Flow Measurement · Free Calculator
Partially Full Pipe Flow Calculator (Manning)
Calculate gravity flow in a circular pipe or culvert running partly full: flow area, wetted perimeter, velocity and flow at any depth, with the Manning equation, compared with the full pipe capacity.
Manning equationGravity sewerDepth ratioCulvert
%
Flow123.08 m³/h (34.19 L/s)
Velocity0.9673 m/s
Flow area0.03534 m²
Hydraulic radius75 mm
Full pipe flow246.16 m³/h
Depth ratio / flow ratio50 % / 50 %
How this result was calculated
- θ = 2 cos⁻¹(1 − 2h/D); A = D²(θ − sin θ) ÷ 8; P = Dθ ÷ 2
- Rh = A ÷ P = 75 mm
- Q = (1/n) A Rh2/3 S1/2 = 34.19 L/s
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Manning Equation for Circular Pipes
θ = 2 cos⁻¹(1 − 2h ÷ D)
A = D² × (θ − sin θ) ÷ 8, P = D × θ ÷ 2, Rh = A ÷ P
Q = (1 ÷ n) × A × Rh2/3 × S1/2
A = D² × (θ − sin θ) ÷ 8, P = D × θ ÷ 2, Rh = A ÷ P
Q = (1 ÷ n) × A × Rh2/3 × S1/2
h is the flow depth, D the pipe inside diameter, θ the central angle of the wetted section in radians, n the Manning roughness, S the slope (m/m) and Q in m³/s with SI units. The maximum flow of a circular pipe occurs at about 94 % depth, slightly above full pipe flow.
Worked example
A 300 mm concrete pipe (n = 0.013) at 0.5 % slope running half full carries about 34.2 L/s at 0.97 m/s, half of the full pipe capacity of 68.4 L/s.
Key insight: open channel flow meters in partly full pipes (area velocity meters) use exactly this geometry: they measure depth and velocity and multiply by the wetted area.
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Frequently Asked Questions
What is the Manning equation?
An empirical formula for gravity flow in open channels and pipes running partly full, relating flow to area, hydraulic radius, slope and roughness.
At what depth does a pipe carry most flow?
At about 94 % of the diameter; above that, the extra wetted perimeter at the crown reduces the flow slightly.
Why is minimum velocity important in sewers?
Velocities of about 0.6 m/s or more keep solids moving and prevent deposits.
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