Three solutions of the Leslie–Ericksen equations for low‐molar mass rod‐like nematic liquid crystals are obtained for pressure‐driven radial outflow between concentric parallel disks. There are two competing hydrodynamic effects on the orientation: extensional flow (strongest in the centerline region) and shear (strongest near the bounding surfaces). At low pressure drops the in‐plane orientation is stable; the centerline orientation is normal to the flow direction. For each radial distance there is a critical pressure drop at which the elongational torques twist the material out‐of‐plane of flow; left and right rotations are possible. The transition from in‐plane mode to out‐of‐plane modes is analogous to the second order Frederiks transition. The two out‐of‐plane modes are characterized by a secondary azimuthal flow. At certain pressure drops all the stationary modes can coexist in the flow cell. The radius of the boundary between in‐ and out‐of‐plane modes increases with increasing pressure drops. There is a minimum pressure drop to observe the transition at the edge of the entrance hole, and there is also another minimum pressure drop at which the out‐of‐plane modes fill the whole flow cell.