Free calculator

Gravity Sewer Capacity — Circular Sewer at Partial Depth

Enter the pipe diameter, roughness, slope, and flow-depth ratio d/D — the calculator returns full-flow and partial-flow discharge and velocity, plus the two checks every sewer design needs: self-cleansing velocity and the d/D ≤ 0.8 design limit.

V = (k/n) · R^2/3 · S^1/2 Q = AV

k	1.0 for SI (m/s), 1.486 for US units (ft/s)
θ = 2 arccos(1 − 2d/D)	wetted angle of the circular section; A = (D²/8)(θ − sin θ), P = Dθ/2
n	Manning's roughness (concrete ≈ 0.013)
S	pipe slope (m/m or ft/ft)

Unit system Diameter D (m) Manning's n Slope S Flow depth ratio d/D (0–1)

For study and checking only. These calculators run entirely in your browser — nothing is sent anywhere. They are meant to verify your hand calculations while you study; on the exam you will work by hand with the NCEES reference handbook.

Worked example: gravity sewer capacity

A 450 mm concrete sewer (n = 0.013) laid at 0.002 flows full. Find the capacity and velocity.

A = π(0.45)²/4 = 0.159 m², R = D/4 = 0.1125 m
Q = (1/0.013) × 0.159 × 0.1125^2/3 × √0.002 ≈ 0.128 m³/s
V = Q/A ≈ 0.80 m/s — above the usual 0.6 m/s self-cleansing minimum ✓

Exam tip: a circular sewer running about 90–95% full actually carries slightly MORE than the full-flow value — check partial-depth ratios before answering "full = max".

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Preparing for exam day? The 110-question FE Civil practice exam is a full 5-hour-20-minute rehearsal with detailed solutions.