Journal of Hydraulic Engineering

An analytic approach is developed for quantifying the distribution of fluid passage times in a heterogeneous porous medium. The basic methodology employed utilizes a diffusion theory description for the displacement of a purely advected fluid subject to a random field of hydraulic conductivity. Within this framework, a governing model is formed using the backward form of the statistical Kolmogorov equation, which yields the inverse Gaussian distribution as a solution to the fluid passage time problem. In proposing the methodology, a rationale is presented for quantifying the associated model parameters using a simple application of the mean and variance to Darcy's law, with subsequent comparisons being made to previous results obtained for perturbation solutions of the associated stochastic partial differential equations. In addition, the validity of the model is discussed within the bounds of a Markovian description for ground‐water flow under a continuum‐based modeling framework. Here, it is argued that acceptably accurate results may be achieved for a statistical Peclet number in excess of 70.

A stochastic analysis for two‐dimensional steady‐state ground‐water flow through a homogeneous random shallow semiconfined aquifer is presented. The flow problems through a semiconfined aquifer with a random leakage factor but subject to deterministic boundary conditions and domain recharge are investigated by perturbation techniques associated with the boundary element method. The leakage factor is related to the physical properties of both the main aquifer and the leaky layer. The hierarchical equations based on the expansion of the potential into the perturbation series are derived and the boundary element method is applied for obtaining the solutions of these equations. The results from the present study are compared with those obtained using the Monte Carlo simulation method as well as the analytical solutions. The perturbation‐based boundary element method does not require the specification of the probability density function of the leakage factor, but only its mean, variance (or standard deviation), and/or higher‐order moments. Therefore, the perturbation‐based boundary element method is particularly useful when the statistical information is incomplete. The results of the present study are quite comparable with those of Monte Carlo simulations, but perturbation‐based boundary element method needs much less computational effort.

The Saint‐Venant equations commonly applied to solving unsteady open‐channel flow problems consist of a continuity equation and a momentum equation. In deriving the momentum equation, the pressure distribution is assumed to be hydrostatic, and the effect of nonuniform cross‐sectional velocity distribution is assumed to be small. Thus, the momentum and pressure correct coefficients $\beta$, $k$, and $k\prime$ are usually assumed to be equal to unity in applications. The effects of these assumptions on the solution of the flow equations have not been explored. The purpose of this paper is to investigate the significance of these assumptions by means of numerically solving the nearly exact unsteady open‐channel flow equations with systematically changing values of the coefficients. The results confirm that the effects of these coefficients are relatively small when the flow is nearly steady and uniform, and their effects increase with flow unsteadiness. These coefficients have a greater impact on the solution for velocity than for depth. The results also indicate more effects for convectively decelerating flow than for accelerating flow, especially when there is significant downstream backwater effect.

The paper presents special measurements of the turbulence characteristics in the river reach just behind the discharge of warm water from a thermalelectric power plant. The measurements of the values of instantaneous longitudinal velocities were taken with special micropropeller meters in 54 different verticals (simultaneously in six points at a vertical). The main characteristics of turbulence and basic hydraulic and morphometric quantities are computed and the analysis of different physical phenomena in the river reach is presented. The analysis concerns the spatial distributions of velociiy and water‐temperature values, kinetic energy of turbulence, turbulence intensity, and the dissipation rate of energy. The quantitative estimations of the scales of turbulence were carried out on the basis of analysis of frequency spectra, autocorrelation, and structural functions. Various empirical formulas were derived and checked.

The mechanism of seawater purging in a tunneled outfall is studied using a 1:83 hydraulic scale model of Boston's proposed wastewater outfall. Purging requires high rates of effluent flow, which is particularly problematic for Boston because of the wide range of expected flow rates caused by combined sewers and seasonal ground‐water infiltration. This study explores some potential solutions to this problem. Model results show riser purging at flows of 5–10% less than predicted for risers (Munro criterion) and tunnel purging at flows about 20% less than predicted (full pipe flow criterion based on riser section invert slope), suggesting that the theoretical criteria are conservative. Construction of a tunnel constriction (Venturi section) just upstream from the risers substantially reduces seawater penetration in the tunnel by creating a condition of densimetric critical flow. Theoretical calculations of the minimum flow rate without tunnel penetration are consistent with observations when downstream mixing is considered. Further tests show that, in combination with the Venturi section, a short‐term increase in effluent flow caused by intermittent dumping of the chlorine contact tanks could significantly reduce the riser purging requirement as well.

The goal of this note is to investigate relationships among the maximum likelihood method (MLE), maximum of entropy (POME) method, and the generalized method of moment (GMM) for four probability density functions. It is shown that MLE and POME constitute a particular case of GMM.

Experiments on settling of kaolin‐distilled water suspensions are carried out in a 5‐m diameter rotating annular flume in which flows were generated by rotating the flume walls in one direction and a top ring in the opposite direction. Suspensions with initial concentrations varying from 250 to 2,000 ppm are allowed to settle under constant bed shear stress conditions. After equilibrium is reached, the suspensions are withdrawn from the flume while the flume volume is maintained constant by adding clear water at an equal rate. Size distributions of the dispersed samples are determined using a Malvern particle size analyzer and concentrations are determined by filtration and weighing. The changes in concentration and size distribution during the initial settling and the subsequent dilution periods are used to investigate two opposing mechanisms of the settling process and to answer the question of whether there is simultaneous deposition and erosion during cohesive sediment settling.

The resistance to flow of a channel is increased significantly by the presence of bends or curves. Existing methods for predicting stage‐discharge relationships for meandering channels give conflicting results and none have been reliably verified with independent data. Three sets of laboratory data, including two only recently acquired, are suitable for evaluating proposed methods. Application of potentially useful methods to reproduce these data shows that ignoring bend losses gives unacceptably high errors in predicting discharge, and some proposed methods give even worse results. The simple SCS method of adjusting Manning's n on the basis of sinuousity is acceptable, although it cannot account for the effects of bend length and radius, cross‐sectional shape, or losses in individual bends. This method can be improved by linearization to remove ambiguities associated with the discontinuities in the original version. The theory proposed by Chang is verified over a wide range of conditions and gives the best results, but would be difficult to apply routinely in practice.

This technical note presents a method to estimate the energy loss on stepped spillways for the jet‐flow regime, which occurs when the ratio of the critical depth $y_c$ to the height of the step $h$ is less than approximately 0.8. It introduces the concept of $\alpha$, the proportional energy loss per step, and using the extensive experimental results of Horner, $\alpha$; was evaluated. It was found that $\alpha$ is a function of $y_c/h$ and $h/l$, where $l$ is the length of the step; and an equation has been developed that describes this variation. It was also found that the energy loss on a stepped spillway with a large number of steps can be very significant in the jet‐flow regime. It also appears that for skimming flow, which occurs for $y_c/h$ larger than about 0.8, the average energy loss per step would be less than that for jet flow.

A riprap sizing criterion for the original Agricultural Research Service (ARS)\‐type low‐drop structure was previously developed. The structure was required to reduce the required rock size. A 1:12 Froude‐scale model of the modified ARS‐type low‐drop structure with a baffle plate was constructed and tested to derive a riprap sizing procedure for stabilizing the stilling basin. Thirty‐four tests with the baffle plate and 12 tests without the baffle plate with varying discharges, submergences and riprap sizes. The drop height and channel geometry remained constant for all tests. The ratio of the approach unit discharge and median stone size was related to the submergence for determining the stable riprap size. The riprap size needed to stabilize the modified stilling basin is approximately 40% smaller than the riprap needed to stabilize the original stilling basin.