Manning's Equation for Flow

Multiply Manning's velocity by the flow area and you have the discharge form, which is what actually sizes a sewer, a channel or a culvert. A trapezoidal channel with n = 0.013, 0.4 m² of flow area, a hydraulic radius of 0.25 m and a 0.16% grade carries 0.488 m³/s, about 29,300 L/min. Solving it for slope is the everyday design case: you know the pipe, you know the flow, and you need the grade the contractor must hold.

The geometry hides the traps. Hydraulic radius for a full circular pipe is exactly D/4, but for a partly full pipe it peaks near 0.81 of full depth — which is why a sewer flowing about 93% full actually carries MORE than the same sewer flowing brim full, and why designers cap pipes at 75–80% depth at peak flow to leave ventilation space for sulfide gases. Note also that Manning assumes uniform, steady, fully turbulent flow; in a backwatered reach, at a drop structure, or in a pipe running under surcharge, it simply does not apply and a proper backwater profile is needed. And be honest about n: a new pipe's 0.011 becomes 0.014 or worse once it carries a slime layer and a few years of grease, so design on the aged value and check the self-cleansing velocity on the new one.