Use of Brink Depth in Discharge Measurement

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.     

Implicit Bidiagonal Scheme for Depth-Averaged Free-Surface Flow Equations

A general fast implicit bidiagonal numerical scheme, based on the MacCormack's predictor-corrector technique requiring the inversion of only block bidiagonal matrices, has been developed and subsequently applied for subcritical and supercritical free-surface flow calculations. The model has been applied to depth-averaged steady flows. There are two main advantages of the proposed method: the technique has fast convergence and utilizes a body fitted nonorthogonal local coordinate system to simulate irregular geometry flows. The model is used to analyze a wide variety of hydraulic engineering problems including flows in a converging-diverging subcritical flume, supercritical expansions at various Froude numbers, and supercritical converging chutes. For each of these test cases, the calculated results are compared with experimental data. The comparisons with measurements as well as with other numerical solutions show that the proposed method is comparatively accurate, fast, and reliable.     

Broad-Crested Weirs with Rectangular Compound Cross Sections

A series of laboratory experiments was performed in order to investigate the effects of width of the lower weir crest and step height of broad-crested weirs of rectangular compound cross section on the values of the discharge coefficient, the approach velocity coefficient, and the modular limit. For this purpose, nine different broad-crested weir models with rectangular compound cross sections and a model with a rectangular cross section were tested in a horizontal laboratory flume of 11.0 m length, 0.29 m width, and 0.70 m depth for a wide range of discharges. The compound cross sections were formed by a combination of three sets of step heights and three sets of lower weir crest widths. The sill-referenced heads at the approach channel and at the tailwater channel were measured in each experiment. The dependence of the discharge coefficient, approach velocity coefficient, and modular limit values on model parameters was investigated, and these quantities were compared with those of the broad-crested weir models with a rectangular cross section.     

Flow Characteristics at Drops

This technical note is an experimental contribution to the study of the supercritical flow at drops. The experimental setup is arranged to measure flow characteristics, which include velocity profiles and several lengths. Because of the similarity of the supercritical flow to the subcritical flow, a basis for the analysis of data is also established. It is found that for a specific discharge increasing the Froude number decreases the relative energy loss, the downstream depth, and the pool depth. For any given value of the Froude number, with increasing discharge the energy loss decreases, but the downstream depth and the pool depth increase. The predictions of flow parameters differ from the measured ones, probably due to the assumptions made in the proposed method, which neglect the entrainment of air at the downstream section and the bed shear stress. An empirical equation is derived to estimate the relative energy loss for supercritical flow. Since the proposed method can be run for any Froude number, it can also be used to predict flow parameters of the subcritical flow with good accuracy.     

Design of a Scroll Vortex Inlet for Supercritical Approach Flow

Vortex drop shafts are used in urban drainage systems to connect two sewers located at considerably different elevations. After their introduction in 1947, these were studied with particular reference to subcritical approach flow. Vortex shafts for supercritical approach flow can also be used, but the intake structure may have relatively high cost due to the complex geometry. The present study includes experimental results of a specific investigation on the changes to be made in the supercritical approach channel if a subcritical vortex intake is used. The experimental investigation analyzes the effect of a hydraulic jump on the performance of vortex intake structure to define appropriate technical solutions, essentially consisting in a negative step to be located along the supercritical approach channel. Design criteria are finally presented for the evaluation of the step height and its distance from the vortex intake structure.     

Simulation of Transcritical Flow in Pipe/Channel Networks

Using finite difference methods in conjunction with the reduced momentum equation and applying boundary condition structure inherent to subcritical flow to all regimes, is an approach that enables efficient numerical simulation of supercritical and transcritical flows in pipe/channel systems. However, as well as certain errors within a single channel due to incomplete equations, this technique also may introduce unwanted effects propagating across a network in both upstream and downstream directions. These may include: unrealistic backwater effects due to improper boundary conditions, nonamplifying oscillations due to jerky jump movement, and other computational instabilities. Practical implications of these are analyzed in detail and are illustrated using a set of examples. Sensitivity analyzes and comparisons with analytical solutions and laboratory experiments are made. The measures to reduce the inaccuracies inevitable in simulation of transcritical flows are discussed.     

Critical Flow over Circular Crested Weirs

The critical flow principle is a useful approach for the hydraulic analysis of round-crested weirs due to their single head-discharge relationships. The hydraulics of circular-crested weirs is examined using simplified models incorporating streamline curvature effects, comparing their predictions with experimental data. A generalized one-dimensional model based on the critical flow in curvilinear motion has been developed. The discharge coefficient increases with the specific energy normalized with the radius of curvature, E/R, when streamline curvature effects are included. The relative flow depth at the crest decreases as E/R increases. The flow at the weir crest is only critical for a normalized specific energy value of E/R ≈ 0.5–0.6. For larger heads, the flow at the weir crest has been found to be supercritical.     

