Abstract
Х.М. Гамзаев, Азербайджанский государственный университет нефти и промышленности, г. Баку, Азербайджан E-mail: xan.h@rambler.ru. K.M. Gamzaev Azerbaijan State Oil and Industry University, Baku, Azerbaijan E-mail: xan.h@rambler.ru
Highlights
Ɋɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɡɚɞɚɱɚ ɩɨ ɨɩɪɟɞɟɥɟɧɢɸ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɫɤɨɪɨɫɬɟɣ ɜ ɩɨɩɟɪɟɱɧɨɦ ɫɟɱɟɧɢɢ ɬɪɭɛɨɩɪɨɜɨɞɚ ɞɥɹ ɧɟɫɬɚɰɢɨɧɚɪɧɨɝɨ ɨɫɟɫɢɦɦɟɬɪɢɱɧɨɝɨ ɩɨɬɨɤɚ ɧɟɫɠɢɦɚɟɦɨɣ ɜɹɡɤɨɣ ɠɢɞɤɨɫɬɢ ɩɪɢ ɧɟɢɡɜɟɫɬɧɨɦ ɭɫɥɨɜɢɢ ɧɚ ɫɬɟɧɤɟ ɬɪɭɛɨɩɪɨɜɨɞɚ
The paper deals with a process of unsteady axisymmetric flow of incompressible viscous liquid in the cylindrical pipeline, described by the nonlinear system of Navier-Stokes differential equations
The set of equations is transformed into one linear parabolic equation with an initial and natural boundary ɑɢɫɥɟɧɧɵɣ ɦɟɬɨɞ ɪɟɲɟɧɢɹ ɨɞɧɨɣ ɧɟɥɨɤɚɥɶɧɨɣ ɡɚɞɚɱɢ ɬɪɭɛɨɩɪɨɜɨɞɧɨɝɨ ɬɪɚɧɫɩɨɪɬɚ ɜɹɡɤɢɯ ɠɢɞɤɨɫɬɟɣ condition on the pipeline axis
Summary
Ɋɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɡɚɞɚɱɚ ɩɨ ɨɩɪɟɞɟɥɟɧɢɸ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɫɤɨɪɨɫɬɟɣ ɜ ɩɨɩɟɪɟɱɧɨɦ ɫɟɱɟɧɢɢ ɬɪɭɛɨɩɪɨɜɨɞɚ ɞɥɹ ɧɟɫɬɚɰɢɨɧɚɪɧɨɝɨ ɨɫɟɫɢɦɦɟɬɪɢɱɧɨɝɨ ɩɨɬɨɤɚ ɧɟɫɠɢɦɚɟɦɨɣ ɜɹɡɤɨɣ ɠɢɞɤɨɫɬɢ ɩɪɢ ɧɟɢɡɜɟɫɬɧɨɦ ɭɫɥɨɜɢɢ ɧɚ ɫɬɟɧɤɟ ɬɪɭɛɨɩɪɨɜɨɞɚ. Ɉɞɧɚɤɨ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɬɟɱɟɧɢɹ ɠɢɞɤɨɫɬɟɣ ɜ ɬɪɭɛɨɩɪɨɜɨɞɚɯ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟɜɨɡɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ, ɤɚɤɨɟ ɢɡ ɷɬɢɯ ɝɪɚɧɢɱɧɵɯ ɭɫɥɨɜɢɣ ɪɟɚɥɢɡɭɟɬɫɹ ɧɚ ɫɬɟɧɤɟ ɬɪɭɛɨɩɪɨɜɨɞɚ. Ɇɚɬɟɦɚɬɢɤɚ ɜɚɠɧɨɟ ɡɧɚɱɟɧɢɟ ɢɦɟɟɬ ɢɫɫɥɟɞɨɜɚɧɢɟ ɩɨ ɨɩɪɟɞɟɥɟɧɢɸ ɡɚɤɨɧɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɫɤɨɪɨɫɬɟɣ ɜ ɩɨɩɟɪɟɱɧɨɦ ɫɟɱɟɧɢɢ ɬɪɭɛɨɩɪɨɜɨɞɚ ɞɥɹ ɧɟɫɬɚɰɢɨɧɚɪɧɵɯ ɩɨɬɨɤɨɜ ɬɪɚɧɫɩɨɪɬɢɪɭɟɦɵɯ ɜɹɡɤɢɯ ɠɢɞɤɨɫɬɟɣ ɩɪɢ ɧɟɢɡɜɟɫɬɧɨɦ ɭɫɥɨɜɢɢ ɧɚ ɫɬɟɧɤɟ ɬɪɭɛɨɩɪɨɜɨɞɚ. Ȼ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɡɚɞɚɱɚ ɨɩɪɟɞɟɥɟɧɢɹ ɩɨɥɹ ɫɤɨɪɨɫɬɟɣ ɞɥɹ ɧɟɫɬɚɰɢɨɧɚɪɧɵɯ ɩɨɬɨɤɨɜ ɜɹɡɤɢɯ ɠɢɞɤɨɫɬɟɣ ɜ ɬɪɭɛɨɩɪɨɜɨɞɚɯ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɤɚɤ ɧɟɥɨɤɚɥɶɧɚɹ ɡɚɞɚɱɚ ɫ ɢɧɬɟɝɪɚɥɶɧɵɦ ɭɫɥɨɜɢɟɦ ɞɥɹ ɭɪɚɜɧɟɧɢɹ ɧɟɫɬɚɰɢɨɧɚɪɧɨɝɨ ɬɟɱɟɧɢɹ ɧɟɫɠɢɦɚɟɦɨɣ ɜɹɡɤɨɣ ɠɢɞɤɨɫɬɢ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ.
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