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Diffusion Theory Applied to Water Flow Data Obtained Using Gamma Ray Absorption¹

ABSTRACT

Unsaturated water flow data obtained using gamma ray equipment were not fit by the equation x = 2 () t. Thus, the data could not be used in the ordinary differential equation obtained by combination of x = 2 () t and the second-order differential equation of diffusion. The discrepancy between the data and x = 2 () t was not great over much of the range; thus, it is possible that this equation could be used in much unsaturated flow work. The data did indicate that diffusivity was a function of water content alone over much of the time of water flow. The relationship between diffusivity and water content followed a nonexponential, curvilinear relationship. The data also suggest that a minimum gradient may be essential in order for unsaturated flow to occur.

¹ Contribution from the Department of Agronomy, Washington Agr. Exp. Sta., Pullman. Scientific Paper No. 2141. Part of a thesis submitted in partial fulfillment of the requirements for the Ph.D. degree at Washington State University. Work was conducted under Project 1234.

² Formerly Graduate Assistant, Washington State University, now Associate Professor, Montana State College; and Professor of Soils, Washington State University, respectively.

Received for publication December 1, 1961. Accepted for publication November 28, 1962.