TWO-DIMENSIONAL DIFFUSION-PROBABILISTIC MODEL OF A SLOW DAM BREAK1

ABSTRACT: A two-dimensional model of a dam-break flood wave is developed by simplifying the St. Venant equations to eliminate local acceleration and inertial terms and combining the simplified equations with continuity to form a diffusion type partial differential equation. This model is cascaded with a two point probability estimate scheme to account for uncertainty in the dam break flood hydrograph and channel roughness. The development and application of the probabilistic model is the main contribution of this paper. The approach is applied to a hypothetical dam break of Long Valley Dam on the Owens River above Bishop, California.     

A two stage batch adsorber design for methylene blue removal to minimize contact time

The adsorption of methylene blue onto bentonite in a batch adsorber has been studied. Three kinetic models, the intraparticle diffusion equation and the pseudo first and second order equations, were selected to follow the adsorption process. Kinetic parameters, rate constants, equilibrium adsorption capacities and related correlation coefficients for each kinetic model were calculated and discussed. It was shown that the adsorption of methylene blue onto bentonite could be described by the pseudo second order equation. Adsorption of methylene blue onto bentonite followed the Langmuir isotherm. A model has been developed for the design of a two stage batch adsorber based on pseudo second order adsorption kinetics. The model has been optimized with respect to operating time in order to minimize total contact time to achieve a specified amount of methylene blue removal using a fixed mass of adsorbent. The results of two stage batch adsorber design studies showed that the required times for specified amounts of methylene blue removal significantly decreased. This design is particularly suitable for low-cost adsorbents/adsorption systems when minimising contact time is a major operational and design criterion and a significant volume of effluent needs to be treated in the minimum amount of time.     

A FINITE ELEMENT MODEL OF CONTAMINANT MOVEMENT IN GROUNDWATER1

ABSTRACT. Transient, two-dimensional solutions are developed which describe the movement and distribution of a conservative substance in a stream-aquifer system. The solutions are obtained by solving sequentially the groundwater flow and mass transport equations. A variational approach in conjunction with the finite element method is used to solve the groundwater flow equation. Galerkin's approach coupled with the finite element method is used to solve the mass transport equation. Linear approximated triangular elements and a centered scheme of numerical integration are employed to calculate the hydraulic head distribution and the concentration of solute in the flow region. The linear approximation used to define the concentration function within each element is not appropriate for cases involving steep concentration gradients. For such cases, higher order approximations are necessary to assure the continuity of gradients across interelemental boundaries. Numerical examples that illustrate the applicability of the model are presented.     

PARALLEL DRAINS FROM THE LAPLACE STANDPOINT1

Where natural drainage is inadequate for keeping the water table below the root zone of the crops being grown, drains are often employed to control water table levels. Such drains are commonly installed in parallel lines at depths and spacings adapted to the needs of the area. Formulas used for determining drain spacings are generally based upon Dupuit-Forchheimer concepts. These developments postulate a saturated, permeable aquifer underlying the irrigated area and an impermeable barrier underlying the aquifer. The basic differential equation expresses the requirement that the flow out through the sides of a vertical column of infinitesmal cross sectional area must be supplied by a corresponding drop of the water table at the top of the column. If variations of transmissivity due to variations of water table level are taken into account the second order differential equation obtained is nonlinear. To avoid the mathematical difficulties posed by this nonlinearity it is customary to neglect the effects of changes of transmissivity due to changes of water table levels. This imposes a restriction that the formulas derived from these linearized differential equations suffer a loss of accuracy if the change of water table levels becomes a considerable portion of the initial saturated depth. Offsetting these difficulties is the tactical advantage that the linearized differential equations are of types long studied in older developments concerned with conduction of heat in solids. The advantages conferred by the possibilities for exploiting the results of investigations in the older discipline are many. An alternative approach is based upon a requirement that there can be no accumulation of water in any elementary cubical volume located in the zone of complete saturation below the water table. The differential equation obtained on this basis, if the aquifer is homogeneous and isotropic, is the one which bears the name of Laplace. It will be the purpose of this paper to explore the possibilities afforded by this approach for evaluating the flow to parallel drains and to compare the results with those obtainable by the Dupuit-Forchheimer method.     

Do Polynomials Adequately Describe the Hypsometry of Monadnock Phase Watersheds?

