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Dupuit–Forchheimer Assumption
The Dupuit–Forchheimer assumption holds that groundwater flows horizontally in an unconfined aquifer and that the groundwater discharge is proportional to the saturated aquifer thickness. It was formulated by Jules Dupuit and Philipp Forchheimer in the late 1800s to simplify groundwater flow equations for analytical solutions. The Dupuit–Forchheimer assumption requires that the water table be relatively flat and that the groundwater be hydrostatic (that is, that the equipotential lines are vertical): :\begin \frac &= -\gamma = -\rho \, g \\ .5em\frac &= 0 \end where \partial P/\partial z is the vertical pressure gradient, \gamma is the specific weight, \rho is the density of water, g is the standard gravity, and \partial h/\partial z is the vertical hydraulic gradient Hydraulic head or piezometric head is a specific measurement of liquid pressure above a vertical datum., 410 pages. See pp. 43–44., 650 pages. See p. 22. It is usually measured as a liquid surface elevati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Groundwater
Groundwater is the water present beneath Earth's surface in rock and soil pore spaces and in the fractures of rock formations. About 30 percent of all readily available freshwater in the world is groundwater. A unit of rock or an unconsolidated deposit is called an aquifer when it can yield a usable quantity of water. The depth at which soil pore spaces or fractures and voids in rock become completely saturated with water is called the water table. Groundwater is recharged from the surface; it may discharge from the surface naturally at springs and seeps, and can form oases or wetlands. Groundwater is also often withdrawn for agricultural, municipal, and industrial use by constructing and operating extraction wells. The study of the distribution and movement of groundwater is hydrogeology, also called groundwater hydrology. Typically, groundwater is thought of as water flowing through shallow aquifers, but, in the technical sense, it can also contain soil moisture, perma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unconfined Aquifer
An aquifer is an underground layer of water-bearing, permeable rock, rock fractures, or unconsolidated materials (gravel, sand, or silt). Groundwater from aquifers can be extracted using a water well. Aquifers vary greatly in their characteristics. The study of water flow in aquifers and the characterization of aquifers is called hydrogeology. Related terms include aquitard, which is a bed of low permeability along an aquifer, and aquiclude (or ''aquifuge''), which is a solid, impermeable area underlying or overlying an aquifer, the pressure of which could create a confined aquifer. The classification of aquifers is as follows: Saturated versus unsaturated; aquifers versus aquitards; confined versus unconfined; isotropic versus anisotropic; porous, karst, or fractured; transboundary aquifer. Challenges for using groundwater include: overdrafting (extracting groundwater beyond the equilibrium yield of the aquifer), groundwater-related subsidence of land, groundwater becoming sa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Groundwater Discharge
Groundwater discharge is the volumetric flow rate of groundwater through an aquifer. Total groundwater discharge, as reported through a specified area, is similarly expressed as: :Q = \fracKA where :''Q'' is the total groundwater discharge ( 3·T−1 m3/s), :''K'' is the hydraulic conductivity of the aquifer ( ·T−1 m/s), :''dh/dl'' is the hydraulic gradient ( ·L−1 unitless), and :''A'' is the area which the groundwater is flowing through ( 2 m2) For example, this can be used to determine the flow rate of water flowing along a plane with known geometry. The discharge potential The discharge potential is a potential in groundwater mechanics which links the physical properties, hydraulic head, with a mathematical formulation for the energy as a function of position. The discharge potential, \Phi 3·T−1 is defined in such way that its gradient equals the discharge vector. Q_x = -\frac Q_y = -\frac Thus the hydraulic head may be calculated in terms of the discharge pot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aquifer
An aquifer is an underground layer of water-bearing, permeable rock, rock fractures, or unconsolidated materials (gravel, sand, or silt). Groundwater from aquifers can be extracted using a water well. Aquifers vary greatly in their characteristics. The study of water flow in aquifers and the characterization of aquifers is called hydrogeology. Related terms include aquitard, which is a bed of low permeability along an aquifer, and aquiclude (or ''aquifuge''), which is a solid, impermeable area underlying or overlying an aquifer, the pressure of which could create a confined aquifer. The classification of aquifers is as follows: Saturated versus unsaturated; aquifers versus aquitards; confined versus unconfined; isotropic versus anisotropic; porous, karst, or fractured; transboundary aquifer. Challenges for using groundwater include: overdrafting (extracting groundwater beyond the Dynamic equilibrium, equilibrium yield of the aquifer), groundwater-related subsidence of land, gro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jules Dupuit
Arsène Jules Étienne Juvenel Dupuit (18 May 1804 – 5 September 1866) was an Italian-born French civil engineer and economist. He was born in Fossano, Italy then under the rule of Napoleon Bonaparte. At the age of ten he emigrated to France with his family where he studied in Versailles — winning a Physics prize at graduation. He then studied in the École Polytechnique as a civil engineer. He gradually took on more responsibility in various regional posts. He received a Légion d'honneur in 1843 for his work on the French road system, and shortly after moved to Paris. He also studied flood management in 1848 and supervised the construction of the Paris sewer system. He died in Paris. Engineering questions led to his interest in economics, a subject in which he was self-taught. His 1844 article was concerned with deciding the optimum toll for a bridge. It was here that he introduced his curve of diminishing marginal utility. As the quantity of a good consumed rises, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philipp Forchheimer
