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This study conducted experiments to investigate the impact of bottom obstacles, specifically broad-crest weir-type and cylindrical obstacles, on the flow within a sewer pipe. It was observed that these two types of obstacles, when possessing the same cross-sectional area and length, exhibited nearly equivalent hydraulic responses for both supercritical and subcritical flows. The obstacle height was found to be the primary factor responsible for choking and the transition between different flow regimes. The results of the one-dimensional analysis show that the threshold value of obstacle height depends on the approaching flow conditions, including the Froude number and the filling ratio that is defined as the flow depth to the pipe diameter. In the context of a partially blocked sewer, the relationships established by using the one-dimensional model between the size of the bottom obstacle and the inflow characteristics enable the identification of flow regimes, assessment of reduced hydraulic capacity, and evaluation of local energy loss. The findings of this study elucidate the hydraulic behavior of obstructed sewers, contributing to the development of more effective strategies for the identification of obstructions through monitoring data. [ABSTRACT FROM AUTHOR]

Under large unit discharges, stepped chutes are susceptible to cavitation damage due to lack of entrained air. Among various preaeration devices, the simple-structured abrupt contraction aerator (ACA) has a good performance on mild-slope (V:H=1∶5) stepped chutes with a combined flow pattern consisting of a jet and a local hydraulic jump. To advance the understanding of ACA hydraulics, this paper investigates the effects of stepped chute slope and slit location on jet dynamics. A series of physical experiments were carried out on a steep-slope (V:H=4∶5) stepped chute with varied slit locations. It was found that a jet was generated by ACA, and sufficiently aerated flow skimmed over the chute bottom with no black water, indicating an effective reduction of cavitation damage. The slit location had little effect on the flow patterns and aeration but might raise the flow profiles and enlarge the jet. Based on the experimental data, the empirical formulas for maximum height and distance of the jet are finally presented to provide references for sidewall design. [ABSTRACT FROM AUTHOR]

These differences become more important for the thicker probes with HT ht and HT ht , as shown by the authors ([9]). The study used dual-tip conductivity probes with two identical needle sensors having a longitudinal separation distance HT ht , mounted with a transverse separation distance HT ht (Fig. The bubble count rate HT ht was defined as the average number of bubbles encountered by each sensor per second. At two elevations ( HT ht in the shear layer and HT ht in the recirculation zone), the probability distribution functions (PDFs) of the raw signal are presented in Fig. [Extracted from the article]

This paper focuses on air–water interactions during pipe filling. The air–water mixed flow is related to a mobile hydraulic jump in the horizontal pipe section. The trapped water–air front at the crown of the pipe bridge determines the upstream boundary conditions for the stratified flow, suppressed hydraulic jump, and slug flow regions in the horizontal pipe section. The velocity field, the water level, and the pressure were measured at different stages of the transitional flow process. A full-scale two-phase computational fluid dynamics model, with two-equation eddy viscosity turbulence to account for small scales of motion, was used to predict the air pocket dynamics. The paper suggests that in the case of a frozen upstream water–air front, the formation of a hydraulic jump downstream can be explained by long-wave-type instability, which is confirmed by the free-surface supercritical flow Froude number condition. The hydraulic jump that merges stratified flow and slug flow is characterized by the speed of the surge wave, which is determined by the pressure, cross-sectional area of water flow, and density changes. A mixing efficiency parameter was introduced to explain the dissipation of turbulent energy due to the air–water mixing front of the suppressed hydraulic jump. [ABSTRACT FROM AUTHOR]

A major challenge of prototype air-water flow measurement is the limited endurance of fragile phase-detection needle sensors in a high-momentum flow with risks of debris damage and particulate erosion. In the present study, a thick-tip conductivity probe is manufactured with sturdier needle sensors than the commonly used laboratory-sized probes. The large sensor tip had low chance to pierce small air bubbles and water droplets, leading to deterioration in the signal output quality, which prevents derivation of basic air-water flow properties using the conventional signal processing technique. To extract valid phase information from the low-quality signal, calibration experiments were conducted in laboratory with reference to a regular-sized probe, to explore a proper signal processing method for the thick-tip probe. The method was validated, and the thick-tip probe was deployed in a field hydraulic jump measurement, allowing for access to the air-water flow characteristics of the prototype D-type jump with a Reynolds number of 1.88×106. Despite the effort of signal calibration and compensation, the use of the thick-tip probe does not guarantee accurate bubble size measurement and requires higher sampling frequencies. Therefore, probes with fine sensor tips are still preferable in prototype measurement. [ABSTRACT FROM AUTHOR]

