A mathematical model for the process of incompressible viscous liquid unsteady turbulent flow in a pipeline is proposed, based on the semi-empirical theory of Prandtl turbulence. As part of this model, the problem of identifying the pipeline hydraulics is formulated. It is assumed that slippage of the flow on the pipeline wall meets the condition of Navier law. This problem belongs to the class of inverse problems related to the restoration of the parabolic equations right parts’ dependence on time. Next, a difference analogue of the formulated problem is constructed, and a special representation associated with the solution of two linear difference problems of the second order is proposed to solve the obtained difference problem. The result is an explicit formula to determine the approximate value of the differential pressure along the length of the pipeline for each discrete value of the time variable. On the basis of the proposed computational algorithm, numerical experiments for model problems were carried out.
How to Cite
pipeline transport, turbulent conditions, hydraulics, semi-empirical theory of turbulence, non-local integral condition, inverse problem
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