металлургия и материаловедение metallurgy and materials

МЕТАЛЛУРГИЯ И МАТЕРИАЛОВЕДЕНИЕ
METALLURGY AND MATERIALS TECHNOLOGY
Ɉɝɥɨɛɥɢɧ Ƚ. ȼ., ɋɬɭɥɨɜ ȼ. ȼ.
G.V.Ogloblin, V.V.Stulov
ɆɈȾȿɅɖ ȼ ȼɈɁȾɍɒɇɈɆ ɉɈɌɈɄȿ
A MODEL IN THE AIRFLOW
Ɉɝɥɨɛɥɢɧ Ƚɚɪɢɣ ȼɚɫɢɥɶɟɜɢɱ – ɤɚɧɞɢɞɚɬ ɩɟɞɚɝɨɝɢɱɟɫɤɢɯ ɧɚɭɤ, ɡɚɫɥɭɠɟɧɧɵɣ ɭɱɢɬɟɥɶ ɊɎ, ɞɨɰɟɧɬ ɤɚɮɟɞɪɵ ɬɟɨɪɢɢ ɢ ɦɟɬɨɞɢɤɢ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɨɛɪɚɡɨɜɚɧɢɹ Ⱥɦɭɪɫɤɨɝɨ ɝɭɦɚɧɢɬɚɪɧɨ-ɩɟɞɚɝɨɝɢɱɟɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ (Ɋɨɫɫɢɹ, Ʉɨɦɫɨɦɨɥɶɫɤ-ɧɚ-Ⱥɦɭɪɟ). E-mail: [email protected].
Mr. Gariy V. Ogloblin – PhD in Education, the Honored Teacher of the Russian Federation, Assistant Professor at the Department of theory and methodology of engineering
education, The Budget Amur Humanitarian&Educational State University (Komsomolsk
on Amur) E-mail: [email protected]
ɋɬɭɥɨɜ ȼɹɱɟɫɥɚɜ ȼɢɤɬɨɪɨɜɢɱ – ɞɨɤɬɨɪ ɬɟɯɧɢɱɟɫɤɢɯ ɧɚɭɤ, ɩɪɨɮɟɫɫɨɪ, ɡɚɫɥɭɠɟɧɧɵɣ ɢɡɨɛɪɟɬɚɬɟɥɶ
ɊɎ, ɡɚɦɟɫɬɢɬɟɥɶ ɞɢɪɟɤɬɨɪɚ ɩɨ ɧɚɭɱɧɨɣ ɪɚɛɨɬɟ ɂɧɫɬɢɬɭɬɚ ɦɚɲɢɧɨɜɟɞɟɧɢɹ ɢ ɦɟɬɚɥɥɭɪɝɢɢ ȾȼɈ ɊȺɇ
(Ɋɨɫɫɢɹ, Ʉɨɦɫɨɦɨɥɶɫɤ-ɧɚ-Ⱥɦɭɪɟ). E-mail: [email protected].
Mr. Vycheclav V. Stulov – Doctor of Engineerings, Professor, the Honored Inventor of the Russian Federation, Deputy Director for Research, Institute for Machine Engineering and Metallurgy of the Far-Eastern
Branch of Russian Academy ofSciences(Komsomolsk-on-Amur). E-mail: [email protected]
Ⱥɧɧɨɬɚɰɢɹ. ɋ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɠɢɞɤɢɯ ɤɪɢɫɬɚɥɥɨɜ ɜɵɩɨɥɧɟɧɨ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɨɛɬɟɤɚɧɢɹ ɬɪɺɯ ɬɟɥ
ɩɨɬɨɤɨɦ ɜɨɡɞɭɯɚ. ɉɪɢɜɟɞɟɧɨ ɫɪɚɜɧɟɧɢɟ ɫ ɪɟɡɭɥɶɬɚɬɚɦɢ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɩɨ ɬɪɚɞɢɰɢɨɧɧɨɣ ɦɟɬɨɞɢɤɟ.
Summary. Using liquid crystals, the authors have modeled the airflow of three bodies. A comparison with
the results of modeling by a traditional technique is presented.
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɦɨɞɟɥɶ, ɜɨɡɞɭɲɧɵɣ ɩɨɬɨɤ, ɠɢɞɤɢɟ ɤɪɢɫɬɚɥɥɵ, ɞɟɬɟɤɬɨɪ.
Key words: model, airflow, liquid crystals, detector.
