Again following Middleman, we would like the enhancement in the inner fluid flowrate for a fixed pipe size and pressure gradient. We realize that while adding more outside fluid reduces shear, and thus increases flow, it also reduces the area available for flow and thus could ultimately reduce the flow of the inner flow.
Thus a fair measure of the enhancement is the ratio of the volumetric flow of the inner fluid for the lubricated case to its volumetric flow when η=0, that is when there is no outside fluid.