Showing papers in "Journal of Hydraulic Engineering in 2014"

Evaluation of Existing Equations for Local Scour at Bridge Piers

Abstract: Twenty-three of the more recent and commonly used equilibrium local scour equations for cohesionless sediments were evaluated using compiled laboratory and field databases. This investigation assembled 569 laboratory and 928 field data. A method for assessing the quality of the data was developed and applied to the data set. This procedure reduced the laboratory and field data to 441 and 791 values, respectively. Because the maturity of the scour hole at the time of measurement for the field data was unknown, they were only used to evaluate underprediction by the equations. A preliminary quality control screening of the equilibrium scour methods/equations reduced the number of equations from the initial 23 to 17. For this screening procedure the equations were used to compute scour depths for a wide, but practical, range of structure, flow, and sediment parameters. Those methods/equations yielding unreasonable (negative or extremely large) scour depths were eliminated from further consideration. The remaining 17 methods/equations were then analyzed using both laboratory and field data. Plots of underprediction error versus total error for the laboratory data and underprediction error for field data versus total error for laboratory data along with error statistics calculations assisted in the ranking of the equations. Equations from previous publications were melded and slightly modified to provide the best performing equation in that it yields the least total error and close to the least under-prediction error of those tested. The new equation is termed the Sheppard/Melville (S/M) equation in this paper.

Modeling Elastically Deforming Leaks in Water Distribution Pipes

Abstract: In this study, the relationship between the conventional power equation and the fixed and variable area discharges (FAVAD) equation for modeling leakage as a function of pressure was investigated. It is shown that different leakage exponent (or N1) values are obtained for the same leak when measured at different pressures. An analytical exploration of the two equations shows that the leakage exponent tends to 0.5 when the system pressure tends to zero, and to 1.5 when the system pressure tends to infinity. A dimensionless leakage number LN is defined as the ratio between the variable and fixed portions of a leak, and it is shown that a single function can be used to describe the relationship between the leakage number and leakage exponent. This model was combined with previous research to accurately predict the leakage exponents of several published studies in cases where elastic deformation occurred.

Flow Patterns and Turbulence Structures in a Scour Hole Downstream of a Submerged Weir

Abstract: Scouring downstream of submerged weirs is a common problem resulting from the interaction of the three-dimensional turbulent flow field around the structures and the mobile channel bed. This paper presents the distributions of flow patterns, bed shear stresses, and turbulence structures in the approach flow and the scour hole downstream of a submerged weir. The experiments were conducted under the clear-water scour condition for an equilibrium scour hole. The experimental results show that the flow structures are considerably changed by the presence of the structure. A large recirculation zone and a flow reattachment region are formed downstream of the submerged weir. Strongly paired cellular secondary flows are observed in the scour hole. The turbulence structures ahead of the recirculation zone govern the dimensions of the scour hole.

Estimation of Concentration and Load of Suspended Bed Sediment in a Large River by Means of Acoustic Doppler Technology

Abstract: Fil: Latosinski, Francisco Guillermo Universidad Nacional del Litoral Facultad de Ingenieria y Ciencias Hidricas Departamento de Hidraulica; Argentina Consejo Nacional de Investigaciones Cientificas y Tecnicas Centro Cientifico Tecnologico Conicet - Santa Fe; Argentina

New Modularity-Based Approach to Segmentation of Water Distribution Networks

Abstract: Complex and/or large size water distribution networks (WDNs) require the division of the hydraulic system into modules to simplify the analysis and the management tasks. In the modern science of networks, the modularity index has been proposed to detect communities, i.e., groups/clusters of nodes characterized by stronger interconnections. The modularity index is a measure of the strength of the network division into communities and it is maximized to identify them. Therefore, the division into modules of WDNs, also named segmentation, could be performed by using the modularity index as metric to identify cluster of nodes. Nevertheless, modularity index needs to be revised considering the specificity of the hydraulic systems, which are infrastructure networks. In fact, the division into modules for infrastructure networks, although it can be based on the identification of clusters of nodes, is not aimed at investigating network features. Differently, the aim is the practical issue of simplifying s...

