The classic solution of gravity flow hydraulics is via a backwater analysis. This type of analysis starts at the network outlet under free discharge, submerged, or tailwater control, and proceeds in an upstream direction.

Steep pipes tend to "interrupt" the backwater analysis, and reset the hydraulic control to critical depth at the upstream end of the steep pipe. A frontwater analysis may be needed for a steep profile (such as an S2), with the backwater analysis recommencing from the upstream structure.