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Файл:Современные проблемы металлургии и материаловедения гидродинамика и массообмен в многофазных системах металлургии. Учебное пособие
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3. ɇɚ ɩɨɜɟɪɯɧɨɫɬɢ ɱɚɫɬɢɰɵ ɢɦɟɸɬɫɹ ɞɜɟ ɤɪɢɬɢɱɟɫɤɢɟ ɬɨɱɤɢ. ɑɬɨ
ɷɬɨ ɡɚ ɬɨɱɤɢ ɢ ɝɞɟ ɨɧɢ ɪɚɫɩɨɥɚɝɚɸɬɫɹ?
4. ȼ ɤɚɤɢɯ ɬɨɱɤɚɯ ɫɤɨɪɨɫɬɶ ɩɨɬɨɤɚ ɢɞɟɚɥɶɧɨɣ ɠɢɞɤɨɫɬɢ, ɨɛɬɟɤɚɸ-
ɳɟɝɨ ɫɮɟɪɢɱɟɫɤɭɸ ɱɚɫɬɢɰɭ, ɢɦɟɟɬ ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɢ ɱɟɦɭ
ɨɧɨ ɪɚɜɧɨ?
5. Ɇɨɠɟɬ ɥɢ ɫɤɨɪɨɫɬɶ ɩɨɬɨɤɚ ɢɞɟɚɥɶɧɨɣ ɠɢɞɤɨɫɬɢ ɩɪɢ ɨɛɬɟɤɚɧɢɢ
ɫɮɟɪɢɱɟɫɤɨɣ ɱɚɫɬɢɰɵ ɛɵɬɶ ɛɨɥɶɲɟ ɫɤɨɪɨɫɬɢ ɷɬɨɣ ɠɢɞɤɨɫɬɢ ɧɚ
ɛɟɫ-
ɤɨɧɟɱɧɨɦ ɭɞɚɥɟɧɢɢ ɨɬ ɱɚɫɬɢɰɵ?
6. Ʉɚɤ ɢɡɦɟɧɹɟɬɫɹ ɞɚɜɥɟɧɢɟ ɜ ɩɨɬɨɤɟ ɢɞɟɚɥɶɧɨɣ ɠɢɞɤɨɫɬɢ, ɩɪɢ
ɫɢɦɦɟɬɪɢɱɧɨɦ ɨɦɵɜɚɧɢɢ ɫɮɟɪɢɱɟɫɤɨɣ ɱɚɫɬɢɰɵ?
7. ȼ ɱɺɦ ɡɚɤɥɸɱɚɟɬɫɹ ɩɚɪɚɞɨɤɫ Ⱦɚɥɚɦɛɟɪɚ? Ʉɚɤ ɨɧ ɨɛɴɹɫɧɹɟɬɫɹ?
8. ɑɟɦɭ ɪɚɜɧɚ ɦɚɫɫɚ ɠɢɞɤɨɫɬɢ, ɩɪɢɫɨɟɞɢɧɺɧɧɚɹ ɤ ɞɜɢɠɭɳɟɣɫɹ
ɫɮɟɪɟ?
9. ȼ ɩɪɨɰɟɫɫɟ ɞɜɢɠɟɧɢɹ ɜ ɩɨɬɨɤɟ ɠɢɞɤɨɫɬɢ ɫɮɟɪɢɱɟɫɤɚɹ ɱɚɫɬɢɰɚ
ɜɵɬɟɫɧɹɟɬ ɱɚɫɬɶ ɠɢɞɤɨɫɬɢ ɢ ɫɨɝɥɚɫɧɨ ɡɚɤɨɧɭ ɫɨɯɪɚɧɟɧɢɹ ɷɧɟɪɝɢɢ
ɜɨ-
ɜɥɟɤɚɟɬ ɜ ɞɜɢɠɟɧɢɟ ɱɚɫɬɶ ɠɢɞɤɨɫɬɢ. Ʉɚɤ ɫɨɨɬɧɨɫɹɬɫɹ ɦɟɠɞɭ ɫɨɛɨɣ
ɦɚɫɫɵ ɜɵɬɟɫɧɟɧɧɨɣ ɢ ɩɪɢɫɨɟɞɢɧɺɧɧɨɣ ɱɚɫɬɟɣ ɠɢɞɤɨɫɬɢ?
10. ɋɨɫɬɚɜɶɬɟ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɫɮɟɪɢɱɟɫɤɨɣ ɱɚɫɬɢɰɵ ɜ ɧɟɩɨɞɜɢɠɧɨɣ ɢɞɟɚɥɶɧɨɣ ɠɢɞɤɨɫɬɢ ɫ ɭɱɺɬɨɦ ɩɪɢɫɨɟɞɢɧɺɧɧɨɣ ɦɚɫɫɵ ɩɪɢ
ɭɫɥɨɜɢɢ ɨɬɫɭɬɫɬɜɢɹ ɫɢɥɵ ɬɹɠɟɫɬɢ.
11. ɋɨɫɬɚɜɶɬɟ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɫɮɟɪɢɱɟɫɤɨɣ ɱɚɫɬɢɰɵ ɜ ɧɟɩɨɞɜɢɠɧɨɣ ɢɞɟɚɥɶɧɨɣ ɠɢɞɤɨɫɬɢ ɫ ɭɱɺɬɨɦ ɩɪɢɫɨɟɞɢɧɺɧɧɨɣ ɦɚɫɫɵ
ɞɟɣɫɬɜɢɹ ɫɢɥɵ ɬɹɠɟɫɬɢ.
12. Ʉɚɤ ɜɵɝɥɹɞɢɬ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɫɮɟɪɢɱɟɫɤɨɣ ɱɚɫɬɢɰɵ ɜ ɩɨɬɨɤɟ ɢɞɟɚɥɶɧɨɣ ɠɢɞɤɨɫɬɢ, ɟɫɥɢ ɞɜɢɠɟɧɢɟ ɩɪɨɢɫɯɨɞɢɬ ɬɨɥɶɤɨ ɩɨɞ
ɞɟɣɫɬɜɢɟɦ ɫɢɥɵ ɬɹɠɟɫɬɢ?
13. ɑɟɦɭ ɪɚɜɧɨ ɭɫɤɨɪɟɧɢɟ ɜ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɤɚɩɥɢ
ɪɬɭɬɢ, ɧɚɱɢɧɚɸɳɟɣ ɩɚɞɚɬɶ ɜ ɜɨɡɞɭɯɟ? ɑɟɦɭ ɪɚɜɧɨ ɧɚɱɚɥɶɧɨɟ ɭɫɤɨɪɟɧɢɟ ɜɨɡɞɭɲɧɨɝɨ ɩɭɡɵɪɶɤɚ, ɧɚɱɢɧɚɸɳɟɝɨ ɜɫɩɥɵɜɚɬɶ ɜ ɫɥɨɟ ɪɬɭɬɢ?
14. Ɂɚɩɢɲɢɬɟ
ɭɪɚɜɧɟɧɢɟ ɇɚɜɶɟ – ɋɬɨɤɫɚ ɜ ɜɟɤɬɨɪɧɨɣ ɮɨɪɦɟ ɞɥɹ
ɫɥɭɱɚɹ ɞɜɢɠɟɧɢɹ ɫɮɟɪɢɱɟɫɤɨɣ ɬɜɺɪɞɨɣ ɱɚɫɬɢɰɵ ɩɪɢ Re << 1.
15. Ʉɚɤ ɧɟɨɛɯɨɞɢɦɨ ɪɚɫɩɨɥɨɠɢɬɶ ɫɮɟɪɢɱɟɫɤɭɸ ɫɢɫɬɟɦɭ ɤɨɨɪɞɢɧɚɬ, ɱɬɨɛɵ ɨɛɬɟɤɚɧɢɟ ɫɮɟɪɢɱɟɫɤɨɣ ɱɚɫɬɢɰɵ ɩɨɬɨɤɨɦ ɛɵɥɨ ɫɢɦɦɟɬɪɢɱɧɵɦ?
16. ɋɮɨɪɦɭɥɢɪɭɣɬɟ ɝɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ ɞɥɹ ɭɪɚɜɧɟɧɢɹ ɋɬɨɤɫɚ
(ɨɦɵɜɚɧɢɟ ɬɜɺɪɞɨɣ ɫɮɟɪɢɱɟɫɤɨɣ ɱɚɫɬɢɰɵ ɩɨɬɨɤɨɦ ɜ ɩɨɥɡɭɳɟɦ ɪɟ-
ɠɢɦɟ (Re << 1)).
