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Hydraulic Gradient

Hydraulic gradient

This is about the hydraulic head of slow-flowing groundwater, for fluid dynamic oriented definitions of hydraulic head, see hydraulic head (disambiguation page) Hydraulic head is a measure of the amount of energy groundwater, flowing through an aquifer, has per unit weight. The word head indicates that the quantity is expressed in terms of a length of water (1.0 m of head is equivalent to 9.8 kPa or 1 ft of head is equal to 0.43 psi or 3.0 kPa of pressure.) In hydrogeology, it is convention to use gauge pressure (pressure measured greater than atmospheric pressure), when speaking of pressure head (unless absolute pressure is explicitly specified).

Components of hydraulic head

atmospheric pressure atmospheric pressure Hydraulic head, in the context of slow-moving groundwater, is composed of two components. Pressure head is the gauge pressure at a point, in terms of water head and Elevation head is the relative amount of potential an object has due to its vertical position, compared to an arbitrary datum (it always increases 1:1 with elevation). Hydraulic head is the sum of pressure and elevation heads; it is the total energy per unit weight, differences in this energy cause groundwater flow from one place to another (if the flow were not slow , a velocity head would need to be included in the total head as well.) :

h = \psi + z \,

\psi = \frac

In the definition of ψ, p is the pressure (units of force per area, kPa or psi), and γ is the specific weight of water (related to the density as γ = gρ, units of force per volume, N/m³ or lbf/ft³). The first figure illustrates these how these three heads relate for a hydrostatic case (no flow). The top of the hydrostatic column is a water table (atmospheric, or zero pressure head), while the outlet of a tube or hose connected to the bottom is held at the same height as the top of the column. Hydraulic head is constant (no hydraulic head gradient), elevation head increases 1:1 (as it always does), and typically pressure head is determined as the difference of the two. For the hydrostatic case, the two components of hydraulic head can simply be thought of as the water above a point in the aquifer (the hydrostatic pressure of the column of water above) and the water below that point (the elevation pressure, representing the water below).

Hydraulic gradient

The second figure illustrates the same three heads when there is steady-state flow through the column, due to a hydraulic head gradient (indicated by the slope of the red line). The pressure head is still zero at the top of the column (water table conditions), but the tube connected to the outflow from the bottom of the column is held at an elevation of 0.75 m, which produces a net hydraulic head gradient. The gradient is defined as change in hydraulic head per length of flow path, or (h_a − h_b)/L, and has units of length of water per length of flowpath, :

0.25  \frac= \frac

. This gradient is positive (increasing) upward, and Darcy's law indicates that flow would be out the bottom valve on the column (water flows "downhill", from high hydraulic head to low hydraulic head, against the mathematical gradient). Also note that water would flow upward in the second column if the hydraulic head gradient was pushing it that way, even though that is "up" in the column; i.e., if the pressure head gradient (slope of the blue line) overcomes the elevation head gradient (the 1:1 slope of the green line), water will flow "uphill".

Atmospheric Pressure

Even though it is convention to use gauge pressure in the calculation of hydraulic head, it is more correct to use total pressure (gauge pressure + atmospheric pressure), since this is truly what drives groundwater flow. Often detailed observations of barometric pressure are not available at each well through time, so this is often disregarded (contributing to large errors at locations where hydraulic gradients are low or the angle between wells is acute.) The effects which changes in atmospheric pressure have water levels observed in wells has been known for many years. The effect is a direct one, an increase in atmospheric pressure is an increase in load on the water in the aquifer, which increases the depth to water (lowers the water level elevation). Pascal first qualitatively observed these effects in the 1600s, and they were more rigorously described by the soil physicist Edgar Buckingham (working for the USDA) using air flow models in 1907.

Groundwater

Groundwater is water which may be flowing within aquifers below the water table. Within aquifers, the water flows through the pore spaces in unconsolidated sediments and the fractures of rocks. Groundwater is recharged from, and eventually flows to, the surface naturally; natural discharge often occurs at springs and seeps and can form oases or swamps. Groundwater is also often withdrawn for agricultural, municipal and industrial use through man-made wells. The study of the distribution and movement of groundwater is hydrogeology. hydrogeology Groundwater can be a long-term 'reservoir' of the natural water cycle (with residence times from days to millennia), as opposed to short-term water reservoirs like the atmosphere and fresh surface water (which have residence times from minutes to years). The figure shows how deep groundwater (which is quite distant from the surface recharge) can take a very long time to complete its natural cycle. Groundwater is naturally replenished by surface water from precipitation, streams, and rivers when this recharge reaches the water table. It is estimated that the volume of groundwater is fifty times that of surface freshwater; the icecaps and glaciers are the only larger reservoir of fresh water on earth. Usable groundwater is contained in aquifers, which are subterranean areas (or layers) of permeable material (like sand and gravel) that channel the groundwater's flow. Aquifers can be confined or unconfined. If a confined aquifer follows a downward grade from a recharge zone, groundwater can become pressurized as it flows. This can create artesian wells that flow freely without the need of a pump. The top of the upper unconfined aquifer is called the water table or phreatic surface, where water pressure is equal to atmospheric pressure. Typically groundwater is thought of as liquid water flowing through shallow aquifers, but technically it can also include soil moisture, permafrost (frozen soil), immobile water in very low permeability bedrock, and deep geothermal or oil formation water. Groundwater is believed to provide lubrication and buoyancy which allow thrust faults to move. Nearly any point in the Earth's subsurface has water in it, to some degree (it may be very dry or mixed with other fluids). Groundwater is not confined only to the Earth, either; subsurface water on Mars is believed to have given rise to some of the landforms observed there. Ground water makes up about twenty percent of the world's fresh water supply, which is about .61 percent of the entire world's water supply. (Environment Canada Website)

Problems with groundwater

Groundwater overdraft

Groundwater is a highly useful and abundant resource, but in arid or semi-arid regions it cannot renew itself as rapidly as it is being withdrawn by humans. If groundwater is extracted intensively from water wells, as for irrigation or municipal use in arid or semi-arid regions, it may not recover to its pre-development state. The most evident problem that may result from this is a lowering of the water table beyond the reach of existing wells. Wells must consequently be deepened to reach the groundwater; in some places (e.g., California, Texas and India) the water table has dropped hundreds of feet due to well pumping. A lowered water table may, in turn, cause other problems such as subsidence.

Subsidence

In its natural equilibrium state, the groundwater in the pore spaces of the aquifer supports some of the weight of the overlying sediments. When groundwater is depressurized or even removed from aquitards, where the materials are very compressible and pore pressures can be high, compaction may occur. This compaction, typically called subsidence, may be partially recoverable if pressures rebound, but much of it is not. Thus the aquifer is permanently reduced in capacity, and the surface of the ground may also subside. The city of New Orleans, Louisiana is actually below sea level today, and its subsidence is partly caused by removal of ground water from the various aquifers beneath it.