Contribution of Trapped Air, Deck Superelevation, and Nearby Structures to Bridge Deck Failure during a Tsunami

Abstract: Failure of the Utatsu concrete girder highway bridge in Minamisanriku, Miyagi Prefecture during the 2011 Great East Japan Tsunami was puzzling because the bridge decks were not pushed off their piers but rather were flipped off the landward side of the bridge piers after being deeply submerged by the surging tsunami. To determine what caused this to happen, two simulations were conducted. The first was a large-scale Delft shallow-water simulation (beginning with published tsunami source free surface deviation) to determine the behavior of the tsunami (time series of flow depth and speed) at the bridge site. The second was a small-scale two-dimensional (2D) (profile view) software volume-of-fluid (VOF) simulation of flow over the bridge deck, with boundary conditions taken from the Delft model. The VOF model then allowed calculation of lift force, drag force, and overturning moment on the bridge deck. Results show that factors contributing to failure included the presence of a seawall near the bridge, inclination (superelevation) of the deck upward toward the ocean, sediment entrained in the water, and air trapped between girders.

Performance Model of Archimedes Screw Hydro Turbines with Variable Fill Level

Abstract: Archimedes screw generators (ASGs) are beginning to be widely adopted at low-head hydro sites in Europe due to their high efficiency, competitive costs, and low environmental impact. ASGs are particularly appropriate for low-head sites. Power is transferred from a water flow to an Archimedes screw by the distribution of static pressure produced by the water volumes between the flights of the screw. Two theoretical models based on quasi-static pressure analysis are developed to predict the performance of ASGs. The first model uses idealized geometry, while the second incorporates the geometric properties of a rotating Archimedes screw, including slope, pitch, and inner and outer diameter. The second model was also formulated to simulate the performance of Archimedes screws operating across a full range of fill levels from empty to overfull. Both models predict that if all friction losses and entry and exit effects are neglected, the Archimedes screw can convert all potential energy in a water flow ...

Two-Dimensional Features of Viscoelastic Models of Pipe Transients

Abstract: Transients in pressurized polymeric pipes are analyzed by means of a two-dimensional (2D) Kelvin-Voigt viscoelastic model, calibrated by means of a microgenetic algorithm on the basis of pressure traces. The reliability of the proposed model is then tested by comparing numerical and experimental profiles of the axial component of the local velocity, the latter measured by means of an ultrasonic Doppler velocimeter. Differences between transients in viscoelastic and elastic pipes are pointed out by considering a 2D model in which an elastic behavior is assumed for pipe material. The comparison between the two 2D models allows attribution of the faster decay of pressure oscillations and velocity profiles to viscoelasticity because of the time-shift between pressure oscillation and retarded circumferential strain. The 2D analysis shows that the viscoelastic model generally presents flatter velocity profiles with respect to the elastic model.

Using both free surface effect and sediment transport mode parameters in defining the morphology of river dunes and their evolution to upper stage plane beds, doi: 10.1061/(ASCE)HY.1943-7900.0000873

Abstract: Dunes are common bed forms in sand bed rivers and are of central interest in water management purposes. Due to flow separation and associated energy dissipation, dunes form the main source of hydraulic roughness. A large number of dune dimension data sets was compiled and analyzed in this study—414 experiments from flumes and the field—showing a significantly different evolution of dune height and length in flows with low Froude numbers (negligible free surface effects) and flows with high Froude numbers (large free surface effects). For high Froude numbers (0.32–0.84 ), relative dune heights are observed to grow only in the bed load dominant transport regime and start to decay for u ∗ /w s (suspension number) exceeding 1. Dunes in this case are not observed for suspension numbers greater than 2.5. For low Froude numbers (0.05–0.32), relative dune heights continue to grow from the bed load to suspended load dominant transport regime. Dunes in this case are not observed for suspension numbers greater than 5. It was concluded that for reliable predictions of dune morphology and their evolution to upper stage plane beds, it is essential to address both free surface effects and sediment transport mode.

Mean Flow Characteristics in a Rock-Ramp-Type Fish Pass

Abstract: Detailed mean flow characteristics generated by a staggered arrangement of boulders in a rock-ramp-type naturelike fish pass were investigated experimentally at three different channel slopes (5%, 3%, and 1.5%). The results showed that this type of fish pass can produce adequate water depth and favorable flow velocity suitable for fish passage. Three different characteristic velocity regions were identified, namely, downstream of boulders (wake region), intermediate region, and upstream of boulders. Some general correlations were developed for predicting the flow depth and velocity in a rock-ramp fish pass as a function of normalized discharge. Moreover, a flow-resistance analysis based on basic concepts for wake-interference flow regime in this fish pass has resulted in a general equation for the average velocity. This study improves the understanding of the complex flow characteristics in a rock-ramp fish pass.

