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In this work is described a research project, which central objective was to reduce scouring depth in shorts and vertical abutments of bridges, so in this it was analyzed at trough of a physical model reduced, the scouring depth that generate an water flow in a system performed by a short and vertical abutment of bridge, in a sand channel of hydraulic engineering laboratory of ESIA Zacatenco United, in Mexico; the abutment was modified in his geometry (with wings to 45, 30 y 20º), in order to determine experimentally its influence in local scouring that was generated, with some flow condition; and in the way of essay‐error to reduce the local erosion. In this project, the local erosion depth generated by the original abutment was reduced in a 98 %. [ABSTRACT FROM AUTHOR]

Deep-water coarse-grained channels are embedded within a polygonal fault tier, and the polygonal faults (PFs) present non-polygonal geometries rather than classic polygonal geometry in plan view. However, PFs present differences when they encounter deep-water (coarse-grained vs. fine-grained) channels with different lithology, which has not been further studied to date. 3D seismic data and a drilling well from Beijiao sag of Qiongdongnan basin, South China Sea were utilized to document the plan view and cross-sectional properties of the PFs and their differences and genetic mechanism were investigated. Results show that, first, PFs can be divided morphologically into channel-segmenting PFs and channel-bounding PFs in plan view. The former virtually cuts or segments the axes of channels in high- and low-amplitudes, and the latter nearly parallels the boundaries of the channels. Both are approximately perpendicular to each other. Secondly, channel-bounding PFs that related to low-amplitude channels are much longer than those of high-amplitude ones; channel-segmenting PFs related to low-amplitude channels are slightly longer than the counterparts related to high-amplitude channels. Lastly, the magnitudes (e.g., heights) of the PFs are proportional to the scales (e.g., widths and heights) of low-amplitude channels, whereas the magnitudes of the PFs are inversely proportional to the scales of high amplitude channels. Coarse-grained (high amplitude) channels act as a mechanical barrier to the propagation of PFs, whereas fine-grained (low-amplitude) channels are beneficial to the propagation and nucleation of PFs. Additionally, the genetic mechanism of PFs is discussed and reckoned as combined geneses of gravitational spreading and overpressure hydrofracture. The differences of the PFs can be used to reasonably differentiate coarse-grained channels from fine-grained channels. This study provides new insights into understanding the different geometries of the PFs related to coarse-grained and fine-grained channels and their genetic mechanism. [ABSTRACT FROM AUTHOR]

In this paper, the flow in the vicinity of rectangular side orifices placed in main channels is estimated by means of the FLOW-3D model. To reconstruct the flow free surface, the volume of fluid (VOF) approach is utilized. In addition, the standard k-ε and RNG k-ε turbulence models are employed to predict turbulence flow. According to the results obtained from the numerical modeling, the RNG k-ε turbulence model has higher accuracy than the standard k-ε. The analysis of the numerical modeling results proved that this model forecasts the discharge coefficient of side weirs with suitable accuracy. On the other hand, the mean absolute percent error (MAPE) is calculated equal to 12.204%. Also, the maximum pressure is simulated near the main channel bed. Moreover, the minimum pressure is estimated near the flow free surface. Regarding the numerical simulations, the maximum turbulence energy state occurs near the inlet of the side orifice and by increasing the side orifice dimensions the flow field turbulence energy value increases. [ABSTRACT FROM AUTHOR]

Side orifice is a hydraulic structure provided in the walls of a channel to divert flow from the main channel to another channel. It is used widely in environmental engineering and irrigation engineering. In the present study, numerical simulation has been performed to analyze the flow characteristics of a rectangular side orifice using the CFD program with ANSYS-CFX code. Finite volume method is used to solve the governing equations of the standard k-ε turbulence model in prismatic channels. The CFD model developed has been verified with the available experimental studies of Hussain and his associates. On comparing with experimental observations; it is found that the CFD model simulates the flow through the orifice with good accuracy. Flow pattern for a side orifice has also been analyzed for streamline pattern, velocity distribution, velocity contours. Further, a reverse flow in the main channel has been noticed near the vicinity of the orifice in the main channel. [ABSTRACT FROM AUTHOR]

