Personally I wouldn't even consider a pipe underground. My over flow consists of a v trench lined with stone theat feeds into an 8 inch pipe, and then the water tumbles out of the pipe into a ditch. No erosion and no water working around the pipe as all is above ground. The pipe slants down and is weighed down with stone. Foolproof!

If pigs could fly bacon would be harder to come by and there would be a lot of damaged trees.