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84-1054: Hydrology (from Ancient Greek ὕδωρ ( húdōr )  'water' and -λογία ( -logía )  'study of') is the scientific study of the movement, distribution, and management of water on Earth and other planets, including the water cycle , water resources , and drainage basin sustainability. A practitioner of hydrology is called a hydrologist . Hydrologists are scientists studying earth or environmental science , civil or environmental engineering , and physical geography . Using various analytical methods and scientific techniques, they collect and analyze data to help solve water related problems such as environmental preservation , natural disasters , and water management . Hydrology subdivides into surface water hydrology, groundwater hydrology ( hydrogeology ), and marine hydrology. Domains of hydrology include hydrometeorology , surface hydrology , hydrogeology , drainage-basin management, and water quality . Oceanography and meteorology are not included because water

168-456: A {\displaystyle \Delta p=p_{b}-p_{a}} is in units ( P a ) {\displaystyle \mathrm {(Pa)} } , and L {\displaystyle L} is the length of the sample in units ( m ) {\displaystyle \mathrm {(m)} } , the Darcy's volumetric flow rate Q {\displaystyle Q} , or discharge,

252-424: A line source or area source , such as surface runoff . Since the 1960s rather complex mathematical models have been developed, facilitated by the availability of high-speed computers. The most common pollutant classes analyzed are nutrients , pesticides , total dissolved solids and sediment . Ancient Greek language Ancient Greek ( Ἑλληνῐκή , Hellēnikḗ ; [hellɛːnikɛ́ː] ) includes

336-433: A piezometer . Aquifers are also described in terms of hydraulic conductivity, storativity and transmissivity. There are a number of geophysical methods for characterizing aquifers. There are also problems in characterizing the vadose zone (unsaturated zone). Infiltration is the process by which water enters the soil. Some of the water is absorbed, and the rest percolates down to the water table . The infiltration capacity,

420-543: A pitch accent . In Modern Greek, all vowels and consonants are short. Many vowels and diphthongs once pronounced distinctly are pronounced as /i/ ( iotacism ). Some of the stops and glides in diphthongs have become fricatives , and the pitch accent has changed to a stress accent . Many of the changes took place in the Koine Greek period. The writing system of Modern Greek, however, does not reflect all pronunciation changes. The examples below represent Attic Greek in

504-445: A scalar . (Note the analogy to Ohm's law in electrostatics. The flux vector is analogous to the current density, head is analogous to voltage, and hydraulic conductivity is analogous to electrical conductivity.) For flows in porous media with Reynolds numbers greater than about 1 to 10, inertial effects can also become significant. Sometimes an inertial term is added to the Darcy's equation, known as Forchheimer term. This term

588-458: A 2008 paper by W. King. The papers will either take the coffee permeability to be constant as a simplification or will measure change through the brewing process. Darcy's law can be expressed very generally as: where q is the volume flux vector of the fluid at a particular point in the medium, h is the total hydraulic head , and K is the hydraulic conductivity tensor , at that point. The hydraulic conductivity can often be approximated as

672-410: A gas cap above the oil leg. When the reservoir pressure drops due to oil production, water flows into the oil zone from below, and gas flows into the oil zone from above (if the gas cap exists), and we get a simultaneous flow and immiscible mixing of all fluid phases in the oil zone. The oil field operator may also inject water (or gas) to improve oil production. The petroleum industry is, therefore, using

756-457: A generalized Darcy equation for multiphase flow developed by Muskat et alios. Because Darcy's name is so widespread and strongly associated with flow in porous media, the multiphase equation is denoted Darcy's law for multiphase flow or generalized Darcy equation (or law) or simply Darcy's equation (or law) or flow equation if the context says that the text is discussing the multiphase equation of Muskat . Multiphase flow in oil and gas reservoirs

840-477: A lack of contemporaneous evidence. Several theories exist about what Hellenic dialect groups may have existed between the divergence of early Greek-like speech from the common Proto-Indo-European language and the Classical period. They have the same general outline but differ in some of the detail. The only attested dialect from this period is Mycenaean Greek , but its relationship to the historical dialects and

