Partial Flow Calculator
Discharge, velocity and hydraulic radius at any flow depth in a part-full circular pipe.
Inputs
Results
Discharge at this depth
48.4L/s
50.0% of the full-bore capacity
Circular segment geometry with a horizontal water surface. Results update as inputs change.
Calculation details
Engineering equations
θ = 2 · arccos(1 − 2y / D)
A = (D² / 8) · (θ − sin θ)
P = (D / 2) · θ
V = (1 / n) · (A / P)^(2/3) · S^(1/2), Q = V · A
Variables
- y
- Flow depth measured from the invert (m)
- θ
- Wetted angle at the pipe centre (rad)
- A
- Part-full flow area (m²)
- P
- Wetted perimeter (m)
- R
- Hydraulic radius (m)
- n
- Manning's roughness coefficient
- S
- Pipe grade (m/m)
- D
- Internal pipe diameter (m)
Assumptions
- Part-full circular section with a horizontal water surface.
- Flow depth cannot exceed the internal diameter.
- Manning's equation is applied at the part-full hydraulic radius.
- Discharge peaks slightly before full depth in a circular pipe; the percentage-full figure is depth based.
Worked example
D = 300 mm, y = 150 mm (d/D = 0.5), S = 1%, n = 0.013
θ = π, A = 0.0353 m², P = 0.4712 m, R = 0.075 m
V = (1 / 0.013) × 0.075^(2/3) × 0.010^0.5 = 1.37 m/s
Q = 1.37 × 0.0353 = 0.0484 m³/s = 48.4 L/s
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Results are preliminary engineering estimates based on the stated assumptions. Confirm inputs, assumptions and requirements against the applicable standards and authority requirements before use in design or construction.