Please Help Identify Hose/Pipe !

[Foufdog]

Hi everyone,

Any Idea what the hose/pipe with the blue tape on is called. Please see Pictures below (whoever answers first is a legend)
(I will have another look tomorrow in the daylight to see if I can locate a part no.)

Background
So I have a 2001 Audi A3 1.8T Sport (AUM Engine code I think)

Started her up yesterday morning and Idle was a bit low and rough, pulled away and 1st and second gear a not responsive, juddering/hesitant acceleration almost felt like misfire!

Anyway made it to work okay, checked the engine bay and all visible hoses. Found by touch that one hose seems perished, so I taped it up for now to see if this made any difference. I need to replace anyway so I have added a couple of Pics as I have no idea what the part is called? Car was running better since taping this hose, so possibly related, I will see how it starts again tomorrow incase this is not related at all and from a little research I realise this could be a Throttle Body or Temp switch issue among other things!

Thanks for any help in advance guys

 

[superkarl]

Coolant hose. Goes from the upper rad hose to the oil/water heat exchanger on top of the oil filter

 

[Foufdog]

Thanks superkarl, you are a legend mate, any idea if this would affect the cars idle or acceleration from cold start? (I guess maybe no, as you can tell not that savvy as regards to Engine function) sorry, I am learning though!

 

[superkarl]

No that won't be affecting the running. Not unless it has completely burst through

 

[Foufdog]

No that won't be affecting the running. Not unless it has completely burst through

Thanks, I'll get it replaced anyway and then ask the garage to check the dodgy idle out, think i'll have to leave this to the Mechanics, thanks for your help, probably not as easy a fix as I hoped.