Reaeration is a primary path of reoxygenation in streams, fundamental to environmental and ecological integrity. Previous laboratory studies of reaeration rates in subcritical flows showed large scatter in results, with differences in mass transfer coefficients of more than one order of magnitude between comparable flow conditions. Although supercritical flow is commonly observed in natural streams and engineered channels, systematic measurements of supercritical flow reaeration rates have been unavailable. Experiments in a laboratory open channel flume encompassing sub- and supercritical flows have been undertaken. The subcritical data were consistent with a large body of previous studies. Supercritical flows showed 6–10 times stronger reaeration rates than comparable subcritical conditions, while local rates at hydraulic jumps systematically exceed those in the supercritical flows upstream by a factor up to three. A close relationship between reaeration rates and turbulent dissipation rate is observed, and a systematic Froude number dependency is demonstrated for both sub- and supercritical flows. Observed mass transfer coefficients do not correlate as well with flow Reynolds number and shear Reynolds number. The higher reaeration rates associated with supercritical flows indicates that a change in open channel flow regime for the same Reynolds number may be used to improve water quality. [ABSTRACT FROM AUTHOR]

The dimensionless mean pressure heads (i.e., HT ht or HT ht ) along the stilling basin with various slopes decrease first and then start to increase in the flow direction until it reaches a constant value of 1.0. Especially, Eq. (9) can exhibit a good agreement of the mean pressure distribution when only the sequent flow depth HT ht is known. 1(a), both the mean pressure head HT ht and the streamwise position HT ht are normalized with the critical flow depth HT ht . [Extracted from the article]

Understanding the air demand of a hydraulic jump in a closed conduit is important in hydropower operations and urban sewer designs. In this study, physical experiments are described to study flow regimes and the air demand of a hydraulic jump in a closed conduit with various submerged outlet depths. Flow regimes with a submerged outlet were defined following previous studies based on outlet depth. Free-surface supercritical flow with a hydraulic jump can induce a relative air demand (air flow rate to water flow rate) of approximately 3%–14%. If the hydraulic jump is followed by pressurized pipe flow, the air demand decreases with increasing outlet depth until the return roller is fully developed in the pipe. For the partially submerged hydraulic jump, the relative air demand is significantly reduced to less than 1%. Field measurements of the air demand at the Hugh Keenleyside Dam, British Columbia, were consistent with the experimental measurements for the partially submerged hydraulic jump. The dynamics of the air pocket upstream of the hydraulic jump was studied. If the air supply was constrained by nozzles of various sizes placed on the top of the air vent, the air pressure in the closed conduit decreased and the hydraulic jump was pushed upstream. The energy loss coefficient in the air vent was also studied. [ABSTRACT FROM AUTHOR]

Yet, a recent data set ([10]) investigated the air-water flow properties in weak hydraulic jump with Reynolds number between HT ht and HT ht . Maybe the key outcomes are (1) a need for field measurements of air-water flow in large prototypes; and (2) the necessity for detailed air-water flow measurements in B-jump, to complement the present case study. A double-threshold technique, a differentiation technique, or a combination of signal thresholds and gradient threshold could be more suitable, although some validation would be required. [Extracted from the article]

Suitable Signal Processing for Better Phase Discrimination The discusser indicated that the phase discrimination from the conductivity probe signal, which was adversely affected by the field air-water flow environment, could be improved by adopting more robust signal processing techniques rather than a single-threshold method. Such a method may be also applied to the present case study for potential signal processing refinement, among the other techniques suggested by the discusser, given proper validation for the specific probe and test flow conditions. This is correct, and the employment of any signal processing method requires comprehensive laboratory calibration and validation under better-controlled flow and fluid conditions. [Extracted from the article]

