Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia1836810.22363/2312-9735-2018-26-2-140-154Research ArticleAn Inviscid Analogue of the Poiseuille ProblemKoptevA V<p>Candidate of Physical and Mathematical Sciences, associate professor of Mathematical Department of Institute of Water Way Transport of Admiral Makarov State University of Maritime and Inland Shipping</p>Alex.Koptev@mail.ruAdmiral Makarov State University of maritime and inland shipping1512201826214015421042018Copyright © 2018, Koptev A.V.2018<p>We consider a plane problem of steady-state motion of an ideal incompressible fluid flow in a channel between two parallel planes under the action of a given pressure drop. The problem is considered in Cartesian coordinates. The formulation is analogous to the well-known Poiseuille problem with the difference that an ideal fluid is considered instead of a viscous one. The non-flow condition is set as the boundary ones on the channel walls. So, that the velocity vector is parallel to the bounding surfaces over the channel walls. The pressure drop is set as a given positive quantity. An approach proposed based on the use of the first integral of the Euler equations while preserving nonlinear terms. We represent the derivation of main relations for the case of 2D steady-state motion of an incompressible fluid. The solution of equations for hydrodynamic characteristics in the form of expansions in powers of the Cartesian coordinates was found out by analytical way. The standard programs of Maple package are used to determine the coefficients of decomposition for some values of defining parameters. As a result expressions for hydrodynamic characteristics are obtained and their features investigated. In particular, zones of recurrent motions and zones of intense vortex motion of fluid were revealed.</p>steady-state motionideal incompressible fluidpressure dropEuler equationsintegralexpansion in powersустановившееся движениеидеальная несжимаемая жидкостьперепад давленияуравнения Эйлераинтегралразложение по степеням[L. I. Sedov, Continuum Mechanics. Part 2, Nauka, 1970, in Russian.][N. E. Kochin, I. A. Kibel, N. B. Rose, Theoretical Hydromechanics. Part 1, Fismatlit, 1963, in Russian.][S. V. Vallander, Lectures on Hydroaeromechanics, LGU im. A. A. Zhdanova, 1978, in Russian.][L. G. Loitsyanskiy, Mechanics of Fluid and Gas, Nauka, 2003, in Russian.][O. A. Lodyzhenskaya, The Mathematical Theory of Viscous Incompressible Fluid, Gordon and Breach, 1969.][A. V. Koptev, Structure of Solution of the Navier — Stokes Equations, Bulletin of the National Research Nuclear University MEPI 6 (3).][A. V. Koptev, First Integral of Motion of an Incompressible Fluid, 2015, in Russian.][A. V. Koptev, Integrals of Motion of an Incompressible Medium Flow. From Classic to Modern, New York, 2017.][A. V. Koptev, Nonlinear Effects in Poiseuille Problem, Journal of Siberian Federal University, Math. and Phys. 6 (3).][A. V. Koptev, Theoretical Research of the Flow around Cylinder of an Ideal Incompressible Medium in the Presence of a Shielding Effect, Bulletin of Admiral Makarov State University of Maritime and Inland Shipping 36 (2), in Russian.]