17. ɋɢɥɚ, ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɱɚɫɬɢɰɭ, ɞɜɢɠɭɳɭɸɫɹ ɜ
ɩɨɬɨɤɟ, ɫɨ ɫɬɨ-
ɪɨɧɵ ɧɟɫɭɳɟɣ ɫɪɟɞɵ, ɜɵɪɚɠɚɟɬɫɹ ɨɛɵɱɧɨ ɱɟɪɟɡ ɤɨɷɮɮɢɰɢɟɧɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ C
(ɢɥɢ ɋɯ). ɑɬɨ ɷɬɨ ɡɚ ɜɟɥɢɱɢɧɚ?
ɞ
ɢ
71
18. ɑɟɦɭ ɪɚɜɟɧ ɤɨɷɮɮɢɰɢɟɧɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɥɹ ɬɜɺɪɞɨɣ ɱɚɫɬɢɰɵ,
ɞɜɢɠɭɳɟɣɫɹ ɜ ɠɢɞɤɨɫɬɢ ɩɪɢ Re << 1?
19. Ʉɚɤ ɩɪɨɢɫɯɨɞɢɬ ɪɚɡɝɨɧ ɬɜɺɪɞɨɣ ɱɚɫɬɢɰɵ, ɞɜɢɠɭɳɟɣɫɹ ɜ ɠɢɞ-
ɤɨɫɬɢ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɢɥɵ ɬɹɠɟɫɬɢ, ɞɨ ɭɫɬɚɧɨɜɢɜɲɟɣɫɹ ɫɤɨɪɨɫɬɢ ɩɚɞɟɧɢɹ?
20. ɑɟɦɭ ɪɚɜɧɚ ɫɢɥɚ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɜɢɠɟɧɢɸ ɬɜɺɪɞɨɣ ɱɚɫɬɢɰɵ ɜ
ɠɢɞɤɨɫɬɢ ɩɪɢ Re << 1?
21. ȼ ɤɚɤɢɯ ɫɥɭɱɚɹɯ ɩɪɢ ɞɜɢɠɟɧɢɢ ɤɚɩɥɢ ɜ ɞɪɭɝɨɣ ɠɢɞɤɨɫɬɢ ɭ
ɧɟɺ
ɫɨɯɪɚɧɹɟɬɫɹ ɫɮɟɪɢɱɟɫɤɚɹ ɮɨɪɦɚ?
22. ɋɨɫɬɚɜɶɬɟ ɦɚɬɟɦɚɬɢɱɟɫɤɭɸ ɦɨɞɟɥɶ ɞɜɢɠɟɧɢɹ ɤɚɩɥɢ ɜ ɞɪɭɝɨɣ
ɠɢɞɤɨɫɬɢ ɩɪɢ Re << 1.
23. Ʉɚɤ ɢɡɜɟɫɬɧɨ, ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɤɚɩɥɢ, ɞɜɢɠɭɳɟɣɫɹ ɜ ɩɨɬɨɤɟ
ɠɢɞɤɨɫɬɢ, ɨɬɫɭɬɫɬɜɭɟɬ ɩɪɨɫɤɚɥɶɡɵɜɚɧɢɟ ɮɚɡ. Ʉɚɤ ɷɬɨɬ ɮɚɤɬ ɨɬɪɚɠɚɟɬɫɹ ɜ ɭɫɥɨɜɢɢ ɨɞɧɨɡɧɚɱɧɨɫɬɢ, ɫɮɨɪɦɭɥɢɪɨɜɚɧɧɨɦ ɞɥɹ ɦɟɠɮɚɡɧɨɣ
ɝɪɚɧɢɰɵ?
24. Ɉɦɵɜɚɸɳɢɣ ɩɨɬɨɤ ɝɟɧɟɪɢɪɭɟɬ ɜ ɨɛɴɺɦɟ ɤɚɩɥɢ ɬɟɱɟɧɢɟ ɠɢɞɤɨ-
ɫɬɢ. Ʉɚɤɨɣ ɯɚɪɚɤɬɟɪ ɧɨɫɢɬ
ɷɬɨ ɬɟɱɟɧɢɟ ɢ ɤɚɤ ɫɮɨɪɦɭɥɢɪɨɜɚɬɶ ɞɥɹ ɧɟ-
ɝɨ ɭɫɥɨɜɢɹ ɨɞɧɨɡɧɚɱɧɨɫɬɢ?
25. ɑɟɦɭ ɪɚɜɧɚ ɫɢɥɚ ɫɨɩɪɨɬɢɜɥɟɧɢɹ, ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɤɚɩɥɸ ɫɨ
ɫɬɨɪɨɧɵ ɧɟɫɭɳɟɝɨ ɩɨɬɨɤɚ?
26. ɑɟɦɭ ɪɚɜɧɚ ɫɤɨɪɨɫɬɶ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɞɜɢɠɟɧɢɹ ɤɚɩɥɢ ɜ ɜɹɡ-
ɤɨɣ ɠɢɞɤɨɫɬɢ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɫɢɥɵ ɬɹɠɟɫɬɢ?
27. ɂɫɩɨɥɶɡɭɹ ɮɨɪɦɭɥɵ ɫɤɨɪɨɫɬɢ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɞɜɢɠɟɧɢɹ ɤɚɩ-
ɥɢ ɢ ɫɢɥɵ ɫɨɩɪɨɬɢɜɥɟɧɢɹ, ɞɟɣɫɬɜɭɸɳɢɟ ɧɚ ɤɚɩɥɸ ɫɨ
ɫɬɨɪɨɧɵ ɧɟɫɭɳɟɝɨ ɩɨɬɨɤɚ, ɩɨɥɭɱɢɬɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɮɨɪɦɭɥɵ ɞɥɹ ɫɥɭɱɚɹ ɞɜɢɠɟɧɢɹ ɝɚɡɨɜɨɝɨ ɩɭɡɵɪɹ ɜ ɠɢɞɤɨɫɬɢ.
28. ȼ ɱɺɦ ɫɨɫɬɨɢɬ ɨɫɨɛɟɧɧɨɫɬɶ ɞɟɣɫɬɜɢɹ ɫɢɥɵ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɫɪɟɞɵ ɧɚ ɞɜɢɠɭɳɭɸɫɹ ɜ ɧɟɣ ɱɚɫɬɢɰɭ ɩɪɢ ɧɟɫɬɚɰɢɨɧɚɪɧɨɦ ɪɟɠɢɦɟ ɞɜɢɠɟɧɢɹ?
29. ɇɚɩɢɲɢɬɟ ɜɵɪɚɠɟɧɢɟ ɫɢɥɵ ɫɨɩɪɨɬɢɜɥɟɧɢɹ, ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ
ɱɚɫɬɢɰɭ ɫɨ ɫɬɨɪɨɧɵ ɧɟɫɭɳɟɣ ɫɪɟɞɵ ɩɪɢ ɫɬɨɤɫɨɜɨɦ ɨɦɵɜɚɧɢɢ ɟɺ
ɢ
ɨɩɢɲɢɬɟ ɮɢɡɢɱɟɫɤɢɣ ɫɦɵɫɥ ɫɥɚɝɚɟɦɵɯ ɷɬɨɣ ɮɨɪɦɭɥɵ.
30. Ʉɚɤ ɨɩɢɫɵɜɚɟɬɫɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɱɚɫɬɢɰɵ ɫ ɩɨɬɨɤɨɦ ɩɪɢ ɧɟɫɬɚɰɢɨɧɚɪɧɨɦ ɞɜɢɠɟɧɢɢ ɱɚɫɬɢɰɵ ɫ ɤɨɧɟɱɧɵɦ ɡɧɚɱɟɧɢɟɦ ɱɢɫɥɚ Ɋɟɣɧɨɥɶɞɫɚ?
31. Ʉɚɤ ɫɨɫɬɚɜɥɹɸɬ ɨɩɢɫɚɧɢɟ ɧɟɫɬɚɰɢɨɧɚɪɧɨɝɨ ɞɜɢɠɟɧɢɹ ɝɚɡɨɜɨɝɨ
ɩɭɡɵɪɹ ɩɪɢ ɤɨɧɟɱɧɵɯ ɡɧɚɱɟɧɢɹɯ ɱɢɫɥɚ Ɋɟɣɧɨɥɶɞɫɚ?
32. ȼ ɱɺɦ ɡɚɤɥɸɱɚɟɬɫɹ ɬɪɭɞɧɨɫɬɶ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɨɩɢɫɚɧɢɹ ɞɜɢɠɟɧɢɹ ɫɢɫɬɟɦɵ ɞɢɫɩɟɪɫɧɵɯ ɱɚɫɬɢɰ ɜ ɧɟɫɭɳɟɦ
ɩɨɬɨɤɟ?