Numerical simulation of undular hydraulic jumps, which occur at an inflow Froude number slightly above unity, remain an important and enigmatic challenge in hydraulic engineering. In this study, a systematic assessment of the two-dimensional (2D) Reynolds averaged Navier Stokes–volume of fluid (RANS-VOF) equations coupled with the k–ω shear stress transport (SST) turbulence model was carried out for the simulation of undular jumps. The modeling strategies adopted for obtaining a stable undular jump profile are highlighted in this paper. The correlation between turbulence intensity at the jump toe and jump characteristics is also demonstrated. Comparison of laboratory observations with results obtained from experiments conducted under different discharge, approach Froude number, and inflow conditions demonstrated that the proposed 2D RANS model can accurately reproduce the key free-surface characteristics corresponding to undular jumps. The model was capable of reproducing the velocity and pressure fields with greater accuracy than the depth-averaged model. The model was also successful in reproducing the bottom recirculation region below the first wave crest for undular jumps with partially developed boundary layer at the jump toe. The proposed 2D RANS-VOF computational fluid dynamics (CFD) model coupled with the k–ω SST turbulence closure equation is, therefore, recommended as an efficient tool for hydraulic computations, especially for the simulation of weak undular jumps. [ABSTRACT FROM AUTHOR]

This paper presents a case study of a prototype B-type hydraulic jump produced downstream an irrigation-regulating gate in a natural river. The inflow Froude number is Fr1=5.1 and the Reynolds number is Re=9×105. Detailed air–water flow properties and free-surface fluctuating features are investigated on site in the central flow region using intrusive phase-detection probes and nonintrusive acoustic displacement meters. Challenges in employing the phase-detection probe in high-momentum natural water are addressed, including the necessary postprocessing for uncertainty mitigation. While good agreement between the present data and previous laboratory measurements is achieved for the air concentration and interfacial velocity distributions, scale effects are observed for bubble frequency, challenging the validity of previous empirical prediction deriving from laboratory experiments. A greater percentage of large bubbles are detected in the full-scale jump. The free-surface fluctuating characteristics are investigated together with the surface wave propagation in the tailwater. The jump length and roller length in the B-jump are discussed with comparison to existing model equations. Although the investigation is limited to one case, it provides the first physical data obtained in full-scale natural water and an important benchmark data set for future study of scale effects in self-aerated open channel flows. [ABSTRACT FROM AUTHOR]

Scientists at the USDA Agricultural Research Service (ARS) Hydraulic Engineering Research Unit (HERU) conducted research on physical models of stilling basins (i.e., Types I, II, III, and IV) associated with stepped chutes to evaluate performance. Tests were conducted with naturally developing unit discharges (0.236 m2/s≤q≤0.930 m2/s) descending a 3(H):1(V) stepped chute flume designed with 0.15-m step heights at near prototype scale and Froude numbers near the stepped chute toe ranging from 4.1≤F≤4.6. Data and visual observations indicated that dissipation features like floor blocks, the end sill, or a dentated end sill effectively reduced wave oscillations and lessened the impact of propagating waves downstream. The study data appear to agree with other published data for stilling basins associated with smooth chutes; thus, design engineers should have confidence in applying the US Bureau of Reclamation (USBR) stilling basin design criteria to basins associated with stepped chutes. Pressure profiles indicated positive values relative to stilling basin floor elevation along the length of all stilling basins. Additionally, pressure peaked near the basin entrance, the floor blocks, and the end sill. [ABSTRACT FROM AUTHOR]

Hydraulic jumps, frequently present in energy dissipation structures, have been thoroughly investigated over the past 70 years. However, studies have focused primarily on the more common and more stable cases of large Froude number jumps. Investigations on low Froude number jumps, usually called transition jumps, are scarce, although they are used in a significant number of run-of-the-river, high-discharge, and low-head dams. This paper addresses the characterization of hydrodynamic pressures of low Froude number jumps. A two-dimensional experimental facility was used for that purpose. Results were compared with those from published studies covering transition jumps and stabilized jumps, to identify differences and similarities between them. The analysis considered common dimensionless statistical parameters, duly nondimensionalized. It was found that, for most of these parameters, low Froude number jumps behave differently from stabilized jumps. This can be attributed mainly to the hydraulic jump's oscillating jet formed under the surface macroturbulent roller, as well as to the partially developed boundary layer of the incoming flow in low-head spillways. [ABSTRACT FROM AUTHOR]

A hydraulic jump in a stilling basin at the base of spillway is typically characterized by preaerated inflow conditions. This paper presents an experimental study of high-Froude-number hydraulic jumps with different preaeration levels. Two characteristic lengths of the jump, namely the jump length and roller length, which are defined in various studies but sometimes not clearly distinguished, are obtained from the same flows by means of free-surface and air-water flow velocity measurements, respectively. The effects of changes in preaeration level are found to be opposite on the jump and roller lengths. Enhanced preaeration allows for a shorter length of the hydraulic jump, and the jump roller is elongated to achieve the same energy-dissipation rate in a shorter distance. The results imply a predominant effect of energy-dissipation enhancement over reductions associated with the extra air-water mixing and bubble-turbulence interplay. Tailwater wave characteristics are presented, showing similar frequencies for the far-field wave fluctuations and upstream jump toe oscillations on the two ends of the jump. [ABSTRACT FROM AUTHOR]

