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Determination of Equivalent Radii for Half-Tube and Whole-Tube Drains in Contact With an Impermeable Barrier¹

ABSTRACT

For soil-drainage problems, we prove that a half-tube of radius a, the diameter of which is coincident with a plane barrier, is equivalent to a whole-tube drain of a smaller radius, b = 2a/ = 0.6366a, installed with its circumference touching the same plane barrier. The value 0.6366a lies between the limits 0.5a and 1.0a found by Kirkham in 1947. The result is applicable by analogy to all types of potential problems, such as those of electricity and heat conduction. The result is useful for applying theoretical results, found for half tubes, to whole tubes as used in practice.

¹ Journal Paper no. J-5807 of the Iowa Agr. & Home Econ. Exp. Sta., Ames, Iowa. Project 998. This investigation was supported in part by Public Health Service Research Grant WP-00070-05 from the Division of Water Supply and Pollution Control.

² Research Associate and Professor, Agronomy Department, Iowa State University.

Received for publication November 15, 1967. Accepted for publication January 3, 1968.