72
33. Ʉɚɤɢɦɢ ɜɟɥɢɱɢɧɚɦɢ ɨɩɟɪɢɪɭɸɬ ɩɪɢ ɨɩɢɫɚɧɢɢ ɞɜɢɠɟɧɢɹ ɫɢ-
ɫɬɟɦɵ ɞɢɫɩɟɪɫɧɵɯ ɱɚɫɬɢɰ ɜ ɧɟɫɭɳɟɦ ɩɨɬɨɤɟ?
34. Ʉɚɤ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɢɥɚ, ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɫɢɫɬɟɦɭ ɞɢɫɩɟɪɫɧɵɯ
ɱɚɫɬɢɰ ɫɨ ɫɬɨɪɨɧɵ ɧɟɫɭɳɟɝɨ ɩɨɬɨɤɚ ɩɪɢ
35. ɂɡɥɨɠɢɬɟ ɮɢɡɢɱɟɫɤɭɸ ɫɭɳɧɨɫɬɶ ɹɱɟɟɱɧɨɣ ɦɨɞɟɥɢ ɞɜɢɠɟɧɢɹ
ɫɢɫɬɟɦɵ ɞɢɫɩɟɪɫɧɵɯ ɱɚɫɬɢɰ ɜ ɧɟɫɭɳɟɦ ɩɨɬɨɤɟ.
36. Ʉɚɤɢɦ ɨɛɪɚɡɨɦ ɹɱɟɟɱɧɚɹ ɦɨɞɟɥɶ ɝɢɞɪɨɞɢɧɚɦɢɤɢ ɫɢɫɬɟɦɵ ɞɢɫ-
ɩɟɪɫɧɵɯ ɱɚɫɬɢɰ ɨɛɥɟɝɱɚɟɬ ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɩɢɫɚɧɢɟ ɷɬɨɝɨ ɞɜɢɠɟɧɢɹ?
37. ȼ ɱɺɦ ɫɦɵɫɥ ɝɪɚɧɢɱɧɨɝɨ ɭɫɥɨɜɢɹ ɏɚɩɩɟɥɹ?
38. ȼ ɱɺɦ ɫɦɵɫɥ ɝɪɚɧɢɱɧɨɝɨ ɭɫɥɨɜɢɹ Ʉɭɜɚɛɚɪɵ?
ɢ
0No
?
1No
4.2. Ɇɚɫɫɨɩɟɪɟɧɨɫ ɜ ɦɧɨɝɨɮɚɡɧɵɯ ɫɢɫɬɟɦɚɯ
4.2.1. Ɉɫɧɨɜɧɵɟ ɞɨɩɭɳɟɧɢɹ
Ɇɟɠɮɚɡɧɵɣ ɬɟɩɥɨɦɚɫɫɨɨɛɦɟɧ ɜ ɦɟɬɚɥɥɭɪɝɢɢ ɨɱɟɧɶ ɱɚɫɬɨ ɫɨɩɪɨɜɨɠɞɚɟɬɫɹ ɮɚɡɨɜɵɦɢ ɩɪɟɜɪɚɳɟɧɢɹɦɢ (ɢɫɩɚɪɟɧɢɟɦ, ɩɥɚɜɥɟɧɢɟɦ, ɤɨɧɞɟɧɫɚɰɢɟɣ) ɢ ɯɢɦɢɱɟɫɤɢɦɢ ɪɟɚɤɰɢɹɦɢ. ɉɪɢɫɬɭɩɚɹ ɤ ɢɡɭɱɟɧɢɸ ɩɪɨɰɟɫɫɨɜ ɦɚɫɫɨɨɛɦɟɧɚ ɜ ɦɧɨɝɨɮɚɡɧɵɯ ɫɢɫɬɟɦɚɯ ɧɚ ɩɟɪɜɨɦ ɷɬɚɩɟ, ɩɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɮɚɡɵ ɹɜɥɹɸɬɫɹ ɧɟɫɠɢɦɚɟɦɵɦɢ ɠɢɞɤɨɫɬɹɦɢ ɢ ɧɚ ɦɟɠɮɚɡɧɨɣ ɝɪɚɧɢɰɟ ɨɬɫɭɬɫɬɜɭɸɬ ɮɚɡɨɜɵɟ ɩɪɟɜɪɚɳɟɧɢɹ, ɚ ɬɚɤɠɟ ɧɟ ɩɪɨɬɟɤɚɸɬ ɯɢɦɢɱɟɫɤɢɟ ɪɟɚɤɰɢɢ
ɉɪɢ ɪɚɡɪɚɛɨɬɤɟ ɦɨɞɟɥɟɣ ɦɚɫɫɨɨɛɦɟɧɚ ɜ ɦɧɨɝɨɮɚɡɧɵɯ ɫɢɫɬɟɦɚɯ
ɧɟɨɛɯɨɞɢɦɨ ɡɧɚɬɶ, ɤɚɤɚɹ ɮɚɡɚ, ɫɩɥɨɲɧɚɹ ɢɥɢ ɞɢɫɩɟɪɫɧɚɹ, ɥɢɦɢɬɢɪɭɟɬ
ɦɚɫɫɨɨɛɦɟɧ. ȿɫɥɢ ɥɢɦɢɬɢɪɭɸɳɟɣ ɹɜɥɹɟɬɫɹ ɫɩɥɨɲɧɚɹ ɮɚɡɚ, ɬɨ ɩɥɨɬɧɨɫɬɶ ɩɨɬɨɤɚ ɦɚɫɫɵ ɡɚɜɢɫɢɬ ɩɪɟɠɞɟ ɜɫɟɝɨ ɨɬ ɝɢɞɪɨɞɢɧɚɦɢɤɢ ɨɦɵɜɚɸɳɟɝɨ ɱɚɫɬɢɰɭ ɩɨɬɨɤɚ, ɚ ɩɪɢ ɥɢɦɢɬɢɪɭɸɳɟɦ ɫɨɩɪɨɬɢɜɥɟɧɢɢ ɞɢɫɩɟɪɫɧɨɣ ɮɚɡɵ ɨɫɧɨɜɧɨɟ ɜɥɢɹɧɢɟ ɧɚ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɦɚɫɫɨɨɛɦɟɧɚ ɨɤɚɡɵɜɚɟɬ ɯɚɪɚɤɬɟɪ
ɱɚɫɬɢɰɵ. ɉɪɢ ɷɬɨɦ ɦɚɫɫɨɨɛɦɟɧ ɜ ɫɢɫɬɟɦɚɯ ɠɢɞɤɨɫɬɶ–ɠɢɞɤɨɫɬɶ ɢɥɢ
ɝɚɡ–ɠɢɞɤɨɫɬɶ ɞɥɹ ɛɨɥɶɲɢɯ ɩɪɨɦɟɠɭɬɤɨɜ ɜɪɟɦɟɧɢ ɜɫɟɝɞɚ ɹɜɥɹɟɬɫɹ
ɧɟɫɬɚɰɢɨɧɚɪɧɵɦ ɩɪɨɰɟɫɫɨɦ. ɂɧɬɟɧɫɢɜɧɨɫɬɶ ɦɚɫɫɨɨɛɦɟɧɚ ɞɥɹ ɷɬɢɯ
ɫɢɫɬɟɦ ɩɨɫɬɨɹɧɧɚ ɬɨɥɶɤɨ ɜ ɧɚɱɚɥɶɧɵɣ ɩɟɪɢɨɞ, ɩɨɤɚ ɤɨɧɰɟɧɬɪɚɰɢɹ
ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɜ ɨɛɴɟɦɟ ɞɢɫɩɟɪɫɧɨɣ ɱɚɫɬɢɰɵ ɩɨɫɬɨɹɧɧɚ. ȼɫɟ
ɷɬɢ ɨɛɫɬɨɹɬɟɥɶɫɬɜɚ ɬɚɤ ɠɟ, ɤɚɤ
ɱɭɬɶ ɩɨɡɠɟ, ɧɟɨɛɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶ, ɩɪɢɫɬɭɩɚɹ ɤ ɪɟɲɟɧɢɸ ɤɨɧɤɪɟɬɧɨɣ ɡɚɞɚɱɢ ɨ ɦɟɠɮɚɡɧɨɦ ɦɚɫɫɨɨɛɦɟɧɟ. ɋɨɡɞɚɧɢɟ ɬɟɨɪɢɢ ɦɚɫɫɨɨɛɦɟɧɚ
ɜ ɦɧɨɝɨɮɚɡɧɵɯ ɫɢɫɬɟɦɚɯ, ɤɨɬɨɪɨɟ ɟɳɺ ɞɚɥɟɤɨ ɧɟ ɡɚɜɟɪɲɟɧɨ, ɩɪɨɢɫɯɨɞɢɬ ɩɭɬɺɦ ɪɚɡɪɚɛɨɬɤɢ ɦɧɨɝɨɱɢɫɥɟɧɧɵɯ ɮɢɡɢɱɟɫɤɢɯ ɦɨɞɟɥɟɣ ɷɬɨɝɨ
ɹɜɥɟɧɢɹ. Ɋɚɫɫɦɨɬɪɢɦ ɧɚɢɛɨɥɟɟ ɩɥɨɞɨɬɜɨɪɧɵɟ ɢɡ ɧɢɯ. ɍɢɬɦɚɧ ɩɪɟɞ-
ɰɢɪɤɭɥɹɰɢɢ ɠɢɞɤɨɫɬɢ ɢɥɢ ɝɚɡɚ ɜ ɨɛɴɺɦɟ ɞɢɫɩɟɪɫɧɨɣ
.
