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hydraulics / closed conduits

Manning partially full circular-pipe calculator.

Estimate the discharge and mean velocity for a free-surface flow depth inside a circular pipe using circular-segment area and wetted-perimeter geometry.

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Depth changes every hydraulic property.

When a circular pipe is only partly full, the flow is a circular segment. The selected depth changes the area, wetted perimeter, hydraulic radius, free-surface width, velocity, and discharge.

Governing equation

With θ = 2cos−1(1 − 2y/D), the flow area is A = D²(θ − sinθ)/8 and the wetted perimeter is P = Dθ/2. The hydraulic radius is R = A/P, then Q = (1/n)AR2/3S1/2.

Part-full circular-pipe relationships and the distinction between gravity-full and partially full flow are discussed in FHWA HDS-4.

Depth is not the whole system.

  • Check inlet control, outlet control, tailwater, surcharge, air entrainment, entrance and exit losses, junctions, bends, blockage, sediment, and maintenance.
  • Confirm that a free-surface Manning model is appropriate; a full pipe under pressure requires a pressure-flow model and hydraulic grade line.
  • Do not assume full-pipe capacity is the maximum at every depth. Circular-pipe discharge and velocity vary differently as depth changes.