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Equations for Approximating Vertical Nonsteady-State Drainage of Soil Columns¹

ABSTRACT

Equations are derived, from a capillary tube model, that predict vertical nonsteady-state drainage from soil columns over the entire time of drainage for which experimental data are available. The model assumes that a soil column is a bundle of capillaries of various radii with the effective conductivity of the column decreasing as drainage progresses. The conductivity is first considered to be a linear function of the average water level in the column, and then considered to be a quadratic function of the water level. Both resulting equations predict drainage reasonably well when particular values are assigned to the ratio of the average height of capillary rise to the column length. A simplified expression is obtained by neglecting an insignificant term and assigning values to constants in the equation in which the conductivity was taken as a quadratic function of the average water level. The equations are compared with experimental data.

¹ Contribution from the Soil & Water Conservation Research Division, ARS, USDA.

² Research Physicist and Research Soil Scientist (Physics), respectively, US Water Conserv. Lab., Phoenix, Ariz.

Received for publication February 13, 1970. Accepted for publication May 12, 1970.