  We experimentally investigate the effects on scaling of
separating/reattaching flows of the ratio $\delta_e/h$, where $\delta_e$ is the
thickness at separation of the incoming boundary layer and $h$ the
characteristic cross-stream scale of the flow. In the present study, we propose
an original approach based on mean mass entrainment, which is the driving
mechanism accounting for the growth of the separated shear layer. The focus is
on mass transfer at the Turbulent/Non-Turbulent Interface (TNTI). In
particular, the scaling of the TNTI, which is well documented in turbulent
boundary layers, is used to trace changes in the scaling properties of the
flow. To emphasise the influence of the incoming boundary layer, two
geometrically similar, descending ramps with sizeably different heights $h$ but
fundamentally similar values of $\delta_e$ are compared. The distribution in
space of the TNTI highlights a sizeable footprint of the incoming boundary
layer on the separated flow, the scaling of which results of the competition
between $h$ and $\delta_e$. On the basis of a simple mass budget within the
neighbourhood of separation, we propose to model this competition by
introducing the scaling factor $C_{h,\delta} = 1 + \delta_e/h$. With this
model, we demonstrate that the relationship between shear layer growth and mass
entrainment rates established for free shear layers (i.e. $\delta_e = 0$) might
be extended to flows where $\delta_e/h > 0$. Since many control systems rely on
mass entrainment to modify separation properties, our findings suggest that the
parameter $\delta_e/h$ needs to be taken into account when choosing the most
relevant strategies for controlling or predicting separating/reattaching flows.