Modeling Flow Exchanges between a Street and an Underground Drainage Pipe during Urban Floods

Abstract: Modelling floods in urban areas generally requires the modelling of both surface and subsurface flows, along with the exchange discharges between these flows. These latter exchanges are studied on an experimental facility at the Ujigawa Open Laboratory of Kyoto University representing a typical urban drainage system with a single street connected through inlets to a drainage pipe located underneath. An exchange model is developed for the cases in which exchange flows are pressurized, applying a head balance between the surface and subsurface layers and using common head loss formulae. Results of the exchange model agree with experimental measurements and show that, for this experimental setup, the exchanges cannot be modelled by fitting a simple and commonly used orifice-type equation. A hydrodynamic model coupling the one-dimensional (1D) and two-dimensional (2D) shallow water equations for, respectively, the pipe and the street flows and including the analytical exchange model is used to simulate the experimental flows. The numerical model can simulate the global characteristics of both street and pipe flows but shows some discrepancies concerning local perturbations of street flow because of the exchange processes.

Turbulence Characteristics in Supercritical Open Channel Flows: Effects of Froude Number and Aspect Ratio

Abstract: An experimental investigation of supercritical uniform and gradually varied open channel flows is presented for a wide range of Froude numbers and flume width-to-flow depth aspect ratios. The instantaneous streamwise and vertical flow velocities were measured in a laboratory flume over the entire width using a two dimensional–laser Doppler anemometry (2D-LDA) system to determine turbulence intensities, and bed and Reynolds shear stresses. The mean velocity patterns show undulation across the flume, indicating the presence of counterrotating secondary current cells. These currents redistribute turbulence intensities and bed and Reynolds shear stresses across the flume. For aspect ratios ≤ 4−5, i.e., narrow open channel flow, the velocity-dip phenomenon is identified both in the streamwise velocity and the Reynolds shear stress distributions. For high aspect ratios, i.e., wide open channel flow, the strength of secondary currents diminish toward the flume center, resulting in a 2D flow farther away ...

Further Developments in Rapidly Decelerating Turbulent Pipe Flow Modeling

Abstract: In the last two decades, energy dissipation in unsteady-state pressurized pipe flow has been examined by various authors, where the instantaneous wall shear stress is split into a quasi-steady and an unsteady shear stress component. The focus of most past studies is on formulating expressions for the unsteady wall shear stress, but there has been less work on the key parameters governing the dominance of unsteady friction in transient flows. This paper derives an expression for the head envelope damping for turbulent flows in smooth and rough pipes and provides new and carefully measured field data for the initial (i.e., pretransient) Reynolds number, R0, that ranges from 97,000 to 380,000. The analytical solutions is derived on the basis of one-dimensional (1D) water hammer equations in which the unsteady component is represented by existing convolutional unsteady friction formulas for both smooth and rough turbulent subregimes. The analytical solution is used to formulate general, encompassing a...

Suction Effects on Sediment Transport in Closed-Conduit Flows

Abstract: Laboratory experiments were conducted to investigate the influence of suction on sediment transport in closed-conduit flows in this study. The results show that the bed load transport rate essentially remains unchanged for small values of suction rates before abruptly increasing beyond a certain threshold. Theoretical analyses of the forces acting on a spherical particle also are conducted and a conceptual model set up to analyze suction effects on particle mobility by considering the near-bed velocities. The model hypothesizes that (1) the bed particle experiences an additional downward vertical drag force induced by suction; and (2) increasing suction will lead to larger horizontal and vertical near-bed velocities, which enhances both the driving force and effective weight of the particle. To qualitatively examine how suction affects the near-bed flow behavior, physical modeling capability software was used to simulate the physical system and the results confirm that the near-bed velocities incr...

Straightforward Transient-Based Approach for the Creep Function Determination in Viscoelastic Pipes

Abstract: This work introduces a simple and straightforward approach for the creep function determination in viscoelastic pipes on the basis of transient flow analysis. The governing equations are expanded and analytically solved for the first half period of the transient. This solution results in a direct formula for the viscoelastic Joukowsky pressure head as a function of the creep function coefficients which are a priori unknown. Utilizing the measured data, only in the first half water hammer period and the proposed viscoelastic Joukowsky formula, the problem unknowns are determined. To investigate the method’s merits and limitations, two experimental polyethylene pipes are taken into account from the literature. The results show that the proposed approach works very well for long enough pipelines which are completely crept in the half period of the transient flow. The method is found to be computationally efficient and easy to implement in comparison with traditional inverse transient analysis techniques.

