V-Notch Weir Calculator
Triangular sharp-crested weir for low-flow measurement. Discharge varies with H to the 5/2 power, giving the V-notch much better resolution than a rectangular weir at small heads.
Defaults: 90° V-notch, 0.5 ft of head, standard discharge coefficient Cd = 0.58.
Why V-notches for low flow
Q ∝ H5/2 for a V-notch versus H3/2 for a rectangular weir. That higher exponent means the head reading is more sensitive to flow at small Q — for a 90° V-notch, going from 0.1 cfs to 0.2 cfs raises H by 32%, while doubling flow over a 1-ft rectangular weir raises H by only 59% as much. So at low flows, you can read the V-notch staff gauge to better precision. That's why every USGS lab flume and small streamflow gauging station uses one.
Standard notch angles
- 22.5° (1:5 H:V slope) — very low flows, < 0.5 cfs at H = 1 ft
- 30° — low flows, ~0.7 cfs at H = 1 ft
- 45° — common for small ditch monitoring
- 60° — common
- 90° (1:1 H:V slope) — most popular, ~2.5 cfs at H = 1 ft
- 120° — high-flow V-notch, used when transitioning to rectangular makes sense
Coefficient Cd
For fully-contracted V-notches (notch sides clear of channel walls and bottom), Cd ≈ 0.58 across angles from 22.5° to 120° at H above 0.2 ft. At smaller heads, surface tension on the nappe matters and Cd can rise to 0.61. ISO 1438 and USBR Water Measurement Manual give angle-specific values for the highest-precision metering.
Range of applicability
Reliable when H is at least 0.2 ft (60 mm) and at most 2 ft (0.6 m) for a 90° notch. Below 0.2 ft, the nappe can cling to the plate (poor ventilation) and surface tension distorts the discharge. Above 2 ft, the V-notch becomes more accurate to model with full physical methods.
Reference: USBR (1997). Water Measurement Manual, Chapter 7. ISO 1438:2017 — Hydrometry — Open channel flow measurement using thin-plate weirs.