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Approximate Solution of a Non-Steady-State Drainage Problem¹

ABSTRACT

Flow in the unsaturated zone during one-dimensional drainage is taken into account approximately by assuming the water content to be a linear function of the hydraulic head. The problem is then treated as one in unsaturated flow. After a brief initial period, the rate of outflow should decrease exponentially with time, with the outflow rate proportional to the soil-water diffusivity. Agreement with experimentally determined outflow rates is reasonable; however, the exact water content distribution cannot be calculated. The treatment is extended to two dimensions by the equivalent of the Dupuit-Forchheimer assumption. The total amount of water in the profile at any horizontal distance from a drain is calculated rather than the position of the water table. The theoretical outflow is in good agreement with results of sand tank and field measurements.

¹ Contribution from Soil and Water Conservation Research Division, ARS, USDA, Riverside, Calif.

² Physicist, U. S. Salinity Laboratory, Riverside, Calif.

Received for publication June 6, 1961. Accepted for publication November 14, 1961.