Regarding oil makeup requirement, and variable displacement oil pumps, here's the oil flow characteristic with respect to somerfeld number.

This is the bearing side flow which is by definition the amount of oil that the bearing needs to receive as make-up from the oil pump.
Take all the fixed dimensions, viscosity and load as fixed, increase "N" (speed), and move to the right...note that the oil requirement reduces.
Here's what happens in actual engines...lifter from a Fed Mogul paper.
he engine requirement drops off, and what's worse, is that a PD oil pump slips more on thinner oils. So to meet the demand at low speeds with thin oils, the pump has to be sized to deliver WAY too much at the top end and pump it through a relief (note this only wastes tens of watts, not HP, as some here claim).

So the logical thing is a variable displacement oil pump that delivers more per revolution at low RPM and less at high RPM...they can be pressure referenced (easy), or mapped.

This is the bearing side flow which is by definition the amount of oil that the bearing needs to receive as make-up from the oil pump.
Take all the fixed dimensions, viscosity and load as fixed, increase "N" (speed), and move to the right...note that the oil requirement reduces.
Here's what happens in actual engines...lifter from a Fed Mogul paper.
he engine requirement drops off, and what's worse, is that a PD oil pump slips more on thinner oils. So to meet the demand at low speeds with thin oils, the pump has to be sized to deliver WAY too much at the top end and pump it through a relief (note this only wastes tens of watts, not HP, as some here claim).

So the logical thing is a variable displacement oil pump that delivers more per revolution at low RPM and less at high RPM...they can be pressure referenced (easy), or mapped.

