Peter,
The exhaust tube is plenty big enough, the problem I judge is that the fan is directly over the shower. This would not be allowed by Code in the States. You are sucking up not only shower "steam" but possibly water as it exits the shower head or splashes. You have two choices as I see it:
1) don't turn on the fan until you are finished with your shower. Inefficient but will stop the cold drips;
2) relocate the fan inlet to outside the shower perimeter.![]()