Use of Brink Depth in Discharge Measurement

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

Relatively Rough Flow Resistance Equations

The definitions of depth and hydraulic radius become ambiguous when bed roughness is large relative to flow depth. Various statistics are currently used to describe bed roughness and many different flow resistance formulas have been developed. The volumetric hydraulic radius Rv and the standard deviation of bed surface elevations dz are rational and unambiguous measures suitable for large relative roughness conditions. Their influence on flow resistance is investigated using conceptual models and digital elevation models of natural alluvial beds. The results show that head-losses for large-scale relative roughness beds can be related to (Rv/dz); the (Rv/dz) exponent of power-law flow resistance equations increases from 1/6 to more than 1/2 as relative roughness increases, and flow velocity can be determined from boundary topography measures, water level and slope, without any calibrated coefficients. An overlooked form of the log law, using standard deviation dz, performs as well as power laws for predicting flow resistance with high relative roughness and it reverts to the conventional log law when relative roughness is low. A field technique for determining Rv and dz is described.     

Numerical Modeling of Free Overfall

Free overfall is treated by using two-dimensional steady potential flow theory. Based on the theory of the boundary value problem of analytical function and the substitution of variables we derive the boundary integral equations in the physical plane for solving the free overfall in a rectangular channel. A numerical iterative method has been developed to solve these boundary integral equations. The free water surface profiles, pressure distribution, and the end-depth ratio are calculated for a wide range of bed slopes, bed roughness, and incoming upstream Froude number. The computed results agree well with the available experimental data.     

Variation of Roughness Coefficients for Unsubmerged and Submerged Vegetation

This paper investigates the variation of the vegetative roughness coefficient with the depth of flow. A horsehair mattress is used in the experimental study to simulate the vegetation on the watercourses. Test results reveal that the roughness coefficient reduces with increasing depth under the unsubmerged condition. However, when fully submerged, the vegetative roughness coefficient tends to increase at low depths but then decrease to an asymptotic constant as the water level continues to rise. A simplified model based on force equilibrium is developed to evaluate the drag coefficient of the vegetal element; Manning's equation is then employed to convert the drag coefficient into the roughness coefficient. The data of this study are compared with those of selected previous laboratory and field tests. The results show a consistent trend of variation for the drag coefficient versus the Reynolds number. This trend can be represented by a vegetative characteristic number k. Given information such as the bed slope, the height of vegetation, and k, one can apply the proposed model to predict the roughness coefficient corresponding to different flow depths.     

Hydraulic Jumps on Rough Beds

This paper presents the results of an experimental investigation on the hydraulic jump on horizontal rough beds. Experiments were carried out to study the effect of bed roughness on both the sequent depth ratio and the roller length. The investigation allowed the writers to positively test the reliability of a new solution of the momentum equation for the sequent depth ratio as a function of the Froude number and the ratio between the roughness height and the upstream supercritical flow depth. The applicability of some empirical relationships for estimating the roller length was also tested.     

Numerical Simulation of Flow over a Rough Bed

This paper presents results of a direct numerical simulation (DNS) of turbulent flow over the rough bed of an open channel. We consider a hexagonal arrangement of spheres on the channel bed. The depth of flow has been taken as four times the diameter of the spheres and the Reynolds number has been chosen so that the roughness Reynolds number is greater than 70, thus ensuring a fully rough flow. A parallel code based on finite difference, domain decomposition, and multigrid methods has been used for the DNS. Computed results are compared with available experimental data. We report the first- and second-order statistics, variation of lift/drag and exchange coefficients. Good agreement with experimental results is seen for the mean velocity, turbulence intensities, and Reynolds stress. Further, the DNS results provide accurate quantitative statistics for rough bed flow. Detailed analysis of the DNS data confirms the streaky nature of the flow near the effective bed and the existence of a hierarchy of vortices aligned with the streamwise direction, and supports the wall similarity hypothesis. The computed exchange coefficients indicate a large degree of mixing between the fluid trapped below the midplane of the roughness elements and that above it.     

Influence of Uncertainties in the Estimation Procedure of Floodwater Level

Despite the recent development of risk-based assessments in flood defense, in practice, flood levels in channels are generally estimated for a design return period by using the discharges of the same return period. The flood levels are also influenced by other factors such as bed roughness, flow area, wetted perimeter, and friction slope which are random in nature. The surveyed cross sections and calibrated values of roughness coefficients are generally used without any allowance for their variability to assess the water levels based on discharge of a selected return period. This simplifies a multivariate random process to a single-variate random process. When the uncertainties of selected influencing parameters were considered in sample studies using Monte Carlo simulation, it was found that the traditional procedures result in an underestimation of water level at high return periods and over estimation of water levels at low return periods. The overall effect is the diffusion of the density function from the center toward the tails of the distribution. Sample studies using the variation in channel roughness and friction slope indicated that the return period of the water level, based on a 100 year return period discharge, varied from 32 to 82 years, depending on the statistical properties of the influencing random parameters. The frequency analysis of water levels was undertaken by analyzing 25–800 million generated data sets.     