Seawater intrusion

Generally, in very humid or undeveloped regions, the shape of the water table mimics the slope of the surface. The recharge zone of an aquifer near the seacoast is likely to be inland, often at considerable distance. In these coastal areas, a lowered water table may induce sea water to reverse the flow toward the sea. Sea water moving inland is called a saltwater intrusion. Alternatively, salt from mineral beds may leach into the groundwater of its own accord.

Mining groundwater

Sometimes the water movement from the recharge zone to the place where it is withdrawn may take centuries (see figure above). When the usage of water is greater than the recharge, it is referred to as mining water (the water is often called fossil water, due to its geologic age). Under those circumstances it is not a renewable resource.

Groundwater pollution

In the Ganges Plain of northern India and Bangladesh, severe natural pollution by arsenic affects 25% of water wells in the shallower of two regional aquifers. The pollution occurs because aquifer sediments contain organic matter (dead plant material) that generates anaerobic (an environment without oxygen) conditions in the aquifer. These conditions result in the microbial dissolution of iron oxides in the sediment and thus the release of the arsenic, normally strongly bound to iron oxides, into the water. As a consequence, arsenic-rich groundwater is often iron-rich, although secondary processes often obscure the association of dissolved arsenic and dissolved iron. Not all groundwater problems are caused by over-extraction. Pollutants dumped on the ground or in landfills may leach into the soil, and work their way down into aquifers. Movement of water within the aquifer is then likely to spread the pollutant over a wide area, making the groundwater unusable. Areas of karst topography on limestone bedrock are especially vulnerable to surface pollution. Sinkholes and underground caverns allow direct groundwater flow without the filtering effect of a permeable aquifer. See environmental engineering and remediation. Water table conditions are of great importance to agricultural irrigation, waste disposal (including nuclear waste), and other ecological issues.

Groundwater

Problems with groundwater

Groundwater overdraft

Subsidence

Seawater intrusion

Mining groundwater

Groundwater pollution

Meter

:This article is about the unit of length. For other uses of metre or meter, see meter (disambiguation). The metre (Commonwealth English) or meter (American English) (symbol: m) is the SI base unit of length. It is defined as the length of the path travelled by light in absolute vacuum during a time interval of 1/299,792,458 of a second. Adding SI prefixes to metre creates multiples and submultiples; for example kilometre (1000 metres; kilo- = 1000) and millimetre (one thousandth of a metre; milli- = 1 / 1 000).

Conversions

1 metre is equivalent to:
- exactly 1/0.9144 yards (approximately 1.0936 yards)
- exactly 1/0.3048 feet (approximately 3.2808 feet)
- exactly 10000/254 inches (approximately 39.370 inches)

History

The word metre is from the Greek metron (μετρον), "a measure" via the French mètre. Its first recorded usage in English is from 1797. In the 18th century, there were two favoured approaches to the definition of the standard unit of length. One suggested defining the metre as the length of a pendulum with a half-period of one second. The other suggested defining the metre as one ten-millionth of the length of the earth's meridian along a quadrant (one-fourth the polar circumference of the earth). In 1791, the French Academy of Sciences selected the meridional definition over the pendular definition because of the slight variation of the force of gravity over the surface of the earth, which affects the period of a pendulum. In 1793, France adopted the metre, with this definition, as its official unit of length. Although it was later determined that the first prototype metre bar was short by a fifth of a millimetre due to miscalculation of the flattening of the earth, this length became the standard. So, the circumference of the Earth through the poles is approximately forty million metres. Earth in a vacuum.]] In the 1870s and in light of modern precision, a series of international conferences were held to devise new metric standards. The Metre Convention (Convention du Mètre) of 1875 mandated the establishment of a permanent International Bureau of Weights and Measures (BIPM: Bureau International des Poids et Mesures) to be located in Sèvres, France. This new organisation would preserve the new prototype metre and kilogram when constructed, distribute national metric prototypes, and would maintain comparisons between them and non-metric measurement standards. This organisation created a new prototype bar in 1889 at the first General Conference on Weights and Measures (CGPM: Conférence Générale des Poids et Mesures), establishing the International Prototype Metre as the distance between two lines on a standard bar of an alloy of ninety percent platinum and ten percent iridium, measured at the melting point of ice. In 1893, the standard metre was first measured with an interferometer by Albert A. Michelson, the inventor of the device and an advocate of using some particular wavelength of light as a standard of distance. By 1925, interferometry was in regular use at the BIPM. However, the International Prototype Metre remained the standard until 1960, when the eleventh CGPM defined the metre in the new SI system as equal to 1,650,763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum. The original international prototype of the metre is still kept at the BIPM under the conditions specified in 1889. To further reduce uncertainty, the seventeenth CGPM of 1983 replaced the definition of the metre with its current definition, thus fixing the length of the metre in terms of time and the speed of light: :The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. Note that this definition exactly fixes the speed of light in a vacuum at 299,792,458 metres per second. Definitions based on the physical properties of light are more precise and reproducible because the properties of light are considered to be universally constant.

Timeline of definition

- 1790 May 8 — The French National Assembly decides that the length of the new metre would be equal to the length of a pendulum with a half-period of one second.
- 1791 March 30 — The French National Assembly accepts the proposal by the French Academy of Sciences that the new definition for the metre be equal to one ten-millionth of the length of the earth's meridian along a quadrant (one-fourth the polar circumference of the earth).
- 1795 — Provisional metre bar constructed of brass.
- 1799 December 10 — The French National Assembly specifies that the platinum metre bar, constructed on 23 June 1799 and deposited in the National Archives, as the final standard.
- 1889 September 28 — The first CGPM defines the length as the distance between two lines on a standard bar of an alloy of platinum with ten percent iridium, measured at the melting point of ice.
- 1927 October 6 — The seventh CGPM adjusts the definition of the length to be the distance, at 0 °C, between the axes of the two central lines marked on the prototype bar of platinum-iridium, this bar being subject to one standard atmosphere of pressure and supported on two cylinders of at least one centimetre diameter, symmetrically placed in the same horizontal plane at a distance of 571 millimetres from each other.
- 1960 October 20 — The eleventh CGPM defines the length to be equal to 1,650,763.73 wavelengths in vacuum of the radiation corresponding to the transition between the 2p¹⁰ and 5d⁵ quantum levels of the krypton-86 atom.
- 1983 October 21 — The seventeenth CGPM defines the length to be distance travelled by light in vacuum during a time interval of 1/299 792 458 of a second.

