Cipoletti Weir Flow
Open-channel flow over a trapezoidal (Cipoletti) weir from crest length and head.
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The engineering
A Cipoletti weir is a sharp-crested trapezoidal notch with sides sloped 1 horizontal to 4 vertical. That slope is chosen so the extra flow through the sloping ends compensates for end contraction — the result behaves like a fully contracted rectangular weir but with a simple linear-in-L discharge equation, no contraction correction needed.
Keep the head-to-length ratio modest (H ≤ L/3 is the comfortable zone, L/2 the hard limit) and measure H well upstream — about 4H back from the crest — so you read the undisturbed pool, not the drawdown curve. Also make sure the nappe is ventilated and fully aerated; a clinging sheet reads high.
Where this math comes from
The weir is named for Cesare Cipoletti, an Italian hydraulic engineer who around 1887 worked out the trapezoidal notch for irrigation canals in the Po and Adige basins. His insight was geometric: give the sides a 1:4 batter and the side flow makes up almost exactly for the loss caused by end contractions, so discharge stays proportional to crest length.
The U.S. Bureau of Reclamation adopted and calibrated the design for Western irrigation districts, publishing the coefficient and installation rules in its Water Measurement Manual — still the standard reference field hydrographers reach for when setting a weir box.
- 1887Cesare CipolettiDevelops the 1:4 trapezoidal weir to eliminate end-contraction correction.
- 1929U.S. Bureau of ReclamationPublishes calibrated Cipoletti coefficients for irrigation delivery.
- 1997USBR Water Measurement Manual (3rd ed.)Pins the standard discharge equation and installation criteria used today.
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