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Файл:Методология расчётов гидродинамических параметров шахтных автоматизированных стационарных установок с центробежными нагнетателями. Монография
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– ɞɥɹ ɤɨɧɬɪɨɥɹ ɬɟɦɩɟɪɚɬɭɪɵ ɩɨɞɲɢɩɧɢɤɨɜ, ɨɛɦɨɬɨɤ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɹ ɢ ɦɚɫɥɚ – ɚɩɩɚɪɚɬɭɪɨɣ ȺɄɌ-2 ɫ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɬɟɪɦɨɞɚɬɱɢɤɚɦɢ
(ɜɡɚɦɟɧ ɌȾɅ-2 ɢ ȾɌɊ-3);
– ɞɥɹ ɤɨɧɬɪɨɥɹ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ – ɪɚɫɯɨɞɨɦɟɪɨɦ ȾɆɂ-Ɋ ɫ
ɫɭɠɚɸɳɟɣ ɜɫɬɚɜɤɨɣ ɩɨɥɧɨɝɨ ɞɚɜɥɟɧɢɹ;
– ɞɥɹ ɤɨɧɬɪɨɥɹ ɞɚɜɥɟɧɢɹ (ɞɟɩɪɟɫɫɢɢ) ɜɟɧɬɢɥɹɬɨɪɚ – ɧɚɩɨɪɨɦɟɪɨɦ
ȾɆɂ-Ɍ ɢɥɢ ɚɩɩɚɪɚɬɨɦ ȾɄɌȼ ɫ ɢɧɞɭɤɰɢɨɧɧɵɦɢ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹɦɢ.
2. Ⱦɥɹ ɧɚɫɨɫɧɵɯ ɭɫɬɚɧɨɜɨɤ ɝɥɚɜɧɨɝɨ ɜɨɞɨɨɬɥɢɜɚ
ɲɚɯɬɵ – ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɩɨɞɚɱɢ ɞɪɨɫɫɟɥɢɪɨɜɚɧɢɟɦ ɬɪɭɛɨɩɪɨɜɨɞɧɨɣ ɫɟɬɢ (ɩɪɢ ɝɥɭɛɢɧɟ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɞɨ 28 %):
– ɩɨɞɜɨɞɨɦ ɪɚɫɱɺɬɧɨɝɨ ɤɨɥɢɱɟɫɬɜɚ ɜɨɡɞɭɯɚ ɜɨ ɜɫɚɫ ɧɚɫɨɫɚ (ɩɪɢ
ɪɟɝɭɥɢɪɨɜɚɧɢɢ ɧɚ ɩɪɢɬɨɤ ɫ ɝɥɭɛɢɧɨɣ 50 %;
– ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɢɡɦɟɧɟɧɢɟɦ ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ ɪɚɛɨɱɟɝɨ ɤɨɥɟɫɚ
ɧɚɫɨɫɚ ɩɪɢ ɩɨɦɨɳɢ ɪɟɝɭɥɢɪɭɟɦɨɝɨ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɢɥɢ ɩɪɢ ɩɨɦɨɳɢ
ɝɢɞɪɚɜɥɢɱɟɫɤɢɯ (ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯ) ɦɭɮɬ (ɩɪɢ ɝɥɭɛɢɧɟ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɞɨ
20 % ɢ ɛɨɥɟɟ).
Ⱦɥɹ
ɪɟɚɥɢɡɚɰɢɢ ɷɬɢɯ ɫɩɨɫɨɛɨɜ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɦɨɝɭɬ ɛɵɬɶ ɪɟɤɨɦɟɧ-
ɞɨɜɚɧɵ:
– ɞɪɨɫɫɟɥɶɧɵɟ ɭɫɬɪɨɣɫɬɜɚ – ɡɚɞɜɢɠɤɢ ɫ ɷɥɟɤɬɪɢɱɟɫɤɢɦ ɩɪɢɜɨɞɨɦ,
ɞɨɩɨɥɧɟɧɧɵɟ ɩɨɬɟɧɰɢɨɦɟɬɪɢɱɟɫɤɢɦ ɞɚɬɱɢɤɨɦ ɩɨɥɨɠɟɧɢɹ ɲɬɨɤɚ ɪɚɛɨɱɟɝɨ
ɨɪɝɚɧɚ;
– ɱɚɫɬɨɬɧɨ ɭɩɪɚɜɥɹɟɦɵɣ ɷɥɟɤɬɪɨɩɪɢɜɨɞ, ɨɬɜɟɱɚɸɳɢɣ ɬɪɟɛɨɜɚɧɢɹɦ
ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɜɨ ɜɥɚɠɧɨɣ ɢ ɜɡɪɵɜɨɨɩɚɫɧɨɣ ɲɚɯɬɧɨɣ ɚɬɦɨɫɮɟɪɟ;
– ɝɢɞɪɚɜɥɢɱɟɫɤɢɟ ɢɥɢ ɦɚɝɧɢɬɧɵɟ ɦɭɮɬɵ (ɩɪɢ ɧɟɪɟɝɭɥɢɪɭɟɦɨɦ ɷɥɟɤɬɪɨɩɪɢɜɨɞɟ) ɫ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɦɢ ɢ ɝɚɛɚɪɢɬɧɵɦɢ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ.
Ⱦɥɹ ɤɨɧɬɪɨɥɹ
ɪɟɝɭɥɢɪɭɟɦɵɯ ɩɚɪɚɦɟɬɪɨɜ ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɩɪɢɦɟɧɟɧɢɟ:
ɚɧɚɥɨɝɨɜɵɯ ɝɢɞɪɨɫɬɚɬɢɱɟɫɤɢɯ ɭɪɨɜɧɟɦɟɪɨɜ ɫ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨ-ɬɪɚɧɫɮɨɪɦɚɬɨɪɧɵɦɢ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹɦɢ ɢ ɫɬɚɧɞɚɪɬɧɵɦ ɬɨɤɨɜɵɦ (ɩɨɬɟɧɰɢɚɥɶɧɵɦ)
ɜɵɯɨɞɨɦ; ɢɧɞɭɤɰɢɨɧɧɵɯ ɪɚɫɯɨɞɨɦɟɪɨɜ ɬɢɩɚ ɂɊ ɫ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ
ɭɫɥɨɜɧɵɦɢ ɩɪɨɯɨɞɚɦɢ; ɦɚɧɨɜɚɤɭɭɦɦɟɬɪɨɜ ɢ ɦɚɧɨɦɟɬɪɨɜ ɬɢɩɚ ȾɆ, ȾɆɂɊ,
Ɇɋ ɫ ɷɥɟɤɬɪɢɱɟɫɤɢɦ ɜɵɯɨɞɨɦ, ɩɪɢɝɨɞɧɵɦ ɞɥɹ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɜ ɋȺɊ.
3. Ⱦɥɹ ɝɢɞɪɨɬɪɚɧɫɩɨɪɬɧɵɯ ɭɫɬɚɧɨɜɨɤ – ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɩɨɞɚɱɢ ɭɝɥɟ-
ɫɨɫɨɜ ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɜɨɡɦɨɠɧɨ ɩɭɬɺɦ
ɢɡɦɟɧɟɧɢɹ ɩɥɨɬɧɨɫɬɢ ɝɢɞɪɨɫɦɟɫɢ,
ɬɪɚɧɫɩɨɪɬɢɪɭɟɦɨɣ ɩɨ ɧɚɩɨɪɧɨɦɭ ɬɪɭɛɨɩɪɨɜɨɞɭ. Ƚɥɭɛɢɧɚ ɪɟɝɭɥɢɪɨɜɚɧɢɹ
ɩɪɢ ɬɚɤɨɦ ɫɩɨɫɨɛɟ ɜ ɫɬɨɪɨɧɭ ɭɦɟɧɶɲɟɧɢɹ ɩɨɞɚɱɢ ɫɨɫɬɚɜɥɹɟɬ ɩɨɪɹɞɤɚ
15…20 % ɨɬ ɧɨɦɢɧɚɥɚ ɢ ɨɝɪɚɧɢɱɟɧɚ ɨɩɚɫɧɨɫɬɶɸ ɨɫɚɠɞɟɧɢɹ ɬɜɺɪɞɵɯ ɱɚɫɬɢɰ ɧɚ ɞɧɨ ɬɪɭɛɨɩɪɨɜɨɞɚ ɩɪɢ ɫɤɨɪɨɫɬɹɯ ɧɢɠɟ ɤɪɢɬɢɱɟɫɤɢɯ ɞɥɹ ɞɚɧɧɨɝɨ
ɤɥɚɫɫɚ ɱɚɫɬɢɰ:
– ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɫ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɣ ɩɪɨɦɵɜɤɨɣ ɭɱɚɫɬɤɚ ɬɪɚɧɫɩɨɪɬ-
ɧɨɝɨ ɬɪɭɛɨɩɪɨɜɨɞɚ ɡɚ ɭɫɬɚɧɨɜɥɟɧɧɵɦ ɞɪɨɫɫɟɥɟɦ (ɧɟɩɨɥɧɚɹ
ɩɪɨɦɵɜɤɚ) ɫ
61
ɩɨɫɥɟɞɭɸɳɢɦ ɞɪɨɫɫɟɥɢɪɨɜɚɧɢɟɦ ɬɪɚɧɫɩɨɪɬɧɨɝɨ ɬɪɭɛɨɩɪɨɜɨɞɚ ɭɩɪɚɜɥɹɟɦɨɣ ɡɚɞɜɢɠɤɨɣ (ɤɚɤ ɢ ɜ ɫɥɭɱɚɟ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɧɚɫɨɫɨɜ). Ɍɚɤɨɣ ɫɩɨɫɨɛ
ɩɪɢɦɟɧɢɦ ɞɥɹ ɭɱɚɫɬɤɨɜɵɯ ɭɝɥɟɫɨɫɧɵɯ ɭɫɬɚɧɨɜɨɤ;
– ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɫ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɣ ɩɨɥɧɨɣ ɩɪɨɦɵɜɤɨɣ ɬɪɚɧɫɩɨɪɬɧɨɝɨ ɬɪɭɛɨɩɪɨɜɨɞɚ ɫ ɩɨɫɥɟɞɭɸɳɢɦ ɟɝɨ ɞɪɨɫɫɟɥɢɪɨɜɚɧɢɟɦ ɩɪɢɦɟɧɹɟɬɫɹ ɧɚ
ɝɢɞɪɨɩɨɞɴɺɦɟ ɢ ɚɧɚɥɨɝɢɱɟɧ ɪɟɝɭɥɢɪɨɜɚɧɢɸ ɩɨɞɚɱ ɝɥɚɜɧɵɯ ɜɨɞɨɨɬɥɢɜɧɵɯ
ɭɫɬɚɧɨɜɨɤ.
