scholarly journals Discussion of “Classroom Activities to Illustrate Concepts of Darcy’s Law and Hydraulic Conductivity” by Roseanna M. Neupauer and Norman D. Dennis

2017 ◽  
Author(s):  
Dejan Brkić ◽  
Vladimir Mitrović
Keyword(s):  
Hydraulic Conductivity ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Available P ◽  
Classroom Activities

No abstract available

Incorporation of Interfacial Areas in Models of Two-Phase Flow

1999 ◽  
Author(s):  
William G. Gray ◽  
Michael A. Celia
Keyword(s):  
Porous Media ◽  
Hydraulic Conductivity ◽  
Single Phase ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Hydraulic Gradient ◽  
Phase Flow ◽  
Single Phase Flow ◽  
Α Phase ◽  
Flow Through

The mathematical study of flow in porous media is typically based on the 1856 empirical result of Henri Darcy. This result, known as Darcy’s law, states that the velocity of a single-phase flow through a porous medium is proportional to the hydraulic gradient. The publication of Darcy’s work has been referred to as “the birth of groundwater hydrology as a quantitative science” (Freeze and Cherry, 1979). Although Darcy’s original equation was found to be valid for slow, steady, one-dimensional, single-phase flow through a homogeneous and isotropic sand, it has been applied in the succeeding 140 years to complex transient flows that involve multiple phases in heterogeneous media. To attain this generality, a modification has been made to the original formula, such that the constant of proportionality between flow and hydraulic gradient is allowed to be a spatially varying function of the system properties. The extended version of Darcy’s law is expressed in the following form: qα=-Kα . Jα (2.1) where qα is the volumetric flow rate per unit area vector of the α-phase fluid, Kα is the hydraulic conductivity tensor of the α-phase and is a function of the viscosity and saturation of the α-phase and of the solid matrix, and Jα is the vector hydraulic gradient that drives the flow. The quantities Jα and Kα account for pressure and gravitational effects as well as the interactions that occur between adjacent phases. Although this generalization is occasionally criticized for its shortcomings, equation (2.1) is considered today to be a fundamental principle in analysis of porous media flows (e.g., McWhorter and Sunada, 1977). If, indeed, Darcy’s experimental result is the birth of quantitative hydrology, a need still remains to build quantitative analysis of porous media flow on a strong theoretical foundation. The problem of unsaturated flow of water has been attacked using experimental and theoretical tools since the early part of this century. Sposito (1986) attributes the beginnings of the study of soil water flow as a subdiscipline of physics to the fundamental work of Buckingham (1907), which uses a saturation-dependent hydraulic conductivity and a capillary potential for the hydraulic gradient.

Measuring the saturated hydraulic conductivity of peat substrates in nursery containers

1994 ◽  
Vol 74 (4) ◽  
pp. 431-437 ◽  
Author(s):  
S. E. Allaire ◽  
J. Caron ◽  
J. Gallichand
Keyword(s):  
Hydraulic Conductivity ◽  
Correction Factor ◽  
Darcy’S Law ◽  
Water Flux ◽  
Darcy's Law ◽  
Saturated Hydraulic Conductivity ◽  
Disruptive Effect ◽  
Flow Measurements ◽  
Flux Measurements ◽  
Made In

Pore size, distribution and continuity are important characteristics for the exchange and storage of air and water in artificial mixes. Saturated hydraulic conductivity (Ks) measurements can be used to obtain such a characterization. However, two difficulties are encountered when using Ks in potting media. First, the validity of Ks may be limited because it may not apply in media composed of coarse material or peat. Second, the structure of peat substrates is very sensitive and in situ measurements of potted peat substrates (i.e. measurements made directly in the pots) should be carried out to avoid any disruptive effect due to handling. Such a measurement, when made in pots, may require the evaluation of the water flux reduction resulting from the container outflow configuration. The objectives of this study were therefore to check the validity of Darcy’s law for peat substrates and to propose an approach for estimating the saturated hydraulic conductivity from flow measurements made in nursery containers. For three different substrates, water flow in artificial mixes followed Darcy’s law for hydraulic gradients ranging from 1.1 to 1.6 cm cm−1. Experimental results showed that the measured fluxes in 5-L nursery container filled at five different substrate heights (9, 11.5, 14, 16.5 and 19 cm) with laterally located drainage holes were significantly different from those measured in pots with the bottom removed (therefore equivalent to measurement currently made in cylinders) at P = 0.0022. Fluxes in containers with bottoms removed were 7–31% higher than in intact pots. Water flux measurements may therefore need to be corrected for this flux reduction in order to accurately estimate hydraulic conductivity from flow experiments run in pots. A correction factor based on the results obtained from a finite difference model was derived and calibrated. Then, this correction factor was used to convert flux measurements made in pots with lateral holes into equivalent flux that would have been obtained had the pot had an open bottom. After correction, no significant flux reductions were found between pots with open bottoms and pots with lateral holes (P = 0.55). A correction factor estimated from Laplace’s equation, once calibrated, can therefore be applied to flux measurements obtained from pots to obtain estimates of Ks of undisturbed potted media. Key words: Hydraulic conductivity, peat substrates, container