ɢ ɪɹɞ ɞɪɭɝɢɯ, ɨ ɤɨɬɨɪɵɯ ɪɟɱɶ ɩɨɣɞɟɬ
73
ɥɨɠɢɥ ɩɥɺɧɨɱɧɭɸ ɦɨɞɟɥɶ ɦɟɠɮɚɡɧɨɝɨ ɦɚɫɫɨɨɛɦɟɧɚ. ɋɨɝɥɚɫɧɨ ɷɬɨɣ
g
D
ɦɨɞɟɥɢ ɩɟɪɟɧɨɫ ɦɚɫɫɵ ɧɚ ɝɪɚɧɢɰɟ ɪɚɡɞɟɥɚ ɮɚɡ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɱɟɪɟɡ
ɩɥɺɧɤɭ. ɉɪɨɰɟɫɫ ɷɬɨɬ ɫɬɚɰɢɨɧɚɪɟɧ, ɩɪɨɬɟɤɚɟɬ ɩɪɢ ɧɚɥɢɱɢɢ ɮɚɡɨɜɨɝɨ
ɪɚɜɧɨɜɟɫɢɹ ɧɚ ɝɪɚɧɢɰɟ ɪɚɡɞɟɥɚ ɮɚɡ ɢ ɨɩɢɫɵɜɚɟɬɫɹ ɨɞɧɨɦɟɪɧɵɦ ɭɪɚɜɧɟɧɢɟɦ ɦɨɥɟɤɭɥɹɪɧɨɣ ɞɢɮɮɭɡɢɢ. ɏɢɝɛɢ ɭɫɨɜɟɪɲɟɧɫɬɜɨɜɚɥ ɩɥɺɧɨɱɧɭɸ ɦɨɞɟɥɶ ɍɢɬɦɚɧɚ. ɋɨɝɥɚɫɧɨ ɏɢɝɛɢ ɩɪɢ ɨɛɬɟɤɚɧɢɢ ɱɚɫɬɢɰɵ ɩɨɬɨɤɨɦ ɧɚ ɜɧɟɲɧɟɣ
ɝɪɚɧɢɰɵ ɩɥɺɧɤɢ ɩɪɨɢɫɯɨɞɢɬ ɧɟɩɪɟɪɵɜɧɨɟ ɨɛɧɨɜɥɟɧɢɟ ɠɢɞɤɨɫɬɢ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɧɚ ɷɬɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɤɨɧɰɟɧɬɪɚɰɢɹ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɧɟ ɪɚɜɧɚ ɤɨɧɰɟɧɬɪɚɰɢɢ ɧɚɫɵɳɟɧɢɹ. Ɇɨɞɟɥɶ ɏɢɝɛɢ
ɧɚɡɜɚɧɚ ɩɟɧɟɬɪɚɰɢɨɧɧɨɣ ɦɨɞɟɥɶɸ ɦɚɫɫɨɨɛɦɟɧɚ. ɇɟɩɪɟɪɵɜɧɵɣ ɩɪɨɰɟɫɫ ɨɛɧɨɜɥɟɧɢɹ ɏɢɝɛɢ ɡɚɦɟɧɢɥ ɫɬɭɩɟɧɱɚɬɵɦ, ɧɚɡɜɚɜ ɪɚɡɦɟɪ ɤɚɠɞɨɣ
ɫɬɭɩɟɧɢ ɜɪɟɦɟɧɟɦ ɨɛɧɨɜɥɟɧɢɹ. ɑɢɫɥɟɧɧɨ ɷɬɨɬ ɢɧɬɟɪɜɚɥ ɪɚɜɟɧ ɜɪɟɦɟɧɢ, ɡɚ ɤɨɬɨɪɨɟ ɱɚɫɬɢɰɚ ɩɪɨɯɨɞɢɬ ɩɭɬɶ,
ɪɚɜɧɵɣ ɟɺ ɞɢɚɦɟɬɪɭ. Ɍɭɪ ɢ
Ɇɚɪɱɟɥɥɨ ɩɪɟɞɥɨɠɢɥɢ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɩɥɺɧɨɱɧɭɸ ɢ ɩɟɧɟɬɪɚɰɢɨɧɧɭɸ
ɦɨɞɟɥɢ ɤɚɤ ɤɪɚɣɧɢɟ ɫɥɭɱɚɢ ɩɪɨɰɟɫɫɚ ɩɟɪɟɧɨɫɚ. ɉɪɟɞɥɨɠɟɧɧɚɹ ɢɦɢ
ɦɨɞɟɥɶ ɬɨɠɟ ɨɫɧɨɜɚɧɚ ɧɚ ɢɞɟɟ ɨɛɧɨɜɥɟɧɢɹ ɩɨɜɟɪɯɧɨɫɬɢ ɩɥɺɧɤɢ, ɧɨ ɫ
ɛɨɥɟɟ ɝɢɛɤɢɦ ɨɩɪɟɞɟɥɟɧɢɟɦ ɩɟɪɢɨɞɚ ɨɛɧɨɜɥɟɧɢɹ. ɋɭɳɟɫɬɜɟɧɧɵɦ
ɧɟɞɨɫɬɚɬɤɨɦ ɩɟɪɟɱɢɫɥɟɧɧɵɯ ɦɨɞɟɥɟɣ ɹɜɥɹɟɬɫɹ ɧɟɭɱɺɬ ɢɥɢ ɜɟɫɶɦɚ
ɫɥɚɛɵɣ ɭɱɺɬ ɪɨɥɢ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ ɜ ɦɚɫɫɨɨɛɦɟɧɟ ɧɚ
ɩɨɜɟɪɯɧɨɫɬɢ
ɱɚɫɬɢɰɵ. ɋ ɷɬɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ ɧɚɢɛɨɥɟɟ ɨɛɨɫɧɨɜɚɧɧɨɣ ɜ
ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɫɱɢɬɚɟɬɫɹ ɦɨɞɟɥɶ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɝɪɚɧɢɱɧɨɝɨ
ɫɥɨɹ. ɂɡɥɚɝɚɟɦɵɟ ɞɨɥɟɟ ɩɪɢɟɦɵ ɪɟɲɟɧɢɹ ɤɨɧɤɪɟɬɧɵɯ ɡɚɞɚɱ ɦɚɫɫɨɨɛɦɟɧɚ ɨɫɧɨɜɚɧɵ ɧɚ ɷɬɨɣ ɦɨɞɟɥɢ.
ɋɨɫɬɚɜɢɦ ɞɥɹ ɤɚɠɞɨɣ ɢɡ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ ɮɚɡ ɜ ɨɬɞɟɥɶɧɨɫɬɢ
ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ, ɨɩɢɫɵɜɚɸɳɭɸ ɤɨɧɜɟɤɬɢɜɧɵɣ ɩɟɪɟɧɨɫ:
– ɬɟɩɥɨɬɵ
dT
2
aT
,
dt
G
dw
dt
1
GG
Q
pw
grad ,
2
(4.108)
U
G
div 0;w
– ɦɚɫɫɵ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ
dC
i
dt
74
2
,
C
ii
g
G
dw
dt
1
GG
Q
pw
grad ,
2
(4.109)
U
div 0.