ȼ ɤɚɱɟɫɬɜɟ ɫɪɟɞɫɬɜ ɪɟɚɥɢɡɚɰɢɢ ɫɩɨɫɨɛɨɜ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɢ ɫɪɟɞɫɬɜ
ɤɨɧɬɪɨɥɹ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɭɝɥɟɫɨɫɨɜ ɩɪɢɦɟɧɹɸɬɫɹ ɬɟ ɠɟ
ɫɪɟɞɫɬɜɚ, ɱɬɨ ɢ ɩɪɢ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɧɚɫɨɫɨɜ ɝɥɚɜɧɨɝɨ ɜɨɞɨɨɬɥɢɜɚ. Ɉɬɥɢɱɢɟ
ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɫɩɨɫɨɛɟ ɩɪɢɫɨɟɞɢɧɟɧɢɹ ɢɡɦɟɪɢɬɟɥɶɧɵɯ ɩɪɢɛɨɪɨɜ ɤ
ɬɪɭɛɨɩɪɨɜɨɞɭ ɱɟɪɟɡ ɝɢɞɪɨɫɬɚɬɢɱɟɫɤɢɟ ɪɚɡɞɟɥɢɬɟɥɢ ɫɪɟɞ.
4. Ⱦɥɹ ɬɭɪɛɨɤɨɦɩɪɟɫɫɨɪɧɵɯ ɭɫɬɚɧɨɜɨɤ ɩɪɢɦɟɧɹɸɬɫɹ ɫɩɨɫɨɛɵ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ ɧɚɝɧɟɬɚɬɟɥɟɣ – ɜ ɨɫɧɨɜɧɨɦ ɞɪɨɫɫɟɥɢɪɨɜɚɧɢɟ ɩɨɞɜɨɞɹɳɟɝɨ ɬɪɭɛɨɩɪɨɜɨɞɚ ɩɨɜɨɪɨɬɧɨɣ ɡɚɫɥɨɧɤɨɣ ɫ ɨɞɧɨɜɪɟɦɟɧɧɨɣ
ɩɪɨɬɢɜɨɩɨɦɩɚɠɧɨɣ ɡɚɳɢɬɨɣ ɧɚ
ɧɚɝɧɟɬɚɧɢɢ.
ȼ ɤɚɱɟɫɬɜɟ ɫɪɟɞɫɬɜ ɤɨɧɬɪɨɥɹ ɢɫɩɨɥɶɡɭɸɬɫɹ ɬɟ ɠɟ ɭɫɬɪɨɣɫɬɜɚ ɢ
ɩɪɢɛɨɪɵ, ɱɬɨ ɢ ɩɪɢ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɝɥɚɜɧɵɯ ɜɟɧɬɢɥɹɬɨɪɧɵɯ ɭɫɬɚɧɨɜɨɤ ɫ
ɰɟɧɬɪɨɛɟɠɧɵɦɢ ɧɚɝɧɟɬɚɬɟɥɹɦɢ.
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3. ȺɇȺɅɂɌɂɑȿɋɄɂȿ ɂɋɋɅȿȾɈȼȺɇɂə ɉȺɊȺɆȿɌɊɈȼ
x
ɗɅȿɄɌɊɈɆȿɏȺɇɂɑȿɋɄɂɏ ɋɂɋɌȿɆ ɋ ɅɈɉȺɋɌɇɕɆɂ
ɌɍɊȻɈɆȺɒɂɇȺɆɂ ɊȺȾɂȺɅɖɇɈȽɈ ɌɂɉȺ
Ʉɚɤ ɨɬɦɟɱɚɥɨɫɶ ɜɵɲɟ, ɞɥɹ ɚɧɚɥɢɬɢɱɟɫɤɢɯ ɢɫɫɥɟɞɨɜɚɧɢɣ ɩɚɪɚɦɟɬɪɨɜ
ɨɬɞɟɥɶɧɵɯ ɡɜɟɧɶɟɜ ɢ ɫɢɫɬɟɦ ɭɩɪɚɜɥɟɧɢɹ ɜ ɰɟɥɨɦ ɧɟɨɛɯɨɞɢɦɨ ɪɟɲɢɬɶ ɪɹɞ
ɡɚɞɚɱ, ɫɪɟɞɢ ɤɨɬɨɪɵɯ ɧɚɢɛɨɥɟɟ ɚɤɬɭɚɥɶɧɵɦɢ ɹɜɥɹɸɬɫɹ: ɪɚɡɪɚɛɨɬɤɚ ɦɟɬɨɞɢɤ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɢ ɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɞɥɹ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɨɩɢɫɚɧɢɹ ɩɪɨɰɟɫɫɨɜ, ɩɪɨɢɫɯɨɞɹɳɢɯ ɧɚ ɨɛɴɟɤɬɚɯ
ɞɢɧɚɦɢɤɟ; ɩɨɞɛɨɪ ɷɦɩɢɪɢɱɟɫɤɢɯ ɮɨɪɦɭɥ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ, ɡɚɞɚɧɧɵɯ ɜ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɝɪɚɮɢɱɟɫɤɢ ɢɥɢ ɬɚɛɥɢɱɧɨ; ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ
ɨɩɢɫɚɧɢɹ ɨɬɞɟɥɶɧɵɯ ɡɜɟɧɶɟɜ ɨɛɴɟɤɬɨɜ ɭɩɪɚɜɥɟɧɢɹ; ɨɩɪɟɞɟɥɟɧɢɟ ɝɪɚɧɢɰɵ
ɩɪɢɦɟɧɟɧɢɹ ɩɨɥɭɱɟɧɧɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɡɚɜɢɫɢɦɨɫɬɟɣ ɢ ɨɰɟɧɤɚ ɬɨɱɧɨɫɬɢ ɨɩɪɟɞɟɥɟɧɢɹ ɧɚ ɢɯ ɨɫɧɨɜɟ ɫɬɚɬɢɱɟɫɤɢɯ ɢ ɞɢɧɚɦɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɧɚ ɜɫɟɦ ɞɢɚɩɚɡɨɧɟ ɢɫɫɥɟɞɨɜɚɧɢɹ ɩɚɪɚɦɟɬɪɨɜ; ɪɚɡɪɚɛɨɬɤɚ
ɞɚɰɢɣ ɩɨ ɩɨɜɵɲɟɧɢɸ ɭɪɨɜɧɹ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɲɚɯɬɧɵɯ
ɫɬɚɰɢɨɧɚɪɧɵɯ ɷɧɟɪɝɨɟɦɤɢɯ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɭɫɬɚɧɨɜɨɤ.
