Help with identifying a part

[Marc b]

I’m hoping someone can help me while working on my a3 8p 1.4 tfsi I have managed to snap a pipe I’m assuming is some kind of air pipe as the was no liquid inside it I have taken some pics to show were it goes on the engine I have tried to look this up but unable to find the name or part number 

Edited December 6, 2023 by Marc b
Photos

[Steve Q]

Have you traced it to see where it goes?

[cliffcoggin]

I see lots of pipes in the pictures but none of them appear to be broken. Which one do you mean? Is it rigid or flexible? Where does it run to and from?