IntroductionPipes that are only partially filled with water exhibit similarities to canals and rivers but are more complex due to the specific geometries of their beds and walls. These structures are prevalent in sewers and under road culverts. Managing sedimentation is crucial for maintaining the optimal operation of sewer systems. Accordingly, it is essential to define specific flow patterns and minimum velocity thresholds to prevent sedimentation. Additionally, these pipes are instrumental in road culverts that facilitate fish passage, requiring that flow velocities be maintained within certain limits to ensure safe passage. Previous studies have focused primarily on utilizing the Manning equation or developing empirical equations to compute average cross-sectional velocity. More sophisticated methods, such as computational fluid dynamics, have been employed to map out detailed flow patterns and identify critical velocity points. However, these methods are often limited by their complexity and the extensive time required to run the models. This research introduces a novel application of quasi-two-dimensional mathematical models to address the flow in partially-filled pipes.MethodologyThe methodology of this study involves applying the Shiono and Knight quasi-two-dimensional model (SKM) to predict flow velocities within partially-filled pipes. This model calculates the lateral distribution of depth-averaged velocities and boundary shear stresses. It incorporates three key coefficients: the Darcy-Weisbach friction factor, turbulent eddy viscosity, and secondary flow coefficient (denoted as f, λ, and β) which are calibrated using data from controlled laboratory experiments. The flow within the pipe is segmented into multiple panels or slices, which serve as computational nodes. Known parameters such as flow depth, lateral slope, and longitudinal slope, along with the three calibrated coefficients, are inputted for each node to compute the velocity. The finite difference method is employed to discretize the governing differential equation, with the resulting matrix solved analytically to obtain the velocity distribution.Results and DiscussionApplication of the SKM to a laboratory-scale partially-filled pipe (Knight and Sterling, 2000) demonstrated that the model accurately predicts lateral velocity profiles at various flow depths, closely aligning with empirical data. This model effectively estimated the minimum, maximum, and average velocities, with calibration constants of 0.07 for eddy viscosity and -0.2 for secondary flow coefficients proving effective. Comparisons of the model's flow discharge predictions with actual measurements showed a maximum error of 5.7% at the lowest flow depth, with an overall average error of 3.6%. These findings underscore the model's robustness and accuracy in simulating real-world conditions.ConclusionThis research has developed a novel analytical approach based on the Shiono and Knight model to perform hydraulic analyses of circular sections with a free surface flow. The results confirm the model's capacity to replicate measured data on velocity distributions and flow discharges accurately. Moreover, this approach enables the calculation of shear stress distribution based on velocity profiles, suggesting its potential for broader applications, including the analysis of specialized sewer pipe sections like egg-shaped pipes.

Severe hydraulic gradients in OPEN CHANNELS cause severe bed erosion and problems caused by sedimentation. Fabric concrete is a unique product with high execution speed that can replace traditional concrete surfaces. According to the mechanical resistance parameters of this product, in addition to its good durability against corrosive factors, one of the applications of fabric concrete is its use on the surface of canals and water course culverts. In this research, first, the flow of OPEN CHANNELS in trapezoidal section is simulated under 9 scenarios, which include 3 common channel geometries in the state of a straight path, a path with bends and deviations, and finally, a channel path with a change in height at the bottom of the channel. In each of the states, 3 different flow regimes have been investigated along with flow turbulence modeling using flow-3d software.Different flow regimes have been investigated along with flow turbulence modeling using flow-3d software. Using ABAQUS software, fabric concrete components and their connection areas have been modeled, and by applying forces equated to the concrete surface and vulnerable connection areas, the amount of created stresses has been checked. The results show that the created stresses are very low compared to the tensile and compressive stress capacity of fabric concrete. In order to validate the hydraulic studies of flow and concrete, the relevant laboratory results have been used.