External links

- [http://www.unitconversion.org/unit_converter/length.html?unit=meter&value=1 Length Converter: convert metre to other units, such as yard, mile, and so on]
- [http://physics.nist.gov/cuu/Units/meter.html History of the metre at the U.S. National Institute of Standards and Technology (NIST)]
- [http://www.mel.nist.gov/div821/museum/timeline.htm Timeline of history of the metre at the NIST]
- [http://www1.bipm.org/en/scientific/length/ Bureau International des Poids et Measures - Lengths] Category:SI base units Category:Units of length ko:미터 ms:Meter ja:メートル simple:Metre th:เมตร

Foot (unit of length)

:For other uses, see Foot (disambiguation). A foot (plural: feet) is a non-SI unit of distance or length, measuring around a third of a metre. There are twelve inches in one foot and three feet in one yard. The international standard symbol for feet is ft (see ISO 31-1, Annex A). The standardization of weights and measures has left several different standard foot measures. The most commonly used foot today is the English foot, used in the United Kingdom and the United States and elsewhere, which is defined to be exactly 0.3048 metre. This unit is sometimes denoted with a prime (e.g. 30′ means 30 feet), often approximated by an apostrophe. Similarly, inches can be denoted by a double prime (often approximated by a quotation mark), so 6′ 2″ means 6 feet 2 inches. In addition to the current standard international foot, there is also a slightly different U.S. survey foot, used only in connection with surveys by the U.S. Coast and Geodetic Survey, it is defined as exactly 1200/3937 m (610 nm greater than 0.3048 m).[http://www.ngs.noaa.gov/PUBS_LIB/FedRegister/FRdoc59-5442.pdf] The foot as a measure was used in almost all cultures. The first known standard foot measure was from Sumeria, where a definition is given in a statue of Gudea of Lagash from around 2575 BC. The imperial foot was adapted from an Egyptian measure by the Greeks, with a subsequent larger foot being adopted by the Romans.

Etymology

The popular belief is that original standard was the length of a man's foot. The original measurement was from King Henry I, who had a foot 12 inches long; he wished to standardise the unit of measurement in England. The average foot length is about 9.4 inches (240 mm) for current Europeans. Approximately 996 out of 1000 British men have a foot that is less than 12 inches long. A plausible explanation for the missing inches is that the measure did not refer to a naked foot, but to the length of footwear. This is consistent with the measure being convenient for practical purposes such as on building sites etc. People almost always pace out lengths whilst wearing shoes or boots, rather than removing them and pacing barefoot.

External link

- http://www.onlineconversion.com/ from feet to international system
- http://www.knowledgedoor.com/1/Library_of_Units_and_Constants/Group_Index/foot_group.htm Foot Foot Foot Category:Human-based units of measure ja:フィート

Psi

Psi has multiple meanings:
- Psi (letter) (Ψ, ψ) of the Greek alphabet
- Psi (Cyrillic) (Ѱ, ѱ), letter of the early Cyrillic alphabet, adopted from Greek
- Psi (instant messenger) software
- Psi is supposed psychic or psionic powers in parapsychology (e.g., used as the symbol for the Psi Corps in the fictional Babylon 5 universe)
- Psi, a character in the game and television series Pokémon
- Schrödinger equation in quantum mechanics, ψ
- J/ψ particle, a subatomic particle
- Ψ in mathematics is the angle between the tangent and the x-axis in the intrinsic coordinates system The abbreviation PSI stands for:
- Paul Scherrer Institute in Villigen, Switzerland
- Permanent Staff Instructor in the British Army
- Permanent Subcommittee on Investigations (PSI) of the U.S. Senate
- Population Services International, an Angolan company
- Program Specific Information, metadata for digital transmission
- Proliferation Security Initiative
- Partito Socialista Italiano, the Italian Socialist Party
- Partit Socialista de les Illes, the Socialist Party of the Islands
- Professors for a Strong Israel The abbreviation psi stands for:
- Pound-force per square inch, a non-SI unit of pressure ja:PSI

Hydrogeology

Hydrogeology (hydro- meaning water, and -geology meaning the study of rocks) is the part of hydrology that deals with the distribution and movement of groundwater in the soil and rocks of the Earth's crust (commonly in aquifers). The term geohydrology is often used interchangeably. Some make the minor distinction between a hydrologist or engineer applying themselves to geology (geohydrology), and a geologist applying themselves to hydrology (hydrogeology).

Introduction

Hydrogeology (like most earth sciences) is an interdisciplinary subject; it can be difficult to account fully for the chemical, physical, biological and even legal interactions between soil, water, nature and man. Although the basic principles of hydrogeology are very intuitive (e.g., water flows "downhill"), the study of their interaction can be quite complex. Taking into account the interplay of the different facets of a multi-component system often requires knowledge in several diverse fields at both the experimental and theoretical levels. This being said, the following is a more traditional (reductionist viewpoint) introduction to the methods and nomenclature of saturated subsurface hydrology, or simply hydrogeology.

Hydrogeology in relation to other fields

Hydrogeology, as stated above, is a branch of the earth sciences dealing with the flow of water through aquifers and other shallow porous media (typically less than 450 m or 1,500 ft below the land surface.) The very shallow flow of water in the subsurface (the upper 3 m or 10 ft) is pertinent to the fields of soil science, agriculture and civil engineering, as well as to hydrogeology. The general flow of fluids (water, hydrocarbons, geothermal fluids, etc.) in deeper formations is also a concern of geologists, geophysicists and petroleum geologists. Groundwater is a slow-moving, viscous fluid (with a Reynolds number less than unity); many of the empirically derived laws of of groundwater flow can be alternately derived in fluid mechanics from the special case of Stokes flow (viscosity and pressure terms, but no inertial term). The mathematical relationships used to describe the flow of water through porous media are the diffusion and Laplace equations, which have applications in many diverse fields. Steady groundwater flow (Laplace equation) has been simulated using electrical, elastic and heat conduction analogies. Transient groundwater flow is analogous to the diffusion of heat in a solid, therefore some solutions to hydrological problems have been adapted from heat transfer literature. Traditionally, the movement of groundwater has been studied separately from surface water, climatology, and even the chemical and microbiological aspects of hydrogeology (the processes are uncoupled). As the field of hydrogeology matures, the strong interactions between groundwater, surface water, water chemistry, soil moisture and even climate are becoming more clear.

Definitions and material properties

Main article: Aquifer In order to further characterize aquifers and aquitards some primary and derived physical properties are introduced below. Aquifers are broadly classified as being either confined or unconfined (water table aquifers), and either saturated or unsaturated; the type of aquifer affects what properties control the flow of water in that medium (e.g., the release of water from storage for confined aquifers is related to the storativity, while it is related to the specific yield for unconfined aquifers).

Hydraulic head

Main article: Hydrualic head (hydrology) Changes in hydraulic head (h) are the driving force which causes water to move from one place to another. It is composed of pressure head (ψ) and elevation head (z). The head gradient is the change in hydraulic head per length of flowpath, and appears in Darcy's law as being proportional to th discharge. Hydraulic head is a directly measurable property; ψ can be measured with a pressure transducer, and z can be measured relative to a surveyed datum (typically the top of the well casing). Commonly, in wells tapping unconfined aquifers the water level in a well is used as a proxy for hydraulic head, assuming there is no vertical gradient of pressure. Often only changes in hydraulic head through time are needed, so the constant elevation head term can be left out (Δh = Δψ). A record of hydraulic head through time at a well is a hydrograph or, the changes in hydraulic head recorded during the pumping of a well in a test are called drawdown.