scholarly journals Comparison between different infiltration models to describe the infiltration of permeable brick pavement system via lab-scale experiment

2021 ◽  
Author(s):  
Jianying Song ◽  
Jianlong Wang ◽  
Wenhai Wang ◽  
Liuwei Peng ◽  
Hongxin Li ◽  
...  
Keyword(s):  
Hydraulic Conductivity ◽  
Darcy’S Law ◽  
Infiltration Rate ◽  
Darcy's Law ◽  
Optimal Model ◽  
Experiment Data ◽  
Runoff Volume ◽  
Infiltration Models ◽  
Scale Experiment ◽  
Horton Model

Abstract Permeable brick pavement system (PBPs) is one of a widely used low impact development (LID) measures to alleviate runoff volume and pollution caused by urbanization. The performance of PBPs on decreasing runoff volume is decided by its permeability, and it was general described by hydraulic conductivity based on Darcy's law. But there is large error when using hydraulic conductivity to describe the infiltration of PBPs, and which infiltration process is not following to the Darcy's law, so it is important to found a more accurate infiltration models to describe the infiltration of PBPs. The Horton, Philip, Green-Ampt, and Kostiakov infiltration models were selected to found an optimal model to investigate infiltration performance of PBPs via lab-scale experiment, and the maximum absolute error (MAE), Bias, and coefficient of determination (R2) were selected to evaluate the models' errors via fitting with experiment data. The results showed that the fitting accuracy of Kostiakov, Philip, and Green-Ampt models was significantly affected by the monitoring area and hydraulic gradients. Meanwhile, Horton model is fitting well (MAE = 0.25–0.32 cm/h, Bias = 0.07–0.11 cm/h, and R2 = 0.98–0.99) with the experiment data, and the parameters of Horton model often can be achieved by monitoring, such as the maximum infiltration rate and the stable infiltration rate. Therefore, the Horton model is an optimal model to describe the infiltration performance of PBPs, which can also be adopt to evaluate hydrological characterization of PBPs.

scholarly journals Averaging hydraulic head, pressure head, and gravitational head in subsurface hydrology, and implications for averaged fluxes, and hydraulic conductivity

2009 ◽  
Vol 13 (7) ◽  
pp. 1123-1132 ◽  
Author(s):  
G. H. de Rooij
Keyword(s):  
Porous Media ◽  
Hydraulic Conductivity ◽  
Darcy’S Law ◽  
Superposition Principle ◽  
Darcy's Law ◽  
Flow In Porous Media ◽  
General Definition ◽  
Closure Problem ◽  
Conservation Of Energy ◽  
Closed Expression

Abstract. Current theories for water flow in porous media are valid for scales much smaller than those at which problem of public interest manifest themselves. This provides a drive for upscaled flow equations with their associated upscaled parameters. Upscaling is often achieved through volume averaging, but the solution to the resulting closure problem imposes severe restrictions to the flow conditions that limit the practical applicability. Here, the derivation of a closed expression of the effective hydraulic conductivity is forfeited to circumvent the closure problem. Thus, more limited but practical results can be derived. At the Representative Elementary Volume scale and larger scales, the gravitational potential and fluid pressure are treated as additive potentials. The necessary requirement that the superposition be maintained across scales is combined with conservation of energy during volume integration to establish consistent upscaling equations for the various heads. The power of these upscaling equations is demonstrated by the derivation of upscaled water content-matric head relationships and the resolution of an apparent paradox reported in the literature that is shown to have arisen from a violation of the superposition principle. Applying the upscaling procedure to Darcy's Law leads to the general definition of an upscaled hydraulic conductivity. By examining this definition in detail for porous media with different degrees of heterogeneity, a series of criteria is derived that must be satisfied for Darcy's Law to remain valid at a larger scale.

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