Hypsometry has been shown to be a useful tool in geomorphic analysis of watersheds with the use of third‐degree polynomial equations to express the hypsometric curve. Despite its usefulness with watersheds in the equilibrium stage, the third‐degree polynomial has been found to be inadequate to describe the hypsometry of Monadnock phase watersheds. Three other equations — a modified third‐degree polynomial with a rational term, a sigmoidal model, and a double exponential — were used to determine hypsometric attributes of 32 Monadnock phase watersheds and compared to the third‐degree polynomial form. The three other equations were found to be better fits for Monadnock phase watersheds than the third‐degree polynomial equation, regardless of which ratio — area or elevation — was plotted as the independent variable. Due to the occasional failure of each functional form to give logical values for hypsometric attributes, the importance of using more than one form equation is discussed. After determining the best‐fit equation for each watershed, the usefulness of hypsometric attributes is discussed in relation to erosion processes within Monadnock phase watersheds.     

NONLINEAR DUPUIT EQUATIONS FOR THE PHREATIC SURFACE OF A SEMI-INFINITE AQUIFER1

ABSTRACT. We present a new approach to the nonlinear equations for the phreatic surface of groundwater flow from or into a reservoir. The differential equation is converted into an equivalent integral equation, which is then solved by a method of iteration. We obtain exact results for both drawdown and infiltration, including the special case of groundwater penetration into dry soil.     

Persistence of fermentative process to phenolic toxicity in groundwater

The fermentation process is an important component in the biodegradation of organic compounds in natural and contaminated systems. Comparing with terminal electron-accepting processes (TEAPs), however, research on fermentation processes has to some extent been ignored in the past decades, particularly on the persistence of fermentation process in the presence of toxic organic pollutants. Both field and laboratory studies, presented here, showed that microbial processes in a groundwater-based system exhibited a differential inhibitory response to toxicity of phenolic compounds from coal tar distillation, thus resulting in the accumulation of volatile fatty acids (VFAs) and hydrogen. This indicated that fermentation processes could be more resistant to phenol toxicity than the subsequent TEAPs such as methanogenesis and sulfate reduction, thus providing us with more options for enhancing bioremediation processes.     

DIGITAL SIMULATION OF THE EFFECT OF THERMAL DISCHARGE ON STREAM WATER QUALITY1

A modified transient version of the Streeter-Phelps model along with the energy balance equation is employed to analyze the effects of waste heat discharge from power plants on stream water quality. Analysis is also made to examine the effects of the upstream water quality and stream velocity on the downstream DO concentration level. The resulting coupled nonlinear hyperbolic partial differential equations representing the energy, BOD and DO concentrations are solved by the method of characteristics and simulated on a digital computer. Final numerical results indicate that the allowable quantity of thermal discharge does heavily depend on the upstream quality.     

酸雨条件下黄壤对镉的释放动力学研究

对不同酸雨条件下黄壤对镉释放的研究发现,吸附态镉释放的过程可以分为快反应和慢反应两个阶段。在以常用动力学方程实验数据进行拟合的基础上,创建了反三角函数方程。结果表明,反三角函数方程对多种酸雨条件下黄壤吸附态镉释放过程的拟合度最佳,此外多项式方程、双常数方程也能较好地描述这一过程。     

高梯度磁分离的过滤性能计算

文章分析了高梯度磁分离器的粒子捕获机理给出了性能计算方法。首先从ＨＧＭＳ的单线模型出发，导出表征ＨＧＭＳ性能的基本量磁速Ｖｍ，然后求出捕获半径ＲＣＯ，得出一系列磁性粒子的轨迹曲线，并且考虑了在ＨＧＭＳ工作状态时的粒子保持情况；再由物质平衡原理得出物质平衡方程。由分析ＨＧＭＳ的捕获几率得出速率方程，运用四阶龙格库塔法对磁分离方程进行数值解，求出穿透曲线；最后通过实验，与推导的结果作了比较。对运用高梯度磁分离器设计废水废气处理设备具有实际意义。     

HYSTAR Sediment Model: Distributed Two‐Dimensional Simulation of Watershed Erosion and Sediment Transport Using Time‐Area Routing

