An Inviscid Analogue of the Poiseuille Problem

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.