Help identifying coolant pipe?

[OxfordBiker]

Hello -

Was about to run the new (to us) A8 up to the Lake District this weekend, but pre-flight checks revealed leaking coolant around the expansion tank. I think I've identified the rogue hose, but I'm failing to track down the part number to make sure I order the correct replacement?

If anyone could look at the attached pic and suggest how to identify the hose, and where best to find a replacement I'd be hugely grateful!

Thanks in advance!