For a given width, a labyrinth weir has a developed crest length, thereby increasing the flow capacity for a given upstream headwater. This paper experimentally studies the flow over labyrinth weirs with semicircular and sinusoidal configurations in a rectangular channel under a wide range of flow discharges. The effects of headwater ratio (HT/P), length of weir (L/P), arc radius ratio (R/P) and the number of cycles (N) on the discharge coefficient of semicircular and sinusoidal labyrinth weirs are investigated. Experimental results indicated the decreasing trend of Cd for HT/P>0.35 which is probably related to the progressive development of local submergence. Despite the effects of local submergence, the labyrinth weirs have nearly the same discharge coefficient as broad-crested weirs, and the flow discharge exceeded the linear weirs efficiency by ∼30. Additionally, reliable equations for estimating the discharge coefficient of labyrinth weirs with semicircular and sinusoidal configurations are presented. [ABSTRACT FROM AUTHOR]

The occurrence of local scour around bridge piers or abutments is one of the major reasons for the destruction of bridges. Therefore, this phenomenon should be prevented or at least minimized using some methods, namely using collars in recent years. In the present paper, by proposing a new approach and developing an experimental model of partial collars (collars not fully encircling the abutment), the effect of length and width of collars on reducing scouring and sedimentation pattern around the bridge abutments with vertical walls were investigated under different conditions. Moreover, the obtained results were compared with the results of models with full collars. The results revealed that collar dimensions could have a great impact on its efficiency. In partial collars, if only the upstream face of the abutment is protected and there is no protrusion toward the downstream, there will be no high and acceptable efficiency. However, increasing length and width, its positive efficiency will be enhanced. Although increasing the length of a collar of this type to more than 0.6 times the length of the abutment diminishes the scouring around the bridge abutment, increasing its width not only does reduce the scour depth but also produces a much greater effect on the location of the scouring hole to be farther away from the downstream of the abutment. Furthermore, the efficiency of full collars is also enhanced as their length and width increase. Comparison of the results shows that the efficiency of full collars is less than that of partial collars, despite their greater cross-sectional area. Therefore, partial collars are more cost-effective than full collars due to their lower cross-sectional areas. The average percentage of scour depth reduction for all four flows for different models in the erodible bed and at the base point ranged from 24 to 68% and 24 to 97%, respectively. [ABSTRACT FROM AUTHOR]

Broad-crested weirs (BCW) are commonly used elements of stormwater systems and different open-channel hydraulic structures. Specific features of stormwater drainage channels are small width, low flow depths and, accordingly, small overflow heads at weirs. Dependences of the discharge coefficient of narrow (b = 0.224 m) rectangular sharp-edged broad-crested weirs with vertical walls, threshold height of 0.05 m and threshold length of 0.05-0.2 m were obtained experimentally. The experimental values of the discharge coefficient were approximated by the power-law functions of relative length of the weir. At large values of the relative length of the threshold (L/h> 10), for all weirs was obtained the same tendency of decreasing the discharge coefficient with increasing L/h ratio that can be explained by the enlargement of the hydraulic friction along the weir with increasing L/h ratio. [ABSTRACT FROM AUTHOR]

Successive earthquakes can drive landscape evolution. However, the mechanism and pace with which landscapes respond remain poorly understood. Offset channels in the Carrizo Plain, California, capture the fluvial response to lateral slip on the San Andreas Fault on millennial time scales. We developed and tested a model that quantifies competition between fault slip, which elongates channels, and aggradation, which causes channel infilling and, ultimately, abandonment. Validation of this model supports a transport-limited fluvial response and implies that measurements derived from present-day channel geometry are sufficient to quantify the rate of bedload transport relative to slip rate. Extension of the model identifies the threshold for which persistent change in transport capacity, obliquity in slip, or advected topography results in reorganization of the drainage network. [ABSTRACT FROM AUTHOR]