3.1. Ɇɟɬɨɞɢɤɚ ɩɨɞɛɨɪɚ ɷɦɩɢɪɢɱɟɫɤɢɯ ɮɨɪɦɭɥ
ɞɥɹ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɨɩɢɫɚɧɢɹ ɫɬɚɬɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ
ɨɬɞɟɥɶɧɵɯ ɡɜɟɧɶɟɜ ɢ ɨɛɴɟɤɬɨɜ ɪɟɝɭɥɢɪɨɜɚɧɢɹ
ɉɨɞɛɨɪ ɷɦɩɢɪɢɱɟɫɤɨɣ ɮɨɪɦɭɥɵ ɞɥɹ ɭɫɬɚɧɨɜɥɟɧɧɨɣ ɢɡ ɨɩɵɬɚ
ɮɭɧɤɰɢɨɧɚɥɶɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ y
ɜɵɛɢɪɚɟɬɫɹ ɜɢɞ ɮɨɪɦɭɥɵ, ɚ ɩɨɫɥɟ ɷɬɨɝɨ ɨɩɪɟɞɟɥɹɸɬɫɹ ɱɢɫɥɟɧɧɵɟ ɡɧɚɱɟɧɢɹ
ɩɚɪɚɦɟɬɪɨɜ, ɞɥɹ ɤɨɬɨɪɵɯ ɩɪɢɛɥɢɠɟɧɢɟ ɤ ɞɚɧɧɨɣ ɮɭɧɤɰɢɢ ɨɤɚɡɵɜɚɟɬɫɹ
ɧɚɢɥɭɱɲɢɦ. ȿɫɥɢ ɧɟɬ ɤɚɤɢɯ-ɥɢɛɨ ɬɟɨɪɟɬɢɱɟɫɤɢɯ ɫɨɨɛɪɚɠɟɧɢɣ ɞɥɹ ɩɨɞɛɨɪɚ
ɜɢɞɚ ɮɨɪɦɭɥɵ, ɨɛɵɱɧɨ ɜɵɛɢɪɚɸɬ ɮɭɧɤɰɢɨɧɚɥɶɧɭɸ ɡɚɜɢɫɢɦɨɫɬɶ ɢɡ ɱɢɫɥɚ
ɧɚɢɛɨɥɟɟ ɩɪɨɫɬɵɯ, ɫɪɚɜɧɢɜɚɹ ɢɯ ɝɪɚɮɢɤɢ ɫ ɝɪɚɮɢɤɚɦɢ ɡɚɞɚɧɧɨɣ ɮɭɧɤɰɢɢ.
ɋ ɰɟɥɶɸ ɧɟɞɨɩɭɳɟɧɢɹ ɨɲɢɛɤɢ ɫɥɟɞɭɟɬ, ɜɵɛɪɚɜ ɤɚɤɭɸ-ɥɢɛɨ ɮɨɪɦɭɥɭ,
ɩɪɟɠɞɟ ɱɟɦ ɨɩɪɟɞɟɥɹɬɶ ɡɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ, ɩɪɨɜɟɪɢɬɶ ɜɨɡɦɨɠɧɨɫɬɶ ɟɺ
ɩɪɢɦɟɧɟɧɢɹ ɩɨ ɦɟɬɨɞɭ ɜɵɪɚɜɧɢɜɚɧɢɹ. Ɇɟɬɨɞ ɜɵɪɚɜɧɢɜɚɧɢɹ ɡɚɤɥɸɱɚɟɬɫɹ ɜ
ɩɪɟɞɩɨɥɨɠɟɧɢɢ, ɱɬɨ ɦɟɠɞɭ ɭ ɢ ɯ ɫɭɳɟɫɬɜɭɟɬ ɡɚɜɢɫɢɦɨɫɬɶ ɨɩɪɟɞɟɥɺɧɧɨɝɨ
ɜɢɞɚ, ɧɚɯɨɞɹɬɫɹ ɧɟɤɨɬɨɪɵɟ ɜɟɥɢɱɢɧɵ X = ij(x, y) ɢ Y = ȥ(x, y), ɤɨɬɨɪɵɟ
ɩɪɢ ɫɞɟɥɚɧɧɨɦ ɩɪɟɞɩɨɥɨɠɟɧɢɢ ɫɜɹɡɚɧɵ ɥɢɧɟɣɧɨɣ ɡɚɜɢɫɢɦɨɫɬɶɸ
(ɧɚɩɪɢɦɟɪ, ɟɫɥɢ
y
x
bxa
ȼɵɱɢɫɥɹɹ ɞɥɹ ɡɧɚɱɟɧɢɣ x ɢ y ɫɨɨɬɜɟɬɫɬɜɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɏ ɢ Y ɢ
ɢɡɨɛɪɚɠɚɹ ɢɯ ɝɪɚɮɢɱɟɫɤɢ, ɥɟɝɤɨ ɭɜɢɞɟɬɶ, ɛɥɢɡɤɚ ɥɢ ɡɚɜɢɫɢɦɨɫɬɶ ɦɟɠɞɭ ɏ
ɢ Y ɤ ɥɢɧɟɣɧɨɣ ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɨɞɯɨɞɢɬ ɥɢ ɜɵɛɪɚɧɧɚɹ ɮɨɪɦɭɥɚ ɢɥɢ
ɧɟɬ.
= f(x) ɫɨɫɬɨɢɬ ɢɡ ɞɜɭɯ ɷɬɚɩɨɜ: ɫɧɚɱɚɥɚ
0
, ɬɨ ɛɟɪɭɬ X = x,
x
Y
y
63
ɜ ɫɬɚɬɢɤɟ ɢ ɜ
ɢɥɢ
X1
ɪɟɤɨɦɟɧ-
1
,
Y
y
).
Ɉɩɪɟɞɟɥɟɧɢɟ ɩɚɪɚɦɟɬɪɨɜ. ɇɚɢɛɨɥɟɟ ɬɨɱɧɵɦ ɦɟɬɨɞɨɦ ɨɩɪɟɞɟɥɟɧɢɹ
ɩɚɪɚɦɟɬɪɨɜ ɹɜɥɹɟɬɫɹ ɦɟɬɨɞ ɧɚɢɦɟɧɶɲɢɯ ɤɜɚɞɪɚɬɨɜ. Ɉɞɧɚɤɨ ɜ ɛɨɥɶɲɢɧɫɬɜɟ
ɫɥɭɱɚɟɜ ɦɨɝɭɬ ɛɵɬɶ ɭɫɩɟɲɧɨ ɩɪɢɦɟɧɟɧɵ ɛɨɥɟɟ ɩɪɨɫɬɵɟ ɦɟɬɨɞɵ, ɜ
ɱɚɫɬɧɨɫɬɢ, ɦɟɬɨɞ ɫɪɟɞɧɢɯ. ȿɫɥɢ ɩɨɥɭɱɟɧɧɚɹ ɩɨ ɷɬɨɦɭ ɦɟɬɨɞɭ ɮɨɪɦɭɥɚ
ɨɤɚɠɟɬɫɹ ɧɟɞɨɫɬɚɬɨɱɧɨ ɬɨɱɧɨɣ, ɞɥɹ ɞɚɥɶɧɟɣɲɟɝɨ ɟɺ ɭɬɨɱɧɟɧɢɹ ɭɠɟ ɦɨɠɟɬ
ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧ ɦɟɬɨɞ ɧɚɢɦɟɧɶɲɢɯ ɤɜɚɞɪɚɬɨɜ, ɩɪɢɱɟɦ ɡɧɚɧɢɟ
ɩɪɢɛɥɢɠɺɧɧɵɯ ɡɧɚɱɟɧɢɣ ɩɚɪɚɦɟɬɪɨɜ
ɩɨɡɜɨɥɢɬ ɫɞɟɥɚɬɶ ɜɵɱɢɫɥɟɧɢɹ ɦɟɧɟɟ
ɝɪɨɦɨɡɞɤɢɦɢ. ɉɨ ɦɟɬɨɞɭ ɫɪɟɞɧɢɯ ɫɧɚɱɚɥɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɥɢɧɟɣɧɚɹ
ɡɚɜɢɫɢɦɨɫɬɶ ɦɟɠɞɭ «ɜɵɪɚɜɧɟɧɧɵɦɢ» ɩɟɪɟɦɟɧɧɵɦɢ ɏ ɢ Y, Y = aX + b. Ⱦɥɹ
ɷɬɨɝɨ ɭɫɥɨɜɧɵɟ ɭɪɚɜɧɟɧɢɹ Y
= aXi + b ɞɥɹ ɢɦɟɸɳɢɯɫɹ ɩɚɪ ɡɧɚɱɟɧɢɣ Xi ɢ Yi
i
ɞɟɥɹɬɫɹ ɧɚ ɞɜɟ ɪɚɜɧɵɟ (ɢɥɢ ɩɨɱɬɢ ɪɚɜɧɵɟ) ɝɪɭɩɩɵ ɜ ɩɨɪɹɞɤɟ ɜɨɡɪɚɫɬɚɧɢɹ
ɩɟɪɟɦɟɧɧɨɣ X
ɢɥɢ Yi. ɋɤɥɚɞɵɜɚɹ ɭɪɚɜɧɟɧɢɹ ɤɚɠɞɨɣ ɝɪɭɩɩɵ, ɩɨɥɭɱɢɦ ɞɜɚ
i
ɭɪɚɜɧɟɧɢɹ, ɢɡ ɤɨɬɨɪɵɯ ɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɚ ɢ b. ȼɵɪɚɠɚɹ X ɢ Y ɱɟɪɟɡ
ɩɟɪɜɨɧɚɱɚɥɶɧɵɟ ɩɟɪɟɦɟɧɧɵɟ, ɩɨɥɭɱɢɦ ɢɫɤɨɦɭɸ ɡɚɜɢɫɢɦɨɫɬɶ ɦɟɠɞɭ ɯ ɢ ɭ.
