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.     

THE MARKET FOR MANGANESE DERIVED FROM DEEPSEA NODULES

The potential markets for the manganese which may be derived from deep-sea nodules are assessed. Estimates are made of current consumption patterns of manganese in various forms – standard ferromanganese, low carbon ferromanganese and manganese metal – by the ferrous and nonferrous metallurgical industries. The effects of technological developments, expected to occur between 1980 and 1990, and potential price reductions on the demand for manganese are analysed separately and the combined effects of market growth, technological change, and price reductions are synthesized. Cet article évalue des marches potentiels pour le manganèse qui peut être extrait des nodules du fond des océans. Ces estimations sont basées sur les tendances actuelles de la consommation du manganèse dans ses diverses formes – ferromanganèse normal, ferromanganèse à basse teneur en carbone et manganèse métallique – par les industries des métaux ferreux et non ferreux. Les effects des progrès techniques qui sont attendus entre 1980 et 1990 et la diminution possible des prix du manganèse sont analysés séparément. L'article fait aussi la synthèse des effects combinés de la croissance du marché, des changements technologiques et de la diminution des prix. En este artículo se evalúa el mercado potencial para el manganeso derivado de los nódulos obtenidos del fondo marino. Se analiza las tendencies actuales del consumo de manganeso en sus diversas formas – ferromanganeso estandard, ferromanganeso de bajo contenido de carbón y metal manganeso – por las industries metalúrgicas. Los efectos sobre la demanda de manganeso por el desarrollo tecnológico durante 1980 a 1990 y de la reducción potencial del precio, son analizados separadamente. Se evalúa también el efector combinado del crecimiento del mercado, el cambio tecnológico y las reducciones de precio.     

UNIT HYDROGRAPHS DERWED FROM THE NASH MODEL1

ABSTRACT: Unit hydrograph ordinates are often estimated by deconvoluting excess rainfall pulses and corresponding direct runoff. The resulting ordinates are given at discrete times spaced evenly at intervals equal to the duration of the rainfall pulse. If the new duration is not a multiple of the parent duration, hydrograph interpolation is required. Linear interpolation, piece-wise nonlinear interpolation and graphical smoothing have been used. These interpolation schemes are expedient but they lack theoretical basis and can lead to undesirable results. Interpolation can be avoided if the instantaneous unit hydrograph (IUH) for the watershed is known. Here two issues connected with the classic Nash IUH are examined: (1) how should the Nash parameters be estimated? and (2) under what conditions is the resulting hydrograph able to reasonably represent watershed response? In the first case, nonlinear constrained optimization provides better estimates of the IUH parameters than does the method of moments. In the second case, the Nash IUH gives good results on watersheds with mild shape unit hydrographs, but performs poorly on watersheds having sharply peaked unit hydrographs. Overall, in comparison to empirical interpolation alternatives, the Nash IUH offers a theoretically sound and practical approach to estimate unit hydrographs for a wide variety of watersheds.     

UNDERSTANDING A WATERSHED FROM THE BIOLOGICAL VIEWPOINT1

In watershed management the effects of plants on water cannot be considered a constant and forgotten because: plants of different sizes and forms use water at different rates and plants of the same size differ in their needs for water because of anatomical differences. Many common denominators are present in all watersheds covered by vegetation. Forces exerted on the soil water by vegetation, climate and soil are the same kinds of forces. The differences between watersheds in water yield potential appear to be due to differences in the degree in which these forces are exerted. However, the influence of biotic factors are more individual. The similarities and differences existing between watersheds suggest some principles that can be used as guides to understanding individual watershed problems and as possible guides to determining when, how, and where to treat a given watershed. Eleven principles are given and their application to the definition and solution of biological or vegetational problems of watershed management are discussed.