Borrowed from Steve Maas - his site is
http://www.nonlintec.com/sprite/ 
Directly above the pressure relief oil return is the oil pressure relief valve. On mine, it's adjustable - we've had it as high as 95 psi - we've since cranked it down to ~ 70 psi. What the pump is actually able to produce as far as maximum pressure is unknown, but we know it produces sufficient volume to get us at least 95 on the positive high pressure side, and that by increasing the flow through the valve, we've introduced flow into the return side.
The energy that produces that flow is energy used by the oil pump.
The oil pump has three forces working against it - the constricted columns of oil on the positive pressure side - constricted by the passages at the bearings and the pressure valve, the weight of the oil it is trying to draw from the sump, and the lack atmospheric pressure in the pan - especially if we are to seek out the ideal of a low pressure - or at least well vented - crankcase.
IO, I disagree with your assessment that the relief side of the valve carries no pressure. Pressure is necessary to produce flow - if there were no pressure, what would cause the excess oil to return to the pan?
If you partially constrict a garden hose, the pressure between the spigot and the constriction increases, but there still remains pressure after the constriction. Think of a garden hose nozzle as the constriction, and we'll call a leaky washer at the spigot an oil passage. You can still hose down your car even if your hose has a leaky washer at the spigot because of the remaining pressure after the leaky spigot.
Let's take the analogy one step further. Let's say we're dealing with a birdbath with a small fountain in it, actuated by an electric pump.
We're trying to maintain a fountain height of 6" above the surface of the water.
The pump produces pressure sufficient to throw the water 12".
We install a T in the high pressure side, one line going to the fountain, and the other line has a valve in it, directing fluid to the collection pan.
We adjust the valve to bleed off sufficient water pressure to achieve our 6" fountain height.
One of the demands on the pump is to produce sufficient draw to permit atmospheric pressure to force water into it.
If we want the pump to consume less power, where can we look?
Constricting flow on the low pressure side can give us the proper fountain height, but the pump will work inefficiently - turning the applied power into heat rather than fluid flow - wrong way.
We can better size the pump to the conditions at hand - ie find one through whatever method that provides us our 6" fountain height - but we really don't want to buy 2 dozen pumps to find one that will deliver the height we want, and this method leaves us no margin for error.
So all things being equal, the bypass valve on the HP gets us our best pump performance and the result we're looking for - a 6" fountain height.
But how can we increase the efficiency?
The pressure at the pickup is nominally atmospheric. If we localize a high pressure zone in the intake of the pump by reintroducing the flow from the bypass - which because it is flowing, is under pressure - back into the intake, we create a relative high pressure environment that requires less power to
draw water.
We know that the
volume of liquid has potential, because if it's drained directly into the pan, it raises the level of the water against atmospheric pressure.
We also know that the demand of the pump is more than the amount of fluid we are looking to reintroduce to the input side from the bypass.
By combining the volume of liquid acted on by atmospheric pressure with the higher pressure fluid being wasted at the bypass, we have a higher relative pressure on the input of the pump than would be provided by atmospheric pressure alone.
We've decreased a pumping loss through a feedback loop.
Are there gobs of horsepower here? I doubt it. Is it worth pursuing? Maybe. Will it hurt anything? THAT'S WHY I'M POSTING IT - I'M NOT SURE.

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