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HYDRAULICS AND WATERWORKS FORMULAS 331
TABLE 12.2 Discharge of Triangular Weirs
Notch (vertex) angle Discharge formula*
90° Q 0.685h 2.45
60° Q 1.45h 2.47
30° Q 2.49h 2.48
*h is as defined above in the Francis formula.
Trapezoidal (Cipolletti) Weir
The Cipolletti weir, extensively used for irrigation work, is trapezoidal in
shape. The sides slope outward from the crest at an inclination of 1:4 (horizontal:
vertical). The discharge is
Q 3.367bh 3/2 (12.126)
where b, h, and Q are as defined earlier. The advantage of this type of weir is
that no correction needs to be made for contractions.
Broad-Crested Weir
The discharge of a broad-crested weir is
Q Cbh 3/2 (12.127)
Values of C for broad-crested weirs with rounded upstream corners generally
range from 2.6 to 2.9. For sharp upstream corners, C generally ranges from 2.4
to 2.6. Dam spillways are usually designed to fit the shape of the underside of
a stream flowing over a sharp-crested weir. The coefficient C for such a spill-
way varies considerably with variation in the head, as shown in Table 12.3.
Q, b, and h are as defined for rectangular weirs.
TABLE 12.3 Variations in Head Ratio and
Coefficient of Discharge for Broad-Crested Weirs
Ratio of actual head Coefficient of
to design head discharge
0.20 3.30
0.40 3.50
0.60 3.70
0.80 3.85
1.00 3.98
1.20 4.10
1.40 4.22