G
w
ȼ ɧɚɫɬɨɹɳɟɦ ɪɚɡɞɟɥɟ ɨɫɧɨɜɧɨɟ ɜɧɢɦɚɧɢɟ ɭɞɟɥɹɟɬɫɹ ɩɪɨɰɟɫɫɚɦ
ɤɨɧɜɟɤɬɢɜɧɨɝɨ ɦɚɫɫɨɩɟɪɟɧɨɫɚ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɜ ɞɜɭɯɮɚɡɧɵɯ
ɫɢɫɬɟɦɚɯ. Ʉɨɧɜɟɤɬɢɜɧɵɣ ɩɟɪɟɧɨɫ ɫɭɛɫɬɚɧɰɢɢ ɜɫɟɝɞɚ ɫɜɹɡɚɧ ɜ ɩɪɨɰɟɫɫɚɦɢ, ɩɪɨɬɟɤɚɸɳɢɦɢ ɜ ɞɜɢɠɭɳɟɣɫɹ ɫɪɟɞɟ ɢɥɢ ɦɟɠɞɭ ɧɟɫɤɨɥɶɤɢɦɢ
ɞɜɢɠɭɳɢɦɢɫɹ ɫɪɟɞɚɦɢ. ȼ ɫɜɹɡɢ ɜ ɷɬɢɦ ɡɚɞɚɱɢ ɤɨɧɜɟɤɬɢɜɧɨɝɨ ɩɟɪɟɧɨɫɚ ɦɨɠɧɨ ɪɚɡɞɟɥɢɬɶ ɧɚ ɞɜɟ ɱɚɫɬɢ: ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɭɸ, ɜ ɤɨɬɨɪɨɣ
ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨɥɹ ɫɤɨɪɨɫɬɟɣ
ɞɜɢɠɭɳɢɯɫɹ ɫɪɟɞ, ɢ ɬɟɩɥɨ- ɢɥɢ ɦɚɫɫɨɨɛɦɟɧɧɭɸ, ɜ ɤɨɬɨɪɨɣ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɚɪɚɦɟɬɪɵ ɩɪɨɰɟɫɫɨɜ ɩɟɪɟɧɨɫɚ
ɬɟɩɥɨɬɵ ɢɥɢ ɦɚɫɫɵ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɪɟɡɭɥɶɬɚɬɨɜ ɪɟɲɟɧɢɹ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɱɚɫɬɢ ɡɚɞɚɱɢ. Ƚɢɞɪɨɞɢɧɚɦɢɱɟɫɤɚɹ ɱɚɫɬɶ ɡɚɞɚɱɢ ɪɚɫɫɦɚɬɪɢɜɚɥɚɫɶ ɜ ɧɚɱɚɥɟ ɞɚɧɧɨɣ ɝɥɚɜɵ. ɉɨɥɭɱɟɧɧɵɟ ɩɪɢ ɷɬɨɦ ɪɟɡɭɥɶɬɚɬɵ
ɛɭɞɭɬ ɢɫɩɨɥɶɡɨɜɚɧɵ ɩɪɢ ɪɟɲɟɧɢɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɡɚɞɚɱ ɦɚɫɫɨɩɟɪɟɧɨɫɚ. ɋ ɭɱɺɬɨɦ ɷɬɨɝɨ ɦɨɠɧɨ ɫɱɢɬɚɬɶ, ɱɬɨ
ɭɪɚɜɧɟɧɢɟ ɤɨɧɜɟɤɬɢɜɧɨɣ
ɞɢɮɮɭɡɢɢ ɜ ɫɢɫɬɟɦɟ (4.109) ɧɟ ɫɜɹɡɚɧɨ ɫ ɞɜɭɦɹ ɞɪɭɝɢɦɢ ɭɪɚɜɧɟɧɢɹɦɢ
ɢ ɫɜɟɫɬɢ ɢɫɫɥɟɞɨɜɚɧɢɟ ɩɪɨɰɟɫɫɨɜ ɦɚɫɫɨɩɟɪɟɧɨɫɚ ɤ ɨɬɵɫɤɚɧɢɸ ɪɟɲɟɧɢɹ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ ɞɥɹ ɤɨɧɤɪɟɬɧɵɯ ɫɥɭɱɚɟɜ, ɤɨɬɨɪɵɟ ɨɩɢɫɵɜɚɸɬɫɹ
ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɭɫɥɨɜɢɹɦɢ ɨɞɧɨɡɧɚɱɧɨɫɬɢ. ɗɬɚ ɦɟɬɨɞɢɤɚ ɛɭɞɟɬ
ɢɫɩɨɥɶɡɨɜɚɧɚ ɜ ɞɚɥɶɧɟɣɲɟɦ.
ɋɬɪɨɝɨ ɝɨɜɨɪɹ, ɩɪɟɞɩɨɥɚɝɚɹ ɧɟɡɚɜɢɫɢɦɨɫɬɶ ɭɪɚɜɧɟɧɢɹ ɤɨɧɜɟɤɬɢɜɧɨɣ ɞɢɮɮɭɡɢɢ (4.109) ɨɬ ɞɜɭɯ ɞɪɭɝɢɯ ɭɪɚɜɧɟɧɢɣ ɫɢɫɬɟɦɵ (4.109)
ɦɨɠɧɨ
ɫɞɟɥɚɬɶ ɟɳɺ ɨɞɧɨ ɩɪɟɞɩɨɥɨɠɟɧɢɟ – ɩɨɥɚɝɚɟɦ, ɱɬɨ ɤɢɧɟɦɚɬɢɱɟɫɤɢɣ ɤɨɷɮɮɢɰɢɟɧɬ ɜɹɡɤɨɫɬɢ ɞɜɢɠɭɳɟɣɫɹ ɫɪɟɞɵ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ. ȼ ɫɜɹɡɢ ɫ ɷɬɢɦ ɪɟɡɭɥɶɬɚɬɵ, ɤɨɬɨɪɵɟ
ɛɭɞɭɬ ɩɨɥɭɱɟɧɵ ɜ ɯɨɞɟ ɩɨɫɥɟɞɭɸɳɢɯ ɢɫɫɥɟɞɨɜɚɧɢɣ, ɨɤɚɠɭɬɫɹ
ɧɚɫɬɨɥɶɤɨ ɞɨɫɬɨɜɟɪɧɵ, ɧɚɫɤɨɥɶɤɨ ɭɤɚɡɚɧɧɨɟ ɞɨɩɭɳɟɧɢɟ ɩɪɢɟɦɥɟɦɨ ɜ
ɤɚɠɞɨɦ ɤɨɧɤɪɟɬɧɨɦ ɫɥɭɱɚɟ.
4.2.2. Ɉɫɧɨɜɧɵɟ ɩɨɧɹɬɢɹ ɢ ɨɩɪɟɞɟɥɟɧɢɹ
ɉɪɟɞɫɬɚɜɢɦ ɭɪɚɜɧɟɧɢɟ ɤɨɧɜɟɤɬɢɜɧɨɣ ɞɢɮɮɭɡɢɢ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ
ɯɢɦɢɱɟɫɤɨɣ ɪɟɚɤɰɢɢ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
C
w
G
i
wCDC
grad .
t
w
ii i
2
(4.110)
75
ɉɪɢ ɫɬɚɰɢɨɧɚɪɧɨɦ ɪɟɠɢɦɟ ɩɟɪɟɧɨɫɚ ɦɚɫɫɵ ɩɟɪɜɨɟ ɫɥɚɝɚɟɦɨɟ ɜ ɥɟɜɨɣ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ (4.110) ɨɛɪɚɳɚɟɬɫɹ ɜ ɧɭɥɶ ɢ ɭɪɚɜɧɟɧɢɟ ɩɪɢɧɢɦɚɟɬ ɜɢɞ
G
grad .
wCDC
ii i
2
(4.111)
Ɉɬɧɨɲɟɧɢɟ ɩɨɪɹɞɤɨɜ ɜɟɥɢɱɢɧ ɥɟɜɨɣ ɢ ɩɪɚɜɨɣ ɱɚɫɬɟɣ ɭɪɚɜɧɟɧɢɹ
(4.111) ɞɚɺɬ ɫɥɟɞɭɸɳɢɣ ɤɨɦɩɥɟɤɫ:
'
C
i
G
ow C l w l
(grad)
oD C
2
()
ii
w
0
i
000
'
C
D
i
i
2
l
0
D
(4.112)
.
i
ɗɬɨɬ ɤɨɦɩɥɟɤɫ ɧɚɡɵɜɚɟɬɫɹ ɞɢɮɮɭɡɢɨɧɧɵɦ ɱɢɫɥɨɦ ɉɟɤɥɟ ɢ ɨɛɨɡɧɚɱɚɟɬɫɹ
ȼ ɫɨɨɬɧɨɲɟɧɢɢ (4.112) ɱɟɪɟɡ
ɨɦɵɜɚɸɳɟɣ ɮɚɡɵ ɡɚ ɩɪɟɞɟɥɚɦɢ ɩɨɝɪɚɧɢɱɧɨɝɨ ɫɥɨɹ;
Pe
c
.
