝɪɚɧɢɱɢɬɟɥɶɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɞɥɹ ɤɪɚɬɤɨɜɪɟɦɟɧɧɨɝɨ ɢ ɞɥɢɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ ɟɝɨ ɪɚɛɨɬɵ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɫɢɫɬɟɦɵ ɧɚɞɞɭɜɚ ɞɢɡɟɥɹ.

2.ɉɪɨɢɡɜɟɫɬɢ ɪɚɫɱɟɬ ɢ ɩɨɫɬɪɨɟɧɢɟ ɜɢɧɬɨɜɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɜ ɩɪɟɞɟɥɚɯ ɩɨɥɟɣ ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɵɯ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ɝɥɚɜɧɨɝɨ ɫɭɞɨɜɨɝɨ ɞɢɡɟɥɹ.

3.ɉɪɨɢɡɜɟɫɬɢ ɚɧɚɥɢɡ ɛɟɡɨɩɚɫɧɵɯ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ɝɥɚɜɧɨɝɨ ɫɭɞɨɜɨɝɨ ɞɢɡɟɥɹ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɨɝɪɚɧɢɱɢɬɟɥɶɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɨ ɫɪɟɞɧɟɦɭ ɢɧɞɢɤɚɬɨɪɧɨɦɭ ɞɚɜɥɟɧɢɸ ɜ ɭɫɥɨɜɢɹɯ ɷɤɫɩɥɭɚɬɚɰɢɢ.

1. Ɉɛɳɢɟ ɫɜɟɞɟɧɢɹ

ɉɪɢ ɥɸɛɵɯ ɪɟɠɢɦɚɯ ɪɚɛɨɬɵ ɞɢɡɟɥɹ ɟɝɨ ɦɟɯɚɧɢɱɟɫɤɚɹ ɢ ɬɟɩɥɨɜɚɹ ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɧɟ ɞɨɥɠɧɚ ɩɪɟɜɵɲɚɬɶ ɧɨɦɢɧɚɥɶɧɵɯ ɡɧɚɱɟɧɢɣ. Ɋɚɡɥɢɱɚɸɬ ɞɜɚ ɜɢɞɚ ɨɝɪɚɧɢɱɢɬɟɥɶɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ:

1.ɉɨ ɬɨɩɥɢɜɧɨɦɭ ɧɚɫɨɫɭ: ɧɟ ɞɨɩɭɫɤɚɟɬɫɹ ɞɚɠɟ ɤɪɚɬɤɨɜɪɟɦɟɧɧɚɹ ɩɟɪɟɝɪɭɡɤɚ ɞɢɡɟɥɹ, ɤɪɨɦɟ ɫɥɭɱɚɟɜ, ɫɜɹɡɚɧɧɵɯ ɫ ɭɝɪɨɡɨɣ ɱɟɥɨɜɟɱɟɫɤɨɣ ɠɢɡɧɢ ɢɥɢ ɛɟɡɨɩɚɫɧɨɫɬɶɸ ɫɭɞɧɚ. Ɍɚɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɹɜɥɹɟɬɫɹ ɜɧɟɲɧɹɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɦɚɤɫɢɦɚɥɶɧɨɣ ɦɨɳɧɨɫɬɢ.

2.ɉɨ ɬɟɩɥɨɜɨɣ ɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɧɚɩɪɹɠɟɧɧɨɫɬɢ: ɧɟ ɞɨɩɭɫɤɚɸɬɫɹ ɩɟɪɟɝɪɭɡɤɢ ɞɢɡɟɥɹ ɩɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɞɥɢɬɟɥɶɧɨɣ ɪɚɛɨɬɵ ɧɚ ɞɚɧɧɨɦ ɪɟɠɢɦɟ.

Ⱦɥɹ ɫɭɞɨɜɵɯ ɝɥɚɜɧɵɯ ɞɢɡɟɥɟɣ ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɨɝɪɚɧɢɱɢɜɚɬɶ ɧɚɝɪɭɡɤɭ

ɞɢɡɟɥɹ ɩɨ ɧɨɦɢɧɚɥɶɧɨɦɭ ɤɪɭɬɹɳɟɦɭ ɦɨɦɟɧɬɭ Ɇɟɧɨɦ=const (ɩɨ ɧɨɦɢɧɚɥɶɧɨɦɭ ɫɪɟɞɧɟɦɭ ɢɧɞɢɤɚɬɨɪɧɨɦɭ ɞɚɜɥɟɧɢɸ ɪɿɧɨɦ=const. ɉɪɢ ɷɬɨɦ ɤɪɨɦɟ ɨɝɪɚɧɢɱɟɧɢɹ ɩɨ ɪɿ, ɧɚɤɥɚɞɵɜɚɸɬɫɹ ɨɝɪɚɧɢɱɟɧɢɹ ɩɨ ɦɚɤɫɢɦɚɥɶɧɨɦɭ ɞɚɜɥɟɧɢɸ ɫɝɨɪɚɧɢɹ ɪz ɢ ɬɟɦɩɟɪɚɬɭɪɟ ɜɵɩɭɫɤɧɵɯ ɝɚɡɨɜ Ɍɝ. ɗɬɢ ɪɟɤɨɦɟɧɞɚɰɢɢ ɩɪɢɦɟɧɹɸɬɫɹ ɞɥɹ ɱɟɬɵɪɟɯɬɚɤɬɧɵɯ ɞɢɡɟɥɟɣ ɛɟɡ ɧɚɞɞɭɜɚ.

Ɉɛɴɹɫɧɹɟɬɫɹ ɷɬɨ ɬɟɦ, ɱɬɨ ɩɪɢ ɭɦɟɧɶɲɟɧɢɢ ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ ɢ ɩɪɢ ɧɟɢɡɦɟɧɧɨɣ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɟ q=const ɩɥɨɬɧɨɫɬɶ ɡɚɪɹɞɚ ɜ ɰɢɥɢɧɞɪɟ ɧɟ ɬɨɥɶɤɨ ɧɟ ɭɦɟɧɶɲɚɟɬɫɹ, ɧɨ ɞɚɠɟ ɧɟɫɤɨɥɶɤɨ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɜɫɥɟɞɫɬɜɢɟ ɪɨɫɬɚ ɤɨɷɮɮɢɰɢɟɧɬɚ ɧɚɩɨɥɧɟɧɢɹ ɉɪɨɰɟɫɫ ɫɝɨɪɚɧɢɹ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɛɟɡ ɭɦɟɧɶɲɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɚ ɢɡɛɵɬɤɚ ɜɨɡɞɭɯɚ, ɱɬɨ ɩɪɟɞɨɯɪɚɧɹɟɬ ɞɢɡɟɥɶ ɨɬ ɬɟɩɥɨɜɵɯ ɩɟɪɟɝɪɭɡɨɤ.