Above the higher HT ht values location, a local minimum HT ht value appears at HT ht in all the cross sections measured, which seems to be related to the abrupt change of the flow at the upper edge of the shear region. 6 of the original paper), and the HT ht value tends to be closer to unity. In the region HT ht , the HT ht values at cross sections HT ht to 0.8 m are around 0.2-0.4, increasing their value as the cross section is located further away from the impingement jet. [Extracted from the article]

Advances in dam construction techniques have significantly increased the number of stepped spillways implemented worldwide. Although stepped chutes provide enhanced energy dissipation along the chute, as compared to smooth chutes, an adequate energy dissipater is usually needed at their toe to govern the remaining energy. Stilling basins downstream of stepped spillways are currently designed using the approaches developed for smooth chutes. As a stepped surface alters the structure of the approaching flow, such practice is questionable. This paper reports a study on the effect of stepped chute approach flows on the performance of a classical stilling basin. Physical modeling was conducted using a large-scale facility of a smooth and stepped spillway with a 30° sloping chute. Experiments were performed under different discharges, two step heights, and variable approach flow aeration. The characteristics of the hydraulic jump were described, focusing mainly on flow depth, bottom pressure, and length. The results indicated a significant effect of stepped chute approach flows on bottom pressure and length of the hydraulic jump. Near the jump toe, pronounced fluctuating and extreme pressures were observed after stepped chutes and attributed to the higher turbulence level of the incoming flow. The normalized hydraulic jump lengths were found to be about 17% longer downstream of stepped chutes as compared to smooth chutes. [ABSTRACT FROM AUTHOR]

A new, concise theoretical model for simulation of unsteady, nonhydrostatic two-layer flow is presented. The formulation is systematically developed from the equations of motion of an ideal fluid using a perturbation technique with shallowness as the small parameter. The advantage of this model over many models in the field is that the shape of streamlines, or velocity and pressure distributions, are dictated by the model rather than being predetermined. This model also relaxes further assumptions involved in the previous formulations and can be used to simulate different two-layer flow cases. In some situations, simulation is impossible without considering the nonhydrostatic pressure, one of which is a two-layer approach-controlled flow. A laboratory transient two-layer flow experiment is conducted to examine transition to the approach-controlled flow, and the new equations are successfully applied to model this transient flow using a total variation diminishing (TVD) MacCormack scheme. Furthermore, new equations for single layer unsteady nonhydrostatic flow are presented and two-steady flow cases of flow over an obstacle and an undular hydraulic jump are excellently simulated. [ABSTRACT FROM AUTHOR]

This paper presents a new method that is able to define the hydraulic jump peculiarities in rough-bed conditions. The findings of this paper improve the literature and guidelines on the design of a stilling basin over a rough bed, taking into account both the Froude number and bottom roughness. It starts with experimental evidence on the flow field and considers the characteristic length scale of the phenomenon as drawn from velocity measurements in the hydraulic jump region. The assumption in the length scale leads to different results compared with the known formulas in the literature related to the hydraulic jump on a rough bed. The formulas in the literature consider the effects of gravel roughness only, neglecting the effects due to the incident Froude number in the evaluation of integrated bottom shear stress. The comparison of the presented results with experimental measurements in the literature highlights the reliability and accuracy of this novel method. This method is theoretically based, but because it needs experimental data in application, it can be considered semiempirical. The results presented here allow for the design of hydraulic jump stilling basins over rough beds. [ABSTRACT FROM AUTHOR]

A classical hydraulic jump with Froude number (Fr1=6) and Reynolds number (Re1=210,000) was characterized using the computational fluid dynamics (CFD) codes OpenFOAM and FLOW-3D, whose performance was assessed. The results were compared with experimental data from a physical model designed for this purpose. The most relevant hydraulic jump characteristics were investigated, including hydraulic jump efficiency, roller length, free surface profile, distributions of velocity and pressure, and fluctuating variables. The model outcome was also compared with previous results from the literature. Both CFD codes were found to represent with high accuracy the hydraulic jump surface profile, roller length, efficiency, and sequent depths ratio, consistently with previous research. Some significant differences were found between both CFD codes regarding velocity distributions and pressure fluctuations, although in general the results agree well with experimental and bibliographical observations. This finding makes models with these characteristics suitable for engineering applications involving the design and optimization of energy dissipation devices. [ABSTRACT FROM AUTHOR]

