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A myriad of different blending or switching functions have been developed to blend Reynolds-averaged Navier-Stokes (RANS) and large-eddy-simulation (LES) models properly in order to prevent issues such as modeled stress depletion. This challenge is a large focus of modern hybrid methods along with generating sufficient turbulent statistics in the Reynolds-averaged to large-eddy-simulation interface. This paper investigates these issues by implementing a variety of blending functions in the NASA OVERFLOW computational fluid dynamics solver and comparing them with the existing length-scale blending models. Scenarios considered include a zero pressure gradient flat plate, subcritical flow around a cylinder, and a supersonic reattaching shear layer. Overall, the eddy-viscosity blending methods produce results similar, if not improved, to their length-scale blending counterparts. In particular, it was found that the entropy function gave more control and stability during the transition from RANS to LES. [ABSTRACT FROM AUTHOR]

Submarine channel mouth settings are hardly preserved in the stratigraphic record. Although they are still poorly known with respect to other segments of turbidite systems, conceptual models are being refined in the light of new discoveries in modern and ancient examples. Still, some questions such as the transition between expansion zones and the traditional Channel-Lobe Transition Zone (CLTZ) remains open in ancient systems. Upper Eocene deposits of the Colombian Caribbean (San Jacinto Fold Belt) are interpreted here as a fan-delta-fed, submarine, coarse-grained channel-lobe system. It displays a well-preserved channel inception stage in the shelf break represented by sigmoidal to lens-shaped gravels, and planar cross-stratified pebbly sandstones (foreset and backset) interpreted as cyclic steps in an expansion zone. In a later stage, a classical channel-levee complex was developed, represented by channel fill elements showing sharp- and erosional-based, fining-upward sequences that are meters thick, having basal massive matrix-supported pebble conglomerates (hard—extrabasinal—clasts, rip-up clasts, coastal bioclasts), vertically evolving to liquefied massive to planar-laminated coarse-grained sandstones with phytodetrital carbonaceous laminae. They are interpreted as concentrated flow deposits (high-density turbidites) coming from continental areas or from coastal systems (i.e., delta reworking). Undifferentiated channel belt thin-bedded turbidites associated with levees and terraces deposits are related to these confined systems. The channel-lobe transition zone is characterized by debrites from cohesionless debris flow in a channel-mouth bar setting, representing bypass processes that developed distally into low-angle, planar cross- and sigmoidally-stratified (upstream antidune) pebble-size to coarse-grained sandstones that fill low-angle scours (cut-and-fill structures) in an antidune field setting with supercritical conditions. When the currents lose channel confinement, the setting is characterized by changes from Froude supercritical to subcritical flow conditions in an inner lobe to lobe off-axis environment. Large seasonal fluctuations in precipitation favor high sediment concentrations, promoting the formation of volumetrically significant fan deltas and coarse-grained submarine channels with high erosive capacity; therefore, their record helps refine interpretations of depositional processes, providing criteria for recognizing areas of the turbiditic systems that are hardly preserved. The particular aggradational conditions for the preservation and stratigraphic characterization of the rare exhumed submarine channel mouth systems make it possible to decipher sediment dispersal patterns and thus connect the models proposed here, from supercritical systems to the traditional models of turbiditic systems. • Sedimentary facies from confined to unconfined flows • Evolution of a coarse-grained system from supercritical to subcritical flows • Depositional cyclic steps with supercritical conditions • Debrites to antidune field settings with supercritical to subcritical conditions • Inner lobe to lobe off-axis in subcritical conditions [ABSTRACT FROM AUTHOR]

