Page 80 - AJWEP-22-6

Heidarnejad, et al.

weirs of various geometries, each exhibiting distinct continuous application of the coefficient under varying
hydraulic characteristics that significantly influence flow conditions.
flow behavior. Among these, labyrinth weirs represent Monjezi et al. emphasized the critical role of weirs
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a notable category widely employed in hydraulic in dam safety and investigated the C of direct and
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engineering. These weirs are characterized by their arched weirs in linear and triangular labyrinth forms
intricate platforms, which often adopt geometric through laboratory experiments. Arched weirs, due to
configurations such as triangular, rectangular, or their curved geometry, increase the effective crest length
trapezoidal shapes. The zigzag design of labyrinth weirs at a given width, enhancing discharge capacity. Results
increases the effective crest length relative to linear showed that increasing the ratio of total hydraulic load
weirs, thereby enhancing their discharge efficiency. to weir crest height decreases C in all weirs. However,
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This structural advantage enables them to convey larger arched shapes improved efficiency by up to 21% in
volumes of water under lower upstream hydraulic linear weirs and 57% in labyrinth weirs. However,
heads. Furthermore, labyrinth weirs are recognized for higher hydraulic loads reduced arched weir efficiency
their cost-effectiveness in terms of construction and due to increased downstream standing wave height.
operation. Furthermore, Seyedian et al. investigated the use
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The study of labyrinth weir hydraulics was initially of machine learning models (MLMs) to predict the C
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undertaken by Gentilini, who introduced triangular of triangular labyrinth weirs, a key parameter in flow
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weirs by aligning several oblique weirs in sequence. control. They developed and evaluated three MLMs:
Modern advancements in labyrinth weir design began least-square support vector machine (SVM), quantile
with Taylor and were subsequently refined by Hay regression forest, and Gaussian process regression
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and Taylor. In 1985, the Bureau of Reclamation in (GPR). Using statistical and visual methods, they
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the United States formalized a design methodology to found that GPR outperformed the others, achieving a
assist engineers in designing and constructing labyrinth determination coefficient (R ) of 0.986 and root mean
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weirs for public infrastructure projects. Meanwhile, square error (RMSE) of 0.009. Sensitivity analysis
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Kocahan and Taylor highlighted that labyrinth weirs, revealed the Froude number and weir geometry as the
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despite their passive flow control nature, can convey most influential inputs. Notably, GPR not only provided
significantly higher discharge rates compared to standard the highest accuracy but also offered reliable prediction
ogee weirs during the initial stages of flood events. In a intervals, making it the preferred model for C prediction.
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study, Crookston and Tullis investigated the hydraulic In the study by Zare et al., they conducted an
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efficiency of conventional and inverted labyrinth weirs experimental study on inclined circular labyrinth weirs
in channels, concluding that orientation had no impact with inclination angles of 60°, 70°, 80°, and 90° and
on performance. Subsequently, Christensen and Tullis diameters of 15, 20, 25, and 30 cm under varying flow
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expanded the understanding of flow characteristics over rates. The flow transitioned from free to submerged as
arched labyrinth weirs, while Seamons evaluated the discharge increased, with no air entrainment observed.
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effects of geometric variations on their efficiency and Results showed that increasing the dimensionless ratio
the accuracy of design predictions. of total hydraulic head to weir height reduced the C .
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Due to the intricate three-dimensional flow The 60° inclined weir achieved the highest C , while
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patterns over labyrinth weirs, determining an exact the vertical (90°) weir had the lowest. Although the
analytical solution for the head-discharge relationship 15 cm diameter weir initially exhibited the highest C ,
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remains challenging. For example, Bijankhan diameter changes had a minimal overall impact.
and Kouchakzadeh conducted experimental and Similarly, Nematollahi et al. analyzed eight
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theoretical studies on water flow through triangular sinusoidal labyrinth weirs with varying heights and
plan labyrinth weirs under both free and submerged effective crest lengths to study C and energy loss.
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flow conditions. New experimental data were collected Increasing flow rate or upstream depth decreased both
for free flow, while the transition threshold between free metrics, while greater effective length and inlet-to-outlet
and submerged regimes was identified experimentally. width ratios increased them. Maximum energy loss
Using Buckingham π analysis, a head-discharge occurred at width ratios of 4.60 and 7.67. A 20% increase
relationship was developed for submerged flow. A step- in weir height led to a 19.8% increase in energy loss.
by-step calibration method was introduced to derive a Flow splitters reduced the C but increased energy loss.
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unified discharge coefficient (C ) that applies across free The study also provided equations for C and energy
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flow, submerged flow, and the transition zone, allowing loss with high correlation coefficients.

Volume 22 Issue 6 (2025) 74 doi: 10.36922/AJWEP025120081