If optical or any type of nonintrusive sensing technique can provide adequate information to reproduce two-phase flow boundary conditions, internal air-water flow structures might be predicted by analytical air entrainment models. For full-scale prototype conditions with typically large Reynolds numbers, ensuring good probe sturdiness and signal processing quality, as discussed in the original paper, does not guarantee a successful collection of detailed air-water flow information at large hydraulic structures in operation. As the discussers implied, the effect of sensor size on bubble detection and measurement of air-water flow properties can vary with the flow's Reynolds number at different model scales. [Extracted from the article]

Hydraulic jumps are characterized by strong flow turbulence, flow aeration, and three-dimensional flow motions. Whereas comprehensive research into hydraulic jumps on smooth bed has improved the understanding of flow aeration and turbulence, limited research has been done of hydraulic jumps on rough beds. Herein novel experiments were conducted in hydraulic jumps on uniformly-distributed bed macroroughness. Both air-water flow patterns and basic air-water flow properties were investigated. The hydraulic jumps on the rough bed exhibited some remarkable differences compared with smooth bed jumps including some preaeration of the flow upstream of the jump, an upwards shift of the jump roller and a clear water-flow region underneath the jump. Air-water flow measurements were conducted with a phase-detection probe, showing similar distributions of air-water flow properties for the rough and smooth bed jumps. Comparative analyses highlighted some distinctive effects of the bed roughness including an upwards shift of the hydraulic jump and an increase in bubble count rate and void fractions in the region close to the jump toe. In the second half of the hydraulic jumps, the rough bed led to a clear-water region with large-scale vortices which were advected downstream. The present study highlighted the potential that improved and nonstandard invert designs may have for flow manipulations and design enhancements. [ABSTRACT FROM AUTHOR]

For HT ht in the downstream region, a self-similarity relationship for the bubble frequency distribution is obtained. With increasing air concentration, the bubble size decreases until the local air concentration reaches approximately HT ht , where the local HT ht and subsequently increases to HT ht . [Extracted from the article]

A supercritical open-channel flow can skirt an emerged obstacle by using two distinct forms of workaround: a detached hydraulic jump or a so-called wall-jet-like bow wave. These two forms stem from the properties of supercritical flow and are described in detail. Experiments assess the conditions of appearance of one form or the other, depending on both upstream Froude number and flow-depth to obstacle-width ratio. A conceptual model, based on mass conservation, reproduces and explains the corresponding transition. For the wall-jet-like bow wave, additional information is given regarding water-depth oscillations; the associated Strouhal number show they are caused by reverse spillage on the obstacle face. Implications of the present results on scouring and forces exerted by the flow on structures justify future works on the subject. [ABSTRACT FROM AUTHOR]

One of the main causes of lining damage in stilling basins and at the toe of chute spillways is the global instantaneous uplift forces due to the difference in pressure acting on the upper and the lower surface of protection slabs or rock elements. Spillway stilling basin linings can be built according to two different techniques: using sealed joints or unsealed joints. In the case of sealed joints, the pressure underneath the slab is constant and the uplift force results from the pressure fluctuations acting on the slab. In the case of unsealed joints, the pressure propagation at the lower surface of the slab, being transferred through the joints, should also be considered. The aim of the paper is to study, define, and compare the design criteria in these two cases. In the present study, the pressure field on the slab is evaluated according to a recent method based on the Taylor hypothesis, whereas the pressure propagation under the slab is computed by a new 3D model based on unsteady flow analysis of seepage through porous media. By this approach, it is possible to consider the effect of finite thickness foundation layers, typical in the case of weirs for run-of-river power plants, earth dams, and rock-fill dams. Furthermore, to complete the presented design criteria, the dynamic behavior of anchored slabs is experimentally investigated with reference to the sealed joint case due to a lack of studies in the literature. [ABSTRACT FROM AUTHOR]