River meanders have always been an intriguing subject in fluvial geomorphology because of their ubiquity, dynamism, remarkable forms and practical consequences of their movement. Sometimes a relatively straight channel flowing over bedrock may develop a lone meander bend cut-off which is very out of the place from the surrounding area. The occurrence of a sudden bend along a river may not be a meandering bend but may be manifestation of sudden change in the river dynamism due to many reasons, such as, lithology, change in rainfall regime, tectonics etc. The formation of such features highlights the behavior of river in the past. One such striking feature has been observed along the River Pravara in the Deccan Trap Region, Maharashtra, India. Rivers in Deccan Trap Region do not meander and form cut-offs by rule. It is rocky country where rivers flow in deeply incised bedrock. Hence, the observed feature displays a striking anomaly in this region. Hence, an attempt has been made in the present paper to evaluate the mode of formation of this single cut-off along this channel. Morphological and sedimentological data were generated and analyzed for the channel loop and the link channel to understand the competence of the river in the past and present which were directly or indirectly responsible for the development of this channel anomaly in this reach. Based on the results of the analysis and intensive field observations, it has been inferred that this is a classic example of natural morphological adjustment of a river when a set of events occurred, first retardation of vertical erosion encountering bedrock followed by series of floods to induce the channel to divert from the original path to resume the present course. Presence of a tributary further aided to the process of the loop development. The study can provide additional knowledge to the studies involving anomalous channel cut-offs at any part of the world. [ABSTRACT FROM AUTHOR]

Recently, a new lightning phenomena, termed needles, has been observed in both VHF and in optical along positive lightning leaders. They appear as small (<100 m) leader branches that undergo dielectric breakdown at regular intervals (called twinkles). Providing a coherent and consistent explanation for this phenomenon is challenging as each twinkle is a form of negative breakdown that propagates away from the positive leader. In this study, we provide detailed observations of needles in VHF, observed during two lightning flashes. We show distributions of different needle properties, including twinkle propagation speeds, time between twinkles, and needle lengths, among others. We show a return stroke and multiple recoil leaders that quench needle activity. We also show that nearby needle activity does not seem to correlate together, and that needle twinkling can slow down by 10%–30% per twinkle. We conclude by presenting possibilities for how the positive leader could induce negative propagation away from the positive channel, and we argue that twinkles can propagate like a stepped leader or like a recoil leader depending on the temperature of the needle, which implies that needle twinkles can probably propagate without emitting VHF. Key Points: Detailed distributions of needle properties are presentedPossible physics behind needle production is discussedRecoil leaders quench needle activity [ABSTRACT FROM AUTHOR]

Flume experiments were conducted to understand the role of episodic sediment supply on the threshold of motion, streambed state, and stability in gravel bed channels. We demonstrate the importance of bed surface evolution on grain entrainment and hence channel stability. The grain‐size distribution (GSD) of the bed surface coarsened quickly under no feed conditions to develop an armored surface. Armor continued to experience particle exchange but remained intact throughout the experiment, and was relatively insensitive to subsequent sediment supply pulses. Bed surface structures (coarse‐grain clusters, stone cells, and imbrication) developed during the experiments and continued to respond dynamically to sediment pulses. Thresholds of motion estimated by various methods increased during the experiment and fluctuated in response to changes in sediment supply, though they were poorly predicted either by surface grain‐size changes or by surface structure. This reinforces the idea that the threshold for motion is not constant in poorly sorted gravel‐bed streams, and it confirms that the critical Shields number in transport models represents a bed state parameter, not a grain mobility number. Changes are controlled by a variety of factors including sediment supply regime, the degree of bed structuring, and the history of bed evolution. Our results highlight the importance of sediment supply regime as a control on bed surface evolution and the channel stabilizing function played by surface structures. Key Points: Despite constant flow and little change of surface grain size, critical shear stress changed in response to bed surface stateBed surface structures increased the shear stress required to entrain sedimentThe Shields Number is a bed state parameter [ABSTRACT FROM AUTHOR]