In order to design a vegetation structure to mitigate floods resulting from extreme events like tsunamis, vegetation density and thickness (width) are important parameters. Flow passing through vegetation faces great resistance, which results in a backwater rise on upstream (U/S) vegetation, increases the water slope inside the vegetation, and for some cases, forms a hydraulic jump downstream (D/S) of the vegetation, thus transforming a subcritical flow to supercritical [Pasha, G. A. and Tanaka, N. [2017] "Undular hydraulic jump formation and energy loss in a flow through emergent vegetation of varying thickness and density," Ocean Eng.141, 308–325.]. Like the concepts of critical velocity and critical slope, this paper introduces the concept of "critical resistance of vegetation," which is defined as "resistance offered by vegetation that transforms a subcritical flow to supercritical." An analytical approach to find the water depths U/S, inside, and D/S of vegetation is introduced and validated well by laboratory experiments. Critical resistance was determined against vegetation of variable densities (G ∕ d , where G = spacing of each cylinder in the cross-stream direction, d = diameter of the cylinder), thicknesses (dn, where d = diameter of a cylinder and n = number of cylinders in a stream-wise direction per unit of cross-stream width), and the initial Froude number (Fro). A subcritical flow (F r o = ∼ 0. 5 5 − 0. 7 5 , without vegetation) was transformed to a supercritical flow (D/S vegetation) with a range of Froude numbers of 1.6–1.9, 1.1–1.2, and 0.85–0.98 against G ∕ d ratios of 0.25, 1.09, and 2.13, respectively, thus defining G ∕ d = ∼ 1. 0 as the critical resistance. However, altering vegetation thickness did not change the results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study flow regime changes of Newtonian fluid flow in an open Venturi channel. The simulations are based on the volume of fluid method with interface tracking. ANSYS Fluent 16.2 (commercial code) is used as the simulation tool. The simulation results are validated with experimental results. The experiments were conducted in an open Venturi channel with water at atmospheric condition. The inlet water flow rate was 400 kg/min. The flow depth was measured by using ultrasonic level sensors. Both experiment and simulation were done for the channel inclination angles 0°, −0.7°, and −1.5°. The agreement between computed and experimental results is satisfactory. At horizontal condition, flow in the channel is supercritical until contraction and subcritical after the contraction. There is a hydraulic jump separating the supercritical and subcritical flow. The position of the hydraulic jump oscillates within a region of about 100 mm. Hydraulic jumps coming from the contraction walls to the upstream flow are the main reasons for the conversion of supercritical flow into subcritical flow. An “oblique jump” can be seen where there is a supercritical flow in the contraction. There is a triple point in this oblique jump: the triple point consists of two hydraulic jumps coming from the contraction walls and the resultant wave. The highest flow depth and the lowest velocity in the triple point are found at the oblique jump. [ABSTRACT FROM AUTHOR]

Side weirs are flow diversion or intake devices that are widely used in irrigation and drainage networks and urban sewage systems. Labyrinth weirs have a proven hydraulic advantage due to their increased discharge rate at the same head for a given design condition. A labyrinth weir is defined as a weir crest that is not straight in plan-form. The increased sill length provided by labyrinth weirs effectively reduces upstream head to the particular discharge. In this study, a comprehensive laboratory study was conducted in a physical model of a semi-circular labyrinth side weir and the model is evaluated for three heights and three radii. In this particular study, the hydraulic effects of this shape of side weir in increasing discharge capacity was investigated. The discharge coefficient of semi-circular labyrinth side weirs was determined and the results were analysed to find the influence of the dimensionless parameters of weir height (w/b), weir length (r/b), nape height ((y1-w)/r), and upstream Froude number (Fr1) on discharge coefficient (Cd), based on the experimental conditions and previous studies. It was found that the discharge coefficient of the semi-circular labyrinth side weir gives a relatively high discharge coefficient value compared to other types of classic side weir positioned on a straight channel. Additionally, reliable equations for calculating the discharge coefficient (Cd) of semi-circular labyrinth side weirs are proposed. According to the proposed equation, Cd depends on dimensionless parameters, which are the ratios of r/b, r/w, (y1-w)/r, (y2-w)/r and Fr1. [ABSTRACT FROM AUTHOR]