The paper presents the results from detailed experiments of the statistical structure of turbulence pressure fluctuations at the bottom of hydraulic jumps, with special reference to the spillway stilling basins lining design. Here, the whole spatial correlation structure of the fluctuating pressure field is required in order to evaluate slab stability. This is computed via simultaneous acquisition of the point pressure fluctuations on a dense grid in the hydraulic jump region, requiring a severe experimental work. As an alternative, one can evaluate the pressure spatial correlation structure via autocorrelation using one point pressure acquisition and applying the Taylor hypothesis. To adopt the Taylor hypothesis, one must know the pressure propagation celerity in space that can be obtained by comparing the whole spatial pressure correlation with the pivot point pressure autocorrelation. The experiments were performed by simultaneous pressure acquisitions at the bottom of a hydraulic jump for Froude numbers of the incident flow ranging from 4.9 to 10.3. From experiments, a criterion to define the pressure celerity as a function of the incident flow velocity is presented. The results highlight a good agreement between the relevant pressure statistical parameters as measured and the ones computed using the Taylor hypothesis. The comparison between the slab thicknesses, as computed via Taylor hypothesis, with the ones retrievable in literature, as obtained by direct force measurement on instrumented slabs in laboratory conditions, highlights the accuracy of the proposed approach that presents undeniable practical advantages. [ABSTRACT FROM AUTHOR]

Free surface, axially symmetric shallow flow is analyzed in both the centrifugal and centripetal directions. Referring to the inviscid steady flow over a flat plate characterized by a unique value of specific energy, the analytical sub- and supercritical solutions are determined. Furthermore, the sub- and supercritical steady solutions for the flow with friction over a flat plate are determined, provided that inertial terms are important compared with frictional terms. In the inviscid case, the sub- and supercritical solutions over a bottom topography are determined, provided that the bottom unevenness is compatible with a continuous solution. In the fundamental case of inviscid flow over a flat plate, the discontinuous solution also is analyzed for a direct hydraulic jump imposed by proper boundary conditions. In the simple scheme of an inviscid shock of zero length, the jump position and the sequent depths are analytically derived, thus indicating that all results are uniquely functions of one dimensionless number, i. e., the specific energy ratio between the sub- and supercritical flows. [ABSTRACT FROM AUTHOR]

In an open channel, the transformation from a supercritical flow into a subcritical flow is a rapidly varied flow with large turbulent fluctuations, intense air entrainment, and substantial energy dissipation called a hydraulic jump. New experiments were conducted to quantify its fluctuating characteristics in terms of free-surface and two-phase flow properties for a wide range of Froude numbers (3.8 < F1 < 8.5) at relatively large Reynolds numbers (2.1 × 104 < R < 1.6 × 105). The time-averaged free-surface profile presented a self-similar profile. The longitudinal movements of the jump were observed, showing both fast and very slow fluctuations for all Froude numbers. The air-water flow measurements quantified the intense aeration of the roller. Overall the present findings demonstrated the strong interactions between the jump roller turbulence and free-surface fluctuations. [ABSTRACT FROM AUTHOR]

The flow structure of vertical and horizontal planes in a stilling basin with five parallel offset jets in a twin-layer configuration for four offset ratios () has been investigated. The velocity distribution was measured, processed, and subsequently used to characterize the flow structure. The flow pattern in the stilling basin exhibits a mixing flow pattern of jets and hydraulic jumps. As the downstream water depth increases in the stilling basin, five different flow patterns appear successively: free jets, hydraulic jumps, submerged jets and hydraulic jumps, mixed submerged jets and critical jumps, and mixed submerged jets and submerged jumps. The results indicate that the velocity distributions in the vertical and horizontal planes of the lower-layer orifices and in the potential core region of the upper-layer orifices are similar to the classical jet; in other regions, the velocity distribution is similar to the hydraulic jump. In addition, the energy dissipation ratio increases with the increasing Froude number, with a value of greater than 70% at . The energy dissipation ratio in the stilling basin with five parallel offset jets in a twin-layer configuration is, on average, 5% larger than that of the SBJ basin and 13% larger than that of the classical jump basin. [ABSTRACT FROM AUTHOR]