An erosion and sediment transport component incorporated in the HYdrology Simulation using Time‐ARea method (HYSTAR) upland watershed model provides grid‐based prediction of erosion, transport and deposition of sediment in a dynamic, continuous, and fully distributed framework. The model represents the spatiotemporally varied flow in sediment transport simulation by coupling the time‐area routing method and sediment transport capacity approach within a grid‐based spatial data model. This avoids the common, and simplistic, approach of using the Universal Soil Loss Equation (USLE) to estimate erosion rates with a delivery ratio to relate gross soil erosion to sediment yield of a watershed, while enabling us to simulate two‐dimensional sediment transport processes without the complexity of numerical solution of the partial differential governing equations. In using the time‐area method for routing sediment, the model offers a novel alternative to watershed‐scale sediment transport simulation that provides detailed spatial representation. In predicting four‐year sediment hydrographs of a watershed in Virginia, the model provided good performance with R² of 0.82 and 0.78 and relative error of ?35% and 11% using the Yalin and Yang's sediment transport capacity equations, respectively. Prediction of spatiotemporal variation in sediment transport processes was evaluated using maps of sediment transport rates, concentrations, and erosion and deposition mass, which compare well with expected behavior of flow hydraulics and sediment transport processes.     

DEVELOPMENT OF A BACTERIAL TRANSPORT MODEL FOR COARSE SOILS1

ABSTRACT: A bacterial transport model, developed to analyze bacterial translocation in coarse-grained soils, is presented. The complex governing equation is presented first, followed by analyses of each of the major processes influencing bacterial transport. These analyses suggest simplification of the governing equation is feasible when input data on specific processes are limited or unavailable. Model parameters, including bacterial die-off, bacterial distribution, input bacterial concentration, and saturated hydraulic conductivity, were randomly generated using a procedure known to produce either a normal or log-normal distribution of random numbers. Monte Carlo simulations were completed, and the resulting output was used to generate cumulative frequency distributions showing the probability of bacterial transport beyond various soil depths. Results from these simulations indicate that bacteria have a high probability of traveling through coarse-grained soils when low clay content and soil water temperatures limit bacterial retention and die-off.     

FRICTION SLOPE MODELS FOR M2 PROFILES1

ABSTRACT: Results of studies which have considered the relative merit of various friction slope averaging equations previously used in water surface profile computations are described. Limitations of the most accurate equation known for the M2 profile have indicated that a new equation which gives more emphasis to the upstream energy gradient is desirable. Based upon friction slope curves developed for M2 water surface profiles two new equations, one a parabolic and the other an elliptical approximation, are presented. The behavior of the new equations and of the previously most recommended equation is described by test calculations. The elliptical equation performed more satisfactorily than the harmonic method commonly recommended for M2 profile computations. Insertion of an additional cross-section about 50 feet upstream from a critical depth section was found to reduce computational errors for any energy gradient averaging method.     

A PARAMETRIC MODEL CALIBRATED WITH A PHYSICALLY BASED MODEL FOR RUNOFF PREDICTION FROM UNGAGED STREAMS1

ABSTRACT: Recent developments in the numerical solution of the governing partial differential equations for overland and channel flow should make possible physically based models which predict runoff from ungaged streams. However, these models, which represent the watershed by sets of intersecting planes, are complex and require much computer time. Parametric models exist that have the advantage of being relatively simple, and once calibrated are inexpensive to use and require limited data input. In this study, a procedure was developed for calibrating a parametric model against a physically based model, utilizing base areas of one acre and one square mile, with the expectation that base areas can be combined to model real watersheds. Simulation experiments with the physically based model showed that, for the one-acre base area, the dominant parameter (cell storage ratio, K) related to the slope and friction of the planes, whereas for one square-mile areas, the dominant parameters (K plus a lag factor, L) relate to channel properties. These parameters decreased exponentially as rainfall intensity increased.     

Estimation of Biogas Generation from a Uasb Reactor via Multiple Regression Model

In this study, regression analysis based an estimation model for biogas generated from an up-flow anaerobic sludge blanket (UASB) reactor treating landfill leachate is developed using several leachate parameters, such as pH, conductivity, total dissolved solids, chemical oxygen demand, alkalinity, chloride, total Kjeldahl nitrogen, ammonia, total phosphorus. These landfill leachate parameters are monitorized over a period of 1000 days at 35 ± 1°C in the UASB reactor. In order to develop the best model giving highest estimation performance, eight model equations including different input parameter combinations are analyzed. Based on the results of regression analysis, the best coefficients of the model equation are determined. As a conclusion, the developed model in this study can give accurate biogas amount prediction for the USAB reactor-based leachate treatment system.     

