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. (2019) ДОСЛІДЖЕННЯ РОЗПОДІЛУ ЗАГАЛЬНОЇ ТУРБУЛЕНТНОЇ КІНЕМАТИЧНОЇ В’ЯЗКОСТІ В ТРУБОПРОВОДАХ ПРИ ТУРБУЛЕНТНОМУ РЕЖИМІ. Вісник Національного університету водного господарства та природокористування (4(88)). с. 3-17.

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Анотація

В статті приведено аналіз літературних джерел щодо розвитку теорії руху потоку в трубопроводах при турбулентному режимі. За узагальненими результатами аналізу та за допомогою проведених теоретичних досліджень отримані математичні моделі, які розкривають розподіл загальної кінематичної в’язкості для всіх областей гідравлічного опору при турбулентному режимі руху потоку в трубопроводах.

Title in English

RESEARCH OF TOTAL KINEMATIC TURBULENT VISCOSITY DISTRIBUTION OF TURBULENT FLOW IN PIPES

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 distribution of total kinematic turbulent viscosity for all areas of turbulent flow friction in 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 theequation 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 the laminar flow averaged velocity distribution equation and experimental data of I. Nikuradze and F.O. Shevelіov, we obtained a graph of the distribution of total kinematic turbulent viscosity along the radius of the pipe. The kinematic turbulent viscosity graph was analysed. To determine the kinematic turbulent viscosity, a canonical ellipse equation with unknown parameters ( k , m , n and s ν ) was chosen. The equation of unknown parameters was proposed and their adequacy proved. These parameters are determined on the basis of the coordinates of the points (lg Re; lg (100λ )) on the Nikuradze graph. This graph describes the flow kinematic structure depending on the flow friction. We have used the equation of total kinematic viscosity distribution in the pipes and obtained a kinematic flow structure. According to the Cauchy – Helmholtz theorem, the equation of the averaged velocity profile is obtained, which characterizes the translational motion of fluid particles, their angular velocity, and the velocity of linear and angular deformations. Using the J.V. Boussinesq equation, we obtained the distribution of the tangent stresses and the turbulent diffusion between the layers of fluid. This article, in the first time, we recommended equations that take into account boundary conditions on the pipe inner surface and on the pipe axis. These equations will be described by the author in future papers.

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