ɍȾɄ 532.738:548-14
ȼɜɟɞɟɧɢɟ. ɂɡɜɟɫɬɧɨ, ɱɬɨ ɩɪɢ ɨɛɬɟɤɚɧɢɢ ɜɨɡɞɭɲɧɵɦ ɩɨɬɨɤɨɦ ɬɜɟɪɞɨɝɨ ɬɟɥɚ ɩɨɬɨɤ ɢɫɩɵɬɵɜɚɟɬ ɞɟɮɨɪɦɚɰɢɢ, ɷɬɨ ɩɪɢɜɨɞɢɬ ɤ ɢɡɦɟɧɟɧɢɸ ɫɤɨɪɨɫɬɢ, ɞɚɜɥɟɧɢɹ, ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɩɥɨɬɧɨɫɬɢ ɜ ɫɬɪɭɣɤɚɯ ɩɨɬɨɤɚ [1]. ȼɨɡɞɭɲɧɵɣ ɩɨɬɨɤ ɫɬɚɧɨɜɢɬɫɹ ɧɟɨɞɧɨɪɨɞɧɵɦ, ɜɨɡɧɢɤɚɸɬ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɟ ɫɢɥɵ ɢ ɦɨɦɟɧɬɵ. Ⱦɥɹ ɜɢɡɭɚɥɢɡɚɰɢɢ ɮɢɡɢɱɟɫɤɨɣ ɤɚɪɬɢɧɵ ɩɪɨɰɟɫɫɚ ɨɛɬɟɤɚɧɢɹ
ɜɨɡɞɭɲɧɵɦ ɩɨɬɨɤɨɦ ɬɟɥɚ ɢɫɩɨɥɶɡɭɸɬ ɞɵɦɤɚɧɚɥɵ, ɲɟɥɤɨɜɢɧɤɢ, ɛɭɦɚɠɧɵɟ ɥɟɧɬɵ, ɨɩɬɢɱɟɫɤɢɟ ɦɟɬɨɞɵ ɢ ɬ.ɞ. ɉɨɥɭɱɟɧɧɭɸ ɜɢɞɢɦɭɸ ɤɚɪɬɢɧɤɭ ɩɪɢɧɹɬɨ ɧɚɡɵɜɚɬɶ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɦ
ɫɩɟɤɬɪɨɦ. ɇɚɦɢ ɩɪɟɞɥɚɝɚɟɬɫɹ ɟɳɺ ɨɞɢɧ ɫɩɨɫɨɛ, ɩɨɡɜɨɥɹɸɳɢɣ ɬɚɤɠɟ ɩɨɥɭɱɢɬɶ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɣ ɫɩɟɤɬɪ ɫ ɩɨɦɨɳɶɸ ɞɟɬɟɤɬɨɪɚ ɧɚ ɠɢɞɤɢɯ ɤɪɢɫɬɚɥɥɚɯ.
ɐɟɥɶ ɪɚɛɨɬɵ: ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɨɛɬɟɤɚɧɢɹ ɜɨɡɞɭɯɨɦ ɬɟɥ ɪɚɡɥɢɱɧɨɣ ɤɨɧɮɢɝɭɪɚɰɢɢ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɠɢɞɤɢɯ ɤɪɢɫɬɚɥɥɨɜ.
ɉɪɢɛɨɪɵ ɢ ɦɚɬɟɪɢɚɥɵ: ɮɟɧ ɫ ɬɪɟɦɹ ɪɟɠɢɦɚɦɢ ɪɚɛɨɬɵ, ɦɨɞɟɥɢɪɭɟɦɵɟ ɬɟɥɚ (ɩɥɚɫɬɢɧɚ,
ɰɢɥɢɧɞɪ, ɤɪɵɥɨ), ɞɟɬɟɤɬɨɪ ɧɚ ɠɢɞɤɢɯ ɤɪɢɫɬɚɥɥɚɯ ɯɨɥɟɫɬɟɪɢɱɟɫɤɨɝɨ ɬɢɩɚ.
ɉɚɪɚɦɟɬɪɵ ɜɨɡɞɭɯɚ [3]: t = 40ÛC; ȕ = 1,09 ɤɝ/ɦ3; ɋ = 1000 Ⱦɠ/ɤɝ·Ʉ; Ȝ = 2,72·10-2
ɜɬ/ɦ·Ʉ; Ɋr = 0,71; Ȟ = 17,6·10-6 ɦ2/ɫ; ɚ = 24,8·10-6 ɦ2/ɫ. ɋɤɨɪɨɫɬɶ ɜɨɡɞɭɯɚ ɧɚ ɦɨɞɟɥɢ Vɜ = 0,9
ɦ/ɫ.
ɉɚɪɚɦɟɬɪɵ ɦɨɞɟɥɟɣ: 1) ɉɥɚɫɬɢɧɚ – ɚ · b, ɦɦ. 2) ɐɢɥɢɧɞɪ – R · l, ɦɦ. 3) Ʉɪɵɥɨ – l · b,
ɦɦ.
