I'm led to believe that MEPs have building codes they follow for gutters, that go by roof area. This corner of the website is mostly civils, and we usually ignore this. You might want to crosspost this question to the ME area of the site. I'm sure nobody will object.
Hydrology, Drainage Analysis, Flood Studies, and Complex Stormwater Litigation for Atlanta and the South East -
you can think of gutters as open channel flow with the roof contributing sheet flow into the channel. could manning equation work?
I would make basic assumption that you want the gutters to handle lets say 2" of rainwater. That would give you the volume based on roof area.
Then use manning equation to size it.
