V-Notch Weir Flow Calculator
Convert the head of water over a triangular (V-notch) weir into a flow rate. Enter the notch angle, the measured head above the vertex and the discharge coefficient, and the tool returns the discharge in m³/s and L/s using the standard triangular-weir equation — ideal for gauging small streams, plant effluent and lab flumes.
Enter Values
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How to use this calculator
- Enter the total included angle of the notch θ in degrees (90° is the most common).
- Measure and enter the head H (metres) from the notch vertex up to the undisturbed water surface.
- Enter the discharge coefficient Cd (0.58–0.60 for a sharp 90° notch) and read the flow rate.
How it works
The triangular-weir discharge is Q = (8/15)·Cd·√(2g)·tan(θ/2)·H^(5/2), with g = 9.81 m/s². The tan(θ/2) term captures how wide the V opens, and the H^2.5 dependence makes the weir very sensitive at low heads. Cd lumps together the real-fluid effects (contraction, viscosity, surface tension) that the ideal derivation ignores.
Worked example
Worked example. For a 90° V-notch with a head of 0.15 m and Cd = 0.58: tan(45°) = 1 and √(2×9.81) = 4.4294, so Q = 0.5333 × 0.58 × 4.4294 × 1 × 0.15^2.5 = 0.01194 m³/s, i.e. about 11.94 L/s.
Common mistakes
- Measuring the head at the weir plate where the surface is already drawn down — H must be read upstream, typically about 4–5×H back, where the water is level.
- Using the notch angle as the half-angle; θ is the full included angle, and the formula already halves it inside tan(θ/2).
- Applying the equation outside its valid range — a submerged, un-ventilated or drowned nappe, or a head too small for surface tension to be negligible, breaks the H^2.5 relationship.
Frequently asked questions
What Cd should I use?
For a sharp-crested, fully-ventilated 90° V-notch, Cd is roughly 0.58–0.60. It varies slightly with head and notch angle, so for accurate metering use the coefficient (or the Kindsvater-Shen effective values) from ISO 1438 or your local standard.
Why a V-notch instead of a rectangular weir?
Because discharge scales with H^2.5, a V-notch keeps a measurable head even at very low flows, giving far better resolution for small or highly variable streams than a rectangular weir, which is better suited to larger, steadier flows.
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