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E. Childs, N. Collis-george (1950)
The permeability of porous materialsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 201
L. Richards (1931)
Capillary conduction of liquids through porous mediumsPhysics, 1
J. Philip (1968)
Steady Infiltration From Buried Point Sources and Spherical CavitiesWater Resources Research, 4
D. Evans, D. Kirkham, R. Frevert (1951)
Infiltration and Permeability in Soil Overlying an Impermeable Layer1Soil Science Society of America Journal, 15
G. Topp, E. Miller (1966)
Hysteretic Moisture Characteristics and Hydraulic Conductivities for Glass-Bead Media1Soil Science Society of America Journal, 30
Talsma Talsma (1963)
The control of saline ground waterMededel. Landbouwhogeschool Opzoekingsta. Staat Gent, Wageningen, 63
Celestre Celestre (1964)
Drop irrigation systemTrans. 8th Intern. Congr. Soil Sci., Bucharest
W. Gardner, M. Fireman (1958)
LABORATORY STUDIES OF EVAPORATION FROM SOIL COLUMNS IN THE PRESENCE OF A WATER TABLESoil Science, 85
Evans Evans, Kirkham Kirkham, Frevert Frevert (1951)
Infiltration and permeability in soil overlying an impermeable layerProc. Soil Sci. Soc. Am., 15
Topp Topp, Millar Millar (1966)
Hysteretic moisture characteristics and hydraulic conductivities for glass‐bead mediaProc. Soil Sci. Soc. Am., 30
W. Gardner (1958)
SOME STEADY‐STATE SOLUTIONS OF THE UNSATURATED MOISTURE FLOW EQUATION WITH APPLICATION TO EVAPORATION FROM A WATER TABLESoil Science, 85
J. Philip (1969)
Theory of Infiltration, 5
J. Parr, A. Bertrand (1960)
Water Infiltration Into SoilsAdvances in Agronomy, 12
Steady infiltration from a shallow, circular, inundated area on the horizontal surface of a semi‐infinite porous medium is treated by a method of linearization proposed by J. R. Philip. Using this method, Philip retains most of the properties of the nonlinear system but reduces the differential equation to a linear type governing steady diffusion in a steady uniform flow. On the surface of the medium, the boundary conditions are of mixed type, although linear. These conditions are reduced to a system of dual integral equations solved by a modification of Tranter's method. Expressions for the distributions of vertical flux density, moisture content, and Stokes' stream function are derived, and numerical values of the last two quantities are illustrated graphically. It is found that the total flux depends almost linearly upon a parameter α, defined as the logarithmic derivative of the hydraulic conductivity with respect to capillary potential. Curves of mean flux over various radii (fractions of the total source radius) for various values of α indicate the importance of the guard ring in infiltrometer design.
Water Resources Research – Wiley
Published: Dec 1, 1968
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