Supercritical Flow in 45° Junction Manhole

The flow in a junction manhole is analyzed using hydraulic modeling and a semiempirical approach. A large number of experiments was conducted to obtain insight in the complex hydraulic features of flows in either one or both of the approach junction branches. Given their significance in applications, in addition to supercritical flow conditions, junction flow with mixed approach flows were also considered. The results include information regarding the main wave structure, with detailed discussions of locations and heights of so-called waves A, B, and C. Further, the swell height at the downstream manhole end was determined and it was found that choking of the supercritical flow structure occurs mainly because of a capacity limit at this outlet. Then, both the minimum and maximum flow limitations were determined. If the discharge is smaller than the minimum discharge, there is a transition from supercritical to subcritical junction flow. If, on the other hand, the discharge is larger than the maximum discharge, supercritical junction flow breaks down and a pressurized two-phase flow is established, which can be responsible for dangerous phenomena such as manhole geysering.     

Simulation of the St. Francis Dam-Break Flood

A two-dimensional (2D) simulation of flooding from the 1928 failure of St. Francis Dam in southern California is presented. The simulation algorithm solves shallow-water equations using a robust unstructured grid Godunov-type scheme designed for wetting and drying and achieves good results. Flood extent and flood travel time are predicted within 4 and 10% of observations, respectively. Representation of terrain by the mesh is identified as the dominant factor affecting accuracy, and an iterative process of mesh refinement and convergence checks is implemented to minimize errors. The most accurate predictions are achieved with a uniformly distributed Manning n = 0.02. A 50% increase in n increases travel time errors to 25% but has little effect on flood extent predictions. This highlights the challenge of a priori travel time prediction but robustness in flood extent prediction when topography is well resolved. Predictions show a combination of subcritical and supercritical flow regimes. The leading edge of the flood was supercritical in San Francisquito Canyon, but due to channel tortuosity, the wetting front reflected off canyon walls causing a transition to subcritical flow, considerably larger depths, and a standing wave in one particular reach that accounts for a 30% fluctuation in discharge. Elsewhere, oblique shocks locally increased flood depths. The 2D dam-break model is validated by its stability and accuracy, conservation properties, ability to calibrate with a physically realistic and simple resistance parametrization, and modest computational cost. Further, this study highlights the importance of a dynamic momentum balance for dam-break flood simulation.     

Discharge Coefficient for Sharp-Crested Side Weir in Subcritical Flow

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 Ratio of Side Outflow to Supercritical Channel Flow

This study presents the effects of width changes of a side breach, Froude numbers, and bottom slopes on discharge ratios of a side outflow to the main channel flow when a flow is supercritical. The results compare the differences between theoretical discharge ratios and experimental ones. The differences increase in one of three conditions: increase of the side breach, increase of the bottom slope, and decrease of the Froude number.     

Field Testing of a Simple Flume (SMBF) for Flow Measurement in Open Channels

In this paper the stage–discharge relationship of a new flume named SMBF (Samani, Magallanex, Baiamonte, Ferro), originally proposed by Samani and Magallanez and tested by Baiamonte and Ferro, for measuring flow discharge in open channels is reviewed. The flume is obtained inserting two semicylinders in a rectangular cross section. The results of some experimental runs carried out using horizontal flumes characterized by different values of the contraction ratio (ranging from 0.17 to 0.81) are used for determining the two coefficients of the power stage–discharge equation. The stage–discharge equation is tested using flow measurements carried out in the period between December 2004 and March 2006 in the Sicilian experimental SPA1 basin. Field testing of the SMBF flume is developed using discharge measurements carried out by a Khafagi–Venturi flume placed in the field measurement channel.     

Flood Plain Filling by a Monoclinal Flood Wave

Theoretical equations are derived to estimate the flood wave celerity and the volume of lateral flow leaving the main channel and entering the flood plain for a two-dimensional monoclinal wave. The equations are based on conservation of water mass assuming an idealized compound channel. The parameters that affect the lateral flow volume are the ratio of flood plain depth to the depth in the main channel at the peak discharge, the ratio of the flood plain width to the main channel width, and the ratio of the flood plain roughness to the main channel roughness. The percentage of flood plain volume filled up by lateral flow from the main channel increases as the width ratio decreases, the roughness ratio increases, or as the depth ratio decreases.     

Detailed Study of Binary Law for Open Channels

This paper presents a generalized version of the binary velocity distribution law, which combines the logarithmic law of the inner region with the parabolic law of the outer region. This combination is extended for cases of flow where the maximum velocity occurs at some distance below the free surface in a vertical. The study uses the data collected at the Indian Institute of Science over a long period for all of the four regimes of turbulent open channel flow, namely, subcritical smooth, supercritical smooth, subcritical rough, and supercritical rough. The various conditions and limitations at the junction point of the inner and outer region are derived and discussed in this paper. It is shown that the velocity distribution for the flows of narrow open channels can be described by the logarithmic law for the inner region and the parabolic law for the outer region, but the conditions at the junction point will not always be the same.     

