A weir is a barrier placed across an open channel that forces water to flow over a shaped notch. By measuring the water depth (head) upstream of the notch and applying the appropriate formula, you can determine the flow rate with an accuracy of 2–5 % under good conditions. Weirs are among the most reliable and widely used primary flow measurement devices for irrigation canals, stormwater channels, wastewater treatment plants, and dam spillways.
The three common weir types (rectangular, V-notch triangular, and Cipolletti trapezoidal) each have advantages for different flow ranges and channel geometries. This guide covers the installation requirements that make or break measurement accuracy, the formulas for each type, and the practical considerations that separate a reliable measurement from a guess.
Weir Types and Applications
A rectangular (contracted) weir has a flat-bottomed notch and is the most common type for medium to large flows. The Francis formula gives flow as Q = 3.33 × (L − 0.2nH) × H^1.5, where L is the crest length, H is the head, and n is the number of end contractions (0, 1, or 2). A suppressed rectangular weir (crest extends the full channel width) has no end contractions and uses Q = 3.33 × L × H^1.5.
V-notch (triangular) weirs are best for low flows because the V shape concentrates small flows into a measurable head. The standard 90-degree V-notch formula is Q = 2.49 × H^2.5. The exponent of 2.5 means head changes are more dramatic for small flow changes, improving measurement resolution. Cipolletti weirs have trapezoidal notches with 1:4 side slopes (horizontal:vertical) that compensate for end contraction effects, simplifying the formula to Q = 3.367 × L × H^1.5.
Weir Flow Rate Calculator
Calculate flow rate over rectangular, V-notch, and Cipolletti weirs with rating tables.
Installation Requirements for Accuracy
A weir must create a free-falling nappe (water sheet) downstream of the crest. If the downstream water level submerges the nappe, the standard formulas no longer apply and the weir under-reports flow. Ensure adequate drop. The downstream water level must be at least 2 inches below the crest for a rectangular weir. The nappe should spring clear of the downstream face of the weir plate; ventilate the space under the nappe if needed.
The approach channel must be straight and uniform for at least 10 to 20 times the maximum head upstream of the weir. Turbulence, eddies, or uneven velocity profiles in the approach channel cause measurement errors. The head measurement point (staff gauge or level sensor) must be upstream of the drawdown zone, typically 4 to 6 times the maximum head upstream of the weir plate. Measure head from the weir crest, not from the channel bottom.
Approach Velocity Correction
Standard weir formulas assume negligible approach velocity, meaning the water upstream is essentially still and all the energy is potential (head). If the approach channel is small relative to the flow, the water has significant velocity, and the kinetic energy adds to the effective head. The velocity head is V²/(2g), where V is the average approach velocity and g is 32.2 ft/s².
The corrected effective head is H_eff = H + V²/(2g). For a channel with approach velocity of 1 ft/s, the velocity head is only 0.016 feet, negligible for most practical purposes. But if the approach velocity reaches 3 ft/s (possible in a small channel carrying significant flow), velocity head is 0.14 feet, which can add 5–10 % to the calculated flow. Design the approach pool to be at least 3 times wider and deeper than the weir notch to keep approach velocity corrections small.
Weir Flow Rate Calculator
Calculate flow rate over rectangular, V-notch, and Cipolletti weirs with rating tables.