Four solutions to the Leslie-Ericksen equations for nematic liquid crystals are obtained for pressure-driven radial out-flow between concentric parallel disks and homeotropic director wall anchoring. At low pressure drops the in-plane mode is stable; the centerline director orientation is normal to the flow direction. For each radial distance from the entrance hole there is a critical pressure drop at which the elongational torque twist the director out-ofthe- plane of flow ; left and right rotations are possible. The transition results in the appearance of secondary flows in the azimuthal direction. The radius of the boundary between in-plane and out-of-the-plane modes increases with increasing pressure drops. At higher pressure drops a twist wall develops at the centerline. There is a second critical pressure drop at which the wall collapses with the nucleation and growth of a twist disclination loop. The resulting stable director field is in-plane and flow-aligned throughout the cell.