[Stiglr]

Better yet...

Select all the surfaces between 5:00 and 6:00 on that ringed area. Delete them.
Twist your view around and make sure there aren't any surfaces left on the inside of the "tube".

Then in Vertex mode, select all the vertices that make up the two "edges" of the space you left. (another thing to consider: is the number of vertices describing the "tube" the same on each side of the break? If not, weld some vertices together or add some so that both cross sections of the tube at the break have the same number of vertices)

Vertex> Create Convex Surface. Then, make sure all the ring surfaces are in the same one object with Object > Merge. That should get rid of the problem.