Secondary currents are important mechanisms in OPEN CHANNELS, having major contribution in flow field and its corresponding parameters including boundary shear stress and depth-averaged velocity. Compound OPEN CHANNELS involve extra plan form vortices in the flow field. Curved OPEN CHANNELS generate especial vortices due to the effects of centrifugal force. Precise modeling of secondary currents in curves and meanders is a very important issue in practical applications. Using OPEN source ``OPENFOAM'' software, the flow field in a meandering channel with compound cross section is simulated herein. Reynolds averaged Navier-Stocks equations (RANS) are solved. Applying appropriate boundary conditions over the free-surface, the simpleFoam solver has been used to model the two-phase air-water flow interface, assuming a steady flow condition, and a symmetry boundary condition. The experimental data from FCF belonging to University of Birmingham is selected for verification and validation of the present numerical results. Two turbulent models of Realizable k− varepsilon and SST k− omega are applied. Lateral velocity profiles at the cross sections indicate that at each wave-length of a meander, a vortex forms in the main channel at the apex, directing towards the outer bank near the bed and towards the inner bank near the water free-surface. The secondary current patterns, achieved for curved compound OPEN CHANNELS differ from those of the simple CHANNELS. This is partly due to the interaction of shear stresses occurring at the interfaces between the main channel and the floodplains. Deviation of paths of the main channel and floodplains, downstream of each apex, results in entering the flow from inner bank to the main channel and exiting the flow from the main channel to the outer bank. These flow patterns shift the flow from inner-to the outer bank, downstream of each apex. Therefore, a helicoidally secondary current pattern forms, growing in size and strength farther downstream of the apex region.

This paper describes the application of artificial neural networks to model the longitudinal dispersion coefficient, which is a key hydraulic parameter included in the advective-diffusion equation (ADE).The dimensionless dispersion (Dl/HU*) has been modeled based upon four dimensionless hydraulic parameters, including: the relative roughness (ks/H), the aspect ratio (H/W), the relative shear velocity (U*/U) and the Reynolds number (UH/v). A total of 81 sets of measured data in small and large rivers from the current literature were used to establish and verify the ANN model. The final model has been compared favorably with two recent formulations published in the literature. Comparison of the results showed that the ANN model is able to predict the measured values more precise by (14%) than the other two considered models.

1. Introduction: Channel expansions are common in both natural and artificial OPEN CHANNELS. With increasing crosssectional dimensions in an expansion, the flow decelerates. Under Subcritical flow and steady flow conditions, reducing the flow velocity due to increasing the water pressure and adverse pressure gradient. In this study, the flow hydraulic along the expansive transition of rectangular to trapezoidal under subcritical flow has been investigated experimentally. Also, a three-dimensional numerical simulation of the flow pattern was developed using the fluent software with RSM turbulent model. Water surface and flow velocity profiles at different sections of transition were compared with experimental results. The results showed a good agreement between numerical and experimental results. Then, the efficiency of the transition and coefficient of energy head loss were calculated. The results show that with increasing the upstream Froude number, the efficiency of the transition and coefficient of energy head loss are decreased and increased, respectively. After calibration, the effect of inflow Froude numbers on flow separation zones, secondary currents, and bed shear stress along the transition was investigated numerically...

The modified log-wake law, which was developed for turbulent boundary layers and pipe flows, is extended to turbulent flows in OPEN-CHANNELS. Turbulent velocity profiles in OPEN-CHANNELS can be approximated with three components: (1) the law of the wall that results from the constant bed shear stress; (2) the law of the wake that reflects the effects of gravity, secondary currents and bed roughness; and (3) the cubic correction near the maximum velocity. A procedure to determine the four model parameters from velocity measurements while keeping k=0.41 is presented. The modified log-wake law compares very well with experimental data from Coleman, Lyn, Kironoto and Graf and Sarma et al. It also replicates the measured velocity profiles of the Mississippi River. In particular, it can well fit the velocity dip phenomenon in OPENCHANNELS where the conventional log-wake law fails.

