Journal of Hydraulic Engineering

Pressure management has been used for more than 3 decades to reduce leakage from water distribution systems. While few of these studies have been published, information on the ranges of field study leakage exponents is available. In contrast, several studies on the pressure-leakage relationship of individual leaks have been published, and verified models have been developed for predicting the response of elastically deforming leaks. The main aim of this paper was to determine whether researchers’ current understanding of the pressure-leakage response of individual leaks can be reconciled with the observed pressure-leakage response of district metered areas containing many leaks. To investigate this, a model of the distribution of individual leaks and their parameters was developed based on available literature and expert advice. A repeatability study showed that such a model can indeed produce typical distributions of leakage exponents found in field studies. A sensitivity analysis of the various parameters showed that the average system pressure and condition of the system had the greatest influence on the system leakage exponent. Finally, it was shown that a small fraction of leaks with high leakage numbers (i.e., in highly flexible material or closing under zero pressure conditions) can explain the high background leakage exponents often found in systems with only background leakage.

Regional downstream hydraulic geometry equations are developed using flow with a 1.5-year recurrence interval, and corresponding widths, depths, and velocities. The study includes 634 gauge stations located across Canada and are grouped by characteristics that affect or are correlated with bank and bed stability. Jack-knife analysis was done to test the predictive capabilities of each grouping. For width prediction, grouping the data by geology and vegetative characteristics improved predictions in 14 of the 15 categories, with drainage characteristics and mode of deposition groupings showing the best results. Grouping the data by vegetative characteristics showed the best improvement among noncontiguous categories when considering all of the hydraulic geometry variables (width, depth, and velocity). These groupings are investigated further. The study demonstrates that classifying downstream hydraulic geometry equations by local geology and vegetation improves the predictive capabilities of the equations. It also shows that though regionalization does not need to occur in a contiguous region, regionalization still provides better results due to the limited resolution of nationally available GIS datasets. As demonstrated in previous studies, it is also shown that downstream hydraulic equations can be applied to semialluvial rivers. Finally, multiple regression was tested with width prediction as a function of flow and up to three grouping variables. The interaction of the grouping variables showed no improvement in the results.

Saltation models provide considerable insight into near-bed sediment transport. This paper outlines a simple, efficient numerical model of stochastic saltation, which is validated against previously published experimental data on saltation in a channel of nearly horizontal bed. Convergence tests are systematically applied to ensure the model is free from statistical errors emanating from the number of particle hops considered. Two criteria for statistical convergence are derived; according to the first criterion, at least ${10}^3$ hops appear to be necessary for convergent results, whereas ${10}^4$ saltations seem to be the minimum required in order to achieve statistical convergence in accordance with the second criterion. Two empirical formulas for lift force are considered: one dependent on the slip (relative) velocity of the particle multiplied by the vertical gradient of the horizontal flow velocity component; the other dependent on the difference between the squares of the slip velocity components at the top and bottom of the particle. The former is found to give more stable results. A parameter study indicates that the saltation length has a minimum value with increasing particle diameter (at $D_{*}\sim 12$) for a given transport stage. Variations in the friction coefficient and collision line level have a negligible effect on the saltation statistics within the ranges considered. Regression equations are obtained for each of the saltation characteristics. Finally, the model is used to evaluate the bed-load transport rate, which is in satisfactory agreement with common formulas based on flume data, especially when compared against other saltation-derived expressions.

Liquid streams of chemicals (dosants) such as sodium hypochlorite frequently need to be quickly and thoroughly mixed across a water or wastewater flow. Where no mixing tanks, stirrers, or pumps are available to ensure rapid and complete mixing, the existing flow turbulence in the conduit will be adequate for mixing if the effective available conduit length exceeds a value proportional to $R/(N{f}^{0.5})$, where $R$ is the conduit’s hydraulic radius, $N$ is the number of well-spaced dosing points at the dosing station, and $f$ is the Darcy-Weisbach factor for the conduit. The proportionality varies slightly with the degree of uniformity required of the dosant concentration across the conduit cross section. The analysis, based on consideration of a square conduit, agrees closely with one (by others) based on a conduit of circular cross section. Laboratory and field data support the analysis to a useful extent.

