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Encyclopedia > Hydraulic conductivity

Hydraulic conductivity, symbolically represented as K, is a property of vascular plants, soil or rock, that describes the ease with which water can move through pore spaces or fractures. It depends on the intrinsic permeability of the material and on the degree of saturation. Saturated hydraulic conductivity, Ksat, describes water movement through saturated media. In the earth sciences, permeability (commonly symbolized as Îº, or k) is a measure of the ability of a material (typically, a rock or unconsolidated material) to transmit fluids. ...

## Derivation through Darcy's law GA_googleFillSlot("encyclopedia_square");

Hydraulic conductivity is the proportionality constant in Darcy's law, which relates the amount of water which will flow through a unit cross-sectional area of aquifer under a unit gradient of hydraulic head. It is analogous to the thermal conductivity of materials in heat conduction, or 1/resistivity in electrical circuits. The hydraulic conductivity (K — the English letter "kay") is specific to the flow of a certain fluid (typically water, sometimes oil or air); intrinsic permeability (κ — the Greek letter "kappa") is a parameter of a porous media which is independent of the fluid. This means that, for example, K will go up if the water in a porous medium is heated (reducing the viscosity of the water), but κ will remain constant. The two are related through the following equation In fluid dynamics, Darcys law is a phenomologically derived constitutive equation that describes the flow of a fluid through a porous medium. ... An aquifer is an underground layer of water-bearing permeable rock or unconsolidated materials (gravel, sand, silt, or clay) from which groundwater can be usefully extracted using a water well. ... It has been suggested that Hydraulic head (hydrology) and Head (hydraulic) be merged into this article or section. ... The modern English alphabet consists of the 26 letters[1] of the Latin alphabet: The exact shape of printed letters varies depending on the typeface. ... Technical note: Due to technical limitations, some web browsers may not display some special characters in this article. ...

$K = frac{kappa gamma}{mu}$

where

K is the hydraulic conductivity [LT-1 or m s-1];
κ is the intrinsic permeability of the material [L2 or m2];
γ is the specific weight of water [ML-2T-2 or N m-3], and;
μ is the dynamic viscosity of water [ML-1T-1 or kg m-1 s-1].

In the earth sciences, permeability (commonly symbolized as Îº, or k) is a measure of the ability of a material (typically, a rock or unconsolidated material) to transmit fluids. ... The specific weight of a structure or material is the weight required to carry out a particular task, e. ... Viscosity is a measure of the resistance of a fluid to deformation under shear stress. ...

## Estimation of hydraulic conductivity

### Direct estimation

Hydraulic conductivity can be measured by applying Darcy's law on the material. Such experiments can be conducted by creating a hydraulic gradient between two points, and measuring the flow rate (Oosterbaan and Nijland[1]). In fluid dynamics, Darcys law is a phenomologically derived constitutive equation that describes the flow of a fluid through a porous medium. ...

### Empirical estimation

Shepherd[2] derived an empirical formula for approximating hydraulic conductivity from grain size analyses: Empirical method is generally meant as the collection of a large amount of data on which to base a theory or derive a conclusion in science. ...

K = a(D10)b

where

a and b are empirically derived terms based on the soil type, and
D10 is the diameter of the 10 percentile grain size of the material

Note: Shepherd's Figure 3 clearly shows the use of d50, not d10, measured in mm. Therefore the equation should be K = a(d10)b. His figure shows different lines for materials of different types, based on analysis of data from others with d50 up to 10 mm. DIAMETER is a computer networking protocol for AAA (Authentication, Authorization and Accounting). ... A percentile is the value of a variable below which a certain percent of observations fall. ...

### Pedotransfer function

A pedotransfer function (PTF) is a specialized empirical estimation method, used primarily in the soil sciences, however has increasing use in hydrogeology[3]. There are many different PTF methods, however, they all attempt to determine soil properties, such as hydraulic conductivity, given several measured soil properties, such as soil particle size, and bulk density. Pedotransfer functions (PTF) is a term used in soil science literature, which can be defined as predictive functions of certain soil properties from other easily-, routinely-, or cheaply-measured properties. ... Soil science deals with soil as a natural resource on the surface of the earth including soil formation, classification and mapping; physical, chemical, biological, and fertility properties of soils per se; and these properties in relation to the use and management of soils. ... Particle size, also called grain size, refers to the diameter of individual grains of sediment, or the lithified particles in clastic rocks. ... Bulk density a property of particulate materials. ...

## Experimental approach

There are relatively simple and inexpensive laboratory tests that may be run to determine the hydraulic conductivity of a soil: constant-head method and falling-head method.

The constant-head method is typically used on granular soil. This procedure allows water to move through the soil under a steady state head condition while the quantity (volume) of water flowing through the soil specimen is measured over a period of time. By knowing the quantity Q of water measured, length L of specimen, cross-sectional area A of the specimen, time t required for the quantity of water Q to be discharged, and head h, the hydraulic conductivity can be calculated:

$Q = Avt,$

Using Darcy's Law, $v = Ki,$, In fluid dynamics, Darcys law is a phenomologically derived constitutive equation that describes the flow of a fluid through a porous medium. ...

yields $Q = frac{AKht}{L}$

Solving for K gives,

$K = frac{QL}{Ath}$

The falling-head method is very similar to the constant head methods in its initial setup; however, the advantage to the falling-head method is that can be used for both fine-grained and coarse-grained soils. The soil sample is first saturated under a specific head condition. The water is then allowed to flow through the soil without maintaining a constant pressure head[4].