In spite of some progress in the study of the transition from super- to subcritical flow without a hydraulic jump, many issues remain unclear, particularly in relation to the turbulence structure and dissipative mechanisms in the transition region. This paper therefore is focused on the experimental investigation of the turbulence characteristics in the transition region from super- to subcritical flow without a hydraulic jump. Instantaneous velocities were measured using an acoustic Doppler velocimeter and mean velocities, turbulence intensities, and Reynolds stresses were computed for different geometrical and hydraulic conditions. The turbulence intensities and Reynolds stresses were found to decrease in the transition region downstream and then approach the levels of the fully-developed turbulent open channel flow. The length of this transitional region was found to be three to seven times the tailwater depth for the range of Froude numbers between 1.3 and 4.5. The obtained results imply that the transition is driven by the longitudinal deceleration of the flow in the transition region. [ABSTRACT FROM PUBLISHER]

Side weirs or lateral weirs are widely employed to divert flows from rivers, channels, sewers and reservoirs or to divide flows between components of water treatment systems. The side weir is a fixed structure installed at one side of a channel for water level control in water treatment plants and irrigation and drainage systems. Hydraulic characteristics of a compound sharp-crested triangular–rectangular side weir under subcritical flow were studied in this paper. The concept of the elementary discharge coefficient that is related to the head to weir height ratio was used to determine the flow through the side weir. The advantage of this method is to calculate the channel water surface profile along the weir. Generalized equations for an elementary discharge coefficient for compound triangular–rectangular side weirs were proposed. Experimental results show the accuracy of the proposed equations. [ABSTRACT FROM AUTHOR]

Based on the potential flow theory, a linear shallow-water wave equation which satisfies Laplace equation, free surface and seabed boundary conditions is established. For the slender ship assumption, boundary conditions of different restricted waterways and continuous matched condition across the step depth change between inner and outer regions, these mathematical problems of sub-subcritical, sub-supercritical, and super-supercritical mixed flows are solved analytically by using Fourier integral transform method, meanwhile, analytical models for ship hydrodynamic pressure field in different restricted waterways such as open water, rectangular canal, dredged channel and stepped canal are established. The characteristics of ship hydrodynamic pressure field in different restricted waterways and mixed flows are obtained by numerical calculation, the influences of sidewall or step on SHPF are analyzed. The analytical models are verified by the comparison between the calculated results with the experimental ones as well as the successful degeneration from complex models to simple ones. [ABSTRACT FROM AUTHOR]

Flow through a surface choke can be described as either critical or subcritical. Most of the correlations available to petroleum engineers are for critical flow but in a lot of high rate gas/condensate wells subcritical flow occurs in large choke sizes. Field data of 15 high rate wells producing from 10 gas condensate reservoirs located in Iran were used to extend two main approaches for high rate wells: a plotting technique proposed by Al-Attar to describe the subcritical flow behavior of gas condensates through wellhead chokes and a general Gilbert-type formula obtained by nonlinear regression of data points for high rate gas condensate wells. The present study extends the work of Al-Attar for high rate gas condensate wells flowing through different large choke sizes between 40/64 and 192/64 in. under subcritical flow conditions, in order to develop individual empirical correlations to be applied to predict gas flow rates under a wide range of flow conditions usually encountered during the flow of gas condensates through wellhead chokes in high rate wells .Also, a new Gilbert-type correlation was generated for high rate Iranian gas condensate wells using nonlinear regression based on the same data points. A comparison between these two approaches is done with five different errors parameters. According to five different errors analysis, the results of gas flow rates calculated by the general formula were compared with those calculated by the individual choke size formulae, and the latter were found to be more accurate. The results of this study could be considered in the design and implementation of deliverability tests, pressure transient tests, well control, and long-term well production of high rate gas condensates wells. [ABSTRACT FROM PUBLISHER]