2D Process-Based Morphodynamic Model for Flooding by Noncohesive Dyke Breach

Abstract: Inundation models based on the shallow water equations (SWE) have been shown to perform well for a wide variety of situations even at the limit of their theoretical applicability and, arguably, somewhat beyond. One of these situations is the catastrophic event of floods induced by dyke breach and consequent dyke erosion. The dyke collapse is often not sudden—as assumed by many flood simulations in which the dyke boundary is treated as a “dam-break.” The dyke erosion is a gradual and complex process that delays the onset of the flood, affecting the hydrograph of the flow. To simulate correct temporal passage of a flood, it is important to understand the rate at which these dykes collapse. In this paper, an overtopping flood event combined with dyke erosion is simulated. The model is built upon the two-dimensional (2D) shallow water equations together with sediment-flow interactions and incorporates a sediment transport equation. The model is solved using a second-order Godunov-type finite volume me...

Local Scour around a Model Hydrokinetic Turbine in an Erodible Channel

Abstract: Laboratory experiments were performed to study the effect of an axial-flow hydrokinetic turbine model on an erodible channel under both clear water and live-bed conditions. Clear water experiments were performed at two scales with a local bed shear stress just below the critical state. Live-bed experiments, performed at small scale, examined the interactions between relatively large-scale bedforms and the flow induced by an axial flow turbine. Spatiotemporal topographic measurements were obtained by sonar and by a state-of-the-art high-resolution scanning system integrated into an automated data acquisition carriage designed and fabricated at the St. Anthony Falls Laboratory at the Univ. of Minnesota. Results indicate that the presence of the turbine rotor increases the local shear stress resulting in accelerated and expanded scour development when compared with typical bridge pier scour mechanisms. The inferred key difference is the alteration of the flow patterns in the rotor wake leading to an ...

Large-Scale Experiment and Numerical Modeling of a Riverine Levee Breach

Abstract: This study aims to clarify the mechanism of riverine levee breach and propose a new numerical model for that phenomenon. Large-scale experiments of overtopping breach were performed using an experimental flume located on the floodway of an actual river channel. By taking advantage of the scale of the flume, the levee breach process was monitored with state-of-the-art observation devices under highly precise hydraulic conditions. Four test cases were performed with variations of inflow rate, levee material, and levee shape, and the levee breach was monitored quantitatively using acceleration sensors installed in the levee body. From the results of the experiments, the breach process is categorized into four stages, focusing on the breach progress and hydraulic characteristics. It was determined that the correlation between the breached volume and the hydraulic quantities of velocity, water level, and Shields number can be expressed by an equation similar to that for bed load transport. Finally, a t...

Measurement of Gravel-Bed Topography: Evaluation Study Applying Statistical Roughness Analysis

Abstract: In this two-part study, experiments are conducted to evaluate available topography measurement techniques for gravel beds in a laboratory flume and to study their suitability for statistical roughness analysis. The available instruments for this study include (1) an acoustic bed profiler; (2) a hand-held laser scanner; and (3) two digital consumer cameras forming a stereophotogrammetric system, and are employed to obtain digital elevation models (DEMs) of water-worked gravel beds. In the first part of the study, the three measurement techniques are reviewed and their feasibilities for future grain-scale roughness work assessed, based on the obtained elevation datasets. Water-worked gravel-bed topographies are measured with all three available measurement techniques. The analysis of the DEMs concentrates on using probability distribution functions (PDFs) and second-order structure functions of bed elevations. Roughness coefficients are determined and used as a benchmark for comparison of the three ...

Influence of Cohesion on River Bed Scour in the Wake Region of Piers

Abstract: Studies on scour in the wake region of piers in cohesive sediments containing gravel were not reported in literature, to the best of our knowledge. Results from the laboratory experiments based study on the process of wake scour are presented here. The sediment used for the experiment were of two types: (1) fine gravel mixed with clay in proportions varying from 20% to 60% by weight, and (2) fine gravel and fine sand in equal proportion by weight mixed with clay in proportions varying from 20% to 60% by weight. The experiments revealed that the process of scour as well as depth, shape, and geometry of scour hole developed in such cohesive sediment were significantly different from that of cohesionless sediments. Proportion of clay fraction and unconfined compressive strength of cohesive sediment mixture were found to be the most significant variables controlling the depth of scour in the wake of piers. On the basis of dimensional considerations, relationships have been proposed for the estimation ...