$K = frac{2.3aL}{At}logleft(frac{h_1}{h_2}right)$

## Transmissivity

The transmissivity, T, of an aquifer is a measure of how much water can be transmitted horizontally, such as to a pumping well: An aquifer is an underground layer of water-bearing permeable rock or unconsolidated materials (gravel, sand, silt, or clay) from which groundwater can be usefully extracted using a water well. ...

$T = K_s , b$

Transmissivity is directly proportional to the aquifer thickness. For a confined aquifer, this remains constant, as the saturated thickness remains constant. The aquifer thickness of an unconfined aquifer is from the base of the aquifer (or the top of the aquitard) to the water table. The water table can fluctuate, which changes the transmissivity of the unconfined aquifer. This may provide positive feedback of a pumping well that is pumping more than can be provided by the aquifer, where the transmissivity drops as the well pumps, thus eventually reducing the aquifer to the height of the pumping well screen. It has been suggested that this article or section be merged with Aquifer. ... Cross section showing the water table varying with surface topography as well as a perched water table The water table or phreatic surface is the surface where the water pressure is equal to atmospheric pressure. ... Positive feedback is a feedback system in which the system responds to the perturbation in the same direction as the perturbation (It is sometimes referred to as cumulative causation). ...

Transmissivity should not be confused with similar word transmittance (used in optics), which means fraction of incident light that passes through a sample. In the fields of optics and spectroscopy, transmittance is the fraction of incident light at a specified wavelength that passes through a sample. ... For the book by Sir Isaac Newton, see Opticks. ...

## Relative properties

Because of their high porosity and permeability, sand and gravel aquifers have higher hydraulic conductivity than clay or unfractured granite aquifer. Sand or gravel aquifers would thus be easier to extract water from (e.g., using a pumping well) because of their high transmissivity, compared to clay or unfractured bedrock aquifers. For other uses, see Sand (disambiguation). ... Gravel (largest fragment in this photo is about 4 cm) Gravel is rock that is of a certain particle size range. ... An aquifer is an underground layer of water-bearing permeable rock or unconsolidated materials (gravel, sand, silt, or clay) from which groundwater can be usefully extracted using a water well. ... For other uses, see Clay (disambiguation). ... For other uses, see granite (disambiguation). ... Village pump redirects here, for information on Wikipedia project-related discussions, see Wikipedia:Village pump. ...

Hydraulic conductivity has units with dimensions of length per time (e.g., m/s, ft/day and (gal/day)/ft² ); transmissivity then has units with dimensions of length squared per time. The following table gives some typical ranges (illustrating the many orders of magnitude which are likely) for K values. This article is about the unit of length. ... The gallon (abbreviation: gal) is a unit of volume. ...

Hydraulic conductivity (K) is one of the most complex and important of the properties of aquifers in hydrogeology as the values found in nature:

• range over many orders of magnitude (the distribution is often considered to be lognormal),
• vary a large amount through space (sometimes considered to be randomly spatially distributed, or stochastic in nature),
• are directional (in general K is a symmetric second-rank tensor; e.g., vertical K values can be several orders of magnitude smaller than horizontal K values),
• are scale dependent (testing a m³ of aquifer will generally produce different results than a similar test on only a cm³ sample of the same aquifer),
• must be determined indirectly through field pumping tests, laboratory column flow tests or inverse computer simulation, (sometimes also from grain size analyses), and
• are very dependent (in a non-linear way) on the water content, which makes solving the unsaturated flow equation difficult. In fact, the variably saturated K for a single material varies over a wider range than the saturated K values for all types of materials (see chart below for an illustrative range of the latter).

An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. ... In probability and statistics, the log-normal distribution is the probability distribution of any random variable whose logarithm is normally distributed (the base of the logarithmic function is immaterial in that loga X is normally distributed if and only if logb X is normally distributed). ... Random redirects here. ... Stochastic, from the Greek stochos or goal, means of, relating to, or characterized by conjecture; conjectural; random. ... In mathematics, a tensor is (in an informal sense) a generalized linear quantity or geometrical entity that can be expressed as a multi-dimensional array relative to a choice of basis; however, as an object in and of itself, a tensor is independent of any chosen frame of reference. ... Particle size, also called grain size, refers to the diameter of individual grains of sediment, or the lithified particles in clastic rocks. ... In mathematics, a nonlinear system is one whose behavior cant be expressed as a sum of the behaviors of its parts (or of their multiples. ... The vadose zone, also termed the unsaturated zone, is the portion of Earth between the land surface and the water table, and is thus not considered groundwater (vadose is Latin for shallow). It comprises the unsaturated portion of the soil, regolith or bedrock, as well as the saturated capillary fringe...

