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GMDH-type neural network approach for modeling the discharge coefficient of rectangular sharp-crested side weirs

This comprehensive handbook on the hydraulic design of labyrinth spillways—from theory to current practice—presents a state-of-the-art method for the effective design of labyrinth weirs. The book provides a fundamental understanding of the theory of labyrinth weirs and continues with detailed sections on significant factors that affect the discharge characteristics of labyrinth weirs, such as crest shape, weir height, and sidewall angle. The most common design curves are discussed, and from these a recommendation is developed for only one design curve to be used in future designs. But because site conditions often vary so much from ideal conditions described in this book, a section on site-specific modeling criteria is included for making accurate predictions of prototype performance. In its review of past studies, the book closely examines many long-held concepts, especially concerning the idea of interference, nappe oscillation, and the definition of which head to use in design computations, and revises them in an effort to advance current thinking based on the latest research.

Hydraulic Design of Labyrinth Weirs

Side weirs, also known as lateral weirs, are flow diversion devices widely used in irrigation as a head regulator of distributaries and escapes, land drainage, and urban sewage systems. The studies on the subject have been generally focused on rectangular and triangular side weirs located on a straight channel. However, the same is not true for labyrinth side weirs. The current studies deal with sediment transport and scour problems around side weirs and lateral structures. The investigation of the hydraulic effects of labyrinth side weirs to increase discharge capacity of them has been studied in this particular work. In the study, 2,830 laboratory tests were conducted for determining discharge coefficient of labyrinth side weirs, and results were analyzed to find the influence of the dimensionless weir length L/b , the dimensionless effective length L/l , the dimensionless weir height p/ h1 , triangular labyrinth side weir included angle θ , and upstream Froude number F1 on the discharge coefficient, wa...

Discharge Capacity of Labyrinth Side Weir Located on a Straight Channel

Gene expression programming (GEP) is used as a new method for estimating side weir discharge coefficient.Two sets of experimental data were used to evaluate the models.New equation proposed by GEP can be used for estimating discharge coefficient in rectangular sharp-crested side weirs. In this study, gene expression programming (GEP) is employed as a new method for estimating the side weir discharge coefficient. The accuracy of existing equations in evaluating the side weir discharge coefficient is first examined. Afterward, taking into consideration the dimensionless parameters that affect the estimation of this parameter and sensitivity analysis, five different models are presented. Coefficient determination (R2), root mean square error (RMSE), mean absolute relative error (MARE), scatter index (SI) and BIAS are used for measuring the models' performance. Two sets of experimental data are applied to evaluate the models. According to the results obtained indicate that the model with Froude number (F1), dimensionless weir length (b/B), ratio of weir length to depth of upstream flow (b/y1), and ratio of weir height to its length (p/y1) parameters of R2=0.947, MARE=0.05, RMSE=0.037, BIAS=0.01 and SI=0.067, performed the best. Accordingly, this new equation proposed through GEP can be utilized for estimating the discharge coefficient in rectangular sharp-crested side weirs.

Gene expression programming to predict the discharge coefficient in rectangular side weirs

Side weirs have many possible applications in the field of hydraulic engineering. They are also considered an important structure in hydro systems. In this study, the support vector machine (SVM) technique was employed to predict the side weir discharge coefficient. The performance of SVM was compared with other types of soft computing techniques such as artificial neural networks (ANN) and adaptive neuro fuzzy inference systems (ANFIS). While ANN and ANFIS models provided a good prediction performance, the SVM model with a radial basis function kernel function outperforms them. The best SVM model was developed with a gamma coefficient and epsilon of 15 and 0.3, respectively. The SVM yielded a coefficient of determination ( R 2 ) equal to 0.96 and 0.93 for the training and testing data. Sensitivity analyses of the ANN, ANFIS and SVM models showed that the Froude number and ratio of weir length to the flow depth upstream of the weir are the most effective parameters for the prediction of the discharge coefficient.

Prediction of side weir discharge coefficient by support vector machine technique

To estimate the outflow over a rectangular sharp-crested side weir, the discharge coefficient in the weir equation needs to be known. Although this type of structure has been designed and used extensively by hydraulic engineers, a universally acceptable discharge coefficient does not exist. In this study over 250 laboratory tests were conducted, and the results were analyzed to find the influence of the flow hydraulics and the geometric, channel, and weir shapes on the coefficient. The results show that for subcritical flow the De-Marchi assumption of constant energy is acceptable, and the weir discharge can therefore be used. Furthermore, it was discovered that the De-Marchi coefficient of discharge is a function of the upstream Froude number and the ratios of weir height to upstream depth and weir length to channel width, whereas the channel slope in subcritical flow can be ignored. Hence, an accurate equation for the coefficient of discharge is introduced.

Discharge coefficient for sharp-crested side weir in subcritical flow

Among discharge flowmeters, the rectangular sharp-crested weir is one of the most popular and accurate, as well as being easy to work with. Using the standard weir, with the help of the conventional weir equation and Rehbock's or a similar standard formula for the discharge coefficient (Cd), the flow can be easily calculated. In order to increase the efficiency of the weir, it can be placed obliquely to the flow, increasing the effective weir length (L) and, hence, increasing the discharge for the same water head with the same channel width (B). The results of a comprehensive set of tests for oblique weirs (1·14 ≤ L/B ≤ 2·26 or oblique angles from 29° to 64°) show that for L/B less than 1·41 (oblique angles 45°), Cd decreases with increasing head and is constant for all values of water head while L/B = 1·41 (oblique angle = 45°). On the whole, since with oblique weirs th...

S. M. Borghei

Papers

Discharge coefficient for sharp-crested side weir in subcritical flow

Oblique rectangular sharp-crested weir