71
Материал поступил 01.02.2012
Ɇɟɬɨɞɢɤɚ ɷɤɫɩɟɪɢɦɟɧɬɚ. Ɇɨɞɟɥɢ ɪɚɡɦɟɳɚɸɬ ɧɚ ɞɟɬɟɤɬɨɪɟ, ɢ ɨɬ ɬɟɩɥɨɜɨɝɨ ɝɟɧɟɪɚɬɨɪɚ
ɩɨɞɜɨɞɢɬɫɹ ɧɚɝɪɟɬɵɣ ɜɨɡɞɭɯ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ (ɩɨɜɟɪɯɧɨɫɬɢ ɩɥɚɫɬɢɧɵ, ɨɫɢ ɰɢɥɢɧɞɪɚ, ɪɚɛɨɱɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɤɪɵɥɚ). ȼ ɪɟɡɭɥɶɬɚɬɟ ɧɚ ɷɤɪɚɧɟ ɞɟɬɟɤɬɨɪɚ ɩɨɹɜɥɹɟɬɫɹ ɰɜɟɬɨɜɨɟ ɢɡɨɛɪɚɠɟɧɢɟ
ɩɪɨɰɟɫɫɚ ɨɛɬɟɤɚɧɢɹ ɜɨɡɞɭɯɨɦ ɦɨɞɟɥɟɣ, ɤɨɬɨɪɨɟ ɡɚɜɢɫɢɬ ɨɬ ɫɢɥɵ ɞɚɜɥɟɧɢɹ ɜɨɡɞɭɲɧɨɝɨ ɩɨɬɨɤɚ, ɨɩɪɟɞɟɥɹɟɦɨɝɨ ɩɨ ɮɨɪɦɭɥɟ [3]
F=
,
(1)
ɝɞɟ F – ɫɢɥɚ ɞɚɜɥɟɧɢɹ ɜɨɡɞɭɲɧɨɝɨ ɩɨɬɨɤɚ (ɧ); ɋɯ – ɤɨɷɮɮɢɰɢɟɧɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ, ɡɚɜɢɫɹɳɢɣ
ɨɬ ɮɨɪɦɵ ɬɟɥɚ; – ɩɥɨɬɧɨɫɬɶ ɜɨɡɞɭɯɚ 1,29 ( ; S – ɩɥɨɳɚɞɶ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɩɥɚɫɬɢɧɵ
(ɦ2), Vɩ – ɫɤɨɪɨɫɬɶ ɩɨɬɨɤɚ ɜɨɡɞɭɯɚ (
. Ⱦɥɹ ɬɨɧɤɨɣ ɩɥɚɫɬɢɧɵ ɧɟɛɨɥɶɲɢɯ ɪɚɡɦɟɪɨɜ ɪɚɫɩɨɥɨ-
ɠɟɧɧɨɣ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɜɨɡɞɭɲɧɨɦɭ ɩɨɬɨɤɭ ɋɯ = 1,11 [3].
Ɋɟɡɭɥɶɬɚɬɵ ɢɫɫɥɟɞɨɜɚɧɢɣ. ɇɚ ɪɢɫ. 1, ɚ – 3, ɚ ɩɪɢɜɟɞɟɧɵ ɤɚɪɬɢɧɵ ɨɛɬɟɤɚɧɢɹ ɧɚɝɪɟɬɵɦ
ɜɨɡɞɭɯɨɦ ɬɪɺɯ ɦɨɞɟɥɟɣ. Ⱦɥɹ ɫɪɚɜɧɟɧɢɹ ɧɚ ɪɢɫ. 1, ɛ – 3, ɛ – ɤɚɪɬɢɧɵ ɨɛɬɟɤɚɧɢɹ ɜɨɡɞɭɯɨɦ ɬɟɥ,
ɩɨɥɭɱɟɧɧɵɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɫɭɳɟɫɬɜɭɸɳɢɯ ɦɟɬɨɞɢɤ. ɇɚ ɪɢɫ. 4 – ɝɪɚɞɭɢɪɨɜɚɧɧɚɹ ɲɤɚɥɚ.
ɋɪɚɜɧɟɧɢɟ ɩɨɥɭɱɟɧɧɵɯ ɤɚɪɬɢɧ, ɩɪɢɜɟɞɺɧɧɵɯ ɧɚ ɪɢɫ. 1, ɚ – 3, ɚ ɫ ɢɡɨɛɪɚɠɟɧɢɹɦɢ ɧɚ ɪɢɫ. 1, ɛ –
3, ɛ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɩɪɢɦɟɧɟɧɢɟ ɪɚɡɪɚɛɨɬɚɧɧɨɝɨ ɠɢɞɤɨɤɪɢɫɬɚɥɥɢɱɟɫɤɨɝɨ ɞɟɬɟɤɬɨɪɚ ɢ ɦɟɬɨɞɢɤɢ ɩɪɨɜɟɞɟɧɢɹ ɨɩɵɬɚ ɩɨɡɜɨɥɹɟɬ ɜɢɡɭɚɥɢɡɢɪɨɜɚɬɶ ɫ ɩɨɦɨɳɶɸ ɬɟɦɩɟɪɚɬɭɪ ɩɪɨɰɟɫɫ ɨɛɬɟɤɚɧɢɹ ɬɟɥ ɪɚɡɥɢɱɧɨɣ ɮɨɪɦɵ. ɉɪɢ ɷɬɨɦ ɬɟɦɩɟɪɚɬɭɪɧɨɟ ɩɨɥɟ ɧɚ ɬɪɺɯ ɦɨɞɟɥɹɯ ɩɪɟɞɫɬɚɜɥɟɧɨ ɫɟɦɟɣɫɬɜɨɦ ɢɡɨɬɟɪɦ 27-33 °ɋ. ɍɥɶɬɪɚɮɢɨɥɟɬɨɜɵɣ ɰɜɟɬ 33 °ɋ ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɨɛɥɚɫɬɶ ɩɨɜɵɲɟɧɧɨɝɨ ɞɚɜɥɟɧɢɹ ɩɟɪɟɞ ɦɨɞɟɥɶɸ (ɫɦ. ɪɢɫ. 1 – 3), ɚ ɤɨɪɢɱɧɟɜɵɣ (28 °ɋ) ɢ ɤɪɚɫɧɵɣ (27 °ɋ) – ɦɢɧɢɦɚɥɶɧɨɟ ɞɚɜɥɟɧɢɟ ɢ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɨɛɬɟɤɚɸɳɟɝɨ ɩɨɬɨɤɚ.
