In the present study, nine models were used to investigate the optimal notch geometry of the compound labyrinth weir. Table 1 shows the physical model test for the optimal geometry of the trapezoidal notch and Figure 1(a) shows the three-dimensional geometry of the compound labyrinth weir. In addition, eight models are used to study the hydraulic characteristics of compound labyrinth weirs, as shown in Table 2. These models consisted of rang sidewall angles (α) configurations of 6, 8, 10, 12, 15, 20, 35, and 90° (linear weir for comparison). The quarter-round crest experiments were carried out with the curved edge facing upstream, as shown in Figure 1(b). These models were two cycles (N = 2) of compound labyrinth weirs and the total width (W) was 0.5 m. All models were fabricated from acrylic sheets with a thickness (tw) of 10 mm. The acrylic sheets were cut using a laser machine to obtain precise dimensions and then the parts were assembled using screws. Silicon was used to prevent the leakage of water through all the joints of the models. The walls of the model were fixed on the base of the acrylic with a thickness of 6 mm to assist with installing the weir inside the flume. To avoid the curvature effect, all models were located approximately 1.5 m from the inlet point of the flume. An is the notch area that is defined as An= ΔPL+b1)/2. Aw is the sidewall area of the weir that is defined as Aw=lc P.

Table 1

Physical model test for optimal geometry of trapezoidal notch

Labyrinth geometryModel no.Notch geometry
An/AwΔP/PΔL/Lc
b1 (cm)ΔL (cm)ΔP (cm)
α = 15°
P = 20 cm
B = 40.05 cm
lc-one leg = 41.46 cm
Lc = 173.87 cm
W = 50 cm
N = 2
D = 3.5 cm
A = 2 cm
tw = 1 cm
15.58 17.58 4% 0.1 0.42
6.29 10.29 4% 0.2 0.24
2.52 8.529 4% 0.3 0.20
23.88 25.88 6% 0.1 0.62
10.44 14.44 6% 0.2 0.34
5.29 11.29 6% 0.3 0.27
32.17 34.17 8% 0.1 0.82
14.58 18.58 8% 0.2 0.44
8.05 14.05 8% 0.3 0.33
Labyrinth geometryModel no.Notch geometry
An/AwΔP/PΔL/Lc
b1 (cm)ΔL (cm)ΔP (cm)
α = 15°
P = 20 cm
B = 40.05 cm
lc-one leg = 41.46 cm
Lc = 173.87 cm
W = 50 cm
N = 2
D = 3.5 cm
A = 2 cm
tw = 1 cm
15.58 17.58 4% 0.1 0.42
6.29 10.29 4% 0.2 0.24
2.52 8.529 4% 0.3 0.20
23.88 25.88 6% 0.1 0.62
10.44 14.44 6% 0.2 0.34
5.29 11.29 6% 0.3 0.27
32.17 34.17 8% 0.1 0.82
14.58 18.58 8% 0.2 0.44
8.05 14.05 8% 0.3 0.33
Table 2

Test programme

α (°)P (cm)B (cm)Lc (cm)A (cm)D (cm)Notch geometry
ΔP/PΔL/lcShape of crest
b1 (cm)ΔL (cm)ΔP (cm)
20 100.8 413.6 3.8 52.8 60.8 0.2 0.6 QR
20 75.6 313.5 3.7 37.8 45.8 0.2 0.6 QR
10 20 60.4 253.5 3.6 28.8 36.8 0.2 0.6 QR
12 20 50.2 213.6 3.6 22.8 30.8 0.2 0.6 QR
15 20 40.0 173.8 3.5 16.8 24.8 0.2 0.6 QR
20 20 29.6 134.3 3.4 10.9 18.9 0.2 0.6 QR
35 20 15.6 84.5 3.0 3.4 11.4 0.2 0.6 QR
90 20 – 50 – – 22 30 0.2 0.6 QR
α (°)P (cm)B (cm)Lc (cm)A (cm)D (cm)Notch geometry
ΔP/PΔL/lcShape of crest
b1 (cm)ΔL (cm)ΔP (cm)
20 100.8 413.6 3.8 52.8 60.8 0.2 0.6 QR
20 75.6 313.5 3.7 37.8 45.8 0.2 0.6 QR
10 20 60.4 253.5 3.6 28.8 36.8 0.2 0.6 QR
12 20 50.2 213.6 3.6 22.8 30.8 0.2 0.6 QR
15 20 40.0 173.8 3.5 16.8 24.8 0.2 0.6 QR
20 20 29.6 134.3 3.4 10.9 18.9 0.2 0.6 QR
35 20 15.6 84.5 3.0 3.4 11.4 0.2 0.6 QR
90 20 – 50 – – 22 30 0.2 0.6 QR

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