The method provides hydraulic pressure for mechanical work from an engine lubricating system in an internal combustion engine by supplying oil to an engine lubrication gallery for lubricating the engine and to at least one variable oil demand accessory. Each of the variable oil demand accessories has an individual pressure regulator. The output of the variable displacement pump is regulated based on the sum of fluid flow required by the engine lubricating system and the engine accessories, regardless of the engine output. The demand for fluid is determined by the individual pressure regulators on each of the engine accessories. In a preferred embodiment, an accumulator stores high-pressure fluid to be used to power the hydraulic accessories.