Cistern mechanism help

[grahfcard]

I'm having trouble with the three part machine puzzle in the cistern level. I got the first two parts, with the weights and the pressure boiler mechanism, but I can't do the pipes one. Problem is, I can't find the fourth pipe: I got the two in each of the weight puzzle rooms, and the one in the pressure mechanism room. I fixed them to the wall in the final chamber, but there's one missing. I've looked everywhere, methodically sweeping the rooms, but I can't find it.
It's not an item you can take into your inventory, so it has to be in that map, and not in another one of the Cistern level.
Anyone know where the fourth one might be?