Porosity

Main article: Porosity. Porosity (n) is a directly measurable aquifer property; it is a fraction between 0 and 1 indicating the amount of pore space between unconsolidated soil particles or within a fractured rock. Typically, the majority of groundwater (and anything dissolved in it) moves through the porosity available to flow (sometimes called efective porosity). Porosity does not directly effect the distribution of hydraulic head in an aquifer, but it very strongly effects the migration of dissolved contaminants, since groundwater flow velocities are controlled by it.

Water content

Main page: water content Water content (θ) is also a directly measurable property; it is the fraction of the total rock which is filled with liquid water. This is also a fraction between 0 and 1, but it must also be less than the total porosity. The water content is very important in vadose zone hydrology, where the hydraulic conductivity is a strongly nonlinear function of water content; this complicates the solution of the unsaturated groundwater flow equation.

Hydraulic conductivity

Main article: Hydraulic conductivity. Hydraulic conductivity (k) and transmissivity (T) are indirect aquifer properties (they cannot be measured directly). T is the k integrated over the vertical thickness (b) of the aquifer (T=kb). These properties are measures of an aquifer's ability to transmit water. Intrinsic permeability (κ) is a secondary medium property which does not depend on the viscosity and density of the fluid (k and T are specific to water); it is used more in the petroleum industry.

Specific storage and specific yield

Main article: Specific storage. Specific storage (S_s) and its depth-integrated equivalent, storativity (S=S_sb), are indirect aquifer properties (they cannot be mesured directly); they indicate of the amount of groundwater released from storage due to a unit depressurization of a confined aquifer. They are fractions between 0 and 1. Specific yield (S_y) is also a ratio between 0 and 1 which indicates the amount of water released due to drainage, from lowering the water table in an unconfined aquifer. Typically S_y is orders of magnitude larger than S_s. Often the porosity or effective porosity is used as an approximation to the specific yield.

Governing equations

Darcy's Law

Main Article: Darcy's law Darcy's law is a Constitutive_equation (derived by Henri Darcy, in 1856) which states the amount of groundwater discharging through a given portion of aquifer is proportional to the cross-sectional area to flow, the hydraulic head gradient and the hydraulic conductivity.

Groundwater flow equation

Main Article: Groundwater flow equation The groundwater flow equation, in its most general form, describes the movement of groundwater in a porous medium (aquifers and aquitards). It is known in mathematics as the diffusion equation, and has many analogs in other fields. Many solutions for groundwater flow problems were borrowed or adapted from existing heat transfer solutions. It is often derived from a physical basis using Darcy's law and a conservation of mass for a small control volume. The equation is often used to predict flow to wells, which have radial symmetry, so the flow equation is commonly solved in polar or cylindrical coordinates. The Theis equation is one of the most commonly used and fundamental solutions to the groundwater flow equation; it can be used to predict the head around a pumping well, due to the effects of pumping one or a number of wells.

Calculation of groundwater flow

To use the groundwater flow equation to estimate the distribution of hydraulic heads, or the direction and rate of groundwater flow, this partial differential equation (PDE) must be solved. The most common means of analytically solving the diffusion equation in the hydrogeology literature are:
- Laplace and Fourier transforms (to reduce the number of dimensions of the PDE),
- similarity transform (also called the Boltzmann transform) is commonly how the Theis solution is derived,
- separation of variables, which is more useful for non-Cartesian coordinates, and
- Green's functions, which is another common method for deriving the Theis solution — from the fundamental solution to the diffusion equation in free space. No matter which method we use to solve the groundwater flow equation, we need both initial conditions (heads at time (t) = 0) and boundary conditions (representing either the physical boundaries of the domain, or an approximation of the domain beyond that point). Often the initial conditions are supplied to a transient simulation, by a corresponding steady-state simulation (where the time derivative in the groundwater flow equation is set equal to 0). There are two broad categories of how the (PDE) would be solved; either analytical methods, numerical methods, or something possibly in between. Typically, analytic methods solve the groundwater flow equation under a simplified set of conditions exactly, while numerical methods solve it under more general conditions to an approximation.

Analytic methods

Analytic methods typically use the structure of mathematics to arrive at a simple, elegant solution, but the required derivation for all but the simplest domain geometries can be quite complex (involving non-standard coordinates, conformal mapping, etc.). Analytic solutions typically are also simply an equation, which can give a quick answer based on a few basic parameters. The Theis equation is a very simple (yet still very useful) analytic solution to the groundwater flow equation, typically used to analyze the results of an aquifer test or slug test.

Numerical Methods

The topic of numerical methods is quite large, obviously being of use to most fields of engineering and science in general. Numerical methods have been around much longer than computers have (In the 1920s Richardson developed some of the finite difference schemes still in use today, but they were calculated by hand, using paper and pencil, by human "calculators"), but they have become very important through the availability of fast and cheap personal computers. A quick survey of the main numerical methods used in hydrogeology, and some of the most basic principles is below. There are two broad categories of numerical methods: gridded or discretized methods and non-gridded or mesh-free methods. In the common finite difference method and finite element method (FEM) the domain is completely gridded. The analytic element method (AEM) and the boundary integral equation method (BIEM — sometimes also called BEM, or Boundary Element Method) are only discretized at boundaries or along flow elements (line sinks, area sources, etc.), the majority of the domain is mesh-free. General Properties of Gridded Methods
Gridded Methods like finite difference and finite element methods solve the groundwater flow equation by breaking the problem area (domain) into many small elements (squares, rectangles, triangles, blocks, tetrahedra, etc.) and solving the flow equation for each element (all material properties are assumed constant or possibly linearly variable within an element), then linking together all the elements using conservation of mass across the boundaries between the elements (similar to the divergence theorem). This results in a system which overall approximates the groundwater flow equation, but exactly matches the boundary conditions (the head or flux is specified in the elements which intersect the boundaries). Finite differences are a way of representing continuous differential operators using discrete intervals (Δx and Δt), and the finite difference methods are based on these (they are derived from a Taylor series). For example the first-order time derivative is often approximated using the following forward finite difference, where the subscripts indicate a discrete time location, :

