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) ДО РОЗВИТКУ ТЕОРІЇ РУХУ ПОТОКУ В ТРУБОПРОВОДАХ ПРИ ТУРБУЛЕНТНОМУ РЕЖИМІ. Вісник Національного університету водного господарства та природокористування (3(87)). с. 3-18.

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Анотація

В статті приведено аналіз наукових джерел щодо розвитку теорії руху потоку в трубопроводах при турбулентному режимі. За узагальненими результатами аналізу та за допомогою проведених теоретичних досліджень отримано математичні моделі, які розкривають структуру потоку в залежності від області гідравлічного опору при турбулентному режимі руху потоку в трубопроводах.

Title in English

TО DEVELOPMENT OF THE WATER TURBULENT FLOW THEORY IN PIPES

English abstract

The article deals with 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 kinematic structure of the water turbulent flow in the pipes for different hydraulic friction. We have hypothesized that the average 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 used the kinematic viscosity distribution equation in the tubes and obtained the average velocity profile equation. This equation corresponds to the boundary conditions on the pipe inner surface and on the axis of the pipe. 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. The equation of the tangent stresses components ( yx τ� , zx τ� ) and the tangent stresses equation in radial coordinates ( rx τ� ) were obtained. The equation of the maximum value of the tangent stresses located on the inner surface of the pipe was obtained. The tangent stresses assume a zero value on the pipe axis. The equation of the vortex components ( y ω� , z ω� ) was obtained. We have shown that vortex lines are concentric circles whose centers are located on the pipe axis. The equation of angular velocity of flow particles rotation relative to the vortex lines was obtained. The maximum value of the particle rotation angular velocity on the pipe inner surface is determined. It decreases monotonically to zero on the axis of the pipeline. It is zero on the pipe axis. In this article, all equations reveal the kinematic structure of the water flow. We described these equations by the Reynolds number and the pipe friction number. Such equations are adopted to show the dependencies between the regimes and the flow kinematic structure. These equations make it possible to calculate the distribution profile of the total kinematic viscosity, average velocity, tangential stresses and angular velocity of flow particle rotation.

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