ɚ)
ɛ)
Ɋɢɫ. 1. ɉɪɹɦɨɭɝɨɥɶɧɚɹ ɩɥɚɫɬɢɧɚ ɜ ɜɨɡɞɭɲɧɨɦ ɩɨɬɨɤɟ: ɚ – ɮɢɡɢɱɟɫɤɚɹ ɤɚɪɬɢɧɚ ɨɛɬɟɤɚɧɢɹ
ɩɪɹɦɨɭɝɨɥɶɧɨɣ ɩɥɚɫɬɢɧɵ ɜɨɡɞɭɲɧɵɦ ɩɨɬɨɤɨɦ, ɩɨɥɭɱɟɧɧɚɹ ɫ ɩɨɦɨɳɶɸ ɞɟɬɟɤɬɨɪɚ
ɧɚ ɠɢɞɤɢɯ ɤɪɢɫɬɚɥɥɚɯ; ɛ – ɮɢɡɢɱɟɫɤɚɹ ɤɚɪɬɢɧɚ ɨɛɬɟɤɚɧɢɹ ɩɪɹɦɨɭɝɨɥɶɧɨɣ ɩɥɚɫɬɢɧɵ
ɜɨɡɞɭɲɧɵɦ ɩɨɬɨɤɨɦ, ɩɨɥɭɱɟɧɧɚɹ ɬɪɚɞɢɰɢɨɧɧɵɦ ɫɩɨɫɨɛɨɦ
ɚ)
ɛ)
72
Оглоблин Г.В., Стулов В.В.
МОДЕЛЬ В ВОЗДУШНОМ ПОТОКЕ
Ɋɢɫ. 2. ɐɢɥɢɧɞɪɢɱɟɫɤɨɟ ɬɟɥɨ ɜ ɜɨɡɞɭɲɧɨɦ ɩɨɬɨɤɟ: ɚ – ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɣ ɫɩɟɤɬɪ ɰɢɥɢɧɞɪɚ,
ɩɨɥɭɱɟɧɧɵɣ ɫ ɩɨɦɨɳɶɸ ɠɢɞɤɨɤɪɢɫɬɚɥɥɢɱɟɫɤɨɝɨ ɞɟɬɟɤɬɨɪɚ; ɛ – ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɣ ɫɩɟɤɬɪ
ɰɢɥɢɧɞɪɚ, ɩɨɥɭɱɟɧɧɵɣ ɬɪɚɞɢɰɢɨɧɧɵɦ ɫɩɨɫɨɛɨɦ
ɚ)
ɛ)
Ɋɢɫ. 3. Ⱥɷɪɨɞɢɧɚɦɢɱɟɫɤɢɣ ɫɩɟɤɬɪ ɤɪɵɥɚ ɫɚɦɨɥɺɬɚ. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɞɚɜɥɟɧɢɹ ɩɨ ɩɪɨɮɢɥɸ
ɤɪɵɥɚ: ɚ – ɬɟɪɦɨɝɪɚɦɦɚ ɤɪɵɥɚ ɫɚɦɨɥɺɬɚ; ɛ – ɝɪɚɮɢɱɟɫɤɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ
Ɋɢɫ. 4. Ƚɪɚɞɭɢɪɨɜɚɧɧɚɹ ɲɤɚɥɚ. ɍɥɶɬɪɚɮɢɨɥɟɬɨɜɵɣ ɰɜɟɬ 33 °ɋ, ɫɢɧɹɹ 32 °ɋ, ɝɨɥɭɛɚɹ 31 °ɋ,
ɡɟɥɺɧɚɹ 30 °ɋ, ɠɺɥɬɚɹ 29 °ɋ, ɤɨɪɢɱɧɟɜɚɹ 28 °ɋ, ɤɪɚɫɧɚɹ 27 °ɋ.
