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Laterally Confined, Steady Flows of Water from Sources and to Sinks in Unsaturated Soils¹

ABSTRACT

Laterally confined, steady flows from line and point sources at arbitrary distance below the soil surface and to line and point sinks at arbitrary distance above an impermeable base are analyzed on the basis of the assumption that the hydraulic conductivity is an exponential function of the pressure head. The results include expressions describing the flow pattern, the distribution of the components of the flux, and the distributions of matric flux potential, pressure head, water content, and total head. The horizontal variations are described by trigonometric functions in problems involving line sources and sinks, and by Bessel functions in problems involving point sources and sinks. The regions below and above the sources and sinks are treated separately, subject, of course, to matching along the interface between the two regions. The vertical variations are described by exponential dampings, and surface and base reflections. For the flows to sinks, with each flow pattern there is associated an infinite variety of distributions of the matric flux potential etc., corresponding to different suctions applied at the sinks. Some problems involving partial supply by sources and interception by sinks are also treated.

The application of water along lines and at points is of interest in connection with furrow, subsurface, and drip irrigation. The removal of water along lines and at points is of interest in connection with uptake of water by plant roots and a variety of devices used to extract water and measure fluxes in the laboratory and in the field.

¹ Contribution from the Western Region, ARS-USDA, Riverside, Calif.

² Formerly Soil Scientist, U.S. Salinity Lab., P.O. Box 672, Riverside, CA 92502. Now with the Institute for Soil Fertility, Oosterweg 92, Haren(Gr), The Netherlands.

Received for publication March 15, 1976. Accepted for publication September 7, 1976.