I have two gutters and a sump pump that all tie into a 3" pipe buried on the side of my house that drains into the street. In late winter, after a heavy rain, my sump was running almost constantly. I checked it out and found that every time it kicked on, water would shoot out of the gutter drains. Figured there was a clog. I rented a snake, but it wasn't quite long enough to go the whole distance of the pipe. I tried from the front gutter drain, but snake ended up in back gutter drain. When I tried from rear gutter drain, I ran out of snake. In any event, I either broke up the clog enough or pushed it enough because after that, water was not shooting out of the gutter drains when the sump kicked on and it ran much less after heavy rain.
Since the weather has been nice, I decided to dig up the points where the gutter drains and the sump tie into the drain pipe to check things out. First, there are no "wye" fittings, only T's. Second, the sump and back gutter drain are almost next to each other. Upon digging them up, I found the sump drain actually pointed toward the back gutter drain instead of toward the drain pipe...so ain't no wonder water wanted to shoot out of that. I fixed all of that by pointing the sump drain toward the main drain pipe and makeing that connection a "wye" so the flow heads toward the street.
The front gutter drain also ties via a "T" fitting. After fixing the back mess and having the sump kick on, once I ran it a few times and the drain pipe kind of filled up with water, the next time the sump ran water shot out from a small hole in the top of that front tie-in "T" fitting. Water still comes out at the street, but its like there still has to be some kind of obstruction to cause it to shoot out like that, right? Also, after the sump turns off, the water remaining in the pipe between the front gutter and back gutter drains backward and starts dripping from the fittings at the back gutter drain and sump area. I take it I should glue these joints? Is it that big of a deal that the slope is not set in such a way that the back drain slopes to the street? To fix that, i would have to tear out and fix a 10-15 foot section. I plan on replacing the front gutter drain "T" fitting with a "Wye" fitting too. Thoughts or ideas? I can post pics of these setups if need be.