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Linearized Moisture Flow with Root Extraction for Three Dimensional, Steady Conditions¹

ABSTRACT

A mathematical model is presented to simulate plant water uptake assuming steady-state conditions and an unsaturated hydraulic conductivity as an exponential function of pressure head. By choosing the conductivity to be of this form, the moisture flow equation is linear, allowing analytical solutions to be developed in a closed form. Geometries considered possess radial symmetry and are appropriate to describe trickle irrigation. These include matrix potentials for points, discs, and cylinders which can be taken either as sources or sinks. These provide the basic building blocks to simulate varied steady-state withdrawal patterns. The solution for the cylinder is newly derived; the other solutions were already available. Nonsymmetric cases can result from superpositions. Examples include pressure head distributions for four sink-source combinations.

¹ Arizona Agric. Exp. Stn. Paper no. 327. Support was from Western Regional Project W-128 and funds provided by the U. S. Dep. of the Interior, Office of Water Resources Research, as authorized under the Water Resources Research Act of 1964, Project B-064-ARIZ.

² Professor, Soils, Water, and Engineering Dep.; Professor, Mathematics Dep., and Research Associate, Soils, Water, and Engineering Dep., The Univ. of Arizona, Tucson, AZ 85721.

Received for publication January 23, 1980. Accepted for publication June 12, 1980.

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