ȿɫɥɢ ɩɪɢ ɷɬɨɦ ɟɳɟ ɧɟ ɜɫɟ ɩɚɪɚɦɟɬɪɵ ɛɭɞɭɬ ɨɩɪɟɞɟɥɟɧɵ, ɬɨ ɫɥɟɞɭɟɬ
ɩɪɢɦɟɧɢɬɶ ɜɧɨɜɶ ɬɨɬ ɠɟ ɦɟɬɨɞ, ɜɵɪɚɜɧɢɜɚɹ ɭɠɟ ɞɪɭɝɢɯ ɜɟɥɢɱɢɧ
YX ɢ .
ɉɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɝɪɚɮɢɤɨɜ ɫɥɟɞɭɟɬ ɢɦɟɬɶ ɜɜɢɞɭ, ɱɬɨ ɩɪɢ ɩɨɥɶɡɨɜɚɧɢɢ
ɷɦɩɢɪɢɱɟɫɤɢɦɢ ɮɨɪɦɭɥɚɦɢ ɢɫɩɨɥɶɡɭɟɬɫɹ ɥɢɲɶ ɱɚɫɬɶ ɤɪɢɜɨɣ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɧɟɤɨɬɨɪɨɦɭ ɢɧɬɟɪɜɚɥɭ ɢɡɦɟɧɟɧɢɹ ɧɟɡɚɜɢɫɢɦɨɣ ɩɟɪɟɦɟɧɧɨɣ.
3.2. ɉɨɞɛɨɪ ɷɦɩɢɪɢɱɟɫɤɢɯ ɪɚɫɱɟɬɧɵɯ ɮɨɪɦɭɥ
3.2.1. ɉɨɞɛɨɪ ɮɨɪɦɭɥ ɞɥɹ ɝɢɞɪɚɜɥɢɱɟɫɤɢɯ ɪɚɫɱɟɬɨɜ ɥɨɩɚɫɬɧɵɯ
ɬɭɪɛɨɦɚɲɢɧ ɪɚɞɢɚɥɶɧɨɝɨ ɬɢɩɚ
ɉɪɢ ɝɢɞɪɚɜɥɢɱɟɫɤɢɯ ɪɚɫɱɺɬɚɯ ɧɚɫɨɫɧɵɯ, ɝɢɞɪɨɬɪɚɧɫɩɨɪɬɧɵɯ ɢ
ɜɟɧɬɢɥɹɬɨɪɧɵɯ ɭɫɬɚɧɨɜɨɤ, ɫ ɩɨɫɥɟɞɭɸɳɟɣ ɢɯ ɚɜɬɨɦɚɬɢɡɚɰɢɟɣ ɧɟɨɛɯɨɞɢɦɨ
ɪɚɫɩɨɥɚɝɚɬɶ ɚɧɚɥɢɬɢɱɟɫɤɢɦɢ ɡɚɜɢɫɢɦɨɫɬɹɦɢ ɧɟɤɨɬɨɪɵɯ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ
ɩɚɪɚɦɟɬɪɨɜ, ɡɚɞɚɧɧɵɯ ɜ ɜɢɞɟ ɝɪɚɮɢɤɨɜ ɢ ɬɚɛɥɢɰ, ɩɪɢɜɟɞɟɧɧɵɯ ɜ ɪɚɛɨɬɚɯ
[2–4, 9]. Ʉ ɬɚɤɢɦ ɩɚɪɚɦɟɬɪɚɦ ɨɬɧɨɫɹɬɫɹ:
– ɩɨɩɪɚɜɨɱɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɞɥɹ ɝɢɞɪɚɜɥɢɱɟɫɤɢɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɩɨ
ɮɨɪɦɭɥɚɦ Ɏ.Ⱥ. ɒɟɜɟɥɟɜɚ [2];
– ɤɨɷɮɮɢɰɢɟɧɬ ɦɟɫɬɧɵɯ ɝɢɞɪɚɜɥɢɱɟɫɤɢɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɭɡɥɚ ɩɪɢɟɦɧɚɹ ɫɟɬɤɚ – ɨɛɪɚɬɧɵɣ ɤɥɚɩɚɧ ɧɚ ɜɫɚɫɵɜɚɸɳɟɦ ɬɪɭɛɨɩɪɨɜɨɞɟ;
– ɩɪɢɜɟɞɟɧɧɨɟ ɞɚɜɥɟɧɢɟ ɧɚ ɭɪɨɜɧɟ ɡɟɪɤɚɥɚ ɜɨɞɵ ɜ ɩɪɢɺɦɧɨɦ ɤɨɥɨɞɰɟ
ɫ ɭɱɺɬɨɦ ɞɚɜɥɟɧɢɹ ɧɚɫɵɳɟɧɧɨɝɨ ɩɚɪɚ ɞɥɹ ɩɨɞɫɱɺɬɚ ɤɚɜɢɬɚɰɢɨɧɧɵɯ
ɯɚɪɚɤɬɟɪɢɫɬɢɤ;
– ɤɚɜɢɬɚɰɢɨɧɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɛɵɫɬɪɨɯɨɞɧɨɫɬɢ ɧɚɝɧɟɬɚɬɟɥɹ.
ɗɬɢ ɩɚɪɚɦɟɬɪɵ ɢɫɯɨɞɧɨ ɡɚɞɚɧɵ ɜ ɜɢɞɟ ɬɚɛɥɢɰ, ɦɚɬɟɦɚɬɢɱɟɫɤɚɹ
ɨɛɪɚɛɨɬɤɚ ɤɨɬɨɪɵɯ ɦɟɬɨɞɨɦ ɧɚɢɦɟɧɶɲɢɯ ɤɜɚɞɪɚɬɨɜ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ
ɪɚɫɫɦɨɬɪɟɧɧɨɣ ɦɟɬɨɞɢɤɢ ɞɚɥɚ ɫɥɟɞɭɸɳɢɟ ɪɟɡɭɥɶɬɚɬɵ:
64
– ɩɪɢ ɫɤɨɪɨɫɬɹɯ ɜɨɞɵ V = 1,2 ɦ/ɫ ɜɨ ɜɪɟɦɹ ɪɚɫɱɺɬɨɜ ɤɨɷɮɮɢɰɢɟɧɬɚ
[
Ⱦɚɪɫɢ ɢ ɩɪɢɜɟɞɟɧɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɩɨ ɞɥɢɧɟ ɬɪɭɛɨɩɪɨɜɨɞɚ ɧɭɠɧɨ
2
ɭɦɧɨɠɢɬɶ, ɚ ɪɚɫɯɨɞɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ Ʉ
ɤɨɷɮɮɢɰɢɟɧɬ Ʉ
, ɷɦɩɢɪɢɱɟɫɤɚɹ ɮɨɪɦɭɥɚ ɤɨɬɨɪɨɝɨ ɢɦɟɟɬ ɜɢɞ:
1
KV r
1
V
1, 06 0,09
4,4 %
ɪɚɡɞɟɥɢɬɶ ɧɚ ɩɨɩɪɚɜɨɱɧɵɣ
(V 1,2 ɦ/ɫ); (3.1)
– ɮɨɪɦɭɥɚ ɞɥɹ ɩɨɞɫɱɺɬɚ ɤɨɷɮɮɢɰɢɟɧɬɚ ɦɟɫɬɧɵɯ ɝɢɞɪɚɜɥɢɱɟɫɤɢɯ
ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɜ ɧɚɱɚɥɟ ɜɫɚɫɵɜɚɸɳɟɝɨ ɬɪɭɛɨɩɪɨɜɨɞɚ, ɢɦɟɟɬ ɜɢɞ:
1, 6 3 3 %
ɝɞɟ ȟ
– ɤɨɷɮɮɢɰɢɟɧɬ ɝɢɞɪɚɜɥɢɱɟɫɤɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɫɢɫɬɟɦɵ ɩɪɢɟɦ-
ɋ+Ʉ
ɋ K ɩɬ
d
r (d
= 0,05…0,5 ɦ), (3.2)
ɩɬ
ɧɚɹ ɫɟɬɤɚ-ɨɛɪɚɬɧɵɣ ɤɥɚɩɚɧ;
dɩɬ – ɜɧɭɬɪɟɧɧɢɣ ɞɢɚɦɟɬɪ ɩɨɞɜɨɞɹɳɟɝɨ (ɜɫɚɫɵɜɚɸɳɟɝɨ) ɬɪɭɛɨɩɪɨɜɨɞɚ, ɦ.;
– ɩɪɢɜɟɞɟɧɧɨɟ ɧɚɱɚɥɶɧɨɟ ɞɚɜɥɟɧɢɟ ɧɚ ɭɪɨɜɧɟ ɜɨɞɵ ɜ ɩɪɢɺɦɧɨɦ
ɤɨɥɨɞɰɟ ɜ ɲɚɯɬɟ, ɢɫɩɨɥɶɡɭɟɦɨɟ ɩɪɢ ɚɧɚɥɢɬɢɱɟɫɤɢɯ ɪɚɫɱɺɬɚɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɨɞɜɨɞɹɳɟɝɨ ɬɪɭɛɨɩɪɨɜɨɞɚ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ:
