Why do you need more pressure than the power steering pump is designed to deliver to run the car's steering system?

Brakes don't run off that same pump. They're vacuum boost hydraulic. There's a vacuum pump on the engine to create the vacuum needed for brake boost. Vac is usually measured in inches of mercury pull up a column.

There's also a diesel injector pump that produces 135bar to pop the injectors to put fuel into the cylinders.

Maybe you're confused about the duality of PS fluid? The automatic transmission uses the same fluid as power steering but they're two different systems.

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Cheers!
Scott McPhee

1987 300D