\frac = h'(t_i) \approx \frac

. The forward finite difference approximation is unconditionally stable, but leads to an implicit set of equations (that must be solved using matrix methods, e.g. LU or Cholesky decomposition). The similar backwards difference is only conditionally stable, but it is explicit and can be used to "march" forward in the time direction, solving one grid node at a time (or possibly in parallel, since one node depends only on its immediate neighbors). Rather than the finite difference method, sometimes the Galerkin FEM approximation is used in space (this is different from the type of FEM often used in structural engineering) with finite differences still used in time. Application of Finite Difference Models
[http://water.usgs.gov/nrp/gwsoftware/modflow.html MODFLOW] is a well-known example of a general finite difference groundwater flow model. It was developed by the US Geological Survey (USGS) in 1988 as a modular and extensible simulation tool for modeling groundwater flow. It is free software developed, documented and distributed by the USGS. Many commercial products have grown up around it, providing graphical user interfaces to its text file based interface, and typically incorporating pre- and post- processing of user data. Many other models have been developed to work with MODFLOW input and output, making linked models which simulate several hydrologic processes possible (flow and transport models, surface water and groundwater models and chemical reaction models), because of the simple, well documented nature of MODFLOW. Application of Finite Element Models
Finite Element programs are more flexible in design (triangular elements vs. the block elements most finite difference models use) and there are some programs available ([http://water.usgs.gov/software/sutra.html SUTRA], a 2D or 3D density-dependent flow model by the USGS; [http://www.hydrus2d.com/ Hydrus], a commercial unsaturated flow model; and [http://www.comsol.com/ COMSOL Multiphysics (FEMLAB)] a commercial general modeling environment), but they are not as popular in with practicing hydrogeologists as MODFLOW is. Finite element models are more popular in university and laboratory environments, where specialized models solve non-standard forms of the flow equation (unsaturated flow, density dependant flow, coupled heat and groundwater flow, etc.) Other Methods
These include mesh-free methods like the Analytic Element Method (AEM) and the Boundary Integral Equation Method (BIEM), which are closer to analytic solutions, but they do approximate the groundwater flow equation in some way. The BIEM and AEM exactly solve the groundwater flow equation (perfect mass balance), while approximating the boundary conditions. These methods are more exact and can be much more elegant solutions (like analytic methods are), but have not seen as widespread use outside academic and research groups.

External links and sources

- [http://www.epa.gov/safewater/ EPA drinking water standards]
- [http://water.usgs.gov/ US Geological Survey water resources homepage] — a good place to find free data (for both surface water and groundwater) and free groundwater modeling software like MODFLOW.
- [http://water.usgs.gov/pubs/twri/ US Geological Survery TWRI index] — a series of instructional manuals covering common procedures in hydrogeology. They are freely available online as PDF files.
- [http://typhoon.mines.edu/ International Ground Water Modeling Center (IGWMC)] — an educational repository of groundwater modeling software which offers support for most software, some of which is free. Category:Water Category:Geology Category:Hydrology Category:Civil engineering

Atmospheric pressure

Atmospheric pressure is the pressure above any area in the Earth's atmosphere caused by the weight of air. Standard atmospheric pressure (atm) is discussed in the next section. Air masses are affected by the general atmospheric pressure within the mass, creating areas of high pressure (anti-cyclones) and low pressure (depressions). As elevation increases, fewer air molecules are above. Therefore, atmospheric pressure decreases with increasing altitude. The following relationship is a first-order approximation: :

\log_ P \approx

, where P is the pressure in pascals and h the height in metres. This shows that the pressure at an altitude of 31 km is about 10^(5-2) Pa = 1000 Pa, or 1% of that at sea level¹. A column of air, 1 square inch in cross section, measured from sea level to the top of the atmosphere would weigh approximately 14.7 lbf. A 1 m² column of air would weigh about 100 kilonewtons. See density of air.

Standard atmospheric pressure

Standard atmospheric pressure or "the standard atmosphere" (1 atm) is defined as 101.325 kilopascals (kPa). (see also Standard temperature and pressure) This can also be stated as:
- 29 117/127 inches of mercury ≈ 29.92 inHg
- 760 millimetres of mercury (mmHg) or torrs (Torr)
- 1013.25 millibars (mbar, also mb) or hectopascals (hPa)
- 14.6959 psia or 0 psig (pounds-force per square inch, absolute or gauge) (lbf/in²)
- 2116.2 pounds-force per square foot (lbf/ft²)
- 1 6517/196133 technical atmospheres (at) ≈ 1.03322745 at This "standard pressure" is a purely arbitrary representative value for pressure at sea level, and real atmospheric pressures vary from place to place and moment to moment everywhere in the world. In the United States, compressed air flow is often measured in "standard cubic feet" per unit of time, where the "standard" means the equivalent quantity of air at standard temperature and pressure. However, this standard atmosphere is defined slightly differently: temperature = 68 °F (20 °C), air density = 0.075 lb/ft³ (1.20 kg/m³), altitude = sea level, and relative humidity = 0%. In the air conditioning industry, the standard is often temperature = 32 °F (0 °C) instead. For natural gas, the petroleum industry uses a standard temperature of 60 °F (15.6 °C).

Mean sea level pressure (MSLP or SLP)

Mean sea level pressure (MSLP or SLP) is the pressure at sea level or (when measured at a given height on land) the station pressure reduced to sea level by an appropriate altitude dependant formula. This is the pressure normally given in weather reports on radio, television, and newspapers. When barometers in the home are set to match the local weather reports, they measure pressure reduced to sea level, not the actual local atmospheric pressure. The reduction to sea level means that the normal range of fluctuations in pressure is the same for everyone. The pressures which are considered high pressure or low pressure do not depend on geographical location. This makes isobars on a weather map meaningful and useful tools. The altimeter setting in aviation, set either QNH or QFE, is another atmospheric pressure reduced to sea level, but the method of making this reduction differs slightly. See altimeter.
- QNH barometric altimeter setting which will cause the altimeter to read altitude above mean sea level in the vicinity of an airfield.
- QFE barometric altimeter setting which will cause an altimeter to read height above a particular runway threshold if set to the correct field elevation while on the ground. Average sea-level pressure is 1013.25 hPa (mbar) or 29.921 inches of mercury (inHg). In aviation weather reports (METAR), QNH is transmitted around the world in millibars or hectopascals, except in the United States and Canada where it is reported in inches of mercury. (The United States also reports sea level pressure SLP, which is reduced to sea level by a different method, in the remarks section, not an internationally transmitted part of the code, in hectopascals or millibars. In Canada's public weather reports, sea level pressure is reported in kilopascals, while Environment Canada's standard unit of pressure is hectopascal.) In the weather code, three digits are all that is needed, Decimal points and the one or two most significant digits are omitted: 1013.2 mbar or 101.32 kPa is transmitted as 132; 1000.0 mbar or 100.00 kPa is transmitted as 000; 998.7 mbar or 99.87 kPa is transmitted as 987; etc. The highest sea-level pressure on Earth occurs in Siberia, where the Siberian High often attains a sea-level pressure above 1032.0 mbar. The lowest measurable sea-level pressure is found at the centers of hurricanes (typhoons, baguios).