w ɨɛɨɡɧɚɱɟɧɚ ɯɚɪɚɤɬɟɪɧɚɹ ɫɤɨɪɨɫɬɶ
0
l – ɯɚɪɚɤɬɟɪɧɨɟ
0
ɪɚɫɫɬɨɹɧɢɟ, ɧɚ ɤɨɬɨɪɨɦ ɩɪɨɢɫɯɨɞɢɬ ɢɡɦɟɧɟɧɢɟ ɤɨɧɰɟɧɬɪɚɰɢɢ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɨɬ ɡɧɚɱɟɧɢɹ
C – ɪɚɜɧɨɜɟɫɧɨɣ ɤɨɧɰɟɧɬɪɚɰɢɢ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɱɚɫɬɢɰɵ
ɧɢɹ
(
is
CC C
'
ii is
f
). ȼ ɱɢɫɥɢɬɟɥɟ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɱɢɫɥɚ ɉɟɤɥɟ ɫɬɨɹɬ ɜɟ-
Cf ɜ ɧɟɜɨɡɦɭɳɺɧɧɨɦ ɩɨɬɨɤɟ, ɞɨ ɡɧɚɱɟ-
i
ɥɢɱɢɧɵ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɟ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɤɨɧɜɟɤɬɢɜɧɨɝɨ ɩɟɪɟɧɨɫɚ
ɦɚɫɫɵ, ɚ ɜ ɡɧɚɦɟɧɚɬɟɥɟ – ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɦɨɥɟɤɭɥɹɪɧɨɝɨ ɩɟɪɟɧɨɫɚ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ. ɉɨɷɬɨɦɭ ɩɪɢ
Pe 1c!! ɤɨɧɜɟɤɬɢɜɧɵɣ ɩɟɪɟɧɨɫ
ɦɚɫɫɵ ɩɪɟɨɛɥɚɞɚɟɬ ɧɚɞ ɦɨɥɟɤɭɥɹɪɧɵɦ ɢ ɩɨɫɥɟɞɧɢɦ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ. ɂ, ɧɚɨɛɨɪɨɬ, ɟɫɥɢ
Pe 1c , ɬɨ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɱɢɫɬɨ ɦɨ-
ɥɟɤɭɥɹɪɧɭɸ ɞɢɮɮɭɡɢɸ.
ɉɨɞɟɥɢɜ ɞɢɮɮɭɡɢɨɧɧɨɟ ɱɢɫɥɨ ɉɟɤɥɟ ɧɚ ɱɢɫɥɨ Ɋɟɣɧɨɥɶɞɫɚ, ɩɨɥɭɱɢɦ ɡɧɚɱɟɧɢɟ ɤɪɢɬɟɪɢɹ ɒɦɢɞɬɚ:
wl
00
c
Pe
Re
D
wl
00
Q
i
D
i
. (4.113)
Sc
i
Q
Ɏɢɡɢɱɟɫɤɢɣ ɫɦɵɫɥ ɷɬɨɝɨ ɤɪɢɬɟɪɢɹ ɩɨɞɨɛɢɹ – ɦɟɪɚ ɨɬɧɨɲɟɧɢɹ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɦɨɥɟɤɭɥɹɪɧɨɝɨ ɩɟɪɟɧɨɫɚ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɢ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɦɨɥɟɤɭɥɹɪɧɨɝɨ ɩɟɪɟɧɨɫɚ ɦɚɫɫɵ ɜ ɩɨɬɨɤɟ, ɨɦɵɜɚɸɳɟɦ
ɱɚɫɬɢɰɭ.
76
Ⱦɥɹ ɝɚɡɨɜ ɤɪɢɬɟɪɢɣ ɒɦɢɞɬɚ ɢɦɟɟɬ ɩɨɪɹɞɨɤ ɟɞɢɧɢɰɵ, ɬɨɝɞɚ ɤɚɤ
ɞɥɹ ɦɟɬɚɥɥɭɪɝɢɱɟɫɤɢɯ ɪɚɫɩɥɚɜɨɜ ɫɭɳɟɫɬɜɟɧɧɨ ɛɨɥɶɲɟ ɟɞɢɧɢɰɵ, ɬɚɤ
ɤɚɤ ɤɢɧɟɦɚɬɢɱɟɫɤɢɣ ɤɨɷɮɮɢɰɢɟɧɬ ɜɹɡɤɨɫɬɢ ɷɬɢɯ ɠɢɞɤɨɫɬɟɣ ɢɦɟɟɬ
ɜɟɥɢɱɢɧɭ ɩɨɪɹɞɤɚ 10
ɞɢɮɮɭɡɢɢ ɯɢɦɢɱɟɫɤɢɯ ɷɥɟɦɟɧɬɨɜ ɜ ɠɢɞɤɢɯ ɫɪɟɞɚɯ ɧɟ ɩɪɟɜɵɲɚɸɬ ɩɨ
ɩɨɪɹɞɤɭ ɜɟɥɢɱɢɧ 10
–6 ɦ2
/ɫ, ɚ ɡɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɦɨɥɟɤɭɥɹɪɧɨɣ
–9
ɦ2/ɫ. ɗɬɨ ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ ɨɛɭɫɥɨɜɥɢɜɚɟɬ ɪɚɡ-
ɥɢɱɧɵɟ ɡɧɚɱɟɧɢɹ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɱɢɫɥɚ ɉɟɤɥɟ ɞɥɹ ɠɢɞɤɨɫɬɟɣ ɢ ɝɚɡɨɜ
ɩɪɢ ɨɞɧɨɦ ɢ ɬɨɦ ɠɟ ɡɧɚɱɟɧɢɢ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ ɮɚɡ. ɋɨɝɥɚɫɧɨ (4.113):
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɞɥɹ ɠɢɞɤɨɫɬɟɣ (Sc 1!! ) ɡɧɚɱɟɧɢɟ
c
Pe Re Sc .
(4.114)
i
c
Pe
ɦɨɠɟɬ ɛɵɬɶ
ɛɨɥɶɲɟ ɟɞɢɧɢɰɵ ɞɚɠɟ ɜ ɬɨɦ ɫɥɭɱɚɟ, ɤɨɝɞɚ Re 1 . ɂɧɚɱɟ ɝɨɜɨɪɹ,
ɦɟɠɮɚɡɧɵɣ ɩɟɪɟɧɨɫ ɦɚɫɫɵ ɜ ɠɢɞɤɨɫɬɹɯ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɡɚ ɫɱɺɬ ɤɨɧɜɟɤɬɢɜɧɨɣ ɞɢɮɮɭɡɢɢ ɞɚɠɟ ɩɪɢ ɨɱɟɧɶ ɦɚɥɵɯ ɡɧɚɱɟɧɢɹɯ ɱɢɫɥɚ
Re .
Ⱦɥɹ ɝɚɡɨɜ ɡɧɚɱɟɧɢɟ ɤɪɢɬɟɪɢɹ ɒɦɢɞɬɚ ɩɪɢɦɟɪɧɨ ɪɚɜɧɨ ɟɞɢɧɢɰɟ ɢ ɩɨɷɬɨɦɭ
Pe 1c!
ɬɨɥɶɤɨ ɜ ɬɨɦ ɫɥɭɱɚɟ, ɤɨɝɞɚ Re 1! . Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ
ɩɪɨɰɟɫɫɟ ɦɟɠɮɚɡɧɨɝɨ ɦɚɫɫɨɨɛɦɟɧɚ, ɨɫɭɳɟɫɬɜɥɹɟɦɨɝɨ ɱɟɪɟɡ ɝɚɡɨɜɭɸ
ɮɚɡɭ, ɫɭɳɟɫɬɜɟɧɧɵɦɢ ɹɜɥɹɸɬɫɹ ɤɚɤ ɱɢɫɬɨ ɤɨɧɜɟɤɬɢɜɧɵɣ, ɬɚɤ ɢ ɦɨɥɟɤɭɥɹɪɧɵɣ ɩɟɪɟɧɨɫɵ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ.
ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɩɪɢ ɫɬɚɰɢɨɧɚɪɧɨɦ ɪɟɠɢɦɟ ɦɚɫɫɨɨɛɦɟɧɚ ɜɞɚɥɢ
c
ɨɬ ɦɟɠɮɚɡɧɨɣ ɝɪɚɧɢɰɵ ɜɵɩɨɥɧɹɟɬɫɹ ɭɫɥɨɜɢɟ Pe 1
ɥɹɪɧɵɦ ɩɟɪɟɧɨɫɨɦ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ
!! , ɬ.ɟ. ɦɨɥɟɤɭ-
. Ɍɨɝɞɚ
ɭɪɚɜɧɟɧɢɟ (4.111) ɩɪɢɨɛɪɟɬɚɟɬ ɜɢɞ
www
CCC
iii
www
xyz
www
xyz
0.
