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Collection System MathAdvanced 32 min read

Collection System Math: System Optimization

Multi-stage Collection Class 3 math: designing a self-cleansing pipe slope with Manning's Equation, partial-flow capacity analysis using circular-segment geometry, and I&I quantification per inch-diameter-mile.

By Class 3 you're not just checking a pipe someone else designed — you're using the same formulas in reverse to design the pipe, and you're extending Manning's Equation from full-pipe flow into the more realistic case of a pipe running partially full. This guide layers three distinct multi-stage skills that show up together on the Class 3 exam: self-cleansing slope design, partial-flow capacity analysis, and inflow/infiltration quantification.
Why "Partially Full" Matters
Every gravity sewer you've analyzed so far in this course has been flowing completely full — a convenient simplification, but not reality. Real sewers are deliberately sized to run partially full most of the time, leaving freeboard for peak flows and I&I. To evaluate a real pipe's actual velocity and capacity, you need the geometry of a circular segment: the area and wetted perimeter of the water occupying on

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