🚇 Culvert Flow

Written and maintained by the PhDino author · Last reviewed 21 September 2026 · Checked against 2 independent reference calculations · how PhDino checks its numbers

Related standards: Manning's Equation

Checking a circular culvert's full-flow capacity using Manning's equation.

Manning's equation is the standard formula for estimating flow in an open channel or a gravity (non-pressurized) pipe like a culvert — different from the pressurized-pipe flow covered elsewhere on PhDino, since a culvert usually isn't flowing completely full or under pressure the way a water-supply pipe is.

The equation relates flow velocity to the channel's slope, its hydraulic radius (cross-sectional flow area divided by the wetted perimeter — the part of the boundary actually in contact with the water), and a roughness coefficient n that depends on the pipe or channel material. A smooth concrete pipe has a low n and carries more flow for the same slope and size than a rough corrugated metal pipe would.

For a circular pipe flowing completely full, the hydraulic radius simplifies neatly to one-quarter of the diameter — a standard result of full-circle geometry (wetted perimeter = full circumference, flow area = full circle area, and the ratio between them reduces to D/4).

Key formula

V = (1.49/n) × R^(2/3) × S^(1/2)
Q = V × A
For a full circular pipe: R = D/4

Variables

n

Manning's roughness coefficient, set by pipe/channel material

R

hydraulic radius — flow area divided by wetted perimeter

S

channel or pipe slope

Notes & limitations

• This checks capacity for the pipe flowing completely full, the simplest case to compute in closed form. A culvert flowing partially full needs an iterative solution for the actual flow depth, since the hydraulic radius of a partially-filled circle doesn't reduce to a clean formula the way the full-pipe case does.
• Actual culvert capacity in practice is also affected by inlet control (how well water enters the pipe) as often as by the pipe's own full-flow capacity — a full hydraulic design checks both, not just the barrel capacity computed here.