Stock T4 oil pump
 

Will the stock T4 oil pump produce enough pressure for a 2666cc engine? Will run 2 oil coolers, 1 upfront, the other above the gearbox.

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Normally the 24mm gears will hold it. Blueprint the pump and use harder oil piston pressure springs under both pistons. If the engine is exactly in all tolerances, you'll receive pressures over 2 bars, if hot at idle and up to 7 bars under load!