924-419: A lesser degree. Pamphylian Greek , spoken in a small area on the southwestern coast of Anatolia and little preserved in inscriptions, may be either a fifth major dialect group, or it is Mycenaean Greek overlaid by Doric, with a non-Greek native influence. Regarding the speech of the ancient Macedonians diverse theories have been put forward, but the epigraphic activity and the archaeological discoveries in

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1008-402: A more global approach to the understanding of the behavior of hydrologic systems to make better predictions and to face the major challenges in water resources management. Water movement is a significant means by which other materials, such as soil, gravel, boulders or pollutants, are transported from place to place. Initial input to receiving waters may arise from a point source discharge or

1092-400: A multiphase flow of water, oil and gas in the porous medium of a petroleum reservoir . The generalized multiphase flow equations by Muskat and others provide the analytical foundation for reservoir engineering that exists to this day. In the integral form, Darcy's law, as refined by Morris Muskat , in the absence of gravitational forces and in a homogeneously permeable medium, is given by

1176-466: A new formulation needs to be used. Knudsen presented a semi-empirical model for flow in transition regime based on his experiments on small capillaries. For a porous medium, the Knudsen equation can be given as where N is the molar flux, R g is the gas constant, T is the temperature, D K is the effective Knudsen diffusivity of the porous media. The model can also be derived from

1260-449: A prediction in practical applications. Ground water is water beneath Earth's surface, often pumped for drinking water. Groundwater hydrology ( hydrogeology ) considers quantifying groundwater flow and solute transport. Problems in describing the saturated zone include the characterization of aquifers in terms of flow direction, groundwater pressure and, by inference, groundwater depth (see: aquifer test ). Measurements here can be made using

1344-550: A prefix /e-/, called the augment . This was probably originally a separate word, meaning something like "then", added because tenses in PIE had primarily aspectual meaning. The augment is added to the indicative of the aorist, imperfect, and pluperfect, but not to any of the other forms of the aorist (no other forms of the imperfect and pluperfect exist). The two kinds of augment in Greek are syllabic and quantitative. The syllabic augment

1428-608: A separate historical stage, though its earliest form closely resembles Attic Greek , and its latest form approaches Medieval Greek . There were several regional dialects of Ancient Greek; Attic Greek developed into Koine. Ancient Greek was a pluricentric language , divided into many dialects. The main dialect groups are Attic and Ionic , Aeolic , Arcadocypriot , and Doric , many of them with several subdivisions. Some dialects are found in standardized literary forms in literature , while others are attested only in inscriptions. There are also several historical forms. Homeric Greek

1512-454: A simple proportionality relationship between the volumetric flow rate Q {\displaystyle Q} , and the pressure drop Δ p {\displaystyle \Delta p} through a porous medium . The proportionality constant is linked to the permeability k {\displaystyle k} of the medium, the dynamic viscosity of the fluid μ {\displaystyle \mu } ,

1596-407: A single-phase flow by including viscosity in the single (fluid) phase equation of Darcy. It can be understood that viscous fluids have more difficulty permeating through a porous medium than less viscous fluids. This change made it suitable for researchers in the petroleum industry. Based on experimental results by his colleagues Wyckoff and Botset, Muskat and Meres also generalized Darcy's law to cover

1680-630: A standard subject of study in educational institutions of the Western world since the Renaissance . This article primarily contains information about the Epic and Classical periods of the language, which are the best-attested periods and considered most typical of Ancient Greek. From the Hellenistic period ( c.  300 BC ), Ancient Greek was followed by Koine Greek , which is regarded as

1764-510: A vowel or /n s r/ ; final stops were lost, as in γάλα "milk", compared with γάλακτος "of milk" (genitive). Ancient Greek of the classical period also differed in both the inventory and distribution of original PIE phonemes due to numerous sound changes, notably the following: The pronunciation of Ancient Greek was very different from that of Modern Greek . Ancient Greek had long and short vowels ; many diphthongs ; double and single consonants; voiced, voiceless, and aspirated stops ; and