Atmospheric pressure variation

Atmospheric pressure varies widely on the Earth, and these variations are important in studying weather and climate. See pressure system for the effects of air pressure variations on weather.. The highest recorded atmospheric pressure, 108.6 kPa (1086 mbar or 32.06 inches of mercury), occurred at Tosontsengel, Mongolia, 19 December, 2001². The lowest recorded non-tornadic atmospheric pressure, 87.0 kPa (870 mbar or 25.69 inHg), occurred in the Western Pacific during Typhoon Tip on 12 October, 1979². The record for the Atlantic ocean was 88.2 kPa (882 mbar or 26.04 inHg) during Hurricane Wilma on 19 October 2005. Atmospheric pressure shows a diurnal (daily) rhythm. This effect is very strong in tropical zones, and almost zero in polar areas. A graph shows these rhymic variations in northern Europe on the top of this page. In tropical zones it may reach above 5 mbar variation. These variations follow a circadian (24 h) and at the same time semi-circadian (12 h) rhythm.

Intuitive feeling for atmospheric pressure based on height of water

Atmospheric pressure is often measured with a mercury barometer, and a height of approximately 30 inches of mercury is often used to teach, make visible, and illustrate (and measure) atmospheric pressure. However, since mercury is not a substance that humans commonly come in contact with, water often provides a more intuitive way to conceptualize the amount of pressure in one atmosphere. 1 atmosphere (14.7 lbf/in²) is the amount of pressure that can lift water approximately 33.9 feet (10.3 m). Thus, a diver at a depth 10.3 meters under water in the ocean experiences a pressure of about 2 atmospheres (1 atm for the air and 1 atm for the water). In terms of city water pressure, one atmosphere is approximately one-half to one-fifth the pressure of typical city water mains (i.e., water pressure is around 2 to 5 atmospheres).

References

# US Department of Defense Military Standard 810E # Burt, Christopher C., (2004). Extreme Weather, A Guide & Record Book. W. W. Norton & Company # U.S. Standard Atmosphere, 1962, U.S. Government Printing Office, Washington, D.C., 1962. # U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C., 1976.

External links

- [http://www.atmosculator.com/The%20Standard%20Atmosphere.html? A detailed mathematical model of the 1976 U.S. Standard Atmosphere]

Experiments

- [http://avc.comm.nsdlib.org/cgi-bin/wiki_print.pl? An exercise in air pressure]
- [http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/patm.html#atm Movies on atmospheric pressure experiments] from Georgia State University's HyperPhysics website. (requires Quicktime) Category:Atmosphere Category:Meteorology Category:Units of pressure Category:Diving ko:대기압 ja:気圧

Pressure

:For the psychological or political context, see Peer pressure. Pressure (symbol: p) is the force per unit area acting on a surface in a direction perpendicular to that surface. Mathematically: :

p = F/A\,

where p is the pressure, F is the normal force, and A is the area. Pressure is transmitted to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. It is a fundamental parameter in thermodynamics and it is conjugate to volume. A closely related quantity is the stress tensor σ which relates the vector force F to the vector area A via :

\mathbf=\mathbf

This tensor may be divided up into a scalar part (pressure) and a traceless tensor part shear. The shear tensor gives the force in directions parallel to the surface, usually due to viscous or frictional forces. The stress tensor is sometimes called the pressure tensor, but in the following, the term "pressure" will refer only to the scalar pressure. shear

Example

As an example of varying pressures, a finger can be pressed against a wall without making any lasting impression; however, the same finger pushing a thumbtack can easily damage the wall. Although the force applied to the surface is the same, the thumbtack applies more pressure because the point concentrates that force into a smaller area. Pressure is transmitted to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. Unlike stress, pressure is defined as a scalar quantity. The gradient of pressure is force density. In the human body, baroreceptors monitor blood pressure.

Relative or gauge pressure

For gases, pressure is sometimes measured, not as an absolute pressure, but relative to atmospheric pressure; such measurements are sometimes called gauge pressure. An example of this is the air pressure in a car tire, which might be said to be "220 kPa," but is actually 220 kPa above atmospheric pressure. Since atmospheric pressure at sea level is about 100 kPa, the absolute pressure in the tire is therefore about 320 kPa. In technical work, this is written "a gauge pressure of 220 kPa." Where space is limited, such as on gauges, name plates, graph labels, and table headings, the use of a modifier in parentheses, such as "kPa (gauge)" or "kPa (absolute)," is permitted. In non-SI technical work, a gauge pressure is sometimes written as "32 psig," though the other methods explained above that avoid attaching characters to the unit of pressure are preferred [http://physics.nist.gov/Pubs/SP811/sec07.html#7.4 ¹].

Scalar nature of pressure

In static gas, the gas as a whole does not appear to move, the individual molecules of the gas, which we cannot see, are in constant random motion. Because we are dealing with an extremely large number of molecules and because the motion of the individual molecules is random in every direction, we do not detect any motion. If we enclose the gas within a container, we detect a pressure in the gas from the molecules colliding with the walls of our container. We can put the walls of our container anywhere inside the gas, and the force per unit area (the pressure) is the same. We can shrink the size of our "container" down to an infinitely small point, and the pressure has a single value at that point. Therefore, pressure is a scalar quantity, not a vector quantity. It has a magnitude but no direction associated with it. Pressure acts in all directions at a point inside a gas. At the surface of a gas, the pressure force acts perpendicular to the surface.

Hydrostatic pressure

Hydrostatic pressure is the pressure due to the weight of a fluid. :p = ρgh where ρ (rho) is density of the fluid, g is acceleration due to gravity, and h is height of the fluid above the point being measured. See also Pascal's law.

Stagnation pressure

Stagnation pressure is the pressure a fluid exerts when it is forced to stop moving. Consequently, although a fluid moving at higher speed will have a lower static pressure, it may have a higher stagnation pressure when forced to a standstill. Static pressure and stagnation pressure are related by the Mach number of the fluid. In addition, there can be differences in pressure due to differences in the elevation (height) of the fluid. See Bernoulli's equation. The pressure of a moving fluid can be measured using a Pitot probe, or one of its variations such as a Kiel probe or Cobra probe, connected to a manometer. Depending on where the inlet holes are located on the probe, it can measure static pressure or stagnation pressure.

