This thesis deals with some cases of two-dimensional slow viscous flow in a region bounded by two plates by assuming that the flow is so slow that the inertial effects are negligible.
In the first case, the flow region is bounded by a plane wall and an inclined semi-infinite flat plate at a distance. The motion is caused by the translation of the plane wall parallel to itself. A formal expression for the flow is obtained by solving a pair of simultaneous Wiener-Hopf equations. Streamlines and stress distributions on the plate are determined by evaluating the formal expression. The case in which the flow is caused by a pressure difference between up- and down-stream infinity with a plane wall at rest is also considered. When the plate is not perpendicular to the plane, it is found that separation occurs at the leading edge of the plate for both cases and that for the flow due to pressure difference a viscous eddy of which size diminishes as the inclination angle approaches 90℃ appears adjacent to the broader side of the plate.
In the second case, the flow region is bounded by a plane wall and parallel semi-infinite flat plate at a distance. The motion is caused by the translation of the plane wall parallel to itself. By the conformal mapping of the flow region onto the upper half of a complex plane, the problem can be reduced to solving the Fred-holm integral equation of second kind. Streamlines and stress distributions on the plate and the plane wall are determined. The case in which the flow is caused by a pressure gradient in the region between the plate and the plane wall is also considered. For both cases, it is found that separation occurs at the leading edge of the plate and that there exists no viscous eddy in flow field.
In the third case, slow viscous flow due to the rotation of two finite hinged plates in an unbounded medium is considered under the condition that the fluid velocity remains finite everywhere. The symmetric flow caused when the plates rotate oppositely about the vertex and anti-symmetric flow due to rotation of plates as a whole are considered separately. A formal expression for the flow is obtained by solving a pair of simultaneous wiener-Hopf equations. The velocity induced at infinity is given as a function of the angle between the plates and the asymptotic behaviors of the flow near the vertex are discussed. Normal and shear forces and moment exerted on each plate are also calculated.