Stability Analysis of Semicohesive Streambanks with CONCEPTS : Coupling Field and Laboratory Investigations to Quantify the Onset of Fluvial Erosion and Mass Failure

Abstract: The overarching goal of this study is to perform a comprehensive bank stability analysis that is phenomenologically sound by considering both mass failure and fluvial erosion. The nature of this study is twofold. First, field and experimental analyses are conducted to generate data for channel cross-section properties, soil index properties, and mechanical and erosional strengths at two sites in a representative, midsize, midwestern stream in southeastern Iowa that is subjected to frequent flash floods and characterized by active fluvial erosion and cantilever failure. Second, the channel surveys and data obtained from the field and laboratory analyses are used as input parameters for an established one-dimensional, channel evolution model, namely, the conservational channel evolution and pollutant transport system (CONCEPTS, version 2.0, Langendoen and Alonso 2008), to estimate the factor of safety for mass failure (FSm) and fluvial erosion (FSf) and simulate the bank retreat as a result of eithe...

Detection of localized deterioration distributed along single pipelines by reconstructive MOC analysis

Abstract: The detection of localized deterioration that is distributed along pipelines, including wall thickness reduction caused by large scale corrosion, is essential for targeted pipeline maintenance and the prevention of pipe failure. This paper proposes a novel technique for the detection of distributed deterioration along a pipeline by estimating the distribution of pipeline properties using a measured pressure transient trace. The proposed technique is referred to as reconstructive method of characteristics (MOC) analysis, and it is an inverse process of the traditional forward MOC calculation. The reconstructive MOC analysis reconstructs the MOC grid and estimates the pipe parameters, such as impedance and wave speed, reach by reach from downstream to upstream. Numerical simulations are performed on a pipeline with three pipe sections of impedance changes. These deteriorated sections are accurately detected and located by using the new technique. Experimental verification is also performed by succes...

Numerical Modeling of Turbulent Buoyant Wall Jets in Stationary Ambient Water

Abstract: The main focus of this study is on the near-field flow and mixing characteristics of the thermal and saline wall jets. A numerical study of the buoyant wall jets discharged from submerged outfalls (e.g., from desalination plants) has been conducted. The performance of different Reynolds-averaged Navier-Stokes (RANS) turbulence models has been investigated and various k-e, k-ω, and other turbulence models have been studied. The results of cling length, plume trajectory, temperature dilutions, and temperature and velocity profiles are compared to both available experimental and numerical data. It was found that two models perform best among the seven models chosen in this paper. According to the results from different simulations, the paper proposes corresponding relationships and comparative graphs that are helpful for a better understanding of buoyant wall jets.

Hydraulics, Air Entrainment, and Energy Dissipation on a Gabion Stepped Weir

Abstract: In the last decades the design of stepped spillways regained some interest because of their suitability with new construction methods including gabions. The hydraulic performances of gabion stepped weirs were investigated experimentally in terms of the flow patterns, air-water flow properties, and energy dissipation. A laboratory study was conducted in a 26.6° slope (1V:2H) and 0.10-m step height facility, with both smooth impervious and gabion steps. The visual observations highlighted the seepage flow through the gabions, inducing a modification of the cavity flow especially in the skimming flow regime. In skimming flows, higher velocities were measured at the downstream end of the gabion stepped chute, associated with smaller energy dissipation rates and lower friction factors, compared to the smooth impervious stepped chute data.

Mixing of 30° and 45° Inclined Dense Jets in Shallow Coastal Waters

Abstract: This study experimentally investigates the effect of shallow water depth on the mixing of 30° and 45° inclined dense jets. Three different mixing regimes were identified, namely, the full submergence, plume contact, and centerline impingement regimes. The mixing characteristics in these three regimes, including the jet trajectory and minimum dilution at the water surface (SS) as well as at the return point near the seabed (Sr), were quantified with respect to the densimetric Froude number (F) and cover water depth (H). The nondimensional cover water depth, H/D, was found to be a suitable normalization parameter for shallow water scenarios. The transitional F·D/H among the regimes, the asymptotic limits of the minimum surface dilution at large F, and the various linear coefficients were also determined. Overall, it was found that the surface constraint in the plume contact and centerline impingement regimes, lengthens the jet-spreading distances and reduces the surface dilution, while the bottom di...