Philipp Forchheimer (7 August 1852 in Vienna – 2 October 1933 in Dürnstein, Lower Austria) was an Austrian engineer, a pioneer in the field of civil engineering and practical hydraulics. He was professor in Istanbul, Aachen and Graz. He introduced mathematical methodology to the study of hydraulics, thus establishing a scientific basis for the field. He was director of the Graz University of Technology until 1897. In addition to his teaching, he worked as a consultant for construction projects. He made proposals for the construction of a tunnel under the English Channel. Modification to Darcy's Law Forchheimer proposed a modification to Darcy's Law, describing fluid flow through packed beds in 1901. This also had a significant influence on the development of the Ergun equation. -=u+b\rho, u, u where: dP is the pressure drop across the bed, \mu is the viscosity of the fluid, K permeability (const.), u is the (area-averaged) velocity of the fluid, b is an empirical const ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Groundwater Flow Equation
Used in hydrogeology, the groundwater flow equation is the mathematical relationship which is used to describe the flow of groundwater through an aquifer. The transient flow of groundwater is described by a form of the diffusion equation, similar to that used in heat transfer to describe the flow of heat in a solid (heat conduction). The steady-state flow of groundwater is described by a form of the Laplace equation, which is a form of potential flow and has analogs in numerous fields. The groundwater flow equation is often derived for a small representative elemental volume (REV), where the properties of the medium are assumed to be effectively constant. A mass balance is done on the water flowing in and out of this small volume, the flux terms in the relationship being expressed in terms of head by using the constitutive equation called Darcy's law, which requires that the flow is laminar. Other approaches are based on Agent Based Models to incorporate the effect of complex aqui ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytical Solution
Generally speaking, analytic (from el, ἀναλυτικός, ''analytikos'') refers to the "having the ability to analyze" or "division into elements or principles". Analytic or analytical can also have the following meanings: Chemistry * Analytical chemistry, the analysis of material samples to learn their chemical composition and structure * Analytical technique, a method that is used to determine the concentration of a chemical compound or chemical element * Analytical concentration Mathematics * Abstract analytic number theory, the application of ideas and techniques from analytic number theory to other mathematical fields * Analytic combinatorics, a branch of combinatorics that describes combinatorial classes using generating functions * Analytic element method, a numerical method used to solve partial differential equations * Analytic expression or analytic solution, a mathematical expression using well-known operations that lend themselves readily to calculation * A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Water Table
The water table is the upper surface of the zone of saturation. The zone of saturation is where the pores and fractures of the ground are saturated with water. It can also be simply explained as the depth below which the ground is saturated. The water table is the surface where the water pressure head is equal to the atmospheric pressure (where gauge pressure = 0). It may be visualized as the "surface" of the subsurface materials that are saturated with groundwater in a given vicinity. The groundwater may be from precipitation or from groundwater flowing into the aquifer. In areas with sufficient precipitation, water infiltrates through pore spaces in the soil, passing through the unsaturated zone. At increasing depths, water fills in more of the pore spaces in the soils, until a zone of saturation is reached. Below the water table, in the phreatic zone (zone of saturation), layers of permeable rock that yield groundwater are called aquifers. In less permeable soils, such as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydrostatic
Fluid statics or hydrostatics is the branch of fluid mechanics that studies the condition of the equilibrium of a floating body and submerged body "fluids at hydrostatic equilibrium and the pressure in a fluid, or exerted by a fluid, on an immersed body". It encompasses the study of the conditions under which fluids are at rest in stable equilibrium as opposed to fluid dynamics, the study of fluids in motion. Hydrostatics is a subcategory of fluid statics, which is the study of all fluids, both compressible or incompressible, at rest. Hydrostatics is fundamental to hydraulics, the engineering of equipment for storing, transporting and using fluids. It is also relevant to geophysics and astrophysics (for example, in understanding plate tectonics and the anomalies of the Earth's gravitational field), to meteorology, to medicine (in the context of blood pressure), and many other fields. Hydrostatics offers physical explanations for many phenomena of everyday life, such as why ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equipotential
In mathematics and physics, an equipotential or isopotential refers to a region in space where every point is at the same potential. This usually refers to a scalar potential (in that case it is a level set of the potential), although it can also be applied to vector potentials. An equipotential of a scalar potential function in -dimensional space is typically an ()-dimensional space. The del operator illustrates the relationship between a vector field and its associated scalar potential field. An equipotential region might be referred as being 'of equipotential' or simply be called 'an equipotential'. An equipotential region of a scalar potential in three-dimensional space is often an equipotential surface (or ''potential isosurface''), but it can also be a three-dimensional mathematical solid in space. The gradient of the scalar potential (and hence also its opposite, as in the case of a vector field with an associated potential field) is everywhere perpendicular to the equip ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Specific Weight
The specific weight, also known as the unit weight, is the weight per unit volume of a material. A commonly used value is the specific weight of water on Earth at , which is .National Council of Examiners for Engineering and Surveying (2005). ''Fundamentals of Engineering Supplied-Reference Handbook'' (7th ed.). . Often a source of confusion is that the terms ''specific gravity'', and less often ''specific weight'', are also used for relative density. A common symbol for specific weight is , the Greek letter Gamma. Definition The specific weight, , of a material is defined as the product of its density, , and the standard gravity, : \gamma = \rho \, g The density of the material is defined as mass per unit volume, typically measured in kg/m3. The standard gravity is acceleration due to gravity, usually given in m/s2, and on Earth usually taken as . Unlike density, specific weight is not a fixed property of a material. It depends on the value of the gravitational acceleration, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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