Investigating the Role of Clasts on the Movement of Sand in Gravel Bed Rivers

The bed morphology of mountain rivers is characterized primarily by the presence of distinguishable isolated roughness elements, such boulders or clasts. The objective of this experimental study was to provide a unique insight into the role of an array of clasts in regulating sand movement over gravel beds for low relative submergence conditions, H/dc<1, and flow depth, H, to the diameter of the clast, dc, a process that has not been studied thoroughly. To assess the role of clasts in controlling incoming sand movement, detailed flume experiments were conducted by placing 40 equally spaced clasts atop a well-packed glass bead bed for replicating the isolated roughness flow regime. The experiments were performed for moderate ( ～ 2.50τcr* where τcr* is the critical dimensionless bed shear stress) and high ( ～ 5.50τcr*) applied bed shear stress conditions, representative of gravel bed rivers. For comparison purposes, experiments were also repeated for nearly identical flow conditions but without the presence of clasts to discern the potential effects that clasts may have on sediment movement and hydraulics within the clast array region and also in the upstream section of the clast region where few observations exist. The experimental results revealed the formation of two distinguishable bed morphological features, namely a funnel shaped “sand ridge” upstream from the clast array region and small depositional “sand patches” around individual clasts. The sand patches were formed in the stoss region of the clasts, which contradicted previous observations of depositional patterns around clasts under high relative submergence conditions (H/dc>1) where, in this case, depositional patches were observed to have formed in the clast wake region. Furthermore, most of the incoming sand was found to be intercepted by the evolving sand ridge upstream from the clast array region with implications in the amount of sand entering the clast array region. The exiting bed-load rate was found to be reduced by a factor of ～ 5.0–20, depending on the prevailing flow conditions when experiments with and without clasts were compared under nearly identical flow conditions. The findings of this research, although limited to the isolated roughness regime, may have significant ramifications in stream restoration projects for the design of engineered riffle sections, which typically consist of an array of clasts installed to improve degraded waterways and aquatic habitat.     

Analyzing Turbulence Intensity in Gravel Bed Channels

In this paper, the results of an experimental investigation of the turbulence intensity in gravel bed channels are described. The runs were carried out by measuring, with an acoustic Doppler velocimeter, the turbulence intensity profile along six verticals of a given cross section in a laboratory flume. The analysis of the measured intensity distributions has shown the existence of two different regions, above and below the tops of the roughness elements, in which different intensity profiles occur. Furthermore, the measured profiles have shown a maximum of the turbulence intensity that decreases for increasing values of the roughness height, confirming that the turbulence damping efficiency increases when the roughness elements protrude inside the flow. The applicability of Nezu’s relationship (derived for a hydraulically smooth bed) for the experimental intensity profiles above the roughness elements is positively tested. Finally a new intensity distribution for a rough bed, applicable to the whole water depth, is proposed. In this profile, two coefficients having a known physical meaning (the maximum turbulence intensity and the depth at which this maximum is located) appear.     

Flood Plain Filling by a Monoclinal Flood Wave

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

Subcritical 90° Equal-Width Open-Channel Dividing Flow

Based on experimental observations, for a subcritical, right-angled, equal-width, open-channel dividing flow over a horizontal bed, the contraction coefficient at the maximum width-contracted section in the recirculation region is almost inversely related to the main channel upstream-to-downstream discharge ratio. The energy heads upstream and downstream of the division in the main channel are found to be almost equal. Under the assumption that the velocities are nearly uniformly distributed at the considered boundaries, the depth-discharge relationship follows the commonly used energy equation. The predicted results correlate fairly with the experimental data from this and other studies. The energy-loss coefficient of a division is expressed in terms of discharge ratio, upstream Froude number, and depth ratio. An expression for practical engineering applications is to determine the maximum possible branch-channel discharge at a given upstream discharge with a prescribed downstream Froude number or the maximum possible downstream Froude number if both branch- and main-channel discharges are prescribed.     