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1848-424: Is a governing equation for single-phase fluid flow in a porous medium. Another derivation of Darcy's law is used extensively in petroleum engineering to determine the flow through permeable media — the most simple of which is for a one-dimensional, homogeneous rock formation with a single fluid phase and constant fluid viscosity . Almost all oil reservoirs have a water zone below the oil leg, and some also have

1932-425: Is a comprehensive topic, and one of many articles about this topic is Darcy's law for multiphase flow . A number of papers have utilized Darcy's law to model the physics of brewing in a moka pot , specifically how the hot water percolates through the coffee grinds under pressure, starting with a 2001 paper by Varlamov and Balestrino, and continuing with a 2007 paper by Gianino, a 2008 paper by Navarini et al., and

2016-570: Is a literary form of Archaic Greek (derived primarily from Ionic and Aeolic) used in the epic poems , the Iliad and the Odyssey , and in later poems by other authors. Homeric Greek had significant differences in grammar and pronunciation from Classical Attic and other Classical-era dialects. The origins, early form and development of the Hellenic language family are not well understood because of

2100-467: Is able to account for the non-linear behavior of the pressure difference vs flow data. where the additional term k 1 is known as inertial permeability, in units of length ( m ) {\displaystyle \mathrm {(m)} } . The flow in the middle of a sandstone reservoir is so slow that Forchheimer's equation is usually not needed, but the gas flow into a gas production well may be high enough to justify using it. In this case,

2184-418: Is added to stems beginning with consonants, and simply prefixes e (stems beginning with r , however, add er ). The quantitative augment is added to stems beginning with vowels, and involves lengthening the vowel: Some verbs augment irregularly; the most common variation is e → ei . The irregularity can be explained diachronically by the loss of s between vowels, or that of the letter w , which affected

2268-402: Is affected by the interaction of dissolved oxygen with organic material and various chemical transformations that may take place. Measurements of water quality may involve either in-situ methods, in which analyses take place on-site, often automatically, and laboratory-based analyses and may include microbiological analysis . Observations of hydrologic processes are used to make predictions of

2352-403: Is also defined in units ( m 3 / s ) {\displaystyle \mathrm {(m^{3}/s)} } and the cross-sectional area A {\displaystyle A} in units ( m 2 ) {\displaystyle \mathrm {(m^{2})} } . A number of these parameters are used in alternative definitions below. A negative sign is used in

2436-769: Is an important part of the water cycle. It is partly affected by humidity, which can be measured by a sling psychrometer . It is also affected by the presence of snow, hail, and ice and can relate to dew, mist and fog. Hydrology considers evaporation of various forms: from water surfaces; as transpiration from plant surfaces in natural and agronomic ecosystems. Direct measurement of evaporation can be obtained using Simon's evaporation pan . Detailed studies of evaporation involve boundary layer considerations as well as momentum, heat flux, and energy budgets. Remote sensing of hydrologic processes can provide information on locations where in situ sensors may be unavailable or sparse. It also enables observations over large spatial extents. Many of

2520-458: Is analogous to Fourier's law in the field of heat conduction , Ohm's law in the field of electrical networks , and Fick's law in diffusion theory. One application of Darcy's law is in the analysis of water flow through an aquifer ; Darcy's law along with the equation of conservation of mass simplifies to the groundwater flow equation , one of the basic relationships of hydrogeology . Morris Muskat first refined Darcy's equation for

2604-666: Is called 'East Greek'. Arcadocypriot apparently descended more closely from the Mycenaean Greek of the Bronze Age. Boeotian Greek had come under a strong Northwest Greek influence, and can in some respects be considered a transitional dialect, as exemplified in the poems of the Boeotian poet Pindar who wrote in Doric with a small Aeolic admixture. Thessalian likewise had come under Northwest Greek influence, though to

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2688-448: Is considered by some linguists to have been closely related to Greek . Among Indo-European branches with living descendants, Greek is often argued to have the closest genetic ties with Armenian (see also Graeco-Armenian ) and Indo-Iranian languages (see Graeco-Aryan ). Ancient Greek differs from Proto-Indo-European (PIE) and other Indo-European languages in certain ways. In phonotactics , ancient Greek words could end only in

