ISRA (India) = 4.971 ISI (Dubai, UAE) = 0.829 GIF (Australia) = 0.564 JIF = 1.500 SIS (USA) = 0.912 РИНЦ (Russia) = 0.126 ESJI (KZ) = 8.716 SJIF (Morocco) = 5.667 ICV (Poland) = 6.630 PIF (India) = 1.940 IBI (India) = 4.260 OAJI (USA) =

Topic of the paper is the simulation of fluid outflow from a channel with complex geometry. Subject of the study is the outflow of fluid from a channel with an arbitrary section, in particular, consisting of a parabolic inlet, cylindrical middle and hyperbolic outlet sections. The paper considers the integral form of determining the pressure and the average flow rate of the fluid in a channel with an arbitrary cross section. From the obtained expression for the pressure and from the equation of conservation of mass, given in integral form, it is necessary to determine the pressure and the average flow rate in successively located channels with a parabolic, cylindrical and hyperbolic section. Research methods are based on: Newton’s rheological law; the continuity equation and the Navier-Stokes equation, which are the basic equations of fluid motion; the method of mathematical modeling and the analytical method for their solution. The paper contains integral expressions for the hydrodynamic characteristics of a fluid flow in a channel with an arbitrary section. The pressure and average flow rate in the channel of successively located parabolic, cylindrical, hyperbolic segments are determined. Analytical expressions are obtained for the pressure and average flow rate of the liquid in a channel with an arbitrary cross section. As an example, the pressures and the average flow rate in the channel from the parabolic inlet, cylindrical middle and hyperbolic outlet sections are determined. In perspective, by substituting in them an arbitrary arithmetic expression of the channel cross-section, it is possible to determine the hydrodynamic characteristics of the flow with any geometry of the flow channel.

The article deals with modeling the process of force load generation at an initial periodic change in pressure (a plane problem). The subject of research is a pulsating flow in a flat channel at an initial periodic pressure change. The determination of flow parameters with a periodic change in the inlet pressure; the changes in the structure of the working fluid associated with the release of various particles from the pipe walls, the addition of impurities to prevent leaks, and the high-speed modes, are given in the article considering the law of molecular and molar transfer between layers. Research methods are based on Newton’s rheological law, according to which molecular transfer is described by the law of proportionality of stresses to the derivative of the normal velocity; on the method of accounting for molar transfer by proportionality of stresses to the derivative of normal acceleration; on the method of mathematical modeling and the analytical method for their solutions, based on the provisions of operational calculus. An analytical solution to the problem of pulsating fluid motion in a plane-parallel channel is obtained with allowance for single and group transfer of molecules in the flow. The application of the analytical expressions obtained for the velocities is not limited to the critical Reynolds number, i.e. they are applied for any values of this number. Analytical expressions are obtained for the transverse and longitudinal components of the flow velocity. The resulting solution describes two zones of flow: in the first zone, two types of transfer occur, depending on the flow pattern, either molecular or molar transfer of fluid volumes between the layers prevails. In the second zone, only molecular transfer occurs.

The article is devoted to the development of a mathematical model of dynamic characteristics of a drive with a planetary gear mechanism. The subject of research is a drive with a planetary gear mechanism. The following issues were considered in the article: the synthesis of a planetary gear mechanism; the development of a mathematical model that describes the dynamic characteristics of the system; the determination of the dynamic characteristics of a drive with a planetary gear mechanism. Research is based on the method of determining the number of gear teeth; the method of determining the kinetic energy of the James gearbox; the method of determining the dynamic characteristics of an electric motor. The possible number of satellites is given in the article; the pitch radii of the wheels for a given modulus are defined; the moment of inertia of the mechanism reduced to the movable central wheel is determined; a mathematical model of the motion of a drive with a planetary gear mechanism is developed. Equations of motion of a drive with a planetary gear mechanism were obtained. Assuming, in a particular case, all the links of the drive with the planetary gear mechanism as rigid links, a mathematical model was developed for this system, considering the dynamic characteristics of an electric motor. A mathematical model was developed that describes the dynamic characteristics of the system. Analytical solutions for the developed mathematical model are given.

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