On the problem of fluid motion in channels

Abstract

It is known that if we neglect the vertical acceleration of fluid particles compared to the acceleration of gravity and consider the horizontal components of vertical velocity to be unchanging, then for an approximate solution of the problem of motion of a heavy incompressible ideal fluid, steady uninterrupted pre-critical flow in a channel with a horizontal bottom and vertical walls, we can use the gas-hydrodynamic analogy. This problem is solved, for example, by the method of Academician S. A. Khristianovich for gas flows with subsonic velocities. According to this method, the desired flow is found by means of a plane-parallel flow of incompressible fluid, the boundaries and velocity field of which are close to the boundaries and velocity field of the actual fluid flow in the channel under appropriate conditions. In this paper, we will construct the plane-parallel flow required to study fluid motion in transient smoothly tapering sections of channels with rectilinear vertical walls at the upstream and downstream ends.