2772-488: Is only one of many important aspects within those fields. Hydrological research can inform environmental engineering, policy , and planning . Hydrology has been subject to investigation and engineering for millennia. Ancient Egyptians were one of the first to employ hydrology in their engineering and agriculture, inventing a form of water management known as basin irrigation. Mesopotamian towns were protected from flooding with high earthen walls. Aqueducts were built by

2856-458: Is related to the flux ( q ) by the porosity ( φ ) with the following equation: The Darcy's constitutive equation, for single phase (fluid) flow, is the defining equation for absolute permeability (single phase permeability). With reference to the diagram to the right, the flow velocity is in SI units ( m / s ) {\displaystyle \mathrm {(m/s)} } , and since

2940-437: Is the kinematic viscosity . The corresponding hydraulic conductivity is therefore: Darcy's law is a simple mathematical statement which neatly summarizes several familiar properties that groundwater flowing in aquifers exhibits, including: 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

3024-578: Is thought of as starting at the land-atmosphere boundary and so it is important to have adequate knowledge of both precipitation and evaporation. Precipitation can be measured in various ways: disdrometer for precipitation characteristics at a fine time scale; radar for cloud properties, rain rate estimation, hail and snow detection; rain gauge for routine accurate measurements of rain and snowfall; satellite for rainy area identification, rain rate estimation, land-cover/land-use, and soil moisture, snow cover or snow water equivalent for example. Evaporation

3108-466: Is typically expressed as where ν is the kinematic viscosity of water , q is the specific discharge (not the pore velocity — with units of length per time), d is a representative grain diameter for the porous media (the standard choice is math| d 30 , which is the 30% passing size from a grain size analysis using sieves — with units of length). For stationary, creeping, incompressible flow, i.e. ⁠ D ( ρu i ) / Dt ⁠ ≈ 0 ,

3192-512: Is utilized to formulate operating rules for large dams forming part of systems which include agricultural, industrial and residential demands. Hydrological models are simplified, conceptual representations of a part of the hydrologic cycle. They are primarily used for hydrological prediction and for understanding hydrological processes, within the general field of scientific modeling . Two major types of hydrological models can be distinguished: Recent research in hydrological modeling tries to have

3276-759: The Greek region of Macedonia during the last decades has brought to light documents, among which the first texts written in Macedonian , such as the Pella curse tablet , as Hatzopoulos and other scholars note. Based on the conclusions drawn by several studies and findings such as Pella curse tablet , Emilio Crespo and other scholars suggest that ancient Macedonian was a Northwest Doric dialect , which shares isoglosses with its neighboring Thessalian dialects spoken in northeastern Thessaly . Some have also suggested an Aeolic Greek classification. The Lesbian dialect

3360-637: The Greeks and Romans , while history shows that the Chinese built irrigation and flood control works. The ancient Sinhalese used hydrology to build complex irrigation works in Sri Lanka , also known for the invention of the Valve Pit which allowed construction of large reservoirs, anicuts and canals which still function. Marcus Vitruvius , in the first century BC, described a philosophical theory of

3444-537: The Klinkenberg effect . Using the definition of molar flux, the above equation can be rewritten as This equation can be rearranged into the following equation Comparing this equation with conventional Darcy's law, a new formulation can be given as where This is equivalent to the effective permeability formulation proposed by Klinkenberg: where b is known as the Klinkenberg parameter, which depends on

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3528-448: The dynamic viscosity μ {\displaystyle \mu } in units ( P a ⋅ s ) {\displaystyle \mathrm {(Pa\cdot s)} } and the hydraulic gradient is in units ( P a / m ) {\displaystyle \mathrm {(Pa/m)} } . In the integral form, the total pressure drop Δ p = p b − p

3612-501: The present , future , and imperfect are imperfective in aspect; the aorist , present perfect , pluperfect and future perfect are perfective in aspect. Most tenses display all four moods and three voices, although there is no future subjunctive or imperative. Also, there is no imperfect subjunctive, optative or imperative. The infinitives and participles correspond to the finite combinations of tense, aspect, and voice. The indicative of past tenses adds (conceptually, at least)