An experimental–analytical investigation was performed to explore whether a hydraulic jump in a transition from super- to subcritical flow regime can be avoided. As the free-surface profile passes the critical depth, the transitional point is a singular point. A transition structure was designed based on the energy principle and the singular point theory to gradually increase the flow depth, thereby eliminating the hydraulic jump. This profile was designed for approach flow Froude numbers between 1.5 and 7. To validate the analytical model, a comprehensive experimental study was conducted. Six hydraulic models of transition structures were experimentally investigated on the basis of the theoretical approach. The analytical results agreed well with the experimental results and those of former investigations. Observations indicated that the hydraulic jump is absent for a certain range of the Froude numbers. [ABSTRACT FROM AUTHOR]

Allocated well oil rates are essential well performance evaluation. Flow meters are not reliable at high gas-oil ratio (GOR) and high water-cut (WC). Most of the available formulas are based on Gilbert-type formulas with neglecting the differential pressure across the choke. Adaptive network-based fuzzy inference system (ANFIS), and functional networks (FN) were used to generate different models to predict the production rates for high GOR and WC wells. A set of data (550 wells) was obtained from oil fields in the Middle East. GOR varied from 1,000 to 9,351 scf/stb, WC ranged from 1 to 60%. Around 300 wells were flowing under critical flow conditions, while the rest were subcritical. The developed AI models were compared against the previous published formulas. For each AI method, two models were developed for subcritical flow and critical flow conditions. The average absolute percent error (AAPE) in the subcritical flow for ANFIS and FN were 1.25, and 0.95%, respectively. While in the critical flow, the AAPE values were 1.1, and 1.35% for ANFIS and FN models, respectively. All developed AI models outperform the published formulas by 34%. The findings from this study will significantly assist production engineers to predict the oil rate in real-time without adding any cost or field intervention. • ANFIS and FN models were developed to predict the oil rates from the choke parameters for high GOR and WC fluids. • AAPE is 1.35% in the case of critical flow with water production and GOR up to 9,000 scf/stb and WC up to 40%. • AAPE is less than 1.25% in the case of subcritical models flow with GOR up to 5,000 scf/stb and WC up to 60%. • AI robust models can estimate oil flow rate with about ±1.35% accuracy error and (R2) of 0.92–0.95. [ABSTRACT FROM AUTHOR]

Abstract: This paper widens insight on the comparison between 1D and 2D approaches when simulating flow division at a 90° open-channel junction. For the 1D simulation, existing models regarding this issue are, on the one hand, of empirical nature and depend on the flow regime, thus not practical in the unsteady case. On the other hand, theoretical dividing models are strongly nonlinear, thus do not guarantee compatibility if combined with the shallow water model. By explicitly inducting the mathematical model of the side weir into the source terms of the conservative form of the 1D shallow water equations, the flow bifurcation is represented by considering a crest-free lateral spillway. For the 2D simulation, the whole system (branches and junction) is considered as one system and discretized into triangular cells forming an unstructured mesh. The numerical approximation of the two approaches is performed by a second order Runge–Kutta Discontinuous Galerkin (RKDG) scheme and tested through a pre-defined flow problem to illustrate the effects of the two approaches. The results are validated by experimental data. Comparisons are carried out for a super-, trans- and subcritical bifurcation, respectively, showing the practicality of the 1D approach and the advantage of the 2D approach. [Copyright &y& Elsevier]

Abstract: In this paper, the hydraulic characteristics of a sharp crested trapezoidal side weir have been experimentally and theoretically investigated. It was found that the DeMarchi coefficient of discharge for a sharp crested trapezoidal side weir in subcritical flow is related to the main channel Froude number, the side slope of weir, ratio of weir height to upstream depth of flow and ratio of weir length to upstream depth of flow. Suitable equations for the discharge coefficient are also obtained. [Copyright &y& Elsevier]