9,69 0,93 10 5,7 % 0...1200 ɦ
ɇɇɇ
r
0
3
ɲɲ
, (3.3)
ɝɞɟ ɇ0 – ɧɚɱɚɥɶɧɵɣ ɩɪɨɜɟɞɟɧɧɵɣ ɧɚɩɨɪ ɜɨ ɜɫɚɫɵɜɚɸɳɟɣ ɥɢɧɢɢ ɧɚɫɨɫɚ ɩɪɢ
ɧɭɥɟɜɨɣ ɩɨɞɚɱɟ, ɦ.;
ɇɲ – ɝɥɭɛɢɧɚ ɲɚɯɬɧɨɝɨ ɫɬɜɨɥɚ, ɦ;
– ɤɚɜɢɬɚɰɢɨɧɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɛɵɫɬɪɨɯɨɞɧɨɫɬɢ, ɢɫɩɨɥɶɡɭɟɦɵɣ ɜ
ɮɨɪɦɭɥɟ ɋ.ɋ. Ɋɭɞɧɟɜɚ [2], ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɤɪɢɬɢɱɟɫɤɨɝɨ ɤɚɜɢɬɚɰɢɨɧɧɨɝɨ
ɡɚɩɚɫɚ, ɦɨɠɟɬ ɛɵɬɶ ɪɚɫɫɱɢɬɚɧ ɩɨ ɮɨɪɦɭɥɟ:
600 18, 433 50 1, 2 % 50 ɦɢɧ
ɋ nn r t , (3.4)
0,676
SS
-1
ɝɞɟ nS – ɭɞɟɥɶɧɚɹ ɛɵɫɬɪɨɯɨɞɧɨɫɬɶ ɧɚɫɨɫɚ, ɦɢɧ-1.
3.2.2. ɉɨɞɛɨɪ ɷɦɩɢɪɢɱɟɫɤɢɯ ɮɨɪɦɭɥ ɞɥɹ ɪɚɫɱɟɬɨɜ ɦɟɫɬɧɵɯ
ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɞɪɨɫɫɟɥɢɪɭɸɳɢɯ ɨɪɝɚɧɨɜ
Ⱦɥɹ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɪɟɠɢɦɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɭɫɬɚɧɨɜɨɤ ɫ ɰɟɧɬɪɨɛɟɠɧɵɦɢ ɧɚɝɧɟɬɚɬɟɥɹɦɢ ɜ ɨɫɧɨɜɧɨɦ ɢɫɩɨɥɶɡɭɸɬɫɹ ɞɪɨɫɫɟɥɶɧɵɟ ɭɫɬɪɨɣɫɬɜɚ
ɱɟɬɵɪɺɯ ɬɢɩɨɜ, ɷɦɩɢɪɢɱɟɫɤɢɟ ɮɨɪɦɭɥɵ ɞɥɹ ɩɨɞɫɱɺɬɚ ɦɟɫɬɧɵɯ ɝɢɞɪɚɜɥɢɱɟɫɤɢɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɤɨɬɨɪɵɯ ɢɦɟɸɬ ɜɢɞ:
– ɩɨɜɨɪɨɬɧɚɹ ɡɚɫɥɨɧɤɚ (ɤɥɚɩɚɧ ɞɪɨɫɫɟɥɶɧɵɣ):
[
r , (3.5)
0,103
0,18 5,1 %
ɏ
ɟ
ɝɞɟ X – ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɡɚɫɥɨɧɤɢ. [X] = ij° (ij° = 0…60°);
65
– ɤɪɚɧ ɩɪɨɛɨɱɧɵɣ:
[
[
[
r
0,1298
0,13 4,8 %
ɏ
ɟ
, (3.6)
ɝɞɟ ɏ – ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɩɪɨɛɤɢ. [X] = ij° (ij° = 0…50°);
– ɩɪɹɦɨɬɨɱɧɵɣ ɜɟɧɬɢɥɶ:
0,215 2,1 %ɏ
[
r
1,86 8
, (3.7)
ɝɞɟ ɏ – ɫɬɟɩɟɧɶ ɪɟɝɭɥɢɪɨɜɚɧɢɹ [ɏ] = h/D (h/D = 0,025…0,25 ɫ);
h – ɯɨɞ ɲɬɨɤɚ ɞɪɨɫɫɟɥɢɪɭɸɳɟɝɨ ɨɪɝɚɧɚ;
D – ɜɧɭɬɪɟɧɧɢɣ ɞɢɚɦɟɬɪ ɞɪɨɫɫɟɥɹ.
ɋɚɦɵɦ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɵɦ ɪɟɝɭɥɢɪɭɸɳɢɦ ɢ ɤɨɦɦɭɬɚɰɢɨɧɧɵɦ
ɭɫɬɪɨɣɫɬɜɨɦ ɜ ɩɪɚɤɬɢɤɟ ɷɤɫɩɥɭɚɬɚɰɢɢ ɹɜɥɹɟɬɫɹ ɤɥɢɧɨɜɚɹ ɡɚɞɜɢɠɤɚ (ɡɚɞɜɢɠɤɚ Ʌɭɞɥɨ), ɫɬɚɬɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɤɨɬɨɪɨɣ ɧɨɫɢɬ ɹɪɤɨ ɜɵɪɚɠɟɧɧɵɣ ɧɟɥɢɧɟɣɧɵɣ ɯɚɪɚɤɬɟɪ. ȼ ɷɬɨɣ ɫɜɹɡɢ ɞɥɹ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɨɩɢɫɚɧɢɹ
ɩɨɜɟɞɟɧɢɹ ɤɪɢɜɨɣ
ɦɟɫɬɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɪɚɛɨɱɢɣ ɞɢɚɩɚɡɨɧ ɫɬɟɩɟɧɢ ɨɬɤɪɵɜɚɧɢɹ ɞɪɨɫɫɟɥɢɪɭɸɳɟɝɨ ɨɪɝɚɧɚ ɛɵɥ ɪɚɡɛɢɬ ɧɚ ɞɜɚ ɭɱɚɫɬɤɚ ɜ
ɞɢɚɩɚɡɨɧɚɯ ɢɡɦɟɧɟɧɢɹ ɧɟɡɚɜɢɫɢɦɨɣ ɩɟɪɟɦɟɧɨɣ ɏ ɨɬ 0 ɞɨ 0,1 ɢ ɨɬ 0,1 ɞɨ
1,0. ɉɪɢ ɨɛɪɚɛɨɬɤɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɛɵɥ ɢɫɩɨɥɶɡɨɜɚɧ ɦɟɬɨɞ
ɜɵɪɚɜɧɢɜɚɧɢɹ, ɤɨɬɨɪɵɣ ɩɨɞɬɜɟɪɞɢɥ ɧɚ ɞɚɧɧɵɯ ɭɱɚɫɬɤɚɯ ɯɨɪɨɲɟɟ ɫɨɜɩɚɞɟɧɢɟ ɪɟɡɭɥɶɬɚɬɨɜ ɨɛɪɚɛɨɬɤɢ ɫ ɝɪɚɮɢɤɨɦ ɩɪɹɦɨɣ ɥɢɧɢɢ, ɜɵɩɨɥɧɟɧɧɵɦ ɜ ɩɨ
ɥɭɥɨɝɚɪɢɮɦɢɱɟɫɤɨɦ ɦɚɫɲɬɚɛɟ. ɍɪɚɜɧɟɧɢɟ ɷɬɢɯ ɩɪɹɦɵɯ ɢɦɟɟɬ ɜɢɞ:
ln 10,1 55,5 11 % 0...0,1ɏɏ
r ; (3.8)
222
ln 5,22 7 7,6 % 0,1...1,0ɏɏ
r , (3.9)
111
ɝɞɟ ɏ – ɫɬɟɩɟɧɶ ɨɬɤɪɵɜɚɧɢɹ ɡɚɞɜɢɠɤɢ, ɏ = h/D;
h – ɯɨɞ ɲɬɨɤɚ ɢɫɩɨɥɧɢɬɟɥɶɧɨɝɨ ɨɪɝɚɧɚ;
D – ɩɪɨɯɨɞɧɨɣ ɞɢɚɦɟɬɪ ɡɚɞɜɢɠɤɢ.