This paper separately evaluates two methods from Bayesian Statistics to estimate parameter and model uncertainty in simulations from a one-dimensional (1D) sediment transport model. The first method, multivariate shuffled complex evolution metropolis-uncertainty analysis (MSU), is an algorithm that identifies the most likely parameter values and estimates parameter uncertainty for models with multiple outputs. The second method, Bayesian model averaging (BMA), determines a combined prediction based on three sediment transport equations that are calibrated with MSU and evaluates the uncertainty associated with the selection of the transport equation. These tools are applied to simulations of three flume experiments. For these cases, MSU does not converge substantially faster than a previously used and simpler parameter uncertainty method, but its ability to consider correlation between parameters improves its estimate of the uncertainty. Also, the BMA results suggest that a combination of transport equations usually provides a better forecast than using an individual equation, and the selection of a single transport equation substantially increases the overall uncertainty in the model forecasts.

Current methods utilized in scaling sediment transport in unsteady open-channel flow result in a number of model and scale effects, decreasing the accuracy and applicability of scale models. Identifying the conditions under which the governing equations of sediment transport are self-similar, and require no sediment diameter or density scaling, can reduce scale effects and increase model applicability. Conditions for self-similarity of one-dimensional unsteady suspended sediment transport are identified by applying the one-parameter Lie group of point scaling transformations, both for the general case and with unscaled sediment diameters. Under the scaling ratio relations found when holding sediment diameter to be unscaled, sediment diameter, density, critical and total shear, porosity, kinematic viscosity, and particle Reynolds number are all unscaled. It is shown that under Lie group scaling, the unsteady one-dimensional suspended sediment transport process as an initial-boundary value problem in the prototype domain can be self-similar with that of a variety of different scaled domains. The scaled values of sediment variables at specified temporal and spatial locations can then be upscaled to the corresponding values in the prototype domain.

Generally constructed with materials from the proximal environment and promoting a more natural aesthetic within a stream, rock-weir grade control structures have recently become popular in-stream alternatives. Energy expenditure through rock weirs is increased from in situ, primarily one-dimensional (1D) conditions owing to strong velocity gradients and turbulence losses. Flow modeling methodologies utilizing a 1D assumption are not directly applicable for representing hydraulics through rock weirs; however, such models are readily implemented in engineering practice. An approach altering parameters and cross section configurations within a 1D model, Hydrologic Engineering Center River Analysis System (HEC-RAS), was developed to approximate hydraulic conditions associated with A-shaped, U-shaped, and W-shaped rock-weirs using data from a near-prototype physical model. Manning’s $n$ roughness values were adjusted for minimum energy variance and calibrated to serve as a turbulence model. Predicted total mechanical energy head and water surface elevations were approximated within a mean reach-averaged cross section absolute error of 0.013 m. The developed methodology may be implemented in streams with similar dimensions and flow characteristics to the laboratory, and provides an approach for rock-weir field design.

Coupled shallow water equations integrated with sediment transport and morphological evolution are presented in this paper. The momentum exchange terms that originated from the interaction between flow and sediment, which were ignored by several researchers, are taken into account. The time and space second-order, MacCormack total variation diminishing (TVD) finite difference method is used to solve these equations. A series of numerical simulations compared with laboratory dam-break experiments were carried out. The simulated results are in good agreement with experimental measured results, which demonstrates that the current computational framework is able to determine the dam-break hydraulics over erodible sediment.

This paper presents early findings from laboratory tests and field observations on the failure of spill-through abutments subject to abutment scour. These findings show that geotechnical and hydraulic processes interact to erode embankment soil during abutment scour, producing lesser scour depths than predicted using leading abutment scour equations. A major failure location is the flow waterline beginning at an abutment’s upstream corner where soil is exposed to the highest values of flow velocity and turbulence. Undercutting and toppling of soil blocks occurs sequentially along the face of the spill slope, eroding it back and eventually exposing the abutment column. Further erosion then may breach the embankment. The laboratory findings, based on uniform sand compacted to varying densities and thereby shear strengths, show that soil strength influences scour depth.