Drop in Combined Sewer Manhole for Supercritical Flow

Manholes often contain small drops for various reasons, the most important being submergence. While this may be appropriate for subcritical flow, its effect was considered doubtful for supercritical flow. This note aims at investigating the effect of a manhole drop on the hydraulics of sewer flow. Based on systematic experimental observations, the flow pattern associated with a manhole drop was established. A distinction was also made between small and intermediate drops. Then, the main wave features were analyzed to result in expressions that contain both the upstream filling ratio and the Froude number of the approach flow. In addition, the discharge capacity was also investigated, and selected photographs show typical drop flow in combined sewer manholes. The result of the present study is evident, based on these observations, and recommendations towards future design of combined sewer manholes are also made.     

Discharge Relation for Cutthroat Flume under Free-Flow Condition

A cutthroat flume is commonly used as flow measuring device for open-channel flow due to ease of fabrication and installation. In most of the cases it is difficult to calibrate the flume in the field. Therefore, accurate relation between discharge and upstream head applicable for all sizes of cutthroat flume is needed. Seven different sizes of cutthroat flumes, having different length to throat width ratios, are fabricated and tested in the laboratory under free-flow condition. Selecting groups of different variables describing flow through a cutthroat flume number of dimensionless parameters are formed. Regression analysis of experimental data is carried out between all possible combinations of pairs of dimensionless parameters and the pair giving the best correlation is selected. Using the selected pair, relation between dimensionless parameters of discharge and head is developed. The relation is simple and convenient to use and, at the same time, more accurate compared to methods available in literature for prediction of discharge.     

Upwind Conservative Scheme for the Saint Venant Equations

An upwind conservative scheme with a weighted average water-surface-gradient approach is proposed to compute one-dimensional open channel flows. The numerical scheme is based on the control volume method. The intercell flux is computed by the one-sided upwind method. The water surface gradient is evaluated by the weighted average of both upwind and downwind gradients. The scheme is tested with various examples, including dam-break problems in channels with rectangular and triangular cross-sections, hydraulic jump, partial dam-break problem, overtopping flow, a steady flow over bump with hydraulic jump, and a dam-break flood case in a natural river valley. Comparisons between numerical and exact solutions or experimental data demonstrated that the proposed scheme is capable of accurately reproducing various open channel flows, including subcritical, supercritical, and transcritical flows. The scheme is inherently robust, stable, and monotone. The scheme does not require any special treatment, such as artificial viscosity or front tracking technique, to capture steep gradients or discontinuities in the solution.     

Numerical Study of the Transition Regime between the Skimming and Wake Interference Flows in a Water Flume by Using the Lattice-Model Approach

A numerical study to describe the transition regime between the skimming and wake interference flows due to the influence of an idealized bed roughness in a water flume was carried out here using the lattice model approach. The model reproduced the skimming, transition, and wake interference regimes for different aspect ratios that determine the bed roughness geometry. The simulated turbulent structures were visualized by drawing the trajectories of a large number of passive tracer particles released in the computational domain, and the results agreed with those reported by the research works. The dimensionless streamwise and vertical turbulent intensities were calculated at five test sections. The results obtained supported the visualized flow patterns permitting us to detect the presence of a shear layer developed at the top of the roughness element, whose strength varied according to the flow regime simulated.     

Hydraulic Resistance of Flow in Channels with Cylindrical Roughness

A laboratory study on the hydraulics of flow in an open channel with circular cylindrical roughness is presented. The laboratory study consists of an extensive set of flume experiments for flows with emergent and submerged cylindrical stems of various sizes and concentrations. The results show that the flow resistance varies with flow depth, stem concentration, stem length, and stem diameter. The stem resistance experienced by the flow through the vegetation is best expressed in terms of the maximum depth-averaged velocity between the stems. Physically based formulas for flow resistance, the apparent channel velocity, and flow velocities in the roughness and surface layers are developed. The formulas are validated with the flume data from the present study as well as those from past studies. A method for calculating channel hydraulic conditions using these formulas is presented.     

Discharge Characteristics of Chimney Weir under Free-Flow Conditions

The assumption of a constant coefficient of discharge in the linear head-discharge relationship of a chimney weir is reinvestigated. Based on dimensional analysis and subsequent experiments conducted with three different chimney weirs at various crest heights and channel widths, it is found that the coefficient of discharge in the linear relationship is not a constant, but is found to vary with the ratio of head to altitude, h/d; half-vertex angle in the form of w/d, w being the half crest width; h/(h+P), P being the crest height; and the channel width contraction ratio, w/C, C being the channel width. A linear regression equation correlating the coefficient of discharge with the above variables is proposed that, along with the linear head-discharge relationship, provides an accurate prediction of free-flow discharge.