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First I'll say that my claim to expertise in performance matters is limited and if my logic or facts are flawed I'm happy to be corrected.
"..that if you increase the total surface area of the oil system, a higher-volume pump would be useful to maintain the same pressure?"
No. An oil cooler simply looks like an extra length of pipe that the oil gets pumped through. It will thus add a slight amount of friction. Mine is installed with an oil filter adapter that places it in series with the oil filter. Like any pipe or added length of pipe, it adds a little resistance to the flow, but not enough to matter--try blowing through one, you'll see. Having more volume of oil flowing from a bigger pump will not affect anything.
In fact, the additional flow from the bigger pump will most of the time flow entirely through the relief valve at the pump, that regulates system pressure, and flow volume through the oiling system as a whole will not vary.
That is the essential point that may be tricky to grasp. Oil pressure is a function of system restrictions at lubrication points of the engine like bearings, where the oil is forced through fine passages or orifices, and relief valve setting. Open up the restrictions, for example by increasing bearing clearances as might be done on a racing engine, then more oil will flow and system pressure will drop--but wait! Now the relief valve will move letting less oil bypass and raising pressure to the set-point, up to the volume capacity of the pump of course. More oil would then flow at the same pressure because there is less restriction.
"The specific example of which I'm thinking is adding an oil cooler. This is a very common mod on high-performance engines, and I suspect this may be why race engines typically use higher-volume pumps.
"My thinking is that if the total surface area of all the little oil passages inside the engine is X square inches, and the pump moves enough volume to pressurize the system to Y pounds, then the average pressure within the system is going to be Y/X pounds per square inch. (European readers feel free to substitute metric measurements.)"
OK so far.
"So, if you were to add more oil plumbing that would increase the total surface area to 2X square inches, with the same pump, then your average pressure would be Y/2X, or half what it was originally. To get back to the original pressure, you'd need to move twice the volume, correct?
No. The oil cooler looks like an open pipe compared to the orifices at bearings etc. It is in series with the entire oil flow, at least on mine, so area of restriction to flow is not increased (& pressure reduced); on the contrary it has the effect of reducing restriction area and (& increasing pressure) but only very slightly, it is designed not to resist flow. If it were in parallel with the rest of the oiling system, your point would be true.
It may be that on some engines a cooler is set up in a parallel-flow or bypass configuration, but not ones I am familiar with.
"The shop manual says the oil pump's relief valve opens at 47 - 55 psi, so that sets an upper limit on the system pressure (unless you tinker with the relief valve.) My older, high-mileage V4 generally shows about 40 psi at highway speeds when fully warmed up, but I've seen it get up near 50 when the car is first started on cold days. This suggests to me that the stock pump has enough capacity to fully pressurize a stock engine, but maybe an oil system enlarged with a cooloer or other add-ons would need more volume to keep pressure in the desirable range...?"
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