This paper uses flume experiments to investigate the influence of lateral width confinement on channel morphology, sediment sorting, and bedload transport. Three runs of about 60 hr were carried out under constant feeding rate equal to 0.6 l/s and 8 g/s, with a bimodal mixture of natural sediments, a fixed flume slope of 3%, and width imposed by lateral walls from 0.12 to 0.50 m in order to model three different flow confinement configurations. Despite the three runs transporting at the same rate on average, they presented different gravel‐bed river morphologies and different degrees of bed complexity. The three runs also presented differences in bedload transport rate fluctuations associated with different magnitude and mechanisms of bed storage and release of sediments. The intermediate width configuration (Run 2) was found to have a minimum storage and release of sediments compared with both the wider configuration (Run 1) and the narrower configuration (Run 3). Runs 1 and 3 were characterized by a significant storage and release of sediments resulting in a highly fluctuating bedload transport rate; however, while Run 1 (braiding morphology) stored and released sediments through lateral deposits and bed variations with planimetric sorting, Run 3 (single‐thread channel) stored and released sediments through variations in bed elevation accompanied by vertical sorting. We extrapolated this concept to the full set of gravel‐bed river morphologies, thus speculating about the channel morphology for optimal sediment transfer. Key Points: We perform flume experiments to represent poorly‐sorted gravel‐bed rivers with the same active channel width but different extents of lateral confinementChannel morphologies, geometries, sorting patterns, and bedload transport rates are strongly influenced by lateral width constraintsAmong the three configurations tested, the one with intermediate width confinement promotes a single‐thread to braided pattern and presents less variation in sediment transport rate [ABSTRACT FROM AUTHOR]

The calculation of Chezy's resistance coefficient (CRC) is typically not provided a priori in a design problem, and its value is often selected subjectively from the literature in most open channels and conduits for the uniform flow. The evaluation of this coefficient is crucial to channel design and for computing its normal depth. The primary purpose of this research study is to revisit the mathematical formulation for the resistance coefficient. A general explicit relation of the resistance coefficient in turbulent flow is set with different geometric profiles of conduits and channels, mainly the horseshoeshaped tunnel using the rough model method (RMM). CRC is firmly based on the internal walls' absolute roughness of the channel, the liquid kinematic viscosity, the longitudinal slope, the discharge and the filling rate. Additionally, a simplified method is proposed to determine CRC with a restricted number of variables such as the kinematic viscosity, the absolute roughness, the slope of the conduit, and the discharge. Based on studying the variation of CRC as a function of the filling rate, another explicit expression is provided to compute this coefficient efficiently when its maximum value is reached. To demonstrate how Chezy's resistance coefficient can be calculated in a horseshoe-shaped tunnel, some examples of calculations are proposed. [ABSTRACT FROM AUTHOR]

Keywords: Environmental fluid mechanics; Hydraulic engineering; Open channel flows; Theoretical analysis; Physical modelling; Numerical modelling EN Environmental fluid mechanics Hydraulic engineering Open channel flows Theoretical analysis Physical modelling Numerical modelling 227 232 6 04/27/20 20200401 NES 200401 Presentation Water is an indispensable element for life on Earth, and covers 71% of our planet's surface; further, humans associate water with environment. The scope of the Special Issue (SI) is broad, with four studies on fluvial hydraulics, one on coastal hydraulics, and seven on hydraulic structures. Environmental fluid mechanics, Hydraulic engineering, Open channel flows, Theoretical analysis, Physical modelling, Numerical modelling. [Extracted from the article]

