V-Notch Weir Calculator (Triangular Weir Flow)
Flow over a sharp-crested V-notch weir from the notch angle and the head of water above its vertex, in litres per second and cubic metres per hour.
Results
The dashed line marks the value you entered.
What this tool does
A V-notch weir measures flow by how high the water stands over the point of the notch: the flow rises with the head to the power 5/2, so a small error in reading the head becomes a bigger error in flow, and the V shape gives good accuracy even for small flows because the opening widens with the head. The discharge coefficient Cd is usually taken as 0.58–0.62; for the common 90° notch the formula reduces to about 1.4 × h^(5/2) in m³/s with h in metres. Measure the head in still water a few notch-heads upstream of the plate, not at the notch itself, and the crest must be sharp and the nappe fully ventilated.
Formula
Q = (8 ÷ 15) × Cd × √(2g) × tan(θ/2) × h^(5/2) (sharp-crested triangular weir, Cd ≈ 0.58–0.62)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
th | Angle of the V-notch | ° |
h | Head of water above the notch vertex | cm |
cd | Discharge coefficient Cd | — |
Q | Flow in litres per second | L/s |
QH | Flow in cubic metres per hour | m³/h |
W | Width of the water surface in the notch | cm |
Worked example
- Angle of the V-notch90 °
- Head of water above the notch vertex15 cm
- Discharge coefficient Cd0.6
- Flow in litres per second12.35 L/s
- Flow in cubic metres per hour44.5 m³/h
- Width of the water surface in the notch30.0 cm
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.