9. Standard Contracted Rectangular Weirs

The fully contracted rectangular weir (figure 7-1) is the most frequent standard weir used in irrigation. To be fully contracted, all overflow plate sides and ends must be located at least a distance of 2h1max (two maximum measurement heads) from the approach flow boundaries. Head is measured at a distance of at least 4h1 from the weir.

(a) Discharge Equation for Standard Fully Contracted Rectangular Weirs

The Francis (1883) equation is convenient for weirs operating under favorable prescribed conditions. The Francis equation is:

Q = 3.33h13/2(L-0.2h1)   (7-4)


The Francis equation has a constant discharge coefficient which facilitates computations without the use of tables. However, the coefficient does not remain constant for a ratio of head-to-crest length greater than one-third, and the actual discharge exceeds that given by the equation. Francis' experiments were made on compara-tively long weirs, most of them with a 10-ft crest and heads ranging from 0.4 ft to 1.6 ft. Thus, these equations apply particularly to such weirs. The Bureau of Reclamation (Reclamation) experiments on 6­in, 1­ft, and 2-ft weirs on the Boise Project in Idaho show that the equation also applies fairly well to shorter crest lengths, provided the head of water on the weir is not greater than about one-third the length of the weir.

(b) Discharge of Standard Contracted Rectangular Weirs

Most of the discharges in tables A7-2 through A7-5 were calculated using equation 7-4. For most sizes of these weirs, the values of discharge in table A7-2 end when the measurement head reaches one-third of the crest length, the limit of the equation. Reclamation, Boise Project, calibrated weirs to extend the head range of contracted rectangular weirs. Their calibrations are included in the table for the 6-in, 1-ft, and 2-ft crest lengths and are indicated by shaded entries in the tables.

(c) Limits of Standard Fully Contracted Rectangular Weir

Equation 7-4 should not be used beyond the maximum discharges shown in table A7-2 or for measuring heads greater than one-third the crest lengths. All the requirements in section 5 apply. All the approach flow conditions in chapter 2 apply. The crest height, p, should be at least equal to 2h1max. The side contractions should also be located a distance of 2h1max from the approach channel boundary.

Head is measured upstream at a distance of at least 4h1max from the weir crest. Should any of these criteria be violated, discharge rating using the Kindsvater-Carter method is still possible.