3696-399: The return period of such events. Other quantities of interest include the average flow in a river, in a year or by season. These estimates are important for engineers and economists so that proper risk analysis can be performed to influence investment decisions in future infrastructure and to determine the yield reliability characteristics of water supply systems. Statistical information

3780-455: The 20th century, while governmental agencies began their own hydrological research programs. Of particular importance were Leroy Sherman's unit hydrograph , the infiltration theory of Robert E. Horton , and C.V. Theis' aquifer test/equation describing well hydraulics. Since the 1950s, hydrology has been approached with a more theoretical basis than in the past, facilitated by advances in the physical understanding of hydrological processes and by

3864-1031: The 5th century BC. Ancient pronunciation cannot be reconstructed with certainty, but Greek from the period is well documented, and there is little disagreement among linguists as to the general nature of the sounds that the letters represent. /oː/ raised to [uː] , probably by the 4th century BC. Greek, like all of the older Indo-European languages , is highly inflected. It is highly archaic in its preservation of Proto-Indo-European forms. In ancient Greek, nouns (including proper nouns) have five cases ( nominative , genitive , dative , accusative , and vocative ), three genders ( masculine , feminine , and neuter ), and three numbers (singular, dual , and plural ). Verbs have four moods ( indicative , imperative , subjunctive , and optative ) and three voices (active, middle, and passive ), as well as three persons (first, second, and third) and various other forms. Verbs are conjugated through seven combinations of tenses and aspect (generally simply called "tenses"):

3948-495: The Archaic period of ancient Greek (see Homeric Greek for more details): Μῆνιν ἄειδε, θεά, Πηληϊάδεω Ἀχιλῆος οὐλομένην, ἣ μυρί' Ἀχαιοῖς ἄλγε' ἔθηκε, πολλὰς δ' ἰφθίμους ψυχὰς Ἄϊδι προΐαψεν ἡρώων, αὐτοὺς δὲ ἑλώρια τεῦχε κύνεσσιν οἰωνοῖσί τε πᾶσι· Διὸς δ' ἐτελείετο βουλή· ἐξ οὗ δὴ τὰ πρῶτα διαστήτην ἐρίσαντε Ἀτρεΐδης τε ἄναξ ἀνδρῶν καὶ δῖος Ἀχιλλεύς. The beginning of Apology by Plato exemplifies Attic Greek from

4032-648: The Classical period of ancient Greek. (The second line is the IPA , the third is transliterated into the Latin alphabet using a modern version of the Erasmian scheme .) Ὅτι [hóti Hóti μὲν men mèn ὑμεῖς, hyːmêːs hūmeîs,   Darcy%27s law Darcy's law was first determined experimentally by Darcy, but has since been derived from the Navier–Stokes equations via homogenization methods. It

4116-411: The Darcy's law hydraulic conductivity . In the (less general) integral form, the volumetric flux and the pressure gradient correspond to the ratios: q = Q A {\displaystyle q={\frac {Q}{A}}} ∇ p = Δ p L {\displaystyle \nabla p={\frac {\Delta p}{L}}} . In case of an anisotropic porous media,

4200-487: The Darcy's law hydraulic resistance . The Darcy's law can be generalised to a local form: where ∇ p {\displaystyle \nabla p} is the hydraulic gradient and q {\displaystyle \mathbf {q} } is the volumetric flux which here is called also superficial velocity . Note that the ratio: σ = k μ {\displaystyle \sigma ={\frac {k}{\mu }}} can be thought as

4284-552: The Navier–Stokes equation simplifies to the Stokes equation , which by neglecting the bulk term is: where μ is the viscosity, u i is the velocity in the i direction, and p is the pressure. Assuming the viscous resisting force is linear with the velocity we may write: where φ is the porosity , and k ij is the second order permeability tensor. This gives the velocity in the n direction, which gives Darcy's law for

