Extension of the problem of viscous fluid flow in a corner to the case of flow with curved boundaries

The slow flow of a viscous fluid over the solid surface which intersects another boundary surface at an angle is considered. The flow is axisymmetric and the surface contours are curved. There is no shear stress on the second surface as in the case of a free surface. The flow is investigated near the line of intersection at arbitrary angles. Formulae for the stream function and the normal stress at the boundary are obtained for short distances from the line of intersection. The leading term in the expansion corresponds to the well-known solution of the problem of low in a corner. The second term of the expansion of the normal stress at the free surface takes into account the curvature of the flow boundaries. The axial symmetry of the flow and the curvature of the boundary contours lead to a logarithmic singularity in the normal stress.