Response of Velocity and Turbulence to Sudden Change of Bed Roughness in Open-Channel Flow

The experimental study shows how an open-channel flow would respond to a sudden change (from smooth to rough) in bed roughness. Using a two-dimensional acoustic Doppler velocimeter and a laser Doppler velocimeter, the velocity, turbulent intensities, and Reynolds stress profiles at different locations along a laboratory flume were measured. Additionally, the water surface profile was also measured using a capacitance-type wave height meter. The experimental data show the formation of an internal boundary layer as a result of the step change in bed roughness. The data show that this boundary layer grows much more rapidly than that formed in close-conduit flows. The results also show that the equivalent bed roughness, bed-shear stress, turbulent intensities, and Reynolds stress change gradually over a transitional region, although the bed roughness changes abruptly. The behavior is different from that observed in close-conduit flows, where an overshooting property—which describes the ability of the bed-shear stress to attain a high-peak value over the section with the larger roughness, was reported. A possible reason for the difference is the variation of the water surface profile when an open-channel flow is subjected to a sudden change in bed roughness.     

Three-Dimensional Numerical Simulation of Compound Channel Flows

A three-dimensional numerical study is presented for the calculation of turbulent flow in compound channels. The flow simulations are performed by solving the three-dimensional Reynolds-averaged continuity and Navier–Stokes equations with the k?ε turbulence model for steady-state flow. The flow equations are solved numerically with a general-purpose finite-volume code. The results are compared with the experimental data obtained from the UK Flood Channel Facility. The simulated distributions of primary velocity, bed shear stress, turbulent kinetic energy, and Reynolds stresses are used to investigate the accuracy of the model prediction. The results show that, using an estimated roughness height, the primary velocity distributions and the bed shear stress are predicted reasonably well for inbank flows in channels of high aspect ratio (width/depth ≥ 10) and for high overbank flows with values of the relative flow depth greater than 0.25.     

Bed-Load Effects on Hydrodynamics of Rough-Bed Open-Channel Flows

The extent to which turbulent structure is affected by bed-load transport is investigated experimentally using a nonporous fixed planar bed comprising mixed-sized granular sediment with a d50 of 1.95?mm. Three different sizes of sediment (d50 = 0.77, 1.99, and 3.96?mm) were fed into the flow at two different rates (0.003 and 0.006?kg/m/s), and subsequently transported as bed load. Particle image velocimetry (PIV) was used to determine the turbulence characteristics over the fixed bed during clear water and sediment feed cases. Mean longitudinal flow velocities at any given depth were lower than their clear water counterparts for all but one of the mobile sediment cases. The exception was with the transport of fine grains at the higher feed rate. In this case, longitudinal mean flow velocities increased compared to the clear water condition. The coarse grains tended to augment bed roughness, but fine grains saturated the troughs and interstices in the bed topography, effectively causing the influence of bed irregularities to be smoothed. The PIV technique permitted examination of both temporal and spatial fluctuations in flow variables: therefore many results are presented in terms of double-averaged quantities (in temporal and spatial domains). In particular, the form-induced stress, which arises from spatially averaging the Reynolds averaged Navier–Stokes equations and is analogous to the Reynolds turbulent stress, contributed between 15 and 35% of the total measured shear stress in the roughness layer. Flow around protrusive roughness elements produced a significant proportion of the turbulent kinetic energy shear production, suggesting that this process is highly intermittent near rough beds.     

Side Outflow from Supercritical Channel Flow

Side flow on a flood plain from a side outlet of the main channel is investigated both theoretically and experimentally for supercritical main flow. The side outlet as a model simulates a failure of a river bank in a prototype. The discharge ratios of the side outflow to that of the main channel flow, the water depth, and the velocity at the side outlet are obtained. The theoretical discharge ratio is a function of the Froude number of the main channel flow. The theoretical spreading angle of the side flow and the theoretical relationship between the velocities and the distance from an upstream point of the side outlet are also compared and predicted. All the theoretical results are found to be in good agreement with the experimental data.     

