When should I use a V-notch weir?

V-notch weirs are best for measuring low or highly variable flows. The triangular shape is more sensitive at low flow than rectangular weirs because head varies less for the same flow change.

What V-notch angle is most common?

90° is the standard angle. 60° and 45° are used for very low flows where 90° wouldn't develop enough head for accurate measurement. Larger angles (120°, 135°) for higher flows.

What's the discharge formula?

Q = (8/15)·C_d·√(2g)·tan(θ/2)·H^(5/2). For θ = 90° in US units with C_d = 0.58, this simplifies to Q ≈ 2.49·H^(5/2). The 5/2 exponent makes V-notch flow especially sensitive to head — an advantage for low-flow measurement.

What is the simplified Q equation for a 90° V-notch?

For a fully-contracted 90° V-notch in US units with H in feet: Q (cfs) = 2.49·H^(5/2). At H = 0.5 ft: Q = 0.44 cfs. At H = 1.0 ft: Q = 2.49 cfs. At H = 2.0 ft: Q = 14.1 cfs.

How accurate are V-notch weirs?

With proper installation per ISO 1438, V-notch weirs achieve ±1–2% accuracy in the calibrated range (0.2 ft ≤ H ≤ 2 ft for 90°). Below 0.2 ft, surface tension effects degrade accuracy to ±3–5%. Above the calibrated range, expect ±5%.

Where is the head H measured from?

H is measured from the bottom point (vertex) of the V-notch up to the upstream water surface, at a stilling well located 4·H_max upstream. Use the maximum expected H to set the stilling-well location.

What is a fully-contracted V-notch?

Fully-contracted means the notch is far enough from channel walls and bed that the nappe contracts freely on all sides. Requires: minimum P/H_max ≥ 1 (where P is weir height), and side-distance of ≥ 2·H_max from channel walls. If not fully contracted, C_d shifts upward by 5–8%.

V-Notch Weir Calculator — Triangular Weir Flow

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.

Why V-notches for low flow

Q ∝ H^5/2 for a V-notch versus H^3/2 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.

V-notch discharge table

Pre-computed discharge for fully-contracted V-notches at common heads, using C_d = 0.58 in US units (cfs). Use this to size your stilling well and head-measurement range.

Discharge Q (cfs) for fully-contracted V-notch weirs at standard heads
Head H (ft)	22.5°	30°	45°	60°	90°	120°
0.20	0.009	0.012	0.018	0.026	0.045	0.077
0.30	0.025	0.033	0.050	0.071	0.123	0.213
0.50	0.090	0.119	0.180	0.255	0.441	0.764
0.75	0.247	0.328	0.494	0.703	1.21	2.10
1.00	0.508	0.673	1.014	1.444	2.49	4.32
1.25	0.890	1.179	1.776	2.527	4.36	7.55
1.50	1.400	1.855	2.795	3.978	6.86	11.88
2.00	2.875	3.808	5.737	8.165	14.08	24.39

Computed from Q = (8/15)·0.58·√64.4·tan(θ/2)·H^5/2. For SI (m³/s), multiply by 0.02832 and convert H from ft to m by multiplying by 0.3048.

Standard notch angles — when to use each

V-notch angle selection guide
Angle θ	Best for	Q at H=0.5 ft	Q at H=1 ft
22.5°	Very low flows (lab, baseflow)	0.09 cfs	0.51 cfs
30°	Small streams, baseflow	0.12 cfs	0.67 cfs
45°	Small ditch monitoring	0.18 cfs	1.01 cfs
60°	Common stream gauging	0.26 cfs	1.44 cfs
90°	Most popular, broad range	0.44 cfs	2.49 cfs
120°	Transitions to rectangular range	0.76 cfs	4.32 cfs

Worked examples

Example 1 — 90° V-notch, baseflow stream gauging

Given: 90° fully-contracted V-notch, head H = 0.65 ft, C_d = 0.58, US units.

Find: Discharge Q.

tan(45°) = 1.0; √(2·32.174) = 8.025

Q = (8/15) · 0.58 · 8.025 · 1.0 · (0.65)^2.5

Q = 2.483 · 0.341

Q = 0.846 cfs

Example 2 — Sizing a 60° V-notch for 0.5–2.0 cfs range

Given: Need to measure 0.5–2.0 cfs in a small monitoring well; check 60° vs 90° notch.

Find: Head range for each option, choose by readability.

60°: H_min = (0.5/(2.5·tan30°))^(2/5) = (0.346)^0.4 = 0.71 ft; H_max = (2.0/(2.5·tan30°))^0.4 = 1.16 ft. Range: 0.45 ft.

90°: H_min = (0.5/2.49)^0.4 = 0.527 ft; H_max = (2.0/2.49)^0.4 = 0.916 ft. Range: 0.39 ft.

60° gives more head range and better readability — pick the 60° notch.

Coefficient C_d

For fully-contracted V-notches (notch sides clear of channel walls and bottom), C_d ≈ 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 C_d 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.

V-Notch Weir Calculator