ɉɪɨɜɟɞɺɦ ɚɧɚɥɢɡ ɩɨɞɨɛɢɹ ɩɪɨɰɟɫɫɨɜ ɧɚ ɦɨɞɟɥɢ (ɦ) ɢ ɧɚɬɭɪɟ (ɧ). ɇɚ ɩɪɚɤɬɢɤɟ ɤɪɢɬɟɪɢɢ ɩɨɞɨɛɢɹ ɨɩɪɟɞɟɥɹɸɬɫɹ ɜ ɪɟɡɭɥɶɬɚɬɟ ɚɧɚɥɢɡɚ ɪɚɡɦɟɪɧɨɫɬɟɣ ɩɚɪɚɦɟɬɪɨɜ, ɨɩɢɫɵɜɚɸɳɢɯ
ɩɪɨɰɟɫɫ, ɢɥɢ ɜ ɪɟɡɭɥɶɬɚɬɟ ɚɧɚɥɢɡɚ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ. ȼɵɩɨɥɧɢɦ ɚɧɚɥɢɡ ɪɚɡɦɟɪɧɨɫɬɟɣ ɧɚ ɩɪɢɦɟɪɟ ɡɚɞɚɱ ɨ ɞɚɜɥɟɧɢɢ ɜɨɡɞɭɲɧɨɝɨ ɩɨɬɨɤɚ ɧɚ ɦɨɞɟɥɢ. ɉɪɢ ɷɬɨɦ ɭɫɩɟɯ ɞɟɥɚ ɡɚɜɢɫɢɬ ɨɬ ɩɪɚɜɢɥɶɧɨɫɬɢ ɨɩɪɟɞɟɥɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ, ɜɥɢɹɸɳɢɯ ɧɚ ɩɪɨɰɟɫɫ, ɱɬɨ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɧɬɭɢɰɢɟɣ [4].
ɂɡɦɟɧɟɧɢɟ ɞɚɜɥɟɧɢɹ ¨Ɋ [ɧ/ɦ2] ɩɪɢ ɨɛɬɟɤɚɧɢɢ ɜɨɡɞɭɯɨɦ ɬɟɥ ɡɚɜɢɫɢɬ ɨɬ: ɩɥɨɬɧɨɫɬɢ ɜɨɡɞɭɯɚ ȡ [ɤɝ/ɦ3], ɫɤɨɪɨɫɬɢ ɜɨɡɞɭɲɧɨɝɨ ɩɨɬɨɤɚ Vɜ [ɦ/ɫ], ɩɥɨɳɚɞɢ ɨɛɬɟɤɚɟɦɨɝɨ ɬɟɥɚ S[ɦ2], ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɢ ɜɨɡɞɭɯɚ Ȝ [Ⱦɠ/ɫ·ɦ·Ʉ]. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɛɟɡɪɚɡɦɟɪɧɵɯ ɤɨɦɩɥɟɤɫɨɜ ɩɪɢɦɟɧɹɟɬɫɹ
ɚɥɝɟɛɪɚɢɱɟɫɤɢɣ ɦɟɬɨɞ Ɋɷɥɟɹ [4]:
(2)
¨Ɋ = Ⱥ ȡɚ Vɜɛ SɜȜ2.
ɉɟɪɟɩɢɲɟɦ (2) ɜ ɪɚɡɦɟɪɧɨɫɬɹɯ ɜɟɥɢɱɢɧ:
ɇ/ɦ2 = (ɤɝ/ɦ3)ɚ · (ɦ/ɫ)ɛ · (ɦ2)ɜ · (Ⱦɠ/ɫ·ɦ·Ʉ)2.
(3)
ɋɭɦɦɢɪɨɜɚɧɢɟ ɩɨɤɚɡɚɬɟɥɟɣ ɫɬɟɩɟɧɟɣ ɩɪɢ ɨɞɢɧɚɤɨɜɵɯ ɟɞɢɧɢɰɚɯ ɩɪɢɜɨɞɢɬ ɤ ɫɢɫɬɟɦɟ
ɭɪɚɜɧɟɧɢɣ:
Ⱦɠ……..0 = 2,
(4)
Ʉɝ………1 = ɚ,
(5)
ɋ……….(-2) = - ɛ – 2,
(6)
Ɇ……… (1) = -3ɚ + ɛ + 2ɜ – 2,
(7)
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Ʉ………..0 = -2.