Abstract: Side weirs are frequently used in many water projects. Due to their position with respect to the flow direction, side weirs are categorized as plain, oblique and labyrinth. One of the advantages of an oblique side weir is the increase in the effective length of the weir for overflowing and, therefore, diverting more discharge with the same channel opening, weir height and flow properties (i.e., upstream discharge, upstream Froude number and so on). In this paper, an experimental set-up of a new design of an oblique side weir with asymmetric geometry has been studied. The hydraulic behavior of this kind of oblique side weir, with a constant opening length, different weir heights and asymmetric oblique angle, has been investigated in a subcritical situation. The results from over 200 test measurements show that this kind of weir is up to 2.33 times more efficient with respect to the conventional side weir in a rectangular channel among the tested conditions. Finally, the discharge coefficient as a function of geometrical and flow variables are presented for design engineers. In addition, a more precise relation has been obtained for flow with Froude numbers less than 0.4. [Copyright &y& Elsevier]

This paper details the development of a method for subcritical flow modeling in channel networks by using the implicit finite-difference method. The method treats backwater effects at the junction points on the basis of junction-point water stage prediction and correction (JPWSPC). It is applicable to flows in both looped and nonlooped channel networks and has no requirement on the flow directions. The method is implemented in a numerical model, in which the Saint-Venant equations are discretized by using the four-point implicit Preissmann scheme, and the resulting nonlinear system of equations is solved by using the Newton-Raphson method. With the help of JPWSPC, each branch is computed independently. This guarantees the simplicity, efficiency, and robustness of the numerical model. The model is applied to two hypothetic channel networks and a real-life river network in South China. All the networks contain both branched and looped structures. The simulated results compare well with the results from literature or the measurements. [ABSTRACT FROM AUTHOR]

The subcritical flow behavior of gas condensates through wellhead chokes under different flow conditions are studied by use of an artificial neural network (ANN). The proposed network is trained using the Levenberg-Marquardt back-propagation algorithm and the hyperbolic tangent sigmoid activation function is applied to calculate the output values of the neurons of the hidden layer. The proposed neuromorphic model outperforms the existing empirical correlations both in accuracy and generality. The results of this work are very important in the design of wellhead chokes under a wide range of flow conditions usually encountered during the flow of gas condensates. [ABSTRACT FROM AUTHOR]

Turbidity currents in the ocean are driven by suspended sediment. Yet results from surveys of the modern sea floor and turbidite outcrops indicate that they are capable of transporting as bedload and depositing particles as coarse as cobble sizes. While bedload cannot drive turbidity currents, it can strongly influence the nature of the deposits they emplace. This paper reports on the first set of experiments which focus on bedload transport of granular material by density underflows. These underflows include saline density flows, hybrid saline/turbidity currents and a pure turbidity current. The use of dissolved salt is a surrogate for suspended mud which is so fine that it does not settle out readily. Thus, all the currents can be considered to be model turbidity currents. The data cover four bed conditions: plane bed, dunes, upstream-migrating antidunes and downstream-migrating antidunes. The bedload transport relation obtained from the data is very similar to those obtained for open-channel flows and, in fact, is fitted well by an existing relation determined for open-channel flows. In the case of dunes and downstream-migrating antidunes, for which flow separation on the lee sides was observed, form drag falls in a range that is similar to that due to dunes in sand-bed rivers. This form drag can be removed from the total bed shear stress using an existing relation developed for rivers. Once this form drag is subtracted, the bedload data for these cases collapse to follow the same relation as for plane beds and upstream-migrating antidunes, for which no flow separation was observed. A relation for flow resistance developed for open-channel flows agrees well with the data when adapted to density underflows. Comparison of the data with a regime diagram for field-scale sand-bed rivers at bankfull flow and field-scale measurements of turbidity currents at Monterey Submarine Canyon, together with Shields number and densimetric Froude number similarity analyses, provide strong evidence that the experimental relations apply at field scale as well. [ABSTRACT FROM AUTHOR]