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4368-564: The advent of computers and especially geographic information systems (GIS). (See also GIS and hydrology ) The central theme of hydrology is that water circulates throughout the Earth through different pathways and at different rates. The most vivid image of this is in the evaporation of water from the ocean, which forms clouds. These clouds drift over the land and produce rain. The rainwater flows into lakes, rivers, or aquifers. The water in lakes, rivers, and aquifers then either evaporates back to

4452-495: The amount of groundwater flowing under a dam . Darcy's law is only valid for slow, viscous flow; however, most groundwater flow cases fall in this category. Typically any flow with a Reynolds number less than one is clearly laminar, and it would be valid to apply Darcy's law. Experimental tests have shown that flow regimes with Reynolds numbers up to 10 may still be Darcian, as in the case of groundwater flow. The Reynolds number (a dimensionless parameter) for porous media flow

4536-550: The aorist. Following Homer 's practice, the augment is sometimes not made in poetry , especially epic poetry. The augment sometimes substitutes for reduplication; see below. Almost all forms of the perfect, pluperfect, and future perfect reduplicate the initial syllable of the verb stem. (A few irregular forms of perfect do not reduplicate, whereas a handful of irregular aorists reduplicate.) The three types of reduplication are: Irregular duplication can be understood diachronically. For example, lambanō (root lab ) has

4620-530: The atmosphere or eventually flows back to the ocean, completing a cycle. Water changes its state of being several times throughout this cycle. The areas of research within hydrology concern the movement of water between its various states, or within a given state, or simply quantifying the amounts in these states in a given region. Parts of hydrology concern developing methods for directly measuring these flows or amounts of water, while others concern modeling these processes either for scientific knowledge or for making

4704-419: The augment when it was word-initial. In verbs with a preposition as a prefix, the augment is placed not at the start of the word, but between the preposition and the original verb. For example, προσ(-)βάλλω (I attack) goes to προσ έ βαλoν in the aorist. However compound verbs consisting of a prefix that is not a preposition retain the augment at the start of the word: αὐτο(-)μολῶ goes to ηὐ τομόλησα in

4788-438: The center of Greek scholarship, this division of people and language is quite similar to the results of modern archaeological-linguistic investigation. One standard formulation for the dialects is: West vs. non-West Greek is the strongest-marked and earliest division, with non-West in subsets of Ionic-Attic (or Attic-Ionic) and Aeolic vs. Arcadocypriot, or Aeolic and Arcado-Cypriot vs. Ionic-Attic. Often non-West

4872-441: The definition of the flux following the standard physics convention that fluids flow from regions of high pressure to regions of low pressure. Note that the elevation head must be taken into account if the inlet and outlet are at different elevations. If the change in pressure is negative, then the flow will be in the positive x direction. There have been several proposals for a constitutive equation for absolute permeability, and

4956-615: The dialect of Sparta ), and Northern Peloponnesus Doric (including Corinthian ). All the groups were represented by colonies beyond Greece proper as well, and these colonies generally developed local characteristics, often under the influence of settlers or neighbors speaking different Greek dialects. After the conquests of Alexander the Great in the late 4th century BC, a new international dialect known as Koine or Common Greek developed, largely based on Attic Greek , but with influence from other dialects. This dialect slowly replaced most of

5040-401: The first-principle-based binary friction model (BFM). The differential equation of transition flow in porous media based on BFM is given as This equation is valid for capillaries as well as porous media. The terminology of the Knudsen effect and Knudsen diffusivity is more common in mechanical and chemical engineering . In geological and petrochemical engineering, this effect is known as

5124-673: The forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek ( c.  1400–1200 BC ), Dark Ages ( c.  1200–800 BC ), the Archaic or Epic period ( c.  800–500 BC ), and the Classical period ( c.  500–300 BC ). Ancient Greek was the language of Homer and of fifth-century Athenian historians, playwrights, and philosophers . It has contributed many words to English vocabulary and has been

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5208-689: The future behavior of hydrologic systems (water flow, water quality). One of the major current concerns in hydrologic research is "Prediction in Ungauged Basins" (PUB), i.e. in basins where no or only very few data exist. The aims of Statistical hydrology is to provide appropriate statistical methods for analyzing and modeling various parts of the hydrological cycle. By analyzing the statistical properties of hydrologic records, such as rainfall or river flow, hydrologists can estimate future hydrologic phenomena. When making assessments of how often relatively rare events will occur, analyses are made in terms of