(8)
Ɋɟɲɟɧɢɟ (4) – (8) ɞɚɺɬ: 2 = 0, ɚ = 1, ɛ = 2, ɜ = 1, ɨɛɨɡɧɚɱɢɜ S = ɏ2, ɝɞɟ ɏ – ɯɚɪɚɤɬɟɪɧɵɣ
ɪɚɡɦɟɪ, ɩɨɞɫɬɚɜɢɦ ɜ ɨɫɧɨɜɧɨɟ ɭɪɚɜɧɟɧɢɟ (2), ɩɨɥɭɱɢɦ:
¨Ɋ = ȺȡVɜ2 · ɏ2
(9)
ɢɥɢ
¨Ɋ/ ȡ Vɜ2 = ȿu = Aɏ2 ,
(10)
ɝɞɟ ȿu – ɱɢɫɥɨ ɗɣɥɟɪɚ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɟɟ ɦɟɪɭ ɨɬɧɨɲɟɧɢɹ ɫɢɥ ɞɚɜɥɟɧɢɹ ɢ ɢɧɟɪɰɢɢ ɜ ɩɨɬɨɤɟ
ɜɨɡɞɭɯɚ. ɇɚ ɦɨɞɟɥɢ ¨Ɋ = F/S, ɝɞɟ F – ɫɢɥɚ ɞɚɜɥɟɧɢɹ ɩɨɬɨɤɚ, ɨɩɪɟɞɟɥɹɟɦɚɹ ɩɨ ɮɨɪɦɭɥɟ (1). ɇɚ
ɦɨɞɟɥɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ¨Ɋɦ = ɋɯ·ȡVɜ2/2, ɝɞɟ ɋɯ – ɤɨɷɮɮɢɰɢɟɧɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɩɨɬɨɤɭ, ɨɩɪɟɞɟɥɹɟɦɵɣ ɩɨ ɫɩɪɚɜɨɱɧɢɤɭ ɢɥɢ ɪɚɫɱɺɬɧɵɦ ɩɭɬɺɦ [3]. ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɪɢ ɢɡɜɟɫɬɧɵɯ ɧɚ ɦɨɞɟɥɢ ȡ,
Vɜ, ɋɯ, ɏɦ ɨɩɪɟɞɟɥɹɟɬɫɹ ɞɢɚɩɚɡɨɧ ɡɧɚɱɟɧɢɣ (ȿu). ɉɪɢ (ȿu)ɦ = (ȿu)ɧ; (ɋɯ)ɦ = (ɋɯ)ɧ; Ɇɯ = ɏɧ /ɏɧ
ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɚɪɚɦɟɬɪɵ ɞɥɹ ɧɚɬɭɪɧɨɝɨ ɨɛɪɚɡɰɚ ɏɧ, ȡɧ, (Vɜ)ɧ.
ɇɚ ɪɢɫ. 1, ɚ ɩɪɟɞɫɬɚɜɥɟɧɚ ɬɟɪɦɨɝɪɚɦɦɚ ɜɨɡɞɭɲɧɨɝɨ ɩɨɬɨɤɚ, ɨɛɬɟɤɚɸɳɟɝɨ ɩɪɹɦɨɭɝɨɥɶɧɭɸ ɩɥɚɫɬɢɧɭ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɠɢɞɤɢɯ ɤɪɢɫɬɚɥɥɨɜ. Ɍɟɪɦɨɝɪɚɦɦɚ ɩɪɟɞɫɬɚɜɥɟɧɚ ɢɡɨɬɟɪɦɚɦɢ
ɪɚɡɧɨɣ ɰɜɟɬɧɨɫɬɢ. Ⱦɥɹ ɪɚɫɲɢɮɪɨɜɤɢ ɬɟɪɦɨɝɪɚɦɦɵ ɧɟɨɛɯɨɞɢɦɚ ɝɪɚɞɭɢɪɨɜɚɧɧɚɹ ɲɤɚɥɚ ɞɥɹ
ɞɚɧɧɨɝɨ ɬɢɩɚ ɠɢɞɤɢɯ ɤɪɢɫɬɚɥɥɨɜ. ɇɚ ɪɢɫ. 4 ɩɪɟɞɫɬɚɜɥɟɧɚ ɝɪɚɞɭɢɪɨɜɚɧɧɚɹ ɲɤɚɥɚ ɞɥɹ ɩɪɢɦɟɧɹɟɦɨɝɨ ɞɟɬɟɤɬɨɪɚ. ɋɨɩɨɫɬɚɜɥɹɹ ɰɜɟɬɚ ɢɡɨɬɟɪɦ ɫɨ ɲɤɚɥɨɣ ɬɟɦɩɟɪɚɬɭɪ, ɨɩɪɟɞɟɥɹɟɦ ɬɟɦɩɟɪɚɬɭɪɧɨɟ ɩɨɥɟ ɤɚɠɞɨɣ ɢɡɨɬɟɪɦɵ. ɂɡɨɬɟɪɦɵ ɯɚɪɚɤɬɟɪɢɡɭɸɬ ɥɢɧɢɢ ɬɨɤɚ ɜɨɡɞɭɲɧɨɝɨ ɩɨɬɨɤɚ.