Acoustic Doppler velocity meters (ADVMs) provide an alternative to more traditional flow measurement devices and procedures such as flumes, weirs, and stage rating for irrigation and drainage canals. However, the requirements for correct calibration are extensive and complex. A three-dimensional computational fluid dynamics (CFD) model was used to design a subcritical rapidly varied flow contraction that provides a consistent linear relationship between the upward-looking ADVM sample velocity and the cross-sectional average velocity in order to improve ADVM accuracy without the need for in situ calibration. CFD simulations validated the subcritical contraction in a rectangular and trapezoidal cross section by showing errors within +1.8 and -2.2%. Physical testing of the subcritical contraction coupled with an upward-looking ADVM in a large rectangular flume provided laboratory validation with measurement errors within ±4% without calibration. [ABSTRACT FROM AUTHOR]

An iterative step method for solving the nonlinear ordinary differential equation, governing spatially varied flows with decreasing discharge, like the flow over side weirs, is developed. In the procedure, starting at a known flow depth and discharge in the control section, the analytical integration of the dynamic equation with bed and friction slope is carried out. The specific energy, the weir coefficient and the velocity distribution coefficient are considered as local variables, then for the explicit integration, the respective average values along the short side weir elements are assumed. The water surface profiles and the discharges for flow over side weirs, obtained with the proposed relation and valid for rectangular channels, are compared with experimental data for subcritical and supercritical flow conditions. The validation of the method is accomplished by the comparison with the solution obtained by De Marchi’s classical hypothesis, about the specific energy, which is constant along a side weir. In addition, the influence of the coefficient velocity distribution is considered. [ABSTRACT FROM AUTHOR]

The energy loss of the vertical drop with subcritical flow in the upstream channel has been studied experimentally with a physical model of 0.20 m drop height. Experimental data were collected in a range where few data exist. Based on a similarity between a turbulent surface jet and the flow over the drop, a model is developed using the theories of the shear layer and fully developed surface jet to estimate the energy loss. The results were compared with previous and current experimental data and were found to agree well with the proposed model. [ABSTRACT FROM AUTHOR]

Ratings relating stage and flow discharge have been traditionally established through measurements of discharge and concurrent stage. Inherent in this approach are several difficulties and shortcomings that have resulted in widely recognized problems in developing and applying ratings, such as looped ratings. Purely empirical methods that attempt to improve the agreement between ratings and measurements have met with limited success. This paper suggests a theoretical basis for discharge ratings that reflects the hydraulics of unsteady, nonuniform, subcritical flow. Simplification of the Saint-Venant equations for rating applications results in an approximation of the dynamics of flow that is summarized in the hydraulic performance graph, from which discharge ratings can be developed and updated theoretically. The resulting ratings apply a quasi-steady approximation of the flow, along with semiempirical correction factors developed for the site to estimate the discharge using the same information that is needed for “stage-fall-discharge ratings,” while addressing some of the shortcomings of this type of rating. Comparison of ratings developed using the resulting procedure against laboratory and field observations yields encouraging results. [ABSTRACT FROM AUTHOR]

Abstract: The paper deals with the classical non-linear problem of steady two-dimensional waves on water of finite depth. The problem is formulated so that it describes all waves without stagnation points on the free-surface profiles that are bounded themselves and have bounded slopes. By virtue of reducing the problem to an integro-differential equation the following three results are proved. First, there are no waves when the flow is critical. Second, there are no waves having profiles totally above the upper boundary of the uniform subcritical stream. Finally, only two types of the free-surface behaviour are possible at positive (or/and negative) infinity: the profile either oscillates infinitely many times around the upper boundary of the subcritical uniform stream or asymptotes the upper level of a uniform stream (subcritical or supercritical). The latter assertion is proved under additional assumption that the slope of the free surface is a uniformly continuous function. [Copyright &y& Elsevier]

