Partially Full Pipe Flow Calculator (Manning, Circular Sewer & Storm Pipes)

How it works

θ = 2·arccos(1 − 2y/D) · A = D²/8 · (θ − sin θ) · wetted perimeter P = D·θ/2 · R = A/P · Q = (1/n)·A·R^(2/3)·S^(1/2) (SI; 1.486/n in US units) · full pipe: Qfull = (1/n)·(πD²/4)·(D/4)^(2/3)·S^(1/2) · Froude number = V/√(g·A/T), T = D·sin(θ/2).

Gravity sewers and storm drains rarely run full; they are open channels with a circular cross-section. Manning’s equation applies at any depth once the flow area and wetted perimeter of the circular segment are known. Because the wetted perimeter grows quickly near the crown, the maximum flow occurs at about 94% of the diameter (about 1.08 × Qfull) and the maximum velocity at about 81%. Design codes such as the Ten States Standards ask for a minimum velocity of 0.6 m/s (2 ft/s) at design flow so solids do not settle.

Worked example

A 300 mm concrete pipe (n = 0.013) on a 1% slope flowing 75% full: θ = 2·arccos(−0.5) = 4.189 rad, A = 0.09/8 × (4.189 + 0.866) = 0.0569 m², P = 0.628 m and R = 0.0905 m. Q = (1/0.013) × 0.0569 × 0.0905^(2/3) × 0.1 = 88.18 L/s at 1.55 m/s. Flowing full the pipe carries 96.70 L/s, so it is at 91.2% of its full capacity and comfortably self-cleansing.

Sources: Manning formula — partially full circular conduits · Recommended Standards for Wastewater Facilities (Ten States Standards), §33 Design and Construction of Gravity Sewers

Frequently asked questions