Triangular (V-Notch) Weir Calculator
Enter the discharge coefficient Cd, notch angle θ and head H to compute the flow of a triangular (V-notch) weir from Q = (8/15)·Cd·tan(θ/2)·√(2g)·H^(5/2).
Input Data
Results
At a glance:A triangular weir (V-notch weir) is a common open-channel measuring structure for small flows: a V-shaped (triangular) notch is cut into a vertical plate so water overflows through it. Because the V-notch is narrow near the surface and widens toward the vertex, even a small flow produces a measurable head H, giving high reading accuracy for low and widely varying discharges. The discharge formula is Q = (8/15) × Cd × tan(θ/2) × √(2g) × H^(5/2), where Q is flow (m³/s), Cd the discharge coefficient (dimensionless), θ the full notch angle (°), g gravitational acceleration (9.81 m/s²) and H the head from the notch vertex to the upstream free surface (m). The core is H^(5/2): compared with a rectangular weir's H^(3/2), the extra power comes from integrating the depth-varying width (wider higher up) times the depth-varying velocity √(2gh) over the height. tan(θ/2) reflects how open the notch is — a wider angle passes more flow at the same head; the 90° notch (tan45°=1) is simplest and most common. Cd is about 0.58-0.60 for a 90° V-notch. Example: Cd=0.58, θ=90° (tan45°=1), H=0.3 m: Q=(8/15)×0.58×1×√(19.62)×0.3^2.5 ≈ 0.30933×4.429×0.049295 ≈ 0.0675 m³/s (≈67.5 L/s).
Formula
Triangular (V-notch) weir: Q = (8/15) × Cd × tan(θ/2) × √(2g) × H^(5/2), g = 9.81.
Cd discharge coefficient (≈0.58), θ full notch angle (°), H head over weir (m).
Requires free overflow with ventilated nappe; 90° notch tan(θ/2)=1 is most common.
$$Q = \dfrac{8}{15}\,C_d\,\tan\!\dfrac{\theta}{2}\,\sqrt{2g}\;H^{5/2}$$How to Use
- Enter the discharge coefficient Cd (≈0.58 for a 90° V-notch).
- Enter the full notch angle θ (°, commonly 90) and the head H (m).
- The tool computes Q = (8/15)Cd·tan(θ/2)·√(2g)·H^(5/2).
Case Studies
Irrigation channel metering
A 90° V-notch with H=0.3 m gives Q≈0.0675 m³/s (≈67.5 L/s).
The H^(5/2) law makes the head readable even at low flow.
Used for small canals, drainage ditches and lab flumes.
Low-flow monitoring
During dry seasons a triangular weir still gives a usable head for tiny flows.
Wider angles (e.g. 120°) increase capacity but reduce low-flow sensitivity.
Narrower angles improve small-flow precision at the cost of range.
FAQ
Why does a triangular weir use H^(5/2)?
The V-notch width grows linearly with height, so integrating the width (∝ height) times the velocity √(2gh) over the height yields H^(5/2) — one power higher than a rectangular weir's H^(3/2), giving better sensitivity to small flows.
What is Cd?
The discharge coefficient (~0.58-0.60 for a 90° V-notch), which corrects for contraction, viscosity and approach-velocity effects. It varies slightly with H and weir geometry.
What are the installation requirements?
Free overflow with a ventilated (air-entrained) nappe, the downstream level below the notch vertex, a stilling well for head measurement (~4-5H upstream), a sharp-edged symmetric notch, and a vertical plate with no leakage.
Why is it preferred for small flows?
At low discharge the narrow top of the V keeps the head H substantial, so readings stay accurate; rectangular weirs would have too small a head to measure reliably.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.