Bosch fuel pressure accumulator: What is the extra hose connection for and how to connect?

Isn’t that the answer you are looking for?

I had to change mine 3 years ago because they started leaking from the 90° stuff.
As Steve said, on my European model they were only “connected” to atmosphere.
No more leak since then and no fuel on the ground

 

Bo, Steve M and roger21 are correct...the function of the pressure accumulator is to hold FI pressure forward to the engine Fuel Distributor to reduce the chance of hot engine compartment temps to heat or boil the fuel and create a "warm engine hard start issue" (vapor lock). Much the same as a radiator operating at above boiling point, fuel under pressure will not vaporize as easily....the rubber diaphragm inside the accumulator retains pressure for minutes/hours after the engine stops to prevent fuel boil.
The rubber diaphragm inside stretches and expands, then slowly contracts as pressure bleeds off, to do this it needs to be vented to outside air pressure to be able to move. If at some time the diaphragm dries and cracks or develops a pin-hole, fuel will leak out and indicate that to the owner as a fuel smell or puddle on the garage floor. The design and production of the car left these pipes open for that purpose, however, most US delivered cars had a rubber hose connected and routed back into the fuel tank. My accumulators on my '85 400i have been open to the air since new, no harm, just a sort of "warning light" if I ever smell fuel or see a puddle, I know what the cause is and replace the accumulators right away.

Gary