Inlet size: Consider these four simple bodies with identical cooling passages and exits.
A and B are low Vi/Vo inlets (inlet velocity divided by freestream velocity = ratio). C and D are high Vi/Vo inlets.
In terms of
cooling, all four inlets perform the same. They all flow the same mass and slow it to the same internal velocity just prior to the heat exchanger body, trading dynamic pressure for static pressure. (Iimagine cylinder fins or a radiator core at the end of the streamlines). A and B slow the flow externally, so velocity through the inlet is slow. C and D do it internally; flow through the inlet is near to or even higher than freestream. The high velocity means some loss due to internal drag, as compared to the near-frictionless external diffusion. With all else equal, C and D would exhibit more cooling drag, i.e more momentum loss.
A and B require less physical distance between the plane of the inlet opening and the plane of the exchanger. The cowl can be shorter. The shape of the duct inside the entrance is non-critical. If entrance velocity is slow enough, it doesn't even need a duct.
C and D require more physical distance between the inlet and the exchanger, as it needs an appropriate diverging duct for best performance. The internal duct cannot diverge too quickly without risking flow separation. If the flow separates into turbulence, the energy in the dynamic flow is wasted, and the resulting static pressure is reduced. In our application, the duct length requirement dictates an extended propeller hub.
Now let's consider
external drag. Body A is a mess. The body shape did not allow the flow to remain attached at the inlet lip. It's much the same separation problem a high Vi/Vo inlet would have
internally if the duct diverged too quickly. The result here is turbulent flow over much of the body. Drag is high.
Good lip shape means flow remains attached to the outside of Body B, at a cost of some greater frontal area. (Take a good look at at the side profile of your standard Vans inlet.)
Body C is our F1 Reno Racer example. The engine is packaged very tightly, as is the sole occupant, so overall frontal area is at an absolute minimum. There is no downside to a prop extension, so the design choice is to stretch out the cowl, use the high Vi/Vo inlet, and keep the cowl skinny.
Body D is a high Vi/Vo inlet, with prop extension and ductwork, grafted on a body where overall frontal area was driven by the size and shape of the engine and/or passenger compartment. External drag will be similar to B, or a little better. The difference would not be due to the inlets or the external shape immediately adjacent to the inlets, but rather the less blunt portions of the cowl inboard of the inlets.
I'm just a student working toward intern; always to happy to hear from the pros.
...building up back pressure in the plenum and spilling that air out over the lip of the inlet. How much drag is represented by that spillage? Or do we even care to quantify it, since we may not be able to do anything about it?
That would be body A above. It's been quantified (NACA-TR-1038, Fig 12), and the answer to to pay attention to external cowl shape in the vicinity of the inlet, not the actual size of the inlet. Short version: being well shaped, bodies B, C, and D above would all maintain a reasonable level of attached flow when operating above roughly 0.3 Vi/Vo, and as you describe, the adverse external pressure outside the lip is further reduced as inlet flow is increased (i.e. exit area is increased, allowing more velocity through the fixed inlet).