Units

The SI unit for pressure is the pascal (Pa), equal to one newton per square metre (N·m^-2 or kg·m^-1·s^-2). This special name for the unit was added in 1971; before that, pressure in SI was expressed in units such as N/m². Non-SI measures (still in use in some parts of the world) include the pound-force per square inch (psi) and the bar. The cgs unit of pressure is the barye (ba). It is equal to 1 dyn·cm^-2. Pressure is still sometimes expressed in kgf/cm² or grams-force/cm² (sometimes as kg/cm² and g/cm² without properly identifying the force units). But using the names kilogram, gram, kilogram-force, or gram-force (or their symbols) as a unit of force is expressly forbidden in SI; the unit of force in SI is the newton (N). The technical atmosphere (symbol: at) is 1 kgf/cm². Some meteorologists prefer the hectopascal (hPa) for atmospheric air pressure, which is equivalent to the older unit millibar (mbar). Similar pressures are given in kilopascals (kPa) in practically all other fields, where the hecto prefix is hardly ever used. In Canadian weather reports, the normal unit is kPa. The obsolete unit inch of mercury (inHg) is still sometimes used in the United States. Blood pressure is still measured in millimetres of mercury in most of the world, and lung pressures in centimeters of water are still common. These obsolete manometric units of pressure are based on the pressure exerted by the weight of some "standard" fluid under some "standard" gravity. They are effectively attempts to define a unit for expressing the readings of a manometer. When millimetres or inches of mercury are used today, they have precise definitions that can be expressed in terms of SI units. The water-based units depend on the density of water, a measured, rather than defined, quantity. The standard atmosphere (atm) is an established constant. It is approximately equal to typical air pressure at earth mean sea level and is defined as follows. :standard atmosphere = 101325 Pa = 101.325 kPa = 1013.25 hPa. A rule of thumb commonly used by scuba divers is that one atmosphere is approximately equal to the pressure exerted by ten metres of water. Non-SI units presently or formerly in use include the following.
- atmosphere.
- manometric units:
- centimetre, inch, and millimetre of mercury (Torr).
- millimetre, centimetre, metre, inch, and foot of water.
- imperial units:
- kip, ton-force (short), ton-force (long), pound-force, ounce-force, and poundal per square inch.
- pound-force, ton-force (short), and ton-force (long) per square foot.
- non-SI metric units:
- bar, millibar.
- kilogram-force, or kilopond, per square centimetre (technical atmosphere).
- gram-force and tonne-force (metric ton-force) per square centimetre.
- barye (dyne per square centimetre).
- kilogram-force and tonne-force per square metre.
- sthene per square metre (pieze).

External links

- [http://calc.skyrocket.de/en/ Online unit converter] - conversion of many different units.
- [http://avc.comm.nsdlib.org/cgi-bin/wiki_grade_interface.pl?An_Exercise_In_Air_Pressure An exercise in air pressure]
- [http://www.grc.nasa.gov/WWW/K-12/airplane/pressure.html Pressure being a scalar quantity] Category:Diving Category:Meteorology Category:Physical quantity Category:Thermodynamics ko:압력 ms:Tekanan ja:圧力

Psi

Newton

---- The newton (symbol: N) is the SI unit of force. It is named after Sir Isaac Newton in recognition of his work on classical mechanics.

Definition

A newton is the amount of force required to accelerate a mass of one kilogram at a rate of one metre per second squared. :1 N = 1 kg·m·s^–2

SI multiples

Explanation

The notions of mass and force are often confused in everyday life, but must be kept separate in science and engineering. The newton was first used around 1904, but not until 1948 was it officially adopted by the General Conference on Weights and Measures (CGPM) as the name for the MKS unit of force. Rather fittingly, given the story about how Newton arrived at his theory of gravity after contemplating why an apple falls downwards, the mass of a small apple exerts a force of about 1 newton on Earth.

Conversions

Hydrostatic pressure

Fluid pressure is the pressure on an object submerged in a fluid, such as water. The pressure can be provided from a number of sources: #the shear weight of the fluid, such as in scuba diving, when the diver goes deeper into the water, the water pressure increases; or in the earth's atmosphere, as a plane goes higher, the air pressure decreases; #a pump, such as when water "pumped" into a water tower; or #a compressor, such as in a small water supply system in a rural well for a house connected to an air compressor. Fluid pressure occurs in one of two situations: (1) an open condition, such as the ocean, or a swimming pool, or (2) a closed condition, such as a water line or a gas line. Open conditions are considered to be "static" or not moving (even in the ocean where there are waves and currents) because the fluid is essentially "at rest." The pressure in open conditions conform with principles of fluid statics. Closed bodies of fluid are either "static," when the fluid is not moving, or "dynamic," when the fluid is moving, like through a pipe. The pressure in closed conditions conform with the principles of fluid dynamics. The concepts of fluid pressure are predominately attributed to the discoveries of Blaise Pascal and Daniel Bernoulli. These concepts are given in greater detail in the remainder of this article.

Concepts of fluid pressure

There are two components to pressure: force and area. The more force, the larger the pressure; the more area, the smaller the pressure. As such, the force on an object in contact with fluid depends on three factors (as summarized in Bernoulli's equation): #Is the fluid at rest or moving? If moving, how fast and in what direction in relation to the object? #What is the vertical distance from the surface of the fluid (if a liquid) to the object? #Are there any sources of pressure, such as from a pump or compressor?

Hydrostatic pressure

In the case where the fluid is at rest, called fluid statics or hydrostatics (from hydro meaning "water" and static meaning "at rest"), the force acting on the object is the sheer weight of the fluid above, up to the water's surface—such as from a water tower. The resulting hydrostatic pressure is isotropic: the pressure acts in all directions equally, according to Pascal's law: ::

p = \rho g h\,

::where: ::
- ρ (rho) is the density of the fluid (the practical density of fresh water is 1000 kg/m³); ::
- g is the acceleration due to gravity (practical value 10 m/s² ); ::
- h is the height of the water column in meters. In the following example. Assume a column 1 meter high, the pressure on the floor of the column will be as follow: ::

p = \rho g h = 1000 \cdot 10 \cdot 1 = 10,000

Pa. The pressure increases linear with the water depth.

Fluid dynamic pressure

Next, when the fluid is moving in a pipe, called fluid dynamics or hydrodynamics (dynamics meaning "moving" or "changing"), the interaction of the fluid with the walls of the pipe creates friction and energy loss. In fluid dynamics, the fluid pressure is anisotropic (not isotropic), i.e. the pressure is not the same in all directions. The anisotrophy is mainly caused by the friction losses, so the further an object is away from the surface of the fluid (assuming the fluid is moving from the fluid surface to the object), the less pressure there will be on that object in the fluid. (Note: There are other reasons for the anisotrophy that are beyond the scope of this article.) These concept are mathematically explained by Bernoulli's equation, and is applicable to all fluids. Consider this simplified example: assume a 10 m high water tower with a large reservoir, that would give us a static pressure of 100,000 Pa (100 kPa or 100,000 N/m² at ground level. Now connect a 100-meter long horizontal pipe to the bottom of the column. From experiment it is known that the friction loss in this typical pipe, depending on material and diameter, is 100 Pa per meter of pipe length. So for the 100 meter pipe, that would be 10 kPa of pressure loss. So the pressure at the end of our pipe would be 100 kPa - 10 kPa = 90 kPa.

Pressure source

Finally, when a pressure source (such as an air pressure tank, a pump, or the human heart) is attached to the system, that pressure adds to the static pressure. In very small systems, such as in the human body or in a domestic water supply system, all of the pressure is derived from the pressure source (the heart or an air compressor), and none (or very little) is due to fluid static force.