5292-403: The gas and the porous medium structure. This is quite evident if we compare the above formulations. The Klinkenberg parameter b is dependent on permeability, Knudsen diffusivity and viscosity (i.e., both gas and porous medium properties). 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

5376-495: The given distance L {\displaystyle L} over which the pressure drop is computed, and the cross-sectional area A {\displaystyle A} , in the form: Q = k A μ L Δ p {\displaystyle Q={\frac {kA}{\mu L}}\Delta p} Note that the ratio: R = μ L k A {\displaystyle R={\frac {\mu L}{kA}}} can be defined as

5460-561: The historical Dorians . The invasion is known to have displaced population to the later Attic-Ionic regions, who regarded themselves as descendants of the population displaced by or contending with the Dorians. The Greeks of this period believed there were three major divisions of all Greek people – Dorians, Aeolians, and Ionians (including Athenians), each with their own defining and distinctive dialects. Allowing for their oversight of Arcadian, an obscure mountain dialect, and Cypriot, far from

5544-476: The historical circumstances of the times imply that the overall groups already existed in some form. Scholars assume that major Ancient Greek period dialect groups developed not later than 1120 BC, at the time of the Dorian invasions —and that their first appearances as precise alphabetic writing began in the 8th century BC. The invasion would not be "Dorian" unless the invaders had some cultural relationship to

5628-464: The hydrologic cycle, in which precipitation falling in the mountains infiltrated the Earth's surface and led to streams and springs in the lowlands. With the adoption of a more scientific approach, Leonardo da Vinci and Bernard Palissy independently reached an accurate representation of the hydrologic cycle. It was not until the 17th century that hydrologic variables began to be quantified. Pioneers of

5712-430: The important areas of hydrology is the interchange between rivers and aquifers. Groundwater/surface water interactions in streams and aquifers can be complex and the direction of net water flux (into surface water or into the aquifer) may vary spatially along a stream channel and over time at any particular location, depending on the relationship between stream stage and groundwater levels. In some considerations, hydrology

5796-463: The inflow performance calculations for the well, not the grid cell of the 3D model, are based on the Forchheimer equation. The effect of this is that an additional rate-dependent skin appears in the inflow performance formula. Some carbonate reservoirs have many fractures, and Darcy's equation for multiphase flow is generalized in order to govern both flow in fractures and flow in the matrix (i.e.

5880-403: The maximum rate at which the soil can absorb water, depends on several factors. The layer that is already saturated provides a resistance that is proportional to its thickness, while that plus the depth of water above the soil provides the driving force ( hydraulic head ). Dry soil can allow rapid infiltration by capillary action ; this force diminishes as the soil becomes wet. Compaction reduces

5964-523: The modern science of hydrology include Pierre Perrault , Edme Mariotte and Edmund Halley . By measuring rainfall, runoff, and drainage area, Perrault showed that rainfall was sufficient to account for the flow of the Seine. Mariotte combined velocity and river cross-section measurements to obtain a discharge value, again in the Seine. Halley showed that the evaporation from the Mediterranean Sea

6048-525: The most famous one is probably the Kozeny equation (also called Kozeny–Carman equation ). By considering the relation for static fluid pressure ( Stevin's law ): p = ρ g h {\displaystyle p=\rho gh} one can decline the integral form also into the equation: Q = k A g ν L Δ h {\displaystyle Q={\frac {kAg}{\nu L}}\,{\Delta h}} where ν

6132-508: The older dialects, although the Doric dialect has survived in the Tsakonian language , which is spoken in the region of modern Sparta. Doric has also passed down its aorist terminations into most verbs of Demotic Greek . By about the 6th century AD, the Koine had slowly metamorphosed into Medieval Greek . Phrygian is an extinct Indo-European language of West and Central Anatolia , which