Dredging of navigation channels in estuaries affects estuarine morphology and ecosystems. In the Western Scheldt, a two‐channel estuary in the Netherlands, the navigation channel is deepened and the sediment is relocated to other parts of the estuary. We analyzed the response of an intertidal flat to sediment disposals in its adjacent channel. Decades of high‐frequency monitoring data from the intertidal flat show a shift from erosion toward accretion and reveal a sequence of cascading eco‐morphological consequences. We document significant morphological changes not only at the disposal sites, but also at the nearby intertidal flats. Disposals influence channel bank migration, driving changes in the evolution of the intertidal flat hydrodynamics, morphology, and grain sizes. The analyzed disposals related to an expansion of the channel bank, an increase in bed level of the intertidal flat, a decrease in flow velocities on this higher elevated flat, and locally a decrease in grain sizes. These changes in turn affect intertidal flat benthic communities (increased in quantity in this case) and the evolution of the adjacent salt marsh (retreated less or even expanded in this case). The shifts in evolution may occur years after dredged disposal begins, especially in zones of the flats farther away from the disposal locations. The consequences of sediment disposals that we identify stress the urgency of managing such interventions with integrated strategies on a system scale. Key Points: Channel disposals result in a nonlocal sequence of eco‐morphological consequences for adjacent intertidal flatsSediment disposals in a channel turned the adjacent eroding intertidal flat into an accreting and expanding intertidal flatThe bed level increase is associated with reduction in grain size, increased quantity of benthic macrofauna, and salt marsh progradation [ABSTRACT FROM AUTHOR]

We investigate two-phase (oil and water) flow in head-on microfluidic devices, which consist of two identical channels as inlets and the “long leg” as a constriction channel leading to a wider outlet section. Over an exceptionally broad range of flow rates of 10-4–10 μl/min in 10–100 μm (hydraulic diameter) microchannels, corresponding to capillary numbers of 10-6–10-1, a two-phase flow map is presented. A rich flow behavior was found. The flow patterns observed were dripping, jetting, and threading. These phenomena are interpreted as caused by capillary instability, squeezing, and shearing by considering the contribution of different forces acting at the oil/water interface. This device provides us with a broad choice to generate droplets of different sizes and frequencies by modifying either the geometrical design or the flow rates. [ABSTRACT FROM AUTHOR]

The configurational entropy of interacting particles adsorbed on one-dimensional channels arranged in a triangular cross-sectional structure is studied by combining Monte Carlo simulation and thermodynamic integration method. Three different energies have been considered in the adsorption process: (1) εo, constant interaction energy between a monomer and an adsorption site; (2) wL, interaction energy between nearest-neighbor particles adsorbed along a single channel, and (3) wT, interaction energy between particles adsorbed across nearest-neighbor channels. Special attention is devoted to the case of repulsive transversal interactions (wT>0), for which a rich variety of ordered phases are observed in the adlayer, depending on the value of the parameters kBT/wT (being kB the Boltzmann constant) and wL/wT. The influence of each ordered structure on the configurational entropy of the adlayer has been analyzed and discussed in the context of the lattice-gas model. [ABSTRACT FROM AUTHOR]

This paper presents new data obtained by speleological surveys and ground-penetrating radar (GPR) on a cut-and-closure conduit in Scott Turnerbreen, a small cold glacier in Svalbard, Norwegian Arctic. We use these data to propose criteria for the identification of cut-and-closure conduits from GPR data. In addition, we describe subglacial and englacial structures exposed in the conduit, which shed light on the former dynamic behaviour of the glacier. The glacier bed consists of a thick layer of subglacial traction till, from which till-filled fractures extend upward into the ice. These observations show that Scott Turnerbreen was formerly warm-based, and are consistent with a surge or surge-like behaviour. The channel system was also imaged using GPR. Varying channel morphologies have distinctive signatures on GPR profiles, allowing the identification and mapping of englacial drainage systems in situations where direct access is impossible. [ABSTRACT FROM AUTHOR]

