Enter values to see results
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m³/s
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L/s
Enter values to see results
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m³/s
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L/s
The Weir Flow Calculator estimates the volumetric flow rate (discharge) over a weir — a barrier placed across an open channel to measure or control flow. Weirs are among the oldest and most reliable flow-measurement devices in hydraulic engineering, used in rivers, irrigation canals, water treatment plants, and laboratory flumes worldwide.
This calculator supports two common weir types. For a rectangular (suppressed) weir: $$Q = \frac{2}{3} C_d \, b \sqrt{2g} \, H^{3/2}$$ For a V-notch (triangular) weir: $$Q = \frac{8}{15} C_d \tan\!\left(\frac{\theta}{2}\right) \sqrt{2g} \, H^{5/2}$$
Here C_d is the discharge coefficient (typically 0.58–0.65), b is the weir width, θ is the V-notch angle, H is the head above the weir crest, and g is gravitational acceleration. V-notch weirs are preferred for measuring low flows because the H^(5/2) relationship provides excellent sensitivity at small heads.
Both formulas derive from integrating the velocity profile (Torricelli's theorem, v = √(2gh)) across the weir opening:
Rectangular weir: The opening width is constant at b, so integrating the velocity from 0 to H: $$Q = C_d \int_0^H b \sqrt{2g h} \, dh = \frac{2}{3} C_d b \sqrt{2g} H^{3/2}$$
V-notch weir: The opening width varies linearly with depth as $$w(h) = 2(H-h)\tan(\theta/2)$$. Integrating: $$Q = \frac{8}{15} C_d \tan\!\left(\frac{\theta}{2}\right) \sqrt{2g} H^{5/2}$$
The discharge coefficient C_d accounts for the contraction of the nappe (the sheet of water) and velocity distribution effects. Standard values are ~0.62 for rectangular and ~0.58 for 90° V-notch weirs, but calibration is recommended for accurate measurement.
The flow rate is highly sensitive to head H. For a rectangular weir, Q scales as H^(3/2), so a 10% head increase raises discharge by about 15%. For V-notch weirs, the H^(5/2) dependence makes them even more sensitive — excellent for detecting small flow changes. A higher discharge coefficient indicates less flow contraction and more efficient passage over the crest.
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Results
A 2 m wide rectangular weir with 0.3 m head and Cd = 0.62 passes about 380 L/s (0.38 m³/s).
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Results
A 90° V-notch weir with only 15 cm head yields ~3 L/s. The H^(5/2) relationship makes it sensitive enough to measure such small flows accurately.
A weir is a low dam or barrier across an open channel designed to raise the upstream water level and create a predictable head-discharge relationship. By measuring the water height (head) above the weir crest, the flow rate can be calculated from a known formula.
V-notch weirs are best for low-flow measurement because their H^(5/2) relationship provides high sensitivity at small heads. Rectangular weirs handle larger flows and are simpler to construct. For very large flows, broad-crested weirs may be more appropriate.
For a sharp-crested rectangular weir, Cd ≈ 0.60–0.65 (Rehbock formula gives more precise values). For a 90° V-notch weir, Cd ≈ 0.58. The coefficient depends on head, weir geometry, and approach conditions; calibration improves accuracy.
A suppressed (full-width) weir spans the entire channel width, so there is no lateral contraction. A contracted weir is narrower than the channel, causing the nappe to contract horizontally. Contracted weirs require additional correction factors (Francis formula) not included in this calculator.
The basic formulas assume negligible approach velocity. When the approach channel is relatively small, the velocity head should be added to H, giving an effective head H_eff = H + v_a²/(2g). This correction becomes important when H exceeds about one-third of the upstream depth.
The nappe is the sheet of water flowing over the weir crest. For accurate measurement, the nappe should be fully aerated (ventilated) underneath. A clinging or submerged nappe changes the head-discharge relationship and invalidates the standard formulas.
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