A hydraulic jump is a common phenomenon that can be observed in open channel flows such as rivers and spillways. It can cause damage of the downstream bed and bank of the channel due to the process of continuous erosion and degradation. In order to reduce the hydraulic jump destruction, the energy in the hydraulic jump must be dissipated as much as possible. One method to increase dissipation of energy is using a corrugated bed. In order to know the effect of a corrugated bed on the hydraulic jump, a smoothed particle hydrodynamics (SPH) model is applied to investigate the characteristics of hydraulic jumps in various corrugated beds. A variety of corrugated beds that are smooth, triangular, trapezoidal, and sinusoidal are considered. The opening of a gate is changed to adjust the hydraulic jump. The conjugate depth ratio, the jump length, the bottom shear stress distribution, and the energy dissipation are reported. The results of the present study are in a good agreement with previous studies. Energy dissipation is compared among corrugated beds and a smooth bed. It is found that the sinusoidal bed can dissipate more energy than other beds. As a result, corrugated beds can be used to enhance energy dissipation of hydraulic jump in the open channel. In general, the proposed SPH model is capable of simulating the effect of corrugated beds on hydraulic jump characteristics. [ABSTRACT FROM AUTHOR]

In urban drainage systems, it is usually necessary to split the storm water discharge among different sewer branches because of limited flow capacity of either hydraulic structures or sewer lines. For this purpose, sewer sideweirs and leaping weirs are generally used as diversion overflow structures. For supercritical approach flow, the former is not recommended because of the occurrence of hydraulic jumps, whereas the latter requires an outlet located below the approach flow sewer bottom. To overcome these constraints, a novel compact hydraulic structure is proposed. It consists of a frontal rectangular intake, representing the diversion sewer inlet, located in the approach flow sewer and parallel to its bottom. A 6.67:1 scale model was tested over a range of hydraulic and geometrical parameters to determine its head-discharge relationship, developing a dimensionless equation relating the diversion discharge to the geometrical properties of the intake under supercritical flow conditions. The limited hydraulic structure size provides cost-effectiveness and ease of installation and maintenance. [ABSTRACT FROM AUTHOR]

Hydraulic jumps at the tail end of spillways are usually induced by baffle blocks or other obstacles. Such jumps can also be induced by jets that oppose the main flow. Another application is to back up turbidity currents in reservoirs by means of opposing jets. This measure can be adopted when transfer tunnels feed water into the reservoir at a higher elevation near the dam. Stopping the turbidity current increases the local sedimentation rate. To reconcile the shallow water equations for turbidity currents with those for open channel flows, mass-based scales for the depth and velocity of both types of flows are outlined. The continuity and momentum equation for flows opposed by jets are then stated in terms of these scales and expressed by a single curve for both gravity currents and free surface flows. The corresponding results for free surface flows agree well with those of experiments carried out for this study. An application to turbidity currents is provided as well. [ABSTRACT FROM AUTHOR]

Stricter environmental regulations have led to new wastewater treatment plants and a centralization of existing wastewater treatment plants. Therefore, pressurized wastewater mains have become an indispensable link between the collection systems and the treatment plants. In urban areas in particular, these pipelines include many inverted siphons to cross other infrastructure, like railways, motorways, other pipelines, and buildings. Accumulation of air in downward sloping sections of these wastewater mains reduces the transport capacity significantly. A dominant air transport mechanism is the air-entraining hydraulic jump at the tail of an accumulated air pocket. The novelty of this paper is a systematic investigation of the influence of surface tension on the air discharge in downward sloping pipe sections. Experiments have been performed with clean water, surfactant-added water, and wastewater. The experiments with surfactant-added water confirm that the air discharge increases significantly at lower surface tension. However, the lower surface tension of wastewater does not enhance the air transport in comparison with the air transport in clean water. [ABSTRACT FROM AUTHOR]

This paper presents the results of an experimental investigation on the roller length of both classical and B-jumps on smooth beds. Using the measurements conducted in this investigation and those available in the literature, a new relationship is proposed for estimating the roller length of classical and B-jumps on smooth beds. Finally, it is demonstrated that the proposed equation is also applicable to estimate the roller length of hydraulic jumps on rough horizontal beds. [ABSTRACT FROM AUTHOR]

An experimental study was conducted investigating submerged hydraulic jumps with baffle blocks. An extensive series of tests were completed that covered a range of Froude numbers, submergence factors, and block arrangements. Dimensional analysis was used to interpret the results and study the effect of each parameter. Two flow regimes, the deflected surface jet (DSJ) and reattaching wall jet (RWJ), were observed. The occurrence of a particular regime depends on the block shape and location as well as the Froude number and submergence factor. The DSJ regime was found to dissipate more energy due to the formation of the deflected jet and its impingement on the water surface. The DSJ regime is almost as efficient in dissipating energy as the free hydraulic jump. This flow regime also had a smaller reverse flow region compared to the RWJ regime. Empirical equations were derived for predicting the critical values of the submergence factor at which each flow regime forms. The efficiency of the submerged hydraulic jump with blocks in dissipating energy was compared with that of free without blocks as a function of submergence factor. [ABSTRACT FROM AUTHOR]