The analysis of Urban Drainage Network Performance in Maximum Discharge Storage in the City becomes an urgent matter, the approach that will be conducted in this research is explanatory, which is explaining natural phenomena that happened and synthesizing the relation of parameter stream, existing drainage network, and potential puddle. The result of analysis shows several inundation area in the rainy season in sub- Catchment Citepus, the cause is identified as there has not been a drainage channel that connects it to the main canal that caused the drainage network hard to be evaluated, the water rope are clogged beside the road, dimensional channel cannot handle runoff discharge, various clog on several crossway, the narrowing and swallowing of channel because of sedimentation, and several different utility with the transversal and parallel in position causing it to become a place where garbage stacks up. Several channel section's capacity are unable to contain discharge, but several channel are still able to contain but in factuality of the field there are still rash that caused inundation in several main section roadway in Bandung. [ABSTRACT FROM AUTHOR]

Abstract Identifying river segments with apparently distinct geomorphic characteristics but relatively homogeneous internal features may be critically helpful in designing network analysis for characterization, environmental assessment and river management. Automatic segmentation procedures using geographic tools and statistical methods provide objective and replicable results. In particular, multivariate procedures may be appropriated for different purposes such as coping with the multiple dimensionality of river systems. Although there is an increasing number of studies dealing with segmentation using different sets of morphological variables, the influence that the selected variables have on segmentation results is rarely assessed. In this context, we defined five combinations of frequently used geomorphic variables (i.e., channel slope, active channel width, valley bottom width, channel confinement and specific stream power), and compared the obtained segmentation results. We study the upper Esla River network, covering a total length of 294 km, with the largest two rivers regulated by large dams. Variables were measured at successive river sections 200 m apart. Five segmentation results were obtained in which we compared the number and characteristics of the segments, and the internal variability and the suitability of predicting river dynamics (i.e., occurrence of bare and vegetated gravel bars). The number of segments per kilometer of river and their average length were different among segmentations but varied much more across rivers than across segmentations. In general, segmentations including channel slope and active channel width performed better in predicting the occurrence of bare gravel bars than segmentations based on stream power or valley confinement. When splitting the initial data set into regulated and non-regulated segments, differences in predicting the occurrence of gravel bars were found, with better results in the case of non-regulated rivers. Channel slope and active channel width showed a reduced explanatory power for the regulated reaches. Finally, we conclude that primary geomorphic variables such as channel slope and active channel width were more efficient than secondary variables such as stream power, which may encompass more information but needed additional data and the use of empirical models, with greater effort and much uncertainty. In the case of regulated rivers, automatic segmentation including the affected variables (e.g., active channel width) may help in detecting differences in geomorphic sensitivity to river adjustments across the resulting segments downstream from the dams. Our results offer valuable insights into the selection of geomorphic variables for river segmentation analysis, in which trade-offs between the information gained and the effort required must be considered according to the respective research targets. Highlights • Automatic segmentation of rivers provides objective and replicable results • Five sets of geomorphic variables with an increasing gradient of effort were designed • Easily quantified primary variables can act as surrogate for more complex variables • Flow regulation alters the efficiency of variables determining geomorphic units [ABSTRACT FROM AUTHOR]

