Potential Flow into Circumferential Openings in Drain Tubes

Abstract

A theoretical analysis of the effect of the spaces between drain tube units as used in the artificial drainage of soil is given. The problem is one of potential flow; therefore, the results are applicable to heat flow, etc. The basic problem solved is that for axially symmetric flow from an external cylindrical boundary at constant potential to a series of equal, equally spaced openings at a lower potential, all located axially on, and comprising a part of, the otherwise impervious drain tube. The radii of the open sections and impermeable sections of the drain tube are equal. The basic problem is extended