Ɏɢɨɥɟɬɨɜɚɹ ɢɡɨɬɟɪɦɚ ɢɫɩɵɬɵɜɚɟɬ ɪɟɡɤɨɟ ɢɡɦɟɧɟɧɢɟ ɩɟɪɟɞ ɩɥɚɫɬɢɧɨɣ, ɱɬɨ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɪɟɡɤɨɦɭ ɢɡɦɟɧɟɧɢɸ ɫɤɨɪɨɫɬɢ, ɢ ɧɚɩɪɚɜɥɟɧɢɹ ɞɜɢɠɟɧɢɹ. Ⱦɚɜɥɟɧɢɟ ɜɨɡɪɚɫɬɚɟɬ ɩɟɪɟɞ ɩɥɚɫɬɢɧɨɣ ɢ
ɩɚɞɚɟɬ ɡɚ ɧɟɣ. ɂɡɨɬɟɪɦɵ ɫɢɧɹɹ, ɝɨɥɭɛɚɹ, ɡɟɥɺɧɚɹ ɢ ɬ.ɞ. ɨɝɢɛɚɸɬ ɩɥɚɫɬɢɧɭ, ɫɨɯɪɚɧɹɹ ɫɜɨɸ ɧɟɪɚɡɪɵɜɧɨɫɬɶ. ɇɚ ɪɢɫ. 1, ɛ ɩɪɟɞɫɬɚɜɥɟɧ ɬɪɚɞɢɰɢɨɧɧɵɣ ɫɩɨɫɨɛ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. Ʌɢɧɢɢ ɬɨɤɚ
ɜɨɡɞɭɲɧɨɝɨ ɩɨɬɨɤɚ ɢɫɩɵɬɵɜɚɸɬ ɞɨɜɨɥɶɧɨ ɪɟɡɤɨɟ ɢɡɦɟɧɟɧɢɟ ɩɟɪɟɞ ɩɥɚɫɬɢɧɨɣ, ɩɨɬɨɤ ɦɟɧɹɟɬ
ɫɤɨɪɨɫɬɶ ɢ ɧɚɩɪɚɜɥɟɧɢɟ ɞɜɢɠɟɧɢɹ, ɩɪɨɢɫɯɨɞɢɬ ɭɩɥɨɬɧɟɧɢɟ ɢ ɨɛɬɟɤɚɧɢɟ ɟɝɨ ɧɚ ɤɪɚɹɯ ɩɥɚɫɬɢɧɵ. ȼɫɺ ɷɬɨ ɫɨɩɪɨɜɨɠɞɚɟɬɫɹ ɩɨɜɵɲɟɧɢɟɦ ɞɚɜɥɟɧɢɹ ɩɟɪɟɞ ɩɥɚɫɬɢɧɨɣ ɢ ɟɝɨ ɭɦɟɧɶɲɟɧɢɟɦ ɡɚ
ɧɟɣ. Ɂɚ ɩɥɚɫɬɢɧɨɣ ɨɛɪɚɡɭɟɬɫɹ ɨɛɥɚɫɬɶ, ɝɞɟ ɥɢɧɢɢ ɬɨɤɚ ɩɪɟɜɪɚɳɚɸɬɫɹ ɜ ɜɢɯɪɢ. Ⱥɧɚɥɨɝɢɱɧɨ
ɩɨɥɭɱɚɟɦ ɬɟɪɦɨɝɪɚɦɦɵ ɞɥɹ ɰɢɥɢɧɞɪɚ (ɫɦ. ɪɢɫ. 2, ɚ) ɢ ɫɪɚɜɧɢɜɚɟɦ ɟɺ ɫ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɦ
ɫɩɟɤɬɪɨɦ, ɩɨɥɭɱɟɧɧɵɦ ɬɪɚɞɢɰɢɨɧɧɵɦ ɦɟɬɨɞɨɦ (ɫɦ. ɪɢɫ. 2, ɛ). ɋɩɟɤɬɪ ɤɪɵɥɚ ɫɚɦɨɥɺɬɚ ɩɪɟɞɫɬɚɜɥɟɧ ɧɚ ɪɢɫ. 3, ɚ, ɤɨɬɨɪɵɣ ɩɨɥɭɱɟɧ ɫ ɩɨɦɨɳɶɸ ɠɢɞɤɨɤɪɢɫɬɚɥɥɢɱɟɫɤɨɝɨ ɞɟɬɟɤɬɨɪɚ, ɚ ɧɚ
ɪɢɫ. 3, ɛ – ɬɪɚɞɢɰɢɨɧɧɵɦ ɫɩɨɫɨɛɨɦ.