(4.115)
Ɋɟɲɟɧɢɟɦ ɭɪɚɜɧɟɧɢɹ (4.115) ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɹ:
,, const
Cxyz C
ii
. (4.116)
f
ɋɨɝɥɚɫɧɨ (4.116) ɜ ɹɞɪɟ ɩɨɬɨɤɚ, ɝɞɟ ɞɨɦɢɧɢɪɭɟɬ ɤɨɧɜɟɤɬɢɜɧɵɣ ɩɟɪɟɧɨɫ, ɤɨɧɰɟɧɬɪɚɰɢɹ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɩɨɫɬɨɹɧɧɚ. ɉɨ ɦɟɪɟ ɩɪɢɛɥɢɠɟɧɢɹ ɤ ɦɟɠɮɚɡɧɨɣ ɝɪɚɧɢɰɟ ɭɦɟɧɶɲɚɟɬɫɹ ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɧɟɫɭɳɟɣ ɫɪɟɞɵ ɢ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɪɨɥɶ ɤɨɧɜɟɤɬɢɜɧɨɣ ɞɢɮɮɭɡɢɢ ɜ ɩɟɪɟɧɨɫɟ ɦɚɫɫɵ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ, ɚ ɪɨɥɶ ɦɨɥɟɤɭɥɹɪɧɨɣ
ɞɢɮɮɭɡɢɢ ɜ ɷɬɨɦ ɩɪɨɰɟɫɫɟ ɜɨɡɪɚɫɬɚɟɬ. Ɉɱɟɜɢɞɧɨ, ɜɛɥɢɡɢ ɩɨɜɟɪɯɧɨɫɬɢ ɨɛɬɟɤɚɟɦɨɝɨ
ɬɟɥɚ ɫɭɳɟɫɬɜɭɟɬ ɡɨɧɚ ɧɟɤɨɬɨɪɨɣ ɬɨɥɳɢɧɵ, ɜ ɤɨɬɨɪɨɣ
ɩɥɨɬɧɨɫɬɢ ɩɨɬɨɤɨɜ ɦɚɫɫɵ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ, ɨɛɭɫɥɨɜɥɟɧɧɵɟ ɤɨɧ-
77
ɜɟɤɰɢɟɣ ɢ ɦɨɥɟɤɭɥɹɪɧɨɣ ɞɢɮɮɭɡɢɟɣ, ɫɪɚɜɧɢɦɵ ɩɨ ɜɟɥɢɱɢɧɟ. ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɨɫɬɭɥɚɬɨɦ Ɏɢɤɚ grad
ɟɧɬ ɦɨɥɟɤɭɥɹɪɧɨɣ ɞɢɮɮɭɡɢɢ
G
mD C
ii i
D ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ ɦɚɥɵɦ, ɞɥɹ ɬɨɝɨ
i
, ɩɨɫɤɨɥɶɤɭ ɤɨɷɮɮɢɰɢ-
ɱɬɨɛɵ ɩɨɬɨɤ ɦɚɫɫɵ, ɩɟɪɟɧɨɫɢɦɵɣ ɦɨɥɟɤɭɥɹɪɧɨɣ ɞɢɮɮɭɡɢɟɣ, ɛɵɥ
ɫɪɚɜɧɢɦ ɩɨ ɜɟɥɢɱɢɧɟ ɫ ɩɨɬɨɤɨɦ ɦɚɫɫɵ, ɩɟɪɟɧɨɫɢɦɨɣ ɤɨɧɜɟɤɬɢɜɧɨɣ
ɞɢɮɮɭɡɢɟɣ, ɝɪɚɞɢɟɧɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɡɨɧɟ ɞɨɥɠɟɧ
ɛɵɬɶ ɛɨɥɶɲɢɦ. Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ, ɱɬɨ ɜ ɷɬɨɣ ɡɨɧɟ ɤɨɧɰɟɧɬɪɚɰɢɹ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɞɨɥɠɧɚ ɪɟɡɤɨ ɢɡɦɟɧɹɬɶɫɹ ɜ ɧɚɩɪɚɜɥɟɧɢɢ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɦ ɦɟɠɮɚɡɧɨɣ ɝɪɚɧɢɰɟ. Ɂɨɧɚ ɜɛɥɢɡɢ ɦɟɠɮɚɡɧɨɣ
ɝɪɚɧɢɰɵ, ɝɞɟ
ɢɦɟɟɬ ɦɟɫɬɨ ɛɨɥɶɲɨɣ ɝɪɚɞɢɟɧɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ,
ɧɨɫɢɬ ɧɚɡɜɚɧɢɟ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɝɪɚɧɢɱɧɨɝɨ ɫɥɨɹ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ,
ɧɚɢɛɨɥɟɟ ɫɭɳɟɫɬɜɟɧɧɨɟ ɢɡɦɟɧɟɧɢɟ ɤɨɧɰɟɧɬɪɚɰɢɢ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɩɪɨɢɫɯɨɞɢɬ ɜ ɞɢɮɮɭɡɢɨɧɧɨɦ ɩɨɝɪɚɧɢɱɧɨɦ ɫɥɨɟ, ɜ ɬɨ ɜɪɟɦɹ ɤɚɤ
ɡɚ ɟɝɨ ɩɪɟɞɟɥɚɦɢ ɨɧɚ ɩɨɱɬɢ ɧɟ ɦɟɧɹɟɬɫɹ.
ɉɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɩɨ ɚɧɚɥɨɝɢɢ ɫ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɢɦ ɩɨɝɪɚɧɢɱ-
ɧɵɦ ɫɥɨɟɦ ɬɨɥɳɢɧɚ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɝɪɚɧɢɱɧɨɝɨ
ɫɥɨɹ ɦɚɥɚ ɢ ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɶɲɟ ɥɢɧɟɣɧɵɯ ɪɚɡɦɟɪɨɜ ɨɛɬɟɤɚɟɦɨɣ ɞɢɫɩɟɪɫɧɨɣ ɱɚɫɬɢɰɵ. ȼ ɫɜɹɡɢ ɫ ɷɬɢɦ ɦɨɠɧɨ ɫɱɢɬɚɬɶ, ɱɬɨ ɤɨɧɰɟɧɬɪɚɰɢɹ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɢɡɦɟɧɹɟɬɫɹ ɬɨɥɶɤɨ ɜ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɝɪɚɧɢɱɧɨɝɨ ɫɥɨɹ ɢ ɩɪɟɧɟɛɪɟɱɶ ɟɺ ɢɡɦɟɧɟɧɢɟɦ ɩɨ ɲɢɪɢɧɟ. ɋ ɭɱɺɬɨɦ ɢɡɥɨɠɟɧɧɨɝɨ, ɭɪɚɜɧɟɧɢɟ (4.111) ɞɥɹ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɝɪɚɧɢɱɧɨɝɨ ɫɥɨɹ ɩɪɢɧɢɦɚɟɬ ɜɢɞ
22
CC CC
ww ww
wwD
ii ii
xyi
xy
ww
§·
(4.117)
¨¸
22
xy
ww
©¹
.
ɍɪɚɜɧɟɧɢɟ (4.117) ɨɩɢɫɵɜɚɟɬ ɩɪɨɰɟɫɫ ɫɬɚɰɢɨɧɚɪɧɨɝɨ ɤɨɧɜɟɤɬɢɜɧɨɝɨ ɪɟɠɢɦɚ ɦɚɫɫɨɩɟɪɟɧɨɫɚ ɜ ɞɢɮɮɭɡɢɨɧɧɨɦ ɩɨɝɪɚɧɢɱɧɨɦ ɫɥɨɟ. Ⱦɥɹ
ɟɝɨ ɞɚɥɶɧɟɣɲɟɝɨ ɭɩɪɨɳɟɧɢɹ ɨɰɟɧɢɦ ɩɨɪɹɞɤɢ ɜɟɥɢɱɢɧ ɟɝɨ ɫɥɚɝɚɟɦɵɯ.
ɉɪɨɢɡɜɨɞɧɵɟ, ɜɯɨɞɹɳɢɟ ɜ ɩɪɚɜɭɸ ɱɚɫɬɶ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ, ɢɦɟɸɬ ɫɥɟɞɭɸɳɢɟ ɩɨɪɹɞɤɢ:
2
G – ɬɨɥɳɢɧɚ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɝɪɚɧɢɱɧɨɝɨ ɫɥɨɹ;
ɝɞɟ
ɞ
r – ɯɚɪɚɤɬɟɪɧɵɣ ɪɚɡɦɟɪ ɞɢɫɩɟɪɫɧɨɣ ɱɚɫɬɢɰɵ, ɨɦɵɜɚɟɦɨɣ ɩɨɬɨɤɨɦ;
0
CC C
' – ɢɡɦɟɧɟɧɢɟ ɤɨɧɰɟɧɬɪɚɰɢɢ ɰɟɥɟɜɨɝɨ ɤɨɦɩɨɧɟɧɬɚ
ii is
f
w
Cr'
Cxw
i
~
2
2
0
2
Cyw
C'
i
ɢ
i
i
~
2
w
, (4.118)
2
G
ɞ
ɜ ɩɪɟɞɟɥɚɯ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɝɪɚɧɢɱɧɨɝɨ ɫɥɨɹ.