ɇɚ ɨɫɧɨɜɚɧɢɢ (3.8) ɢ (3.9) ɫɬɚɬɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɞɪɨɫɫɟɥɹ ɧɚ
ɞɜɭɯ ɭɱɚɫɬɤɚɯ ɚɩɩɪɨɤɫɢɦɢɪɨɜɚɧɚ ɜɵɪɚɠɟɧɢɹɦɢ ɜ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɣ
ɮɨɪɦɟ ɡɚɩɢɫɢ:
24343
[
2
185
[
1
ɏɟ55,5
(ɭɱɚɫɬɨɤ II: X = 0…0,1); (3.10)
ɏɟ7
(ɭɱɚɫɬɨɤ I: X = 0,1…1,0). (3.11)
ɗɬɨ ɩɪɢɟɦɥɟɦɨ ɞɥɹ ɞɚɥɶɧɟɣɲɟɝɨ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɞɚɧɧɵɯ ɮɨɪɦɭɥ ɜ
ɤɚɱɟɫɬɜɟ ɨɫɧɨɜɧɵɯ ɪɚɫɱɺɬɧɵɯ ɩɪɢ ɢɫɫɥɟɞɨɜɚɧɢɢ ɩɪɨɰɟɫɫɨɜ ɞɪɨɫɫɟɥɢɪɨɜɚɧɢɹ ɬɪɭɛɨɩɪɨɜɨɞɧɵɯ ɫɟɬɟɣ.
-
66
3.3. Ɇɟɬɨɞɢɤɚ ɨɩɪɟɞɟɥɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɫɬɚɬɢɱɟɫɤɨɣ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜɟɧɬɢɥɹɬɨɪɧɨɣ ɭɫɬɚɧɨɜɤɢ
ȼɵɛɨɪ ɜɢɞɚ ɮɨɪɦɭɥɵ ɨɫɧɨɜɚɧ ɧɚ ɚɧɚɥɢɡɟ ɝɪɚɮɢɤɨɜ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɰɟɧɬɪɨɛɟɠɧɵɯ ɜɟɧɬɢɥɹɬɨɪɨɜ ɢ ɧɚ ɨɛɳɢɯ ɩɨɥɨɠɟɧɢɹɯ
ɬɟɨɪɢɢ ɥɨɩɚɫɬɧɵɯ ɬɭɪɛɨɦɚɲɢɧ. Ɂɚɜɨɞɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɬɚɤɢɯ ɜɟɧɬɢɥɹɬɨɪɨɜ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɟɦɟɣɫɬɜɨ ɢɧɞɢɜɢɞɭɚɥɶɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ P
SV
=
= f(Q), ɩɨɥɭɱɟɧɧɵɯ ɩɪɢ ɪɚɡɧɵɯ ɭɝɥɚɯ ɭɫɬɚɧɨɜɤɢ ɥɨɩɚɬɨɤ ɧɚɩɪɚɜɥɹɸɳɟɝɨ
ɚɩɩɚɪɚɬɚ ĬɇȺ ɢ ɪɚɡɧɵɯ ɱɚɫɬɨɬɚɯ ɜɪɚɳɟɧɢɹ ɜɚɥɚ ɪɚɛɨɱɟɝɨ ɤɨɥɟɫɚ n.
Ɂɚɜɢɫɢɦɨɫɬɶ P
ɩɚɪɚɛɨɥɭ ɫ ɜɟɪɬɢɤɚɥɶɧɨɣ ɨɫɶɸ ɫɢɦɦɟɬɪɢɢ:
= f(Q) ɩɪɢ ĬɇȺ = const ɝɪɚɮɢɱɟɫɤɢ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ
SV
20
, (3.12)
QBQAPP
SVSV
ɫɨɜɟɪɲɟɧɧɨ ɢɞɟɧɬɢɱɧɚ ɧɚɩɨɪɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɰɟɧɬɪɨɛɟɠɧɨɝɨ ɫɟɤɰɢɨɧɧɨɝɨ ɧɚɫɨɫɚ, ɩɨɥɭɱɟɧɧɨɣ ɜ ɢɧɫɬɢɬɭɬɟ ɦɟɯɚɧɢɤɢ ɢɦ. Ɇ.Ɇ. Ɏɟɞɨɪɨɜɚ ɢ ɢɫɩɨɥɶɡɭɟɦɨɣ ɩɪɨɟɤɬɧɵɦɢ ɨɪɝɚɧɢɡɚɰɢɹɦɢ ɩɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɢ ɪɟɤɨɧɫɬɪɭɤɰɢɢ ɲɚɯɬ Ⱦɨɧɛɚɫɫɚ. ȼ ɮɨɪɦɭɥɟ (3.12) ɩɪɢɧɹɬɵ ɨɛɨɡɧɚɱɟɧɢɹ: P
ɫɬɚɬɢɱɟɫɤɨɟ ɞɚɜɥɟɧɢɟ, ɪɚɡɜɢɜɚɟɦɨɟ ɜɟɧɬɢɥɹɬɨɪɨɦ, ɉɚ;
0
– ɧɚɱɚɥɶ-
P
SV
–
SV
ɧɨɟ ɞɚɜɥɟɧɢɟ ɩɪɢ Q = 0, ɉɚ; Q – ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɜɟɧɬɢɥɹɬɨɪɚ, ɦ3/ɫ;
Ⱥ ɢ ȼ – ɷɦɩɢɪɢɱɟɫɤɢɟ ɤɨɷɮɮɢɰɢɟɧɬɵ:
[A] = ɉɚ / (ɦ3/ɫ), [ȼ] = ɉɚ/(ɦ6/ɫ2).
0
ȼ ɭɪɚɜɧɟɧɢɢ (3.12) ɨɩɪɟɞɟɥɟɧɢɸ ɩɨɞɥɟɠɚɬ ɤɨɷɮɮɢɰɢɟɧɬɵ
P
SV
, Ⱥ ɢ ȼ
ɜ ɨɛɥɚɫɬɢ ɩɪɨɦɵɲɥɟɧɧɨɝɨ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɜɟɧɬɢɥɹɬɨɪɚ, ɲɢɪɢɧɚ ɤɨɬɨɪɨɣ
ɡɚɜɢɫɢɬ ɨɬ ɩɪɢɧɹɬɨɝɨ ɫɩɨɫɨɛɚ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɜɟɧɬɢɥɹɬɨɪɚ. Ʉɚɤ ɨɬɦɟɱɚɥɨɫɶ, ɩɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɰɟɧɬɪɨɛɟɠɧɵɦ
ɜɟɧɬɢɥɹɬɨɪɚɦ ɢɦɟɸɬ ɦɟɫɬɨ ɞɜɚ ɫɩɨɫɨɛɚ ɪɟɝɭɥɢɪɨɜɚɧɢɹ: ɢɡɦɟɧɟɧɢɟɦ ɭɝɥɚ
ɭɫɬɚɧɨɜɤɢ ɥɨɩɚɬɨɤ ɧɚɩɪɚɜɥɹɸɳɟɝɨ ɚɩɩɚɪɚɬɚ ɢ ɢɡɦɟɧɟɧɢɟɦ ɱɚɫɬɨɬɵ
ɜɪɚɳɟɧɢɹ ɜɚɥɚ ɩɪɢɜɨɞɧɨɝɨ ɷɥɟɤɬɪɨɞɜɢɝɚɬɟɥɹ. ɇɚɢɛɨɥɶɲɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɩɨɥɭɱɢɥ ɩɟɪɜɵɣ ɫɩɨɫɨɛ. ȼ
ɷɬɨɦ ɫɥɭɱɚɟ ɨɛɥɚɫɬɶ ɩɪɨɦɵɲɥɟɧɧɨɝɨ
ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɜɟɧɬɢɥɹɬɨɪɚ ɨɝɪɚɧɢɱɢɜɚɟɬɫɹ ɤɪɢɜɨɣ, ɩɪɨɜɟɞɟɧɧɨɣ ɱɟɪɟɡ
