The orienting properties of incompressible discotic nematic liquid crystals for creeping flows between converging and diverging planar walls (Jeffrey-Hamel) are analyzed using the Leslie-Ericksen theory. The dependence of director orientation on the reactive parameter ;t and the flow kinematics is presented. Closed form stationary solutions for the director orientation are found when elastic effects are neglected. Stationary numerical solutions for the velocity and director fields using the full Leslie-Ericksen theory are presented. The director field in converging flow is characterized by azimuthal (radial) centerline orientation, by being asymmetric with respect to the azimuthal (radial) direction, and by having an allowed orientation range that spans two halfquadrants (full quadrants). In the limiting case of perfectly flat disk (~= -oo) the flow-induced director orientation in converging flow is the azimuthal direction, while in diverging flow the director rotates by a full zr radians. By reducing the vertex angle between the walls to vanishingly small values, converging flow solutions properly reduce to those of flow between parallel plates, but diverging flows are expected to lead to a new instability.