This article proposes a numerical method for solving the problem of an axisymmetric methane jet propagation in an infinite wake air flow. The dimensionless equations of the turbulent boundary layer of reacting gases in von Mises coordinates and the k-e turbulence model were used in modeling. The equations for N components of the gas mixture were reduced to two equations by introducing the Schwab-Zeldovich functions. To solve the problem in von Mises coordinates, a two-layer, six-point implicit finite-difference scheme was used, which provided the second order of accuracy of the approximation in coordinates. An iterative process was realized due to the nonlinearity of the equations for the conservation and transfer of substances. The effect of the radius of fuel nozzle on the indices of turbulent jet and flame was investigated. It was found that in an infinite wake flow of fuel with a decrease in the nozzle radius, the rate of chemical reaction and the highest temperature in the calculation area decrease, and the amount of unburnt fuel increases.

The paper proposes a numerical method for solving the problem of the gas-dynamic state of a main gas pipeline linear section, which is characterized by a path change in the diameter and leveling height of the pipeline axis. The quasi-one-dimensional equations of gas pipeline transport are derived with account for the local and convective components of the inertia force, the quadratic law of resistance and the force of gravity at a variable cross-sectional area of the pipeline. At the inlet to the section, a time change in hydrostatic pressure is set, and at the outlet from the section a mass rate of gas flow is set. The initial distribution of gas-dynamic indices was taken for a stationary mode of operation. The equations were transformed to the equations of direct and reverse traveling waves presented in dimensionless variables, and approximated by an implicit scheme, taking into account the direction of excitation propagation. The iterative processes were formed by virtue of the nonlinearity of equations and boundary conditions, A calculation program was developed that allowed studying the process dynamics depending on the time change in the inlet pressure and the outlet mass flow rate under a path change in the diameter and leveling height of the pipeline axis. The results of separate calculations on transient processes were presented, when, at the section outlet the mass flow rate increases abruptly, and the pipe diameter has a local increase according to a sinusoidal law.

A new task is set and solved about the flow of fluid in the canal with a break and considering the vortex and cavitation zones. Systematic calculations of stationary flow characteristics and cavity for cavitation flow in the channel.

The article discusses the task of regulating the flow in the channel with a lateral outflow. A form of retraction channel is recommended to ensure a smooth flow. Solving the issues with water distribution along the channel route and determining the shape of these channels, providing non-cavitation and non-water current, comes down to the problem of the flow of the ideal incompressible liquid in the channels with a side drain.