ɬɨɱɤɢ ɢɧɞɢɜɢɞɭɚɥɶɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɞɥɹ ɤɚɠɞɨɝɨ ɭɝɥɚ ɭɫɬɚɧɨɜɤɢ
ɥɨɩɚɬɨɤ ɧɚɩɪɚɜɥɹɸɳɟɝɨ ɚɩɩɚɪɚɬɚ ɢ ɦɢɧɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɄɉȾ, ɪɚɜɧɨɝɨ
0.6. Ƚɪɚɧɢɰɚɦɢ ɷɬɨɣ ɨɛɥɚɫɬɢ ɹɜɥɹɸɬɫɹ ɬɨɱɤɢ ɫ ɤɨɨɪɞɢɧɚɬɚɦɢ X1(Q1; P
X
; P
2(Q2
), ɩɨɥɭɱɟɧɧɵɟ ɧɚ ɩɟɪɟɫɟɱɟɧɢɹɯ ɤɪɢɜɵɯ P
SV2
= f(Qi) ɢ Ș
SVi
= 0,6,
min
SV1
) ɢ
ɤɚɤ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 3.1. ɋ ɰɟɥɶɸ ɨɩɪɟɞɟɥɟɧɢɹ ɭɤɚɡɚɧɧɵɣ ɜɵɲɟ ɩɚɪɚɦɟɬɪɨɜ ɫɨɫɬɚɜɢɦ ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ, ɢɫɩɨɥɶɡɭɹ ɦɟɬɨɞ ɬɪɟɯ ɬɨɱɟɤ. Ɇɟɬɨɞ
ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɫɥɟɞɭɸɳɟɦ. ɇɚ ɤɪɢɜɨɣ P
ɬɨɱɟɤ X
Q
0
ɢ X2 ɨɩɪɟɞɟɥɹɟɦ ɬɨɱɤɭ ɏ0 ɫ ɤɨɨɪɞɢɧɚɬɚɦɢ X0(Q0; P
1
ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
= f(Q) ɩɪɢ ĬɇȺ = const, ɤɪɨɦɟ
SV
SV0
QQQ
21
, ɚ ɜɟɥɢɱɢɧɚ P
2
67
0
). ȼɟɥɢɱɢɧɚ
SV0
ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɤɪɢɜɨɣ PSV = f(Q) ɩɪɢ Q = Q0 (ɪɢɫ. 3.1). ȼ ɩɪɟɞɩɨɥɨɠɟɧɢɢ, ɱɬɨ ɤɪɢɜɚɹ, ɡɚɞɚɧɧɚɹ ɭɪɚɜɧɟɧɢɟɦ (3.12), ɩɪɨɯɨɞɢɬ ɱɟɪɟɡ ɜɵɛɪɚɧ-
ɧɵɟ ɬɨɱɤɢ X
ɫɢɫɬɟɦɵ ɭɪɚɜɧɟɧɢɣ:
ɢ ɏ2, ɏ0, ɩɚɪɚɦɟɬɪɵ
1
ɂɡ ɫɢɫɬɟɦɵ (3.13) ɫɥɟɞɭɟɬ:
PP
ɝɞɟ
P
'
1
SVSV
QQ
01
SVSVi
0
2
B
0
01
,
P
'
2
0
, Ⱥ ɢ ȼ ɦɨɝɭɬ ɛɵɬɶ ɨɩɪɟɞɟɥɟɧɵ ɢɡ
P
SV
0
0
SVSV
0
SVSV
''
QQ
SVSV
PP
SVSV
02
.
QQ
02
2
½
QBQAPP
11
°
°
2
QBQAPP
(3.13)
¾
00
°
2
QBQAPP
°
22
¿
PP
21
; (3.14)
12
QQBPA ' ; (3.15)
011
2
, (3.16)
QBQAPP
000
ɇɚɢɛɨɥɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɵɦ ɫɩɨɫɨɛɨɦ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ ɰɟɧ-
0
P
SV
ɬɪɨɛɟɠɧɵɯ ɜɟɧɬɢɥɹɬɨɪɨɜ ɹɜɥɹɟɬɫɹ ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɢɡɦɟɧɟɧɢɟɦ ɭɝɥɚ ɭɫɬɚɧɨɜɤɢ ɥɨɩɚɬɨɤ
ɧɚɩɪɚɜɥɹɸɳɟɝɨ ɚɩɩɚɪɚɬɚ. Ⱦɥɹ
ɟɝɨ ɪɟɚɥɢɡɚɰɢɢ ɫɥɟɞɭɟɬ ɞɥɹ
ɤɚɠɞɨɝɨ ɬɢɩɚ ɜɟɧɬɢɥɹɬɨɪɚ
ɧɚɣɬɢ ɨɛɨɛɳɺɧɧɵɟ ɡɚɜɢɫɢɦɨɫɬɢ
ɧɚɣɞɟɧɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɨɬ ɭɝɥɚ
ɭɫɬɚɧɨɜɤɢ ɥɨɩɚɬɨɤ ɧɚɩɪɚɜɥɹɸɳɟɝɨ ɚɩɩɚɪɚɬɚ. ɋ ɷɬɨɣ ɰɟɥɶɸ,
ɧɚɣɞɟɧɧɵɟ ɩɨ ɮɨɪɦɭɥɚɦ
(3.14), (3.15) ɢ (3.16)
ɜɢɞɟ
Ɋɢɫɭɧɨɤ 3.1. Ʉ ɨɩɪɟɞɟɥɟɧɢɸ ɤɨɨɪɞɢɧɚɬ
ɭɡɥɨɜɵɯ ɬɨɱɟɤ
ɩɚɪɚɦɟɬɪɵ ɢɡɨɛɪɚɠɚɸɬ ɜ
ɝɪɚɮɢɤɚ y = f(
Ĭ ), ɝɞɟ Ĭ – ɫɬɟ-
ɩɟɧɶ ɨɬɤɪɵɬɢɹ ɧɚɩɪɚɜɥɹɸɳɟɝɨ
ɚɩɩɚɪɚɬɚ:
68
Ĭ
– ɬɟɤɭɳɟɟ ɡɧɚɱɟɧɢɟ ɭɝɥɚ ɭɫɬɚɧɨɜɤɢ ɥɨɩɚɬɤɢ;
ɝɞɟ Ĭ
i
Ĭ
– ɦɚɤɫɢɦɚɥɶɧɵɣ ɭɝɨɥ ɭɫɬɚɧɨɜɤɢ ɥɨɩɚɬɤɢ, ɩɪɢ ɤɨɬɨɪɨɦ ɧɚɩɪɚɜ-
max
Ĭ
ɥɹɸɳɢɣ ɚɩɩɚɪɚɬ ɫɱɢɬɚɟɬɫɹ ɩɨɥɧɨɫɬɶɸ ɨɬɤɪɵɬɵɦ (Ĭ
i
, (3.17)
Ĭ
max
= 90°). ɉɪɢ ɷɬɨɦ
max
ɞɢɚɩɚɡɨɧ ɢɡɦɟɧɟɧɢɹ ɫɬɟɩɟɧɢ ɨɬɤɪɵɬɢɹ, ɫɨɝɥɚɫɧɨ ɡɚɜɨɞɫɤɢɦ ɞɚɧɧɵɦ,
ɫɨɫɬɚɜɥɹɟɬ
000,1...333,0 Ĭ .
Ⱦɥɹ ɜɵɛɨɪɚ ɜɢɞɚ ɷɦɩɢɪɢɱɟɫɤɨɣ ɮɨɪɦɭɥɵ ɞɥɹ ɦɨɞɟɥɶɧɨɝɨ ɪɹɞɚ
ɰɟɧɬɪɨɛɟɠɧɵɯ ɜɟɧɬɢɥɹɬɨɪɨɜ ɝɥɚɜɧɨɝɨ ɩɪɨɜɟɬɪɢɜɚɧɢɹ ɲɚɯɬ ɦɨɝɭɬ ɛɵɬɶ
ɩɪɢɧɹɬɵ ɡɚ ɨɫɧɨɜɭ ɬɚɤɢɟ ɡɚɜɢɫɢɦɨɫɬɢ ɤɚɤ: ɥɢɧɟɣɧɚɹ ɮɭɧɤɰɢɹ y = ax+b;
ɫɬɟɩɟɧɧɚɹ ɮɭɧɤɰɢɹ y = ax
b
ɢ ɟɺ ɪɚɡɧɨɜɢɞɧɨɫɬɶ y = axb+c (ɟɫɥɢ ɝɪɚɮɢɤ
ɮɭɧɤɰɢɢ ɫɦɟɳɟɧ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɨɫɢ 0y).
