Pressurized overflow tanks are a European car thing. Once the new tank is in place, you may want to bleed the air from the system.

This bleed procedure works on all vehicles with the N52, N51, N52K and N54 engine, operating with electric cooling water pump.

Fill the system with coolant via the reservoir until the proper level is achieved. It may be necessary to remove a bleeder screw on the reservoir when initially filling the cooling system on some reservoirs. Install the cap and bleeder screw if present, on the reservoir. Turn on the ignition (do not start car), set the heat to maximum and the blower on the lowest setting. Begin by pressing the accelerator pedal to the floor for at least 10 seconds; be sure NOT to start the engine. Release the accelerator pedal and within a moment, the pump can be heard during activation. While the bleed procedure is being performed, inspect for leaks. The procedure can be repeated several times as needed, turning the ignition off for 5 minutes between each bleed procedure.

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2009 35d, 2006 325i & 330i