Хлапук, М. М. та Мошинський, В. С. та Безусяк, О. В. та Волк, Л. Р. та Khlapuk, M. М. та Moshynskyi, V. S. та Bezusiak, О. V. та Volk, L. R. (2020) ДОСЛІДЖЕННЯ ПРОФІЛЮ ОСЕРЕДНЕНОЇ ШВИДКОСТІ ПОТОКУ В ТРУБОПРОВОДАХ ПРИ ТУРБУЛЕНТНОМУ РЕЖИМІ В ОБЛАСТІ ГІДРАВЛІЧНО ГЛАДКОГО ОПОРУ. Вісник Національного університету водного господарства та природокористування (1(89)). с. 3-11.

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Анотація

В статті приведено результати теоретичних досліджень та отримані математичні моделі, які дають можливість побудувати профілі осередненої швидкості потоку в трубопроводах при турбулентному режимі в області гідравлічно гладкого опору.

Title in English

RESEARCH OF THE AVERAGED VELOCITY PROFILE IN PIPES IN THE REGION OF HYDRAULICALLY SMOOTH TURBULENCE

English abstract

The paper presents the analysis of the literature about the development of the water turbulent flow theory in pipes. According to the results of analysis and theoretical studies, we obtained mathematical models. These models describe the profiles of the averaged velocity of turbulent flow in smooth pipes. We have hypothesized that the averaged velocity profile is described by the Navier-Stokes differential equation for the laminar flow regime. We have included kinematic turbulent viscosity in the equation besides molecular kinematic viscosity. This kinematic turbulent viscosity results from the movement of masses from one layer to another, which was recommended by J. V. Boussinesq. On the basis of experimental data I. Nikuradze and F. O. Shevelev, we obtained a distribution of the total kinematic viscosity in the pipes, including the kinematic viscosity on the pipe inner surface and the kinematic turbulent viscosity. We have used the kinematic viscosity distribution equation in the pipes and obtained the averaged velocity profile equation. This equation takes into account the boundary conditions on the inner surface of the pipe and on the axis of the pipe. Its adequacy is proven. The equation of maximum average velocity, the equation of distance from the axis of the pipe to the points having average velocity, the equation of the ratio of maximum velocity to average velocity was obtained. It is proved that the ratio of the distance from the pipe axis to the points having average velocity to the pipe radius r r0 is not constant, as for laminar flow. It depends on the Reynolds number and the pipe friction number and changes to a small value. It is shown that the ratio ux t max uх is not constant, as for the laminar flow, and it depends on the Reynolds number and the pipe friction number. According to the Cauchy-Helmholtz theorem, the obtained equation of the averaged velocity profile characterizes the translational motion of fluid particles in the pipe. The main flow parameters (angular velocity, velocity of linear and angular deformation of fluid particles, distribution of tangent stresses and diffusion) describe the kinematic structure of the turbulent flow. Their theoretical research will be presented in future articles.

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