The study of the patterns of change in the hydrodynamic parameters under the conditions of non-stationary flow at the entry of the cylindrical pipe and the initial arbitrary distribution of velocities in the entry section was conducted based on the boundary layer equations. A boundary problem was formed under the axisymmetric change conditions in the flow. The boundary conditions were chosen in accordance with the pattern of an arbitrary distribution of velocities in the entry section. A general solution of the approximating Navier-Stokes equations is presented depending on the initial conditions and the Reynolds number. In accordance with the type of flow, the boundary conditions of the problem are established, and the boundary-value problem is formulated. Regularities for the change in velocities lengthwise in the entrance region have been obtained for a constant and parabolic velocity distribution in the inlet cross-sections. Analytical solutions have been obtained, allowing to obtain patterns of changes in velocities and pressures toward flow at any section and at any time. For the mentioned cases, the composite graphs of velocity changes in different sections along the length of the entrance transition area were constructed by computer analysis, for different time conditions. With the obtained composite graphs, the patterns of change over the entire length of the transition area of the entrance region were constructed, enabling to obtain fluid flow velocity at any point of the section. The length of the transition zone can be estimated based on the condition of reaching a certain percentage (99%) of the maximum velocity of the flow. The proposed solutions create the conditions for correctly constructing separate units of hydromechanical equipment

The paper touches upon a newly developed methodology for determining the automobile physical wear coefficient, taking into account some technological factors during operation that compose the rolling stock life cycle in the given operating conditions. A concept for determining the operation period of an automobile has been proposed based on maintaining the smooth operation of the rolling stock throughout the life cycle. The quantitative and qualitative indicators of automobile physical wear are determined aimed at solving the problem. The theoretical and scientific experimental research has identified the analytical connections of their interactions and relations. Given the stochastic nature of physical wear coefficient variations, it has been considered as a random value, and the characteristics of its variations pattern have been determined.

Studies of patterns of changes in hydrodynamic parameters of the viscous incompressible fluid in a conical diffuser were conducted. The specificity of the viscous liquid flow in a conical diffuser is that the kinetic energy of the flow, depending on the opening angle, is converted into pressure energy. Depending on Reynolds numbers and diffuser opening angles, the velocity vector field is stationary. With an increase in the Reynolds number, the symmetry of the flow relative to the axis of the diffuser is broken. A general solution to the approximate Navier-Stokes equations is given, based on the diffuser opening angle and the Reynolds number. A method for integrating the boundary value problem has been developed, and the patterns of velocity changes across the diffuser length at a parabolic distribution of velocities in the inlet section are obtained. By integrating partial differential equations that match all boundary conditions, the solution to the boundary value problem can be found. Graphs of changes in radial and axial velocities along the length and with a fixed value of the opening angle are shown; the flow pattern and the transition of a single-mode flow to multimode regimes are obtained. For a fixed opening angle and Reynolds number, the conditions for flow separation from a fixed wall are derived, where the flow velocity changes the sign. A mixing process is observed in the multi-mode region, which is accompanied by numerous pulsation phenomena and an unstable diffuser operation, where the resulting solutions are inappropriate. Based on the results of the studies obtained, it is possible to correctly design a conical diffuser, namely, under the condition of non-separated flow, to choose the opening angle and its length.

The efficiency of commercial automobiles and wheeled military vehicles mainly depends on the choice of maintenance (M) and current repair (CR) concept. In the paper the difficulties of adapting the (M) and (CR) planning strategies to the structural characteristics of modern transport facilities are pointed out. The advantages of using the (M) and (CR) random strategy for transport facilities based on the stochastic nature of failures and malfunctions are substantiated. Considering the failures and malfunctions as random values and identifying the patterns of their distribution based on γ percentage resources, it is proposed to develop a list of regulated maintenance and repair work, periodicity and labor intensity based on a random strategy, which will increase the efficiency of preserving the technical resource of the rolling stock throughout the entire life cycle of the vehicle.