## Ranges of values for natural materials

Table of saturated hydraulic conductivity (K) values found in nature

Values are for typical fresh groundwater conditions — using standard values of viscosity and specific gravity for water at 20°C and 1 atm. See the similar table derived from the same source for intrinsic permeability values.[5] Missing main definition------ someone add if you know it please. ... For other uses, see Viscosity (disambiguation). ... Relative density (also known as specific gravity) is a measure of the density of a material. ... In the earth sciences, permeability (commonly symbolized as Îº, or k) is a measure of the ability of a material (typically, a rock or unconsolidated material) to transmit fluids. ...

 K (cm/s) 10² 101 100=1 10−1 10−2 10−3 10−4 10−5 10−6 10−7 10−8 10−9 10−10 K (ft/day) 105 10,000 1,000 100 10 1 0.1 0.01 0.001 0.0001 10−5 10−6 10−7 Relative Permeability Pervious Semi-Pervious Impervious Aquifer Good Poor None Unconsolidated Sand & Gravel Well Sorted Gravel Well Sorted Sand or Sand & Gravel Very Fine Sand, Silt, Loess, Loam Unconsolidated Clay & Organic Peat Layered Clay Fat / Unweathered Clay Consolidated Rocks Highly Fractured Rocks Oil Reservoir Rocks Fresh Sandstone Fresh Limestone, Dolomite Fresh Granite

Source: modified from Bear, 1972 A centimetre (American spelling centimeter, symbol cm) is a unit of length that is equal to one hundredth of a metre, the current SI base unit of length. ... This article is about the unit of time. ... A foot (plural: feet or foot;[1] symbol or abbreviation: ft or, sometimes, â€² â€“ a prime) is a unit of length, in a number of different systems, including English units, Imperial units, and United States customary units. ... Look up day in Wiktionary, the free dictionary. ... An aquifer is an underground layer of water-bearing permeable rock or unconsolidated materials (gravel, sand, silt, or clay) from which groundwater can be usefully extracted using a water well. ... For other uses, see Sand (disambiguation). ... Gravel (largest fragment in this photo is about 4 cm) Gravel is rock that is of a certain particle size range. ... This article or section does not cite any references or sources. ... Loam is soil composed of a relatively even mixture of three mineral particle size groups: sand, silt, and clay. ... Peat in Lewis, Scotland Peat is an accumulation of partially decayed vegetation matter. ... For other uses, see Clay (disambiguation). ... Petroleum geology is a term used to refer to the specific set of geological disciplines that are applied to the search for hydrocarbons (oil exploration). ... Red sandstone interior of Lower Antelope Canyon, Arizona, worn smooth due to erosion by flash flooding over millions of years Sandstone is a sedimentary rock composed mainly of sand-size mineral or rock grains. ... For other uses, see Limestone (disambiguation). ... For other uses, see Dolomite (disambiguation). ... For other uses, see granite (disambiguation). ...

An Aquifer test is conducted to evaluate an aquifer by stimulating the aquifer through constant pumping, and observing the aquifers response (drawdown) in observation wells. ... Pedotransfer functions (PTF) is a term used in soil science literature, which can be defined as predictive functions of certain soil properties from other easily-, routinely-, or cheaply-measured properties. ...

## References

1. ^ R.J.Oosterbaan and H.J.Nijland, 1994, Determination of the Saturated Hydraulic Conductivity. In: H.P.Ritzema (ed.) Drainage Principles and Applications, ILRI Publication 16, p.435-476. International Institute for Land Reclamation and Improvement, Wageningen, The Netherlands. ISBN 90 70754 3 39.
Free download from the Articles page of waterlog.info.
2. ^ Shephard, R.G. (1989). "Correlations of permeability and grain-size". Ground Water 27 (5): 633–638.
3. ^ Wösten, J.H.M., Pachepsky, Y.A., and Rawls, W.J. (2001). "Pedotransfer functions: bridging the gap between available basic soil data and missing soil hydraulic characteristics" 251: 123–150. doi:10.1016/S0022-1694(01)00464-4.
4. ^ Liu, Cheng "Soils and Foundations." Upper Saddle River, New Jersey: Prentice Hall, 2001 ISBN 0-13-025517-3
5. ^ Bear, J. (1972). Dynamics of Fluids in Porous Media. Dover Publications. ISBN 0-486-65675-6.

Results from FactBites:

 Hydraulic conductivity - Wikipedia, the free encyclopedia (607 words) Hydraulic conductivity is the proportionality constant in Darcy's law, which relates the amount of water which will flow through a unit cross-sectional area of aquifer under a unit gradient of hydraulic head. The hydraulic conductivity (k — the English letter "kay") is specific to the flow of a certain fluid (typically water, sometimes oil or air); intrinsic permeability (κ — the Greek letter "kappa") is a parameter of a porous media which is independent of the fluid. Hydraulic conductivity has units with dimensions of length per time (e.g., m/s, ft/day and gal/(day/ft²)); transmissivity then has units with dimensions of length squared per time.
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