a question
 

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I broke the other end of this double nipple part on my s5, is there any reason its screwed to that solenoid, or can I replace this with just a hardware store nipple
this is probably just a noob question sorry

-thanks for your help

It's just a coolant hose connection. Mounting it to the BAC isn't critical.
Connecting it to the BAC valve transfers some heat between coolant and the solenoid in very cold weather. You shouldn't see any functional difference.

What does the BAC exactly do? I do live in a pretty cold climate, will it warm up enough just being bolted to the engine and under the hood?

It adjusts the idle speed for certain conditions. Cold engine, power steering, AC, electrical load etc.
The heat transfer is not important since you rarely have much temperature difference between the engine and coolant.
Bolting it there was probably more about tidy packaging than function.

thank you!