ȼɵɜɨɞ. ɂɡɨɬɟɪɦɵ, ɫɨɡɞɚɧɧɵɟ ɠɢɞɤɢɦɢ ɤɪɢɫɬɚɥɥɚɦɢ, ɯɚɪɚɤɬɟɪɢɡɭɸɬ ɫɤɨɪɨɫɬɶ ɥɢɧɢɣ
ɬɨɤɚ ɢ ɬɟɦɩɟɪɚɬɭɪɭ. Ɂɧɚɹ ɢɫɯɨɞɧɭɸ ɫɤɨɪɨɫɬɶ ɜɨɡɞɭɲɧɨɝɨ ɩɨɬɨɤɚ, ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ ɥɢɧɢɢ ɬɨɤɚ ɨɞɧɨɣ ɢɡɨɬɟɪɦɵ ɱɟɪɟɡ ɫɨɨɬɧɨɲɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪ ɢ ɫɤɨɪɨɫɬɟɣ, ɚ ɬɚɤɠɟ ɩɨɥɭɱɢɬɶ ɝɪɚɞɢɟɧɬ ɫɤɨɪɨɫɬɟɣ ɩɟɪɟɞ ɩɥɚɫɬɢɧɨɣ ɢ ɡɚ ɩɥɚɫɬɢɧɨɣ. Ⱥɧɚɥɨɝɢɱɧɨ ɡɚɞɚɱɭ ɦɨɠɧɨ ɪɟɲɢɬɶ
ɢ ɞɥɹ ɞɚɜɥɟɧɢɣ ɜ ɥɢɧɢɹɯ ɬɨɤɚ, ɜɡɹɜ ɡɚ ɢɫɯɨɞɧɨɟ ɜɵɪɚɠɟɧɢɟ (1). ɉɪɟɞɥɨɠɟɧɧɚɹ ɦɟɬɨɞɢɤɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɬɟɩɥɨɜɵɯ ɩɨɥɟɣ ɜɨɡɞɭɲɧɵɯ ɩɨɬɨɤɨɜ ɫ ɩɨɦɨɳɶɸ ɠɢɞɤɢɯ ɤɪɢɫɬɚɥɥɨɜ ɩɨɡɜɨɥɹɟɬ
ɩɨɥɭɱɢɬɶ ɤɨɧɟɱɧɵɣ ɪɟɡɭɥɶɬɚɬ ɢ ɨɩɪɟɞɟɥɢɬɶ ɩɚɪɚɦɟɬɪɵ ɞɥɹ ɧɚɬɭɪɧɵɯ ɨɛɪɚɡɰɨɜ.
ɅɂɌȿɊȺɌɍɊȺ
1. Ɉɝɥɨɛɥɢɧ, Ƚ. ȼ. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɬɟɩɥɨɜɵɯ ɩɨɥɟɣ ɜɨɡɞɭɲɧɵɯ ɩɨɬɨɤɨɜ / Ƚ. ȼ. Ɉɝɥɨɛɥɢɧ, ȿ. Ƚ. Ɏɟɞɭɥɨɜ // Ⱥɤɬɭɚɥɶɧɵɟ ɩɪɨɛɥɟɦɵ ɦɚɬɟɦɚɬɢɤɢ, ɮɢɡɢɤɢ, ɢɧɮɨɪɦɚɬɢɤɢ ɜ ɜɭɡɟ ɢ ɲɤɨɥɟ: ɦɚɬɟɪɢɚɥɵ ɜ. ɧ-ɩ. ɤ.
ɝ. Ʉɨɦɫɨɦɨɥɶɫɤ-ɧɚ-Ⱥɦɭɪɟ, 26 ɦɚɪɬɚ 2010 ɝ. – Ʉɨɦɫɨɦɨɥɶɫɤ-ɧɚ-Ⱥɦɭɪɟ: ȺɦȽɉȽɍ, 2010. – ɋ. 28-31.
2. ɋɬɭɥɨɜ, ȼ. ȼ. Ɏɢɡɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɩɪɨɰɟɫɫɨɜ ɩɪɢ ɩɨɥɭɱɟɧɢɢ ɥɢɬɨɣ ɞɟɮɨɪɦɢɪɨɜɚɧɧɨɣ ɡɚɝɨɬɨɜɤɢ / ȼ. ȼ. ɋɬɭɥɨɜ, ȼ. ɂ. Ɉɞɢɧɨɤɨɜ, Ƚ. ȼ. Ɉɝɥɨɛɥɢɧ. – ȼɥɚɞɢɜɨɫɬɨɤ: Ⱦɚɥɶɧɚɭɤɚ, 2009. – 175 ɫ.
3. Ɍɟɩɥɨ- ɢ ɦɚɫɫɨɨɛɦɟɧ. Ɍɟɩɥɨɬɟɯɧɢɱɟɫɤɢɣ ɷɤɫɩɟɪɢɦɟɧɬ: ɫɩɪɚɜ. / ȿ. ȼ. Ⱥɦɟɬɢɫɬɨɜ, ȼ. Ⱥ. Ƚɪɢɝɨɪɶɟɜ,
Ȼ. Ɍ. ȿɦɟɰ [ɢ ɞɪ.]. – Ɇ.: ɗɧɟɪɝɨɢɡɞɚɬ, 1982. – 512 ɫ.
4. Ɇɢɝɚɣ, Ɇ. Ʉ. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɬɟɩɥɨɨɛɦɟɧɧɨɝɨ ɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɨɛɨɪɭɞɨɜɚɧɢɹ / Ɇ. Ʉ. Ɇɢɝɚɣ. – Ʌ.:
ɗɧɟɪɝɨɢɡɞɚɬ, 1987. – 264 ɫ.
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