LIQUID FLOW IN PRISMATIC CHANNELS RESTING ON A PARABOLIC CONTOUR

A set of exact solutions is suggested for the Poisson equation in a plane region of a certain form for describing a fl ow of Newtonian incompressible liquid in a channel at low Reynolds numbers. The motion of an ideal liquid in a region bounded by a rotating contour, torsion of a rod, defl ection of a membrane at zero displacement on the boundary of its region, and heating of a rod under certain conditions are equivalent to a mathematically formulated problem of such a fl ow. A possibility is demonstrated to construct approximate solutions to the said problem for certain sections of a channel, having a parabolic segment of the contour, using exact solutions to this problem. Examples are given for the construction of fl ow regions in a prismatic channel resting on a parabolic contour
A set of exact solutions is suggested for the Poisson equation in a plane region of a certain form for describing a fl ow of Newtonian incompressible liquid in a channel at low Reynolds numbers. The motion of an ideal liquid in a region bounded by a rotating contour, torsion of a rod, defl ection of a membrane at zero displacement on the boundary of its region, and heating of a rod under certain conditions are equivalent to a mathematically formulated problem of such a fl ow. A possibility is demonstrated to construct approximate solutions to the said problem for certain sections of a channel, having a parabolic segment of the contour, using exact solutions to this problem. Examples are given for the construction of fl ow regions in a prismatic channel resting on a parabolic contour
Author:  A. I. Moshinskii
Keywords:  velocity profi le, channel, parabola, cavity
Page:  1246