Although many numerical techniques such as approximate Riemann solvers can be used to analyze subcritical and supercritical flows modeled by hyperbolic-type shallow-water equations, there are some difficulties in practical applications due to the numerical unbalance between source and flux terms. In this study, a revised surface gradient method is proposed that balances source and flux terms. The new numerical model employs the MUSCL–Hancock scheme and the HLLC approximate Riemann solver. Several verifications are conducted, including analyses of transcritical steady-state flows, unsteady dam break flows on a wet and dry bed, and flows over an irregular bathymetry. The model consistently returns accurate and reasonable results comparable to those obtained through analytical methods and laboratory experiments. The revised surface gradient method may be a simple but robust numerical scheme appropriate for solving hyperbolic-type shallow-water equations over an irregular bathymetry. [ABSTRACT FROM AUTHOR]

The behavior of free surface flow at a rectangular free overfall is studied experimentally to obtain a relation between the brink depth and the flow rate. A series of experiments were conducted in a tilting flume with wide range of flow rates covering subcritical, critical, supercritical regimes, and two different roughnesses in order to develop a relationship between the discharge and the brink depth. An equation is proposed to determine the flow rate using the brink depth for a channel of known roughness and bed slope. [ABSTRACT FROM AUTHOR]

This study focuses on the discharge distribution in an intersection of four channels, similar to a city crossroad. The channels and the intersection are all horizontal. Flow enters through two of the channels, and leaves through the other two. The flow is subcritical everywhere, and flow depths are controlled by vertical weirs at the exits of the outlet channels. The main variables that are measured are the flow rates in the four channels. When the weir heights in the outlet channels are the same, the ratio of flow rates in the outlet channels depends only on the ratio of flow rates in the inlet channels; if the outlet conditions are different, other parameters, such as the total flow rate also become important. The flow has also been simulated numerically using a solution of the 1-D Saint Venant equations, with a simple model to predict flow distribution in the intersection. A comparison with the experimental data shows that this model works well for the limited range of experimental conditions studied here. However, further work is needed on a wider range of conditions, closer to real conditions, before the model can be considered valid for practical applications. [ABSTRACT FROM AUTHOR]

A Burgers equation model (BEM) for simulating translatory waves in conveyance channels is extracted from the Saint-Venant equations for small perturbations in initial uniform flow. The present study improves upon the previous model and presents analytical solutions for the simulation of translatory waves occurring in conveyance channels. The BEM is reduced to the linear diffusion equation using the Cole–Hopf transformation and then solved by means of the Green’s function assuming an infinite domain. The simulation studies performed show that the BEM results are comparable to those of the Saint-Venant equations for small perturbations in the initial uniform flow conditions and for Froude numbers within the subcritical region. The BEM could be useful for flood routing and for simulating release of water from a reservoir into a conveyance channel when the flow perturbation is small. [ABSTRACT FROM AUTHOR]

This study presents a simplified approach to determine the end depth of a free overfall in horizontal U-shaped channels. The flow over the free overfall is simulated by that over a sharp-crested weir to calculate the end-depth ratio (EDR). The theoretical model is calibrated by the experimental data by considering the coefficient of velocity a free parameter. The EDR is 0.745 up to nondimensional critical depth 0.50; and then it decreases gradually as the nondimensional critical depth increases. A method to estimate discharge from the end depth is presented. The results obtained using the model agree satisfactorily with the experimental data and results obtained from the previous model of the author. [ABSTRACT FROM AUTHOR]

A numerical model was used to study the effect of change in specific energy height along a side weir on flow. Discharge coefficient was considered as a local variable that includes flow depth and the angle of the deflected water jet along side weir. Hydraulic profile on the weir plane and the hydraulic head on the weir were obtained using two dimensionless parameters ψ and m as a function of Froude number. Flow depths and flow rates were then computed and minimum standard errors were determined based upon these parameters. The agreement between computed values and observations was demonstrated. It was concluded that rates of flow are considerably affected by the variation of specific energy along the side weir when weir head is based on flow depth at the weir plane. Considerable deviations from the constant specific energy assumption may be observed in this case specially when a great change in flow rates exists along side weirs with zero end discharges. [Copyright &y& Elsevier]