Hi Hazelnuts,
Well, at subsonic speeds, it is infinite, in all directions. Any boundary is arbitrary.
Sure it is, but you also wrote:
it can be shown for an elliptic lift distribution that the area of the scoop is equal to a circle with a diameter equal to the wing span.
so the area of the affected stream tube is a finite part of an infinite field - doesn't change my view that one cannot quantify mdot