Compute the discharge over a sharp-crested weir from the measured head, for rectangular, V-notch (triangular), and Cipolletti (trapezoidal) weirs. Weirs are simple, reliable open-channel flow-measurement devices — read off the head H and this calculator returns the flow rate in SI units.
A weir is a notch or obstruction placed across an open channel so that water must flow over it; the depth of water above the crest (the head, H) uniquely determines the discharge. Because head is easy to measure accurately, weirs are among the simplest and most reliable devices for measuring flow in streams, irrigation channels, water-treatment plants, and laboratory flumes. This calculator covers the three standard sharp-crested shapes — rectangular, V-notch, and Cipolletti — in SI units.
A sharp-crested weir converts a single, easily measured quantity — the head H above the crest — into discharge through a calibrated relationship. There are no moving parts, the device is cheap to build, and a stilling well with a staff gauge or transducer reads H directly. The general form is Q = C·(weir shape factor)·H^n, where the exponent n depends on the crest geometry. Accurate readings require the head to be measured upstream of the drawdown, typically about 4H back from the crest, and the weir to discharge freely (a ventilated, fully aerated nappe).
A suppressed rectangular weir (crest spanning the full channel width) follows Q = 1.84·L·H^1.5 in SI units, where L is the crest length and the discharge grows with H to the 1.5 power. The Cipolletti weir is a trapezoidal notch with side slopes of 4 vertical to 1 horizontal; the flared sides compensate for the end contractions of a contracted rectangular weir, so the simple form Q = 1.86·L·H^1.5 applies without an end-contraction correction. Both are good for moderate-to-large flows where a wide crest is practical.
A triangular weir with included angle θ follows Q = (8/15)·C_d·√(2g)·tan(θ/2)·H^2.5, with a typical discharge coefficient C_d ≈ 0.58. For the common 90° notch this reduces to roughly Q ≈ 1.38·H^2.5. The 2.5-power dependence means that at low flows a small change in discharge produces a relatively large change in head, so V-notch weirs give excellent precision for small flows — which is why they are favored for low or widely varying discharges, such as monitoring small streams or treatment-plant effluent.
Use a V-notch for small or highly variable flows where sensitivity matters; use a rectangular or Cipolletti weir for larger, steadier flows where a wide crest is appropriate. For valid readings the weir must be sharp-crested and vertical, the upstream pool must be wide and calm so the approach velocity is negligible, the nappe must spring clear and be aerated, and the head must be small relative to the weir height. Submerged (drowned) flow, an unaerated nappe, or a high approach velocity all introduce error and need separate corrections.
Measure H as the vertical distance from the weir crest (or the vertex of a V-notch) to the undisturbed upstream water surface — taken far enough upstream to be clear of the surface drawdown over the crest, conventionally about 3 to 4 times the maximum head back from the weir. A stilling well connected to that point gives a steady reading.
Because the flow area of a triangular notch grows with the square of the head (the notch widens as the water rises) while the velocity grows with the square root of head; the product gives an H^2.5 relationship. This strong dependence makes the head very sensitive to flow at low discharges, which is exactly why V-notch weirs are chosen for accurate measurement of small flows.
A Cipolletti weir is a trapezoidal sharp-crested weir with sides sloped 1 horizontal to 4 vertical. The outward-sloping sides add flow area that offsets the end contractions a plain contracted rectangular weir would suffer, so discharge stays proportional to crest length and you can use the simple Q = 1.86·L·H^1.5 without an end-contraction correction. It is popular for irrigation measurement.
No — the standard equations here assume the approach velocity in the upstream pool is negligible, which holds when the channel is much larger than the flow over the weir. If the approach velocity is significant, the head should be corrected to a total (velocity) head, or the weir relocated to a larger pool. Always provide a calm, wide approach for accurate measurement.
A suppressed rectangular weir has its crest extending the full width of the channel, so there are no side (end) contractions of the nappe — the Q = 1.84·L·H^1.5 form applies directly. A contracted weir is narrower than the channel, so the nappe contracts at each end, reducing effective crest length; that requires an end-contraction correction (or you use a Cipolletti weir, which is shaped to cancel it).