Extrusion of a plastic material from a circular sector with a small apex angle and a sink at the vertex

The plane inertialess extrusion of a perfect rigid-plastic material from a circular sector, the angle of which serves as a small parameter, is investigated using the asymptotic integration. The flow was initiated by the approach of the two sides of the sector and the existence in it of a sink of specified power. The principal velocity and stress approximations are obtained and the domains of applicability of the asymptotic expansions and the inertialess (quasistatic) solutions are found. Analogies are drawn with the solutions of the classical Prandtl problem and several of its extensions.