6216-487: The perfect stem eilēpha (not * lelēpha ) because it was originally slambanō , with perfect seslēpha , becoming eilēpha through compensatory lengthening. Reduplication is also visible in the present tense stems of certain verbs. These stems add a syllable consisting of the root's initial consonant followed by i . A nasal stop appears after the reduplication in some verbs. The earliest extant examples of ancient Greek writing ( c.  1450 BC ) are in

6300-400: The permeability is a second order tensor , and in tensor notation one can write the more general law: Notice that the quantity q {\displaystyle \mathbf {q} } , often referred to as the Darcy flux or Darcy velocity, is not the velocity at which the fluid is travelling through the pores. It is the specific discharge, or flux per unit area. The flow velocity ( u )

6384-429: The porosity φ is a nondimensional number , the Darcy flux q {\displaystyle \mathbf {q} } , or discharge per unit area, is also defined in units ( m / s ) {\displaystyle \mathrm {(m/s)} } ; the permeability k {\displaystyle k} in units ( m 2 ) {\displaystyle \mathrm {(m^{2})} } ,

6468-458: The porosity and the pore sizes. Surface cover increases capacity by retarding runoff, reducing compaction and other processes. Higher temperatures reduce viscosity , increasing infiltration. Soil moisture can be measured in various ways; by capacitance probe , time domain reflectometer or tensiometer . Other methods include solute sampling and geophysical methods. Hydrology considers quantifying surface water flow and solute transport, although

6552-517: The syllabic script Linear B . Beginning in the 8th century BC, however, the Greek alphabet became standard, albeit with some variation among dialects. Early texts are written in boustrophedon style, but left-to-right became standard during the classic period. Modern editions of ancient Greek texts are usually written with accents and breathing marks , interword spacing , modern punctuation , and sometimes mixed case , but these were all introduced later. The beginning of Homer 's Iliad exemplifies

6636-455: The traditional porous rock). The irregular surface of the fracture walls and high flow rate in the fractures may justify the use of Forchheimer's equation. For gas flow in small characteristic dimensions (e.g., very fine sand, nanoporous structures etc.), the particle-wall interactions become more frequent, giving rise to additional wall friction (Knudsen friction). For a flow in this region, where both viscous and Knudsen friction are present,

6720-440: The treatment of flows in large rivers is sometimes considered as a distinct topic of hydraulics or hydrodynamics. Surface water flow can include flow both in recognizable river channels and otherwise. Methods for measuring flow once the water has reached a river include the stream gauge (see: discharge ), and tracer techniques. Other topics include chemical transport as part of surface water, sediment transport and erosion. One of

6804-603: The variables constituting the terrestrial water balance, for example surface water storage, soil moisture , precipitation , evapotranspiration , and snow and ice , are measurable using remote sensing at various spatial-temporal resolutions and accuracies. Sources of remote sensing include land-based sensors, airborne sensors and satellite sensors which can capture microwave , thermal and near-infrared data or use lidar , for example. In hydrology, studies of water quality concern organic and inorganic compounds, and both dissolved and sediment material. In addition, water quality

6888-409: The volumetric flux density in the n direction, In isotropic porous media the off-diagonal elements in the permeability tensor are zero, k ij = 0 for i ≠ j and the diagonal elements are identical, k ii = k , and the common form is obtained as below, which enables the determination of the liquid flow velocity by solving a set of equations in a given region. The above equation

6972-480: Was Aeolic. For example, fragments of the works of the poet Sappho from the island of Lesbos are in Aeolian. Most of the dialect sub-groups listed above had further subdivisions, generally equivalent to a city-state and its surrounding territory, or to an island. Doric notably had several intermediate divisions as well, into Island Doric (including Cretan Doric ), Southern Peloponnesus Doric (including Laconian ,

7056-617: Was sufficient to account for the outflow of rivers flowing into the sea. Advances in the 18th century included the Bernoulli piezometer and Bernoulli's equation , by Daniel Bernoulli , and the Pitot tube , by Henri Pitot . The 19th century saw development in groundwater hydrology, including Darcy's law , the Dupuit-Thiem well formula, and Hagen- Poiseuille 's capillary flow equation. Rational analyses began to replace empiricism in

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