Limitations of model-fitting methods for kinetic analysis: Polystyrene thermal degradation

In this paper, some clarifications regarding the use of model-fitting methods of kinetic analysis are provided in response to the lack of plot linearity and dispersion in the activation energy values for the thermal degradation of polystyrene found in the literature and some results proposing an nth order model as the most suitable one. In the present work, two model-fitting methods based on the differential and integral forms of the general kinetic equation are evaluated using both simulated and experimental data, showing that the differential method is recommended due to its higher discrimination power. Moreover, the intrinsic limitations of model-fitting methods are highlighted: the use of a limited set of kinetic models to fit experimental data and the ideal nature of such models. Finally, it is concluded that a chain scission model is more appropriate than first order.     

ICP-AES法测定土壤中铬含量的不确定度评定

根据等离子体原子发射光谱(ICP-AES)法测定土壤中铬的过程,建立相应的数学模型并对模型中各个参数进行了不确定度来源分析。结果表明,测定结果的不确定性主要来源于标准曲线的浓度与光谱强度拟合直线方程求铬含量的不确定度、标准溶液和配置标准工作溶液时的不确定度,其次为重复性不确定度;定容体积和样品称量过程的不确定度对测量结果的不确定度贡献相对较小。     

A TEST OF SEVERAL EVAPORATION EQUATIONS FOR WATER TEMPERATURE SIMULATIONS IN LAKES1

ABSTRACT: Evaporative heat loss is an essential component of any heat budget used for the modeling of lake water temperatures. Seven evaporative heat loss equations were tested in a year-round, physically-based temperature and dissolved oxygen model for lakes. Deciding which equation to choose for use in the year-round model was based on the goodness of fit of the simulated vs. measured surface temperatures, which were taken at a depth of 1 m below the water surface. An equation which includes free and forced convection components and which was previously used for cooling ponds gave the best fit between temperature simulations and measurements.     

Multiresource simulation for wildland management

The model presented here is a simulation of the watershed of the Little South Fork of the Cache la Poudre River system located in the Front Range of the Rocky Mountains of Colorado. This simulation model, TERRA, provides information of resource interactions, ecosystem processes, and harvest ramifications for this watershed. The information is generated through sets of difference equations to represent process flows. The model has a modular design that separates the ecologic processes—weather conditions, hydrologic functions, forage and timber production, wildlife and domestic population dynamics, recreation use, and management activities—from the simulation planning overhead—updating, plotting, and printing.The model is designed such that the output is readily usable information for an allocation model and the decision-making process. This is accomplished by allowing different levels of specified management activities as input and producing responses and output on a per unit land area basis.This simulation is a useful research tool for estimating parameter and variable values and levels of management-resource interaction. Lack of a pertinent field data base inhibits the model from actually being used as a management tool in the planning process.Submitted for publication as Paper No. 1217 in the Journal Series of the Agricultural Experiment Station, University of Florida.     

MODIFICATION OF NEILL'S EQUATION FOR STORM‐TIDE DESIGN FLOW ANALYSIS1

ABSTRACT: Design of bridges spanning tidal estuaries or bays requires an estimate of peak tidal flow. One common approach to estimating these flows (Neill's method) uses a first‐order approximation of uniform water surface rise in the water body. For larger water bodies, the assumptions of this method are decreasingly valid. This study develops a simple modification that accounts for the spatial variability in the response of tidal waterways to storm surge flows. The peak tidal flow predicted by Neill's equation is compared to the peak flow determined by numerical simulation of estuaries with simple geometries, ranging from 1 to 25 km in length, using the U.S. Army Corps of Engineers one‐dimensional unsteady flow model, UNET. Results indicate that, under certain conditions, it may be appropriate to apply a correction factor to the peak discharge and peak velocity predicted by Neill's method. An algorithm, developed by nonlinear regression, is presented for computing correction factors based on estuary length, shape, mean depth, and storm‐tide characteristics. The results should permit the design of more reliable, cost‐effective structures by providing more realistic estimates of the potential for bridge scour in tidal waterways, especially when a full solution of the unsteady flow equations is impractical.