Effects of Bed Roughness on Flow around Bed-Mounted Cylinders in Open Channels

This paper presents the results of an experimental study of flow around cylindrical objects on a rough bed in an open channel. This is an extension of a previous study of flow around cylinders on a smooth bed. The purpose of this study is to explore the effects of bed roughness on the characteristics of the deflected flow around cylindrical objects and the resulting bed-shear stress distributions. Similar to the previous study cylindrical objects of equal diameter and four heights were tested under similar flow conditions producing four different levels of submergence. Bed shear stress and deflected flow velocities were measured by a thin yaw-type Preston probe after a set of flow visualization tests. Flow visualization tests showed that the horse-shoe vortex systems on the rough bed occupy a relatively greater width compared to the smooth bed. Unlike smooth bed observations, the flow separation point upstream of the cylinder was not dependent on the level of submergence as the separation points were found to appear within a short range of x = ?1D to ?1.2D. Bed shear stress has been found to increase significantly near the shoulder of the cylinders, and its ratio with respect to the approach bed-shear stress was twice as large compared to the smooth bed case. Mean velocity profiles were analyzed in terms of three-dimensional turbulent boundary layer theories. Bed roughness was found to oppose the effect of the lateral pressure gradient that causes skewing in the boundary layer. Perry and Joubert’s model has been found to be equally accurate on smooth and rough beds for predicting the deflected velocity magnitudes around cylinders. The present study will enhance the knowledge of hydraulics of flow around bed-mounted objects (e.g. fish-rocks) in natural streams.     

Aspect Ratio to Maximize Sediment Transport in Rigid Bank Channels

The continuity equation, Manning’s equation, Einstein’s wall correction procedure and sediment transport equations are combined to indicate channel aspect ratios which maximize sediment transport for a given water discharge in rigid-bank trapezoidal and rectangular channels with fixed slope. Higher aspect ratios are required to maximize sediment transport for channels conveying bed load than for those with a dominant suspended load. A total load equation predicts optimum aspect ratios lying in between those for bed load and suspended load channels. The equations imply that the optimum aspect ratio increases markedly as the channel bank to channel bed roughness ratio increases. The resulting optimum ratios are smaller than the aspect ratios of many natural rivers.     

Sediment Pickup on Streamwise Sloping Beds

This paper presents an experimental investigation on noncohesive sediment pickup under a unidirectional steady-uniform stream flow on streamwise steeply sloping (down slope and adverse) sedimentary beds. The characteristic parameters affecting the sediment pickup, identified based on the physical reasoning and dimensional analysis of the sediment particle movement under stream flow, are the transport-stage parameter, particle parameter, and geometric standard deviation of sediment particles. A large number of experiments (426 runs) were carried out in two long rectangular ducts (closed-conduit flow) with nine types of sediments (six uniform and three nonuniform sediments), having a variation of bed slope from ?15° (adverse slope) to 25° (down slope). In an open channel flow (laboratory flume study), the uniform flow is a difficult, if not impossible, proposition for a steeply sloping channel and is impossible to obtain in an adversely sloping channel. To avoid this problem, the tests were conducted with a closed-conduit flow. Measurements included flow discharge and sediment pickup rate. The bed shear stress for a particular run was computed considering side wall correction. The experimental data were used to determine the equation of sediment pickup function through a regression analysis. The equation is adequate to estimate sediment pickup not only on horizontal and mild slopes but also on steep and adverse slopes.     

Performances of Hydraulics and Bedload Sediment Flushing in Rigid Channel Using Surge Flows

This paper presents an investigation of the performance of the hydraulic and sediment removal of a flushing system in a detention basin. A hydraulic criterion for the design of the flushing system is proposed. An equation for the maximum height of the flushing wave front as a function of the distance from the gate, the initial water depth in the chamber, and the chamber length is proposed. The Lauber and Hager equation for the maximum velocity of a flushing wave is also verified. Effective removal of sediment particles on the bed is a direct function of the bed shear stress generated by the flushing flow. This study reveals that the bed shear stress on the channel bed induced by the flushing flow can be attributed to the hydrostatic pressure, the flow acceleration, and the convection-induced momentum. The shear stress associated with fluid distortion and the turbulent viscosity may be neglected. Significant error would occur if the hydrostatic pressure component were used as an estimate of the bed shear stress on a mild slope channel. The energy slope method may provide an overestimate of the bed shear stress. Finally, an appropriate equation to evaluate the maximum bed shear stress is proposed.     

Supercritical Flow Measurement Using a Small Parshall Flume

An experimental program was conducted to determine if a Parshall flume, developed to accurately measure open-channel subcritical flow, could also be used to measure discharge in a supercritical flow regime. Fifteen experimental configurations were tested using two small Parshall flumes [6-in. (15.2-cm) and 9-in. (22.9-cm) crest width] with varying approach channel slopes, approach channel roughness, and flume convergence. It was determined that a single Parshall flume can be used to measure flow (within ±5%) for both supercritical and subcritical flow regimes for a specified range of flows. The original Parshall flume equation was then modified to incorporate crest width, channel slope, channel roughness, and convergence in the prediction algorithm. Unique expressions were developed for both supercritical and subcritical flow regimes to estimate the discharge. A single expression does not appear feasible for accurate discharge measurement for both flow regimes in a Parshall flume at this time.