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ML-based C for side trapezoidal labyrinth weirs
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Ahmed and Altalib investigated the effects of cycle acceleration due to gravity. The C values are influenced
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number, total arc angle, and semicircular openings by hybrid hydraulic-geometry parameters, prompting
on the C of arched weirs and arched labyrinth weirs. numerous studies and research endeavors to elucidate
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Reducing the number of cycles increased the C by up this effect. Table 1 summarizes a list of C predictors
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to 35.94%, with arched weirs performing better than presented by various researchers.
arched labyrinth weirs. Increasing the total arc angle The adoption of recently developed MLMs as a
improved the coefficient by up to 32.4%. However, state-of-the-art approach has supplanted the need for
semicircular openings reduced performance, with C costly, limited, and time-intensive experimental tests.
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decreases of 19.54% for arched labyrinth weirs and MLMs employ training and testing phases to uncover
12.08% for linear weirs as the opening-to-edge length intricate and hidden relationships between dependent
ratio increased. A predictive equation was developed and independent variables, thereby facilitating accurate
to predict C , showing a strong correlation with forecasting of target variables. Table 2 presents a
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experimental data (R = 0.9). comprehensive summary of various studies aiming to
Masoudi et al. emphasized the importance of flood predict the C in overflows of differing shapes.
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discharge from dam reservoirs, typically managed using As evident from Table 2, accurately determining
weirs. Labyrinth weirs, ideal for narrow valleys and large the C for structures such as labyrinth, piano-key, and
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floods, offer high efficiency due to their extended flow lateral weirs has long been a focus of research due to
paths. This study aimed to enhance the C and efficiency its potential to enhance performance efficiency. The
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of rectangular and trapezoidal labyrinth weirs by use of MLMs has demonstrated superior accuracy
replacing uniform, regular labyrinth cycles (congresses) compared to traditional regression models and empirical
with unequal and irregular ones. Five samples of each equations. In addition, the exploration and development
weir type were tested in two configurations, differing of new configurations inspired by the geometry of the
by the placement of the longest cycle (center vs. sides). labyrinth weir is a burgeoning area of study. To address
Experimental results showed that using unequal and these aspects, this study employs four MLMs–SVM,
irregular congresses improved the C by 40.7% for gene expression programming (GEP), artificial neural
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rectangular weirs and 35.3% for trapezoidal ones. network (ANN), and multivariate adaptive regression
Similarly, Hadi and Majeed investigated the C splines (MARS)–to simulate the C of a trapezoidal-
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of side weirs installed in the side wall of a rectangular arched labyrinth weir (TALW). A review of existing
channel, focusing on trapezoidal labyrinth weirs literature reveals a gap in research specifically focused
with side wall angles of 15°, 30°, 45°, 60°, 75°, and on this topic.
a linear side weir at 90°. Using six physical models,
they developed hydraulic equations relating discharge 2. Materials and methods
and head over the weir. Results showed that the C
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increases with larger side wall angles and is highest 2.1. Data series
at 75°, approaching the value for a straight (90°) weir. The experimental procedures for this research were
Computational fluid dynamic simulations using the conducted in the hydraulic laboratory of the Khuzestan
k-omega shear stress transport model and volume of Water and Power Authority, Iran. The weir models
fluid scheme confirmed the experimental findings, were installed within an 8 m long, 0.6 m wide, and
showing strong agreement. 0.6 m high test flume with transparent Plexiglas walls,
Non-linear weirs demonstrate a superior overflow facilitating the observation of water surface profiles
capacity relative to linear weirs, attributable to their and flow conditions. The flume was operated under
extended crest length. The C plays a critical and free-flow conditions. To ensure the accuracy of the
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notable role in the hydraulic performance of non-linear results, the flume was designed to be watertight and
weirs. The usual discharge equation for a labyrinth weir seamless. The test equipment and components of the
is given in Equation I. flume comprised the flume’s groundwater tank, a digital
flowmeter with an accuracy of 0.2 L/s, a tranquilizer,
2 1.5
Q= CL c 2gH (I) a floating electric pump with a maximum flow rate of
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T
3 140 m /h, and a constant-head tank (Figure 1A). The
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where Q is the overflow rate, Lc is the effective crest digital magnetic flowmeter was calibrated against a 90°
length, H denotes the total upstream head, and g is the V-notch weir installed at the flume outlet. The weir’s
T

Volume 22 Issue 6 (2025) 75 doi: 10.36922/AJWEP025120081