Slot version of ASME Flow Nozzle?

The ASME flow nozzle represents a sort of ideal in the way it converts static pressure into velocity pressure, producing a nearly flat velocity profile across its exit plane. It has a throat profile that follows an ellipse around one quadrant. The major and minor diameters of the ellipse have some relationship (which I can’t seem to find anymore) to the throat diameter of the nozzle.

Is there a version of this for slot nozzles (as opposed to axisymmetric nozzles)? Failing that, if I want to achieve as nearly as practical a flat velocity profile on a slot, is there anything arguably better to try than just a quarter-round profile on the entrance to the slot?

Say, anybody know the elliptical relationship to the throat diameter for the ordinary round flow nozzle?