Calculating the velocity of a viscous fluid that partially fills a cylindrical cavity

Plane-parallel steady motion of a viscous incompressible fluid that partially fills a cylindrical rotating cavity is under consideration. The region occupied by the fluid is simply connected, with two points of a sliding three-phase contact, and the edge angles at which the fluid approaches the walls are specified at these points. The free boundary of the fluid is curvilinear. There is a slip condition at the interface between the fluid and solid wall, which corresponds to proportionality of tangential stresses of a velocity difference of the solid and fluid particles. The flow region is conformally mapped onto a rectangular. The vortex and current function with a given slip coefficient and different rotation velocities of the cylinder are calculated.