Applications

- Artesian well
- Blood pressure
- Plant cell stability

Water table

The water table is the upper limit of abundant groundwater. In the vadose zone, above the water table, the interstices between particles of earth are filled by air, or by air and water (with the exception of the capillary fringe). Below it, every available space is saturated with water. A large amount of water within a body of sand or rock below the water table is called an aquifer. A so-called "perched aquifer" (or perched water table) occurs when the descent of water percolating from above is blocked by a shelf of impermeable rock. The porous media in which groundwaters occur are the complex geologic materials near the earth surface; hence local details of porosity and permeability are as complex as those materials. Generally, the more productive and useful aquifers are in sedimentary geologic formations, though weathered and fractured crystalline rocks yield smaller volumes of groundwater in many environments. Among the most productive groundwater environments are unconsolidated to poorly cemented alluvial materials that have accumulated as valley-filling sediments in major river valleys and geologically subsiding structural basins. The water table is that surface beneath which all interconnected pore space in the rock is water-filled or saturated. Groundwater recharge is the process of adding new water to the groundwater body, as through infiltration of precipitation on the land surface. Discharge is the process of water escaping from the groundwater body, as when the water table intersects the land surface, allowing water to flow out from a spring. In undeveloped regions, or areas with high amounts of precipitation, the water table roughly follows the contour of the overlying land surface, and rises and falls with rainy or dry weather. Springs and oases occur when the water table reaches the surface. Springs commonly form on hillsides, where the earth's slanting surface may "intersect" with the water table. Other, unseen springs are found under rivers and lakes, and account for the sometimes surprisingly well-preserved water levels which occur in times of mild drought. The practice of drilling wells to extract groundwater is dependent on understanding the water table. Because wells must reach the water table, its depth determines the minimum depth of a viable well, and thus the feasibility of drilling it. In areas with a high water table, tunnels and basements are less common due to the risk of flooding. see also:
- Hydrogeology
- Aquifer
- Groundwater Category:Hydrology

Water table

Darcy's law

Darcy's Law is a phenomologically derived constituative equation that describes the flow of a fluid through a porous medium (typically water through an aquifer). The law was formulated by Henry Darcy based on the results of 1855 and 1856 experiments on the flow of water through beds of sand. It, along with the conservation of mass, comprises the groundwater flow equation, which is one the basic building relationships of hydrogeology. Darcy's Law (an expression of conservation of momentum) is a relationship determined experimentally by Henry Darcy, which has since been proved theoretically from simplifications made to the Navier-Stokes equations. It is analogous to Fourier's law in the field of heat conduction, Ohm's law in the field of electrical networks, or Fick's law in diffusion theory. This simple relationship relates the instantaneous discharge rate through a porous medium to the local hydraulic gradient (change in hydraulic head over a distance) and the hydraulic conductivity (k) at that point. :

Q=-kA \frac

It shows that the total discharge, Q (units of volume per time, e.g., cm³/s) is proportional to the hydraulic conductivity, k, the cross-sectional area to flow, A, and the hydraulic gradient (the hydraulic head drop between two points a and b, divided by the distance between them, L). The negative sign is needed because water flows from high head to low head. Dividing both sides of the equation by the area and using more general notation leads to :

q=-k \nabla h

where q is the flux (discharge per unit area, with units of length per time, m/s) and

\nabla h

indicates the mathematical gradient of the hydraulic head. This value of flux is often referred to as the Darcy flux, it is not the velocity which the water traveling through the pores is experiencing. The pore velocity (v) is related to the Darcy flux (q) by the porosity (n). The flux is divided by porosity to account for the fact that only a fraction of the total aquifer volume is available for flow, this pore velocity would be the velocity a conservative tracer would experience if carried by water through the aquifer. :

v=\frac

Darcy's law is a simple mathematical statement which neatly summarizes several familiar properties that groundwater flowing in aquifers exhibits, including:
- if there is no hydraulic gradient (difference in hydraulic head over a distance), no flow occurs (this is hydrostatic conditions),
- if there is a hydraulic gradient, flow will occur from high head towards low head (opposite the direction of increasing gradient - hence the negative sign in Darcy's law),
- the greater the hydraulic gradient (through the same aquifer material), the greater the discharge, and
- the discharge of water will be often be different — through different aquifer materials (or even through the same material, in a different direction) — even if the same hydraulic gradient exists in both cases. A graphical illustration of the use of the steady-state groundwater flow equation (based on Darcy's law and the conservation of mass) is in the construction of flownets, to quantify the amount of groundwater flowing under a dam. Darcy's law is only valid for slow, viscous flow; fortunately, most groundwater flow cases fall in this category. Typically any flow with a Reynold's number less than one is clearly laminar, and it would be valid to apply Darcy's law. Experimental tests have shown that for flow regimes with values of Reynold's number up to 10 may still be Darcian. Reynold's number (a dimensionless parameter) for porous media flow is typically expressed as :

Re = \frac

. Where ρ is the density of water (units of mass per volume), v is the specific discharge (not the pore velocity — with units of length per time), d₃₀ is a representative grain diameter for the porous media (often taken as the 30% passing size from a grain size analysis using sieves - with units of length), and μ is the viscosity of the fluid.

Additional forms of Darcy's Law

For very short time scales, a time derivative of flux may be added to Darcy's law, which results in valid solutions at very small times (in heat transfer, this is called the modified form of Fourier's law), :

\tau \frac+q=-k \nabla h

, where τ is a very small time constant which causes this equation to reduce to the normal form of Darcy's law at "normal" times (> nanoseconds). The main reason for doing this is that the regular groundwater flow equation (diffusion equation) leads to singularities at constant head boundaries at very small times. This form is more mathematically rigorous, but leads to a hyperbolic groundwater flow equation, which is more difficult to solve and is only useful at very small times, typically out of the realm of practical use. Another extension to the traditional form of Darcy's L

Hydraulic gradient

Components of hydraulic head

Hydraulic gradient

Atmospheric Pressure

See also

Groundwater

Problems with groundwater

Groundwater overdraft

Subsidence

Seawater intrusion

Mining groundwater

Groundwater pollution

See also

Groundwater

Problems with groundwater

Groundwater overdraft

Subsidence

Seawater intrusion

Mining groundwater

Groundwater pollution

See also

Meter

Conversions

History

Timeline of definition

See also

External links

Foot (unit of length)

Etymology

See also

External link

Psi

Hydrogeology

Introduction

Hydrogeology in relation to other fields

Definitions and material properties

Hydraulic head

Porosity

Water content

Hydraulic conductivity

Specific storage and specific yield

Governing equations

Darcy's Law

Groundwater flow equation

Calculation of groundwater flow

Analytic methods

Numerical Methods

Further reading

General hydrogeology

Numerical groundwater modeling

Analytic groundwater modeling

See also

External links and sources

Atmospheric pressure

Standard atmospheric pressure

Mean sea level pressure (MSLP or SLP)

Atmospheric pressure variation

Intuitive feeling for atmospheric pressure based on height of water

See also

References

External links

Experiments

Pressure

Example

Relative or gauge pressure

Scalar nature of pressure

Hydrostatic pressure

Stagnation pressure

Units

See also

External links

Psi

Newton

Definition

SI multiples

Explanation

Conversions

See also

Hydrostatic pressure

Concepts of fluid pressure