Sink flow in a sector

A line sink of strength $\alpha Q$ at the vertex of a sector $0<\theta <\alpha$ produces the irrotational outer flowIt satisfies no penetration at the radial walls but violates no slip there, so viscous boundary layers form along both walls.

Near a radial wall, let $x$ measure distance from the sink along the wall and $y$ point into the fluid. Withthe Prandtl boundary-layer equation reduces toOne physical solution has