Multiport Diffusers for Dense Discharges

Abstract: Comprehensive laboratory experiments on multiport diffusers for dense effluents such as brine into stationary receiving waters are reported. Tracer concentration fields were mapped in three dimensions by laser-induced fluorescence (3DLIF). The effect of port spacing is described by s/dF where s is the port spacing, d the nozzle diameter, and F the jet densimetric Froude number. For s/dF>∼2, the jets did not merge, and the results followed expected asymptotic solutions for single jets. For s/dF<2 the jets merged, but did not follow expected asymptotic line source solutions. As the port spacing was reduced, the rise height and other geometrical variables decreased. The dilutions also decreased, but much more rapidly than predicted. These were caused by Coanda effects and merging. The Coanda effect caused an under pressure on the interior jet surfaces which caused them to curve more sharply inwards. This shortened their trajectories, reducing the external surface area available for entrainment. Jet m...

Effects of step pool porosity upon flow aeration and energy dissipation on pooled stepped spillways

Abstract: The hydraulics of stepped spillways with flat steps has been studied for the last three decades, including for embankment dam slopes, but studies of alternative stepped designs are limited. In this study, a pooled stepped spillway was investigated in a relatively large-size facility, and three different pool wall porosities were tested. The flow patterns, the macro- and microscopic air-water flow properties, and the energy dissipation performances were recorded; the results were compared with the flat stepped spillway design for the same chute slope (θ=26.6°). The investigations highlighted a close agreement between air-water flow properties on the configurations in terms of void fraction, turbulence levels, bubble count rate, and chord sizes. The interfacial velocity distributions showed larger interfacial velocity on the pooled step configurations of approximately 5–10% linked with a reduced flow depth. On the porous pooled stepped spillways, the interfacial velocities within the cavity highligh...

Closure of "Skimming, Nonaerated Flow on Stepped Spillways over Roller Compacted Concrete Dams"

Abstract: AbstractThe nonaerated region may occupy a large portion of the skimming flow in steep, stepped spillways, particularly for relatively high unit flow rates. In spite of the numerous contributions on the hydraulic properties at both the inception point of air entrainment and the aerated region, much less is known regarding the flow in the nonaerated region. In this paper, new empirical evidence, based on an extensive data set obtained during several years in a large-scale facility, sheds light on the features of the nonaerated-flow region. Diverse ways to locate and estimate the main hydraulic properties at the inception point are first discussed and compared. Then, expressions capable of characterizing the main flow variables along the nonaerated region are presented, namely, the boundary-layer development, the velocity distribution, the equivalent clear-water depth, the characteristic depth taking into account the free-surface unsteadiness due to turbulence, and the energy dissipation. The energy dissipa...

Stage-Discharge Prediction in Compound Channels

Abstract: The failure of conventional methods for discharge prediction in compound channels results from their ignorance of the loss in conveyance arising from the complicated flow interaction between the main channel and its associated floodplains. In this paper, a new method is presented for assessing the stage-discharge relationship and the discharge distribution in compound channels by considering both the momentum transfer between the upper and lower main channel flows and that between the upper main channel and its adjoining floodplain flows. A calibration using data from the laboratory channels and three natural rivers demonstrates that the presented method can give predictions that agree better with the experimental and field data. The computed results also show that the method not only is well capable of predicting the discharge distributions of the floodplain and the whole main channel, but also of predicting the discharge distribution in the lower main channel. In addition, the momentum transfer ...

Simplistic Design Methods for Moderate-Sloped Stepped Chutes

Abstract: Numerous research contributions have been made on the hydraulic properties for steep, stepped chutes Stepped chutes applied to more moderate slopes like those for aging embankment dams are a growing trend, and research activities as a result have increased in this arena Although numerous stepped chute design guidelines are available, some of them are complicated and somewhat cumbersome to use A multiyear, large-scale physical model study was conducted for a broad range of step height (h) to critical flow depth (dc) ratio and chute slope (θ) (ie, 0035≤h/dc≤227 and 14°≤θ≤266°) The objectives of the study were to (1) evaluate the step height to critical flow depth ratio and the chute slope affect on the surface inception point, clear water and bulked flow depth, air concentration, and energy coefficient; and (2) develop practical, straight-forward design relationships for practicing engineers Detailed flow measurements were collected during testing, and the results were compared in terms of