The Problem with a pitched roof - can it be solved
OK heres a plan of the roof with a pitched roof linking the two xisting roofs. I've marked the problem spot. You get 2 valley gutters coming down to a horizontal box gutter which has to turn a corner.
The area drained by this box gutter is at about 60% of the existing roof area. That amount of water will just flood the box gutter and the force of the water would probably push up a fountain as it goes around the corner.
Maybe there is a different roof configuration - if anyone can think of one please draw it in.:C:U:o