In order to consider flow structure in OPEN CHANNELS, for a fully developed turbulent uniform flow, boundary shear stress and its distribution have been investigated. As the distribution of boundary shear stress around wetted perimeter and the effect of cross sectional shape are very important in sediment transport, so the boundary shear stress distribution have been evaluate4 and compared for different channel cross sections (i.e. rectangular, trapezoidal, circular and v-shaped bottom CHANNELS). The boundary shear stress was measured using a Preston tube having an outer diameter of 4.075mm. The experimental data illustrates that the lateral distribution of boundary shear stress shows that for mild slope CHANNELS, they are fairly flat, but that for the steep slope this is not the case. The analysis of results also shows that the channel cross-section and secondary flows are more effective on boundary shear stress distribution. Of course, this outcome is different for subcritical and super critical flow conditions. For this purpose, the percentage shear force carried by the walls (%SFw) has been used. The result shows that %SFw is favorably correlated with the geometry parameter, P+=Pb/Pw An interesting result is that the eddy viscosity coefficient is a function of flow rate, where the dimensionless eddy viscosity, l, decreases as the flow discharge increases. This matter should be applied in any computational models for OPEN channel flows.

The measurement of velocity in rivers confluences and OPEN-CHANNELS junction is important in terms of hydraulic and environmental aspects. In this research, the performance of data driven models including ANN, ANFIS and GEP in estimating horizontal component of flow velocity in the OPEN-CHANNELS junction was investigated using Khosravinia (2012) laboratory data. In the mentioned study, effects of a 45o side slope in the main channel on hydraulic characteristics of flow were investigated and compared with those at a 90o side slope. In this regard, the velocity field was measured for side slop angles of 45o and 90o using an ADV. For estimating the horizontal component of the flow velocity in the junction region, the discharge ratio and the dimensionless coordinates of measured points in three dimensional space of flow field were used. The performance of the models and comparison of their results were evaluated by coefficient of determination (R2) and root mean square error (RMSE). In addition to statistical indicators, for objective accuracy checking and performance of data driven models, scatterplot, box-plot, and Taylor diagram were used. Comparison of the results of different models using the best pattern indicates that the GEP model with the highest determination coefficient (R2 = 0.967), the lowest root mean square error (RMSE = 0.142) and the lowest mean absolute error (MAE = 0.094) in validation step has shown better performance than other models in (U/U0) estimation for the side slop angle of 45o. Similarly, the mentioned values were achieved 0.956, 0.184 and 0.128 using the GEP model for the side slop angle of 90o. This is while the ANFIS and ANN models ranked second and third. According to the scatterplots of the GEP model, nearly all the points are concentrated around the one-to-one line, which indicates the high level of predictive capability of this model in (U/U0) estimation for the both side slop angles. Also, according to the box plots, the statistical distribution of the GEP model in the lower and upper quartiles and median 50 percentile had a better performance than the other models, for the both side slop angles. The under and over estimation conditions of the ANFIS and ANN models were evident in these ranges. Moreover, according to the Taylor diagrams, the GEP model was closer to the observations and its superiority to the other models was tangible, with the lowest RMSE and the highest correlation coefficient for the both side slop angles. According to the results, GEP model as a powerful model can be used to replace the direct methods of velocity measurement in the junction region. In other words, using the mathematical equations derived from the GEP model in the present study, the longitudinal velocity field in the OPEN-CHANNELS junction for side slopes of 45° and 90° can be predicted accurately.

Composite OPEN channel structures are an expensive infrastructure in terms of material, construction and maintenance, and therefore finding the optimum design becomes an important issue. This paper develops four different models for composite OPEN channel and applies a new optimization algorithm to determine the optimal design of these models. The new algorithm called Charged System Search (CSS) is inspired by the governing laws from electrostatics physics and mechanics. CSS is a multi-agent approach and each agent is a Charged Particle (CP) which can affect others based on their fitness values and their separation distances. The results of the CSS are compared to those of ant colony optimization and the genetic algorithm method to highlight its superiority for determining the optimum design of composite OPEN channel structures.