An undular hydraulic jump on a smooth boundary occurs when the approaching flow Froude number marginally exceeds its critical value of unity. The free surface profiles of undular hydraulic jumps are studied theoretically by using the steady-state flow equation. It is established that the undular hydraulic jump phenomenon takes place because of the instability of the flow and can be described by the instability principle. The threshold of an undular hydraulic jump can be represented by a monotonic increasing curve of approaching flow Froude number versus boundary inclination. The elevation of the undular free surface increases with an increase in boundary inclination, but the amplitude of the free surface waves decreases with downstream distance. The theoretical results are well comparable with the experimental data. [ABSTRACT FROM AUTHOR]

This note presents the general features of velocity and variation in length scales of the transition expanding jump, free jump, and wall jet in the rectangular horizontal open channel. The experiments were performed for a range of Froude numbers from 2 to 6 and at an abrupt expansion ratio of 2. The results indicate that the postdepth y2 required to form an expanding jump is distinctly smaller than that for the corresponding classical jumps. The expanding jump length was 1.25 times the corresponding free jump length. The velocity profiles for the transition jumps were similar to those for the wall jet. For the transitional expanding jumps, the boundary layer thickness δ, normalized by the supercritical flow depth y1, grows more rapidly relative to the free jumps. The normalized boundary layer thickness δ in terms of the length scale of b equal to the flow depth y, where the velocity u is equal to half of the maximum velocity um, against the longitudinal direction x normalized by y1, which was stabilized at 0.31 for expanding jumps. The length scale L, equal to x where the maximum velocity is equal to half of the initial velocity u0, of the free jump was approximately 0.75 that of the corresponding transitional expanding jump. The growth rate of the length scale (b/y1) for the expanding jumps was approximately 2.4 times that of the corresponding wall jet and free jumps. [ABSTRACT FROM AUTHOR]

A new approach for studying forced hydraulic jumps below abrupt symmetric and asymmetric expansions is introduced. Intensive experiments for two expansion ratios, one asymmetry ratio, and different solid sill heights and locations were conducted specifically for the spatial jump case as a critical design case. A new parameter correlating sill height and sill location is presented and found to play an important role in the basin's design, scour, and flow patterns. Using this parameter gives distinguished relationships for predicting sequent depth, energy dissipation, and basin length for the preliminary or operating design in expected or unexpected flow conditions. Empirical equations and experimental regression curves are introduced to predict the sequent depth and the basin length at any sill height and sill location. Scour and flow patterns are intensively studied experimentally and qualitatively described for the symmetric and asymmetric basins with or without sills for the spatial jump. A numerical example is presented to illustrate the applicability of the study in preliminary and operating designs. [ABSTRACT FROM AUTHOR]

The article presents a study on energy dissipation and the turbulence production in hydraulic jumps of low inflow Froude number. It states that jumps' flow conditions below a sluice gate depend both in the inflow Froude and Reynolds number. It also presents the stream wise variation of vertical integral turbulence dissipation through measuring a wind tunnel. Furthermore, several energy equations for the mean flow, turbulence, and hydrostatic pressure to the jump zone are also presented.

A B-jump is defined as the jump having the toe section located on a positively sloping upstream channel and the roller end on a downstream horizontal channel. This jump often occurs in the stilling basins with a horizontal bottom and located downstream of a steep channel. For a B-jump, a completely theoretical approach is not sufficient to solve the momentum equation and to establish the sequent depth ratio. In this paper, by using the laboratory measurements carried out in this investigation, some available empirical relationships useful for estimating the sequent depth ratio are tested. Then, by using the Π theorem of the dimensional analysis and the incomplete self-similarity theory, a generalized functional relationship for estimating the sequent depth ratio for different types of jumps is deduced. The estimate of the coefficient appearing in this relationship is dependent on the particular type of jump. In conclusion, the analysis established that the sequent depth ratio for a B-jump depends on a parameter E accounting for the toe section position, the upstream Froude number F1, and the channel slope. [ABSTRACT FROM AUTHOR]