78
Ɋɚɧɟɟ ɛɵɥɨ ɩɪɢɧɹɬɨ, ɱɬɨ ɬɨɥɳɢɧɚ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɝɪɚɧɢɱɧɨɝɨ
x
x
x
x
ɫɥɨɹ ɧɚɦɧɨɝɨ ɦɟɧɶɲɟ, ɱɟɦ ɯɚɪɚɤɬɟɪɧɵɣ ɪɚɡɦɟɪ ɱɚɫɬɢɰɵ
22
CC
ww
ɝɞɚ ɢɡ (4.118) ɫɥɟɞɭɟɬ, ɱɬɨ
ii
!!
22
yx
ww
. ɗɬɨ ɧɟɪɚɜɟɧɫɬɜɨ ɩɨɡɜɨɥɹɟɬ
ɞ 0
rG , ɬɨ-
ɩɪɟɧɟɛɪɟɱɶ ɩɟɪɜɵɦ ɱɥɟɧɨɦ ɩɪɚɜɨɣ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ (4.117), ɤɨɬɨɪɨɟ
ɩɪɢɨɛɪɟɬɚɟɬ ɜɢɞ
CC C
www
wwD
ii i
xyi
xy
ww
2
.
(4.119)
2
y
w
Ⱦɥɹ ɨɰɟɧɤɢ ɩɨɪɹɞɤɚ ɜɟɥɢɱɢɧ, ɜɯɨɞɹɳɢɯ ɜ ɥɟɜɭɸ ɱɚɫɬɶ ɭɪɚɜɧɟɧɢɹ
(4.119), ɩɪɨɢɡɜɟɞɺɦ ɫɧɚɱɚɥɚ ɨɰɟɧɤɭ ɬɨɥɳɢɧɵ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɝɪɚ-
ɧɢɱɧɨɝɨ ɫɥɨɹ
ɫɤɨɝɨ
G ɢ ɬɟɩɥɨɜɨɝɨ ɬG ɩɨɝɪɚɧɢɱɧɵɯ ɫɥɨɺɜ. ɂɡ ɬɟɨɪɢɢ ɝɢɞɪɨɞɢɧɚ-
r
ɦɢɱɟɫɤɨɝɨ ɩɨɝɪɚɧɢɱɧɨɝɨ ɫɥɨɹ ɢɡɜɟɫɬɧɨ, ɱɬɨ
ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ ɫɥɭɱɚɟ
G ɢ ɫɪɚɜɧɢɦ ɟɺ ɫ ɨɰɟɧɤɚɦɢ ɬɨɥɳɢɧ ɝɢɞɪɨɞɢɧɚɦɢɱɟ-
ɞ
2
()oy G , ɢɦɟɟɦ
ɞ
owQ
()
()
ow
y
y
y
3
G
r
2
QG
ɞ
. ɂɫɩɨɥɶɡɭɹ
3
G
r
. Ɍɚɤ ɤɚɤ ɜ
ɷɬɨ ɫɨɨɬɧɨɲɟɧɢɟ, ɨɩɪɟɞɟɥɢɦ ɩɨɪɹɞɨɤ ɜɬɨɪɨɝɨ ɫɥɚɝɚɟɦɨɝɨ ɫɥɟɜɚ ɜ
ɭɪɚɜɧɟɧɢɢ (4.119):
§·
ow C
w
'
¨¸
yi
w
©¹
QG
ɋ
i
y
ɞ
3
G
r
. (4.120)
Ɉɰɟɧɢɦ ɞɚɥɟɟ ɩɨɪɹɞɨɤ ɜɟɥɢɱɢɧɵ ɩɟɪɜɨɝɨ ɫɥɚɝɚɟɦɨɝɨ ɥɟɜɨɣ ɱɚɫɬɢ
ɭɪɚɜɧɟɧɢɹ (4.119). ɋ ɷɬɨɣ ɰɟɥɶɸ ɢɫɩɨɥɶɡɭɟɦ ɭɪɚɜɧɟɧɢɟ ɧɟɪɚɡɪɵɜɧɨ-
w
ɫɬɢ ɞɥɹ ɩɥɨɫɤɨɝɨ ɞɜɢɠɟɧɢɹ
w
ww
w
x
w
y
ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ,
y
w
w
ww
ɩɪɚɜɭɸ ɢ ɥɟɜɭɸ ɱɚɫɬɶ ɩɨɫɥɟɞɧɟɝɨ ɪɚɜɟɧɫɬɜɚ ɧɚ
2
ow ~
ow o
§·
¨¸
y
©¹
QG
x
w
y
wG
r
ɞ
0
3
G
r
, ɨɤɨɧɱɚɬɟɥɶɧɨ
ɞ
w
w
y
x
0,
ɨɬɤɭɞɚ ɫɥɟɞɭɟɬ, ɱɬɨ
xy
w
w
x
§·
y
¨¸
y
©¹
ow
w
w
§·
ɨɨ
¨¸
ww
©¹
, ɢɥɢ, ɭɦɧɨɠɢɜ
w , ɩɨɥɭɱɢɦ
r
QG
ɞ 0
x
.
3
G
r
Ɍɨɝɞɚ ɩɨɪɹɞɨɤ ɩɟɪɜɨɝɨ ɫɥɚɝɚɟɦɨɝɨ ɜ ɥɟɜɨɣ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ
(4.119) ɪɚɜɟɧ
79
D
§·
ow
¨¸
©¹
ii
x
xr
w
ɞ 0 ɞ
33
GG
rr
0
i
.
(4.121)
rC
QG QG '
ɋ C
w'
ɋɨɩɨɫɬɚɜɢɜ ɩɨɥɭɱɟɧɧɵɟ ɪɟɡɭɥɶɬɚɬ ɫ ɜɵɪɚɠɟɧɢɟɦ (4.120), ɜɢɞɢɦ,
ɱɬɨ ɩɨɪɹɞɤɢ ɨɛɨɢɯ ɫɥɚɝɚɟɦɵɯ ɥɟɜɨɣ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ (4.121) ɨɞɢɧɚɤɨɜɵ. ɉɪɚɜɚɹ ɱɚɫɬɶ ɭɪɚɜɧɟɧɢɹ (4.119) ɢɦɟɟɬ ɩɨɪɹɞɨɤ
2
C
w
i
D
i
~
2
w
y
2
CDw
i
. (4.122)
i
2
wG
ɞ
ɉɪɢɪɚɜɧɢɜɚɹ ɩɨɪɹɞɤɢ ɩɪɚɜɨɣ ɢ ɥɟɜɨɣ ɱɚɫɬɟɣ ɭɪɚɜɧɟɧɢɹ (4.119),
ɩɨɥɭɱɚɟɦ
QG '
C
ɞ
i
32
GG
r
C
'
ii
ɢɥɢ
ɞ
3
G
§·
¨¸
GQ
©¹
ɞ
r
D
1
i
.
(4.123)
Sc
ɂɡ ɬɟɨɪɢɢ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɩɨɝɪɚɧɢɱɧɨɝɨ ɫɥɨɹ ɢɡɜɟɫɬɧɨ, ɱɬɨ
G
1
r
~
r
0
. (4.124)
Re
ɋ ɭɱɺɬɨɦ ɩɨɫɥɟɞɧɟɝɨ ɧɚɣɞɺɦ ɢɡ (4.123) ɞɥɹ ɬɨɥɳɢɧɵ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɝɪɚɧɢɱɧɨɝɨ ɫɥɨɹ
G
ɞ
r
0
~
3
1
Sc Re
. (4.125)
Ⱥɧɚɥɨɝɢɱɧɵɦ ɨɛɪɚɡɨɦ ɦɨɠɧɨ ɩɨɤɚɡɚɬɶ, ɱɬɨ ɞɥɹ ɬɨɥɳɢɧɵ ɬɟɩɥɨɜɨɝɨ ɩɨɝɪɚɧɢɱɧɨɝɨ ɫɥɨɹ ɢɦɟɟɬ ɦɟɫɬɨ ɫɨɨɬɧɨɲɟɧɢɟ
ɝɞɟ
Pr
Q
– ɤɪɢɬɟɪɢɣ ɉɪɚɧɞɬɥɹ.
G
ɬ
r
0
~
3
1
Pr Re
, (4.126)
a
Ⱦɥɹ ɝɚɡɨɜ ɡɧɚɱɟɧɢɟ ɤɪɢɬɟɪɢɟɜ ɉɪɚɧɞɬɥɹ ɢ ɒɦɢɞɬɚ ɩɨɫɬɨɹɧɧɵ ɢ
ɛɥɢɡɤɢ ɤ ɟɞɢɧɢɰɟ. Ɍɨɝɞɚ ɢɡ (4.124) – (4.126) ɫɥɟɞɭɟɬ, ɱɬɨ ɞɥɹ ɝɚɡɨɜ
80
G|G|G. (4.127)
ɞrT
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