Abstract Tidal asymmetry (i.e., unequal ebb and flood intensities and durations) is a dominant factor in the dynamic equilibrium of current-related sediment transport in estuaries. The evolution of estuarine tides and sediment transport is of great importance to the development and utilization of channels in estuaries. Based on field hydrological and sedimentological data collected over multiple years, the hydrodynamic characteristics, suspended sediment concentration (SSC) and grain size, and median grain size of seabed sediments were analyzed to investigate the effects of the construction of a water–sediment regulation scheme (WSRS) in the Sheyang Estuary in China. Our results showed that small grain sizes (fine sand, silt, and clay) dominated and that suspension was the dominant transport mechanism in the area where tidal asymmetry was greatest. Tidal distortion occurred due to the construction of the WSRS. In this flood-dominant system (i.e., before and after the construction of phase I of the WSRS), the flood current velocity was significantly greater than the ebb current velocity, while it also had a shorter duration that caused higher SSCs during the flood current. This likely induced net sediment import to the estuary, which was the main cause of estuary infilling. Furthermore, the net transport of sediment into the estuary caused by the high flood current velocities resulted in the gradual deposition of sediments in the shipping channel of Sheyang Port. Ebb-dominant conditions (i.e., after the construction of phase II of the WSRS) induced net sediment export from the estuary, and sedimentation was significantly reduced. Since the ebb–flood current velocity ratio (R v) and ebb–flood mean SSC ratio (R s) could reflect tidal asymmetry and the direction of residual sediment transport with and without the WSRSs, they were used as important and sensitive indices to investigate hydraulic and sedimentological conditions. Results from this study can be used to improve the monitoring and management of navigation channels by providing insights into new methods of preventing or reducing sediment deposition in estuarine channels (i.e., by employing R v and R s). Highlights • A water–sediment regulation scheme (WSRS) in the Sheyang Estuary was evaluated. • Tidal asymmetry and channel infilling worsened with phase I of WSRS construction. • Overtopping flow and backflow near jetties caused the enhanced asymmetry. • Lengthening and raising of the jetties (phase II) resolved channel infilling. • WSRSs are effective for controlling sediment deposition in shipping channels. [ABSTRACT FROM AUTHOR]

Abstract Channels with parabola-shaped cross-section are widely used in water conservancy and hydropower engineering, agricultural irrigation and drainage engineering, so it is necessary to determine the accurate normal depth values for design of open channels, operation management and analysis of gradually varied flow. However, the governing equations are nonintegrable for cubic and semi-quintic parabola-shaped channels in terms of the wetted perimeters. In this study, the Simpson's numerical integral method is introduced to approximate the two nonintegrable wetted perimeters for cubic and semi-quintic parabola-shaped channels which can meet the requirements of engineering design well in the commonly using range of engineering. Subsequently, the approximate wetted perimeters are substituted into the uniform flow equation and the uniform flow equation deforms optimal model identically. The optimal model parameters are determined by the 1stOpt software based on Marquardt algorithm and two explicit calculation formulas for the normal depths of cubic and semi-quintic channels are proposed. At the same time, two direct calculation formulas for normal depths of semi-cubic and quadratic parabola-shaped channels are presented as well. Four sets of formulas for normal depths of parabola-shaped channels are presented and their maximum relative errors are 0.52%, − 0.37%, − 0.22% and 0.57%, respectively, which have wide range of application, high precision, concise form and can provide some better guidance for engineering design and operation management. Highlights • The Simpson's numerical integral method is firstly introduced to approximate the two nonintegrable wetted perimeters for cubic and semi-quintic parabola-shaped channels accurately. • Two explicit formulae for normal depths of cubic and semi-quintic parabola-shaped channels are obtained with high precision, wide range of application firstly. • Two explicit formulae for normal depths of semi-cubic and quadratic parabola-shaped channels are obtained with higher precision, wider range of application than those of former studies. [ABSTRACT FROM AUTHOR]

Abstract A Two-stage compound channel section is commonly used in ecological channel design. This paper presents the geometric properties of the compound section and the formulae for calculating the cross-section area, wetted perimeter are obtained. Then, the explicit equations of the best hydraulic section for design are derived. Results show the best width-depth ratio of the compound section is related to some geometric parameters. Furthermore, this type of best hydraulic section is compared with the rectangular and trapezoidal sections. Results indicate that the cross-section area and wetted perimeter are less than those of rectangular and trapezoidal sections for a given flow discharge when the ratios of the compound section's roughness coefficient to those of rectangular and trapezoidal sections are less than 1.017 and 0.855, respectively. It means less lining and excavation cost is required for construction. Highlights • Geometric properties of the two-stage compound channel section are presented. • Formulae for calculating the cross-section area, wetted perimeter of the compound section are obtained. • The explicit equations of the best hydraulic section of the compound section for design are derived. • This type of best hydraulic section is compared with the rectangular and trapezoidal sections. • Quantitative values are obtained used to determine the more efficient section of the compound section. [ABSTRACT FROM AUTHOR]