ȼ ɷɬɨɦ ɫɥɭɱɚɟ, ɤɚɤ ɩɨɤɚɡɚɥɢ ɢɫɫɥɟɞɨɜɚɧɢɹ, ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ
ɥɢɧɟɣɧɨɣ ɮɭɧɤɰɢɢ ɜɨɡɦɨɠɧɵ ɢɡɨɛɪɚɠɟɧɢɹ ɜɟɥɢɱɢɧ:
Y
y
ɢ Ĭɏ . ɋɬɟɩɟɧɧɭɸ ɮɭɧɤɰɢɸ ɜɵɪɚɜɧɢɜɚɸɬ, ɩɨɥɨɠɢɜ ɏ = lnx
ɢɥɢ
ĬyY ɢ Ĭɏ
Ĭ
y
ɢ Y = lny (ɢɥɢ
Y
). Ɋɚɡɧɨɜɢɞɧɨɫɬɶ ɫɬɟɩɟɧɧɨɣ ɮɭɧɤɰɢɢ ɜɵɪɚɜɧɢ-
ln
Ĭ
y
Ĭ
º
), ɨɩɪɟɞɟɥɢɜ
c
»
¼
1
, y2 ɢ y3 ɢ
ɜɚɟɬɫɹ ɩɪɢ:
Ĭɏ ln ɢ
cyY ln (ɢɥɢ
ª
ln
Y
«
¬
ɫɧɚɱɚɥɚ ɫ. Ⱦɥɹ ɷɬɨɝɨ ɧɚɯɨɞɹɬ ɧɚ ɝɪɚɮɢɤɟ ɡɚɞɚɧɧɨɣ ɮɭɧɤɰɢɢ ɬɪɢ ɬɨɱɤɢ ɫ
ɚɛɫɰɢɫɫɚɦɢ ɯ
ɩɪɢɧɢɦɚɸɬ
, ɯ2 ɢ
1
ɫ
ɯɯɯ ɢ ɨɪɞɢɧɚɬɚɦɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ y
213
2
yyy
321
(ɬɨɱɤɢ ɯ1 ɢ ɯ2 ɜɵɛɢɪɚɸɬ ɩɪɨɢɡɜɨɥɶɧɨ).
2 yyy
321
ɂɫɩɨɥɶɡɭɹ ɨɩɢɫɚɧɧɭɸ ɦɟɬɨɞɢɤɭ ɞɥɹ ɰɟɧɬɪɨɛɟɠɧɨɝɨ ɜɟɧɬɢɥɹɬɨɪɚ
(ɜ ɱɚɫɬɧɨɫɬɢ, ȼɐ-31,5Ɇ) ɩɨɥɭɱɟɧɵ ɷɦɩɢɪɢɱɟɫɤɢɟ ɮɨɪɦɭɥɵ:
SV
0
91,37 ĬȺ , (3.18)
297,0 Ĭȼ
793,0
238,1
6,5224308 ĬP
, (3.19)
1
. (3.20)
ɉɨɝɪɟɲɧɨɫɬɶ ɚɩɩɪɨɤɫɢɦɚɰɢɢ ɝɪɚɮɢɱɟɫɤɢɯ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɡɚɜɢɫɢɦɨɫɬɹɦɢ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɧɚɣɞɟɧɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɜ ɞɢɚɩɚɡɨɧɟ ɢɡɦɟɪɟɧɢɹ
ɭɝɥɚ ɭɫɬɚɧɨɜɤɢ ɥɨɩɚɬɨɤ ɧɚɩɪɚɜɥɹɸɳɟɝɨ ɚɩɩɚɪɚɬɚ ɨɬ Ĭ = 30° ɞɨ
Ĭ = 90° ɫɨɫɬɚɜɥɹɟɬ ±2,2 %...±4,6 %, ɱɬɨ ɩɪɢɟɦɥɟɦɨ ɞɥɹ ɞɚɥɶɧɟɣɲɢɯ
ɢɫɫɥɟɞɨɜɚɧɢɣ ɞɢɧɚɦɢɱɟɫɤɢɯ ɪɟɠɢɦɨɜ ɪɚɛɨɬɵ ɜɟɧɬɢɥɹɬɨɪɧɨɣ ɭɫɬɚɧɨɜɤɢ,
ɜɨɡɧɢɤɚɸɳɢɯ ɩɪɢ ɟɺ ɩɭɫɤɟ ɢ ɪɟɝɭɥɢɪɨɜɚɧɢɢ.
69
3.4. Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɢɫɫɥɟɞɨɜɚɧɢɟ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɩɪɨɰɟɫɫɚ ɪɚɡɝɨɧɚ
ɂ
ɩɨɬɨɤɚ ɜɨɡɞɭɯɚ ɜ ɜɟɧɬɢɥɹɰɢɨɧɧɨɣ ɫɟɬɢ ɩɪɢ ɩɭɫɤɟ ɜɟɧɬɢɥɹɬɨɪɧɨɣ
ɭɫɬɚɧɨɜɤɢ
ɇɚɱɚɥɶɧɵɦɢ ɭɫɥɨɜɢɹɦɢ ɹɜɥɹɟɬɫɹ ɪɚɛɨɬɚ ɜɟɧɬɢɥɹɬɨɪɚ ɫ ɩɨɥɧɨɫɬɶɸ
ɡɚɤɪɵɬɵɦ ɧɚɩɪɚɜɥɹɸɳɢɦ ɚɩɩɚɪɚɬɨɦ, ɤɨɝɞɚ
ȼ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t = t
ɥɨɩɚɬɤɢ ɧɚɩɪɚɜɥɹɸɳɟɝɨ ɚɩɩɚɪɚɬɚ ɦɝɧɨɜɟɧɧɨ
0
ɭɫɬɚɧɚɜɥɢɜɚɸɬɫɹ ɜ ɩɨɥɨɠɟɧɢɟ «ɨɬɤɪɵɬɨ»
0 Ĭ , n = n
, Q = 0.
H
1 Ĭ , ɚ ɜ ɜɟɧɬɢɥɹɰɢɨɧɧɨɣ ɫɟɬɢ
ɧɚɱɢɧɚɟɬɫɹ ɪɚɡɝɨɧ ɩɨɬɨɤɚ
ɡɚ ɫɱɺɬ ɢɧɟɪɰɢɨɧɧɨɝɨ ɞɚɜɥɟɧɢɹ, ɤɨɬɨɪɵɣ ɹɜɥɹɟɬɫɹ
ɱɚɫɬɶɸ ɫɬɚɬɢɱɟɫɤɨɝɨ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɞɚɜɥɟɧɢɹ,
ɫɨɡɞɚɜɚɟɦɨɝɨ ɜɟɧɬɢɥɹɬɨɪɨɦ. ɂɧɟɪɰɢɨɧɧɨɟ ɞɚɜɥɟɧɢɟ ɩɨɪɨɠɞɚɟɬ ɞɜɢɠɭɳɭɸ
ɫɢɥɭ, ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɤɨɬɨɪɨɣ ɫɤɨɪɨɫɬɶ ɩɨɬɨɤɚ ɜ ɜɵɪɚɛɨɬɤɟ ɢɡɦɟɧɹɟɬɫɹ ɨɬ ɧɭɥɹ
ɞɨ ɧɨɦɢɧɚɥɶɧɨɣ ɜɟɥɢɱɢɧɵ,
ɨɩɪɟɞɟɥɹɟɦɨɣ ɬɨɱɤɨɣ ɩɟɪɟɫɟɱɟɧɢɹ ɧɚɩɨɪɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ –
ɜɟɧɬɢɥɹɬɨɪɚ PSV =
= f(Q) ɢ ɜɟɧɬɢɥɹɰɢɨɧɧɨɣ
Ɋɢɫɭɧɨɤ 3.2. Ʉ ɨɩɪɟɞɟɥɟɧɢɸ ɢɧɟɪɰɢɨɧɧɨɝɨ
ɞɚɜɥɟɧɢɹ
ɫɟɬɢ Pɋ = ȥ(Q), (ɪɢɫ. 3.2).
ɂɧɟɪɰɢɨɧɧɨɟ ɞɚɜɥɟ-
ɧɢɟ Pɂ = ij(Q) ɫɜɹɡɚɧɨ ɫɨ
ɫɬɚɬɢɱɟɫɤɢɦ ɞɚɜɥɟɧɢɟɦ ɜɟɧɬɢɥɹɬɨɪɚ ɢ ɩɨɬɟɪɟɣ ɞɚɜɥɟɧɢɹ ɜ ɜɟɧɬɢɥɹɰɢɨɧɧɨɣ ɫɟɬɢ ɭɪɚɜɧɟɧɢɟɦ ɛɚɥɚɧɫɚ ɞɚɜɥɟɧɢɣ PSV = Pɂ+PC, ɨɬɤɭɞɚ:
ɋ
PPP , (3.21)
CɂSV
2
, (3.22)
QRP
ɝɞɟ R – ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɵɪɚɛɨɬɤɢ, ɉɚ/(ɦ6/ɫ2);
Q – ɩɨɞɚɱɚ ɜɟɧɬɢɥɹɬɨɪɚ, ɦ
ɋ ɭɱɺɬɨɦ (3.12), (3.21) ɢ (3.22), ɩɨɫɥɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɧɚɯɨɞɢɦ:
3
/ɫ.
SVU
2
20
ɢɥɢ
QRBQAPP
qQpQRBP
, (3.23)
70
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