Weir Flow Calculator (V-Notch and Rectangular)
By Santaji GadepatilinUpdated October 27, 2026
A weir is a notch or barrier in an open channel; the height of water flowing over it gives the flow rate. Weirs are common for effluent and irrigation, and are often paired with level transmitters — see measuring flow rate with level sensors. This free weir flow calculator solves for whichever value you leave blank and shows the formula and steps.
How to use the weir flow calculator
Choose the weir type and enter the head — the height of the water surface above the bottom of the notch or the crest. For a V-notch, set the notch angle and discharge coefficient; for a rectangular weir, set the crest length.
Weir flow formulas
V-notch (Kindsvater–Shen form)
Q = (8/15) × Cd × √(2g) × tan(θ/2) × h5/2
Rectangular, contracted (Francis)
Q = 1.84 × (L − 0.2h) × h3/2
with Q in m³/s and L and h in metres.
90° V-notch flow table
| Head | Flow |
|---|---|
| 25 mm | 0.49 m³/h (0.14 L/s) |
| 50 mm | 2.78 m³/h (0.77 L/s) |
| 75 mm | 7.66 m³/h (2.13 L/s) |
| 100 mm | 15.73 m³/h (4.37 L/s) |
| 150 mm | 43.35 m³/h (12.04 L/s) |
| 200 mm | 88.98 m³/h (24.72 L/s) |
| 250 mm | 155.45 m³/h (43.18 L/s) |
| 300 mm | 245.21 m³/h (68.11 L/s) |
Flow rises with h2.5, so doubling the head increases flow about 5.7 times.
Rectangular weir, 0.5 m crest
| Head | Flow |
|---|---|
| 25 mm | 13.0 m³/h |
| 50 mm | 36.3 m³/h |
| 100 mm | 100.5 m³/h |
| 150 mm | 180.9 m³/h |
| 200 mm | 272.5 m³/h |
Installation guidelines
- Sharp, thin crest (bevelled downstream).
- Free-falling, aerated nappe — the water must spring clear of the weir plate.
- Head measured at 4–5 × hmax upstream with a stilling well or level sensor.
- Approach channel straight and wide enough for low approach velocity.
- Minimum head about 50 mm for V-notches to avoid surface-tension errors.
Automating with level sensors
Ultrasonic or radar level transmitters above the weir measure head continuously. The flow computer then applies the weir equation — a common setup for effluent flow monitoring.
Frequently asked questions
What is a V-notch weir used for?
Measuring small and varying flows accurately — the triangular shape gives good resolution at low heads. 90° V-notches are common for effluent and wastewater.
Where should I measure the head?
Upstream of the weir, at a distance of about 4–5 times the maximum head, where the water surface is level and unaffected by drawdown.
What is the Francis formula?
Q = 1.84 (L − 0.2h) h^1.5 in SI units, for a rectangular weir with end contractions on both sides.
How accurate are weir formulas?
Typically within 2–5% when the weir is installed to standard (sharp crest, free fall, ventilated nappe, adequate approach channel).