Хлапук, М. М. та Мошинський, В. С. та Безусяк, О. В. та Волк, Л. Р. та Khlapuk, M. М. та Moshynskyi, V. S. та Bezusіak, O. V. та Volk, L. R. (2020) ДОСЛІДЖЕННЯ РОЗПОДІЛУ ДОТИЧНИХ НАПРУЖЕНЬ СИЛ ТЕРТЯ В ТРУБОПРОВОДАХ ПРИ ТУРБУЛЕНТНОМУ РЕЖИМІ РУХУ РІДИНИ В ГЛАДКІЙ ОБЛАСТІ. Вісник Національного університету водного господарства та природокористування (2(90)). с. 42-49.

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Анотація

В статті приведено результати теоретичних досліджень та отримані математичні моделі, які дають можливість визначити розподіл дотичних напружень в трубопроводах при турбулентному режимі руху рідини в гладкій області.

Title in English

RESEARCH OF THE SHEAR STRESS DISTRIBUTION 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 paper presents the equations of the shear stresses distribution along the radius of in pipes in the region of hydraulically smooth turbulence. The shear stresses of the laminar flow along the radius vary linearly and describe the basic law of uniform laminar flow. For the first time, the equation of shear stress distribution along the radius of turbulent flow is obtained. The shear stresses vary according to the curvilinear law and describe the basic law of uniform turbulent flow. The equation for calculating the maximum shear stresses of turbulent flow near the inner surface of the pipe is obtained. It is proved that they coincide in shape with the equation for calculating the maximum stresses of the laminar flow, but the values will be much larger. The main flow parameters (angular velocity, velocity of linear and angular deformation of fluid particles and diffusion) describe the hydrodynamic structure of the turbulent flow. Their theoretical research will be presented in future articles.

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