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Topics:  Introduction    Equations     Installation Guidelines and Equation Applicability     Error Messages     References

Introduction
Weirs are typically installed in open channels such as streams to determine discharge (flowrate). The basic principle is that discharge is directly related to the water depth (h) in the figure above; h is known as the "head." The Cipoletti (or trapezoidal) weir has side slopes in the vertical to horizontal ratio of 4 to 1. Cipoletti weirs are considered fully contracted and have the installation requirements shown below. The discharge coefficient for Cipoletti weirs is 3.367 (in English units), and it does not depend on L or P like it does for a rectangular weir. Though the discharge coefficient formulation is simpler than for rectangular weirs, its accuracy is not as good - about ±5% (USBR, 1997). Cipoletti is sometimes spelled Cipoleti, Cipolleti, Cipolletti, Cippoleti, Cippolleti, Cippoletti, and Cippolletti.

Equation
The Cipoletti weir equation is shown below for Q in cfs (ft³/s) and head and length in feet units (USBR, 1997).  Our calculation allows you to work in a variety of units.

Note that L is measured along the bottom of the weir (called the crest), not along the water surface.

Installation Guidelines and Equation Applicability (USBR, 1997)            Top of Page
Weir side slopes should have a vertical to horizontal ratio of 4 to 1.

Head (h) should be measured at a distance of at least 4h upstream of the weir.

It doesn't matter how thick the weir is except where water flows through the weir. The weir should be between 0.03 and 0.08 inches (0.8 to 2 mm) thick in the opening. If the bulk of the weir is thicker than 0.08 inch, the downstream edge of the opening can be chamfered at an angle greater than 45^o (60^o is recommended) to achieve the desired thickness of the edges. You want to avoid having water cling to the downstream face of the weir.

Water surface downstream of the weir should be at least 0.2 ft. (6 cm) below the weir crest (i.e. below the bottom of the opening).

Measured head (h) should be greater than 0.2 ft. (6 cm) but less than L/3.

P is measured from the bottom of the upstream channel and should be greater than 2h_max where h_max is the maximum expected head.

b is measured from the sides of the channel and also should be greater than 2h_max.

Error Messages given by calculation                                Top of Page
"All inputs must be positive".  This is an initial check of user input.

References
USBR (1997). U.S. Department of the Interior, Bureau of Reclamation. Water Measurement Manual. 1997. 3ed. Available from http://www.usbr.gov/pmts/hydraulics_lab/pubs/wmm/index.htm .

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