The results of ε for the sidewall angles range from 6 to 35° and the quarter-round crest are shown in Figure 7. In general, ε is larger when α is small. According to total capacity, labyrinth weirs with larger sidewall angles are less efficient. For each α, the labyrinth weir efficiency (ε) increases with increasing Ht′/P′. This is because nappe interference and aeration behind the nappe flow decrease when Ht′/P′ increase. For comparison between the efficiency of the compound and conventional labyrinth weirs, the percentage of the improvement in efficiency was 10, 8.9, 7.8, 7.2, 6.6, 5, and 4% for α = 6, 8, 10, 12, 15, 20, and 35°, respectively. The best curve-fit coefficients of Equation (13) and the coefficient of determination (R2) are presented in Table 4. These equations are valid for 0.07 ≤ Ht′/P′ < ∼ 0.85. Equation (13) assists in determining the efficiency of the compound and conventional labyrinth weirs:
formula
(13)
Table 4

Curve-fit coefficients for efficiency of the compound and conventional labyrinth weirs validated for 0.07 ≤ Ht′/P′ < ∼0.85

Compound labyrinth weir
Conventional labyrinth weir
α(°)abR2abR2
0.37 1.41 0.99 0.36 1.49 0.99 
0.33 1.51 0.99 0.32 1.65 0.99 
10 0.30 1.60 0.99 0.30 1.80 0.99 
12 0.27 1.81 0.99 0.26 2.03 0.99 
15 0.25 1.99 0.99 0.24 2.22 0.99 
20 0.24 2.15 0.99 0.24 2.36 0.99 
35 0.23 2.16 0.99 0.233 2.91 0.99 
Compound labyrinth weir
Conventional labyrinth weir
α(°)abR2abR2
0.37 1.41 0.99 0.36 1.49 0.99 
0.33 1.51 0.99 0.32 1.65 0.99 
10 0.30 1.60 0.99 0.30 1.80 0.99 
12 0.27 1.81 0.99 0.26 2.03 0.99 
15 0.25 1.99 0.99 0.24 2.22 0.99 
20 0.24 2.15 0.99 0.24 2.36 0.99 
35 0.23 2.16 0.99 0.233 2.91 0.99 
Figure 7

Efficiency versus Ht′/P′ for compound and conventional labyrinth weirs for 6° ≤ α ≤ 35° and quarter-round crest. The data have been collected from the present study.

Figure 7

Efficiency versus Ht′/P′ for compound and conventional labyrinth weirs for 6° ≤ α ≤ 35° and quarter-round crest. The data have been collected from the present study.

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