The author obtains a low Reynolds number matched Stokes-Oseen solution for a particular two-dimensional semi-bounded flow. It takes place in a semi-infinite body of viscous incompressible liquid. It is caused by the steady rectilinear motion of a circular cylinder in the otherwise quiescent liquid. This cylinder moves in a direction perpendicular to its axis and parallel to a solid plane. In the limiting case of infinite gap between the obstacle and the plane the solution reduces to that obtained by Proudman and Pearson (6).Unlike an unbounded flow, the one analyzed is characterized by a vanishing disturbance in the far field. It follows that with respect to axes fixed to the cylinder the momentum of the stream is unchanged. Therefore the forces and moments experienced by the cylinder are equal to those exerted by the solid plane. It is conjectured that the case analysed is a representative example of many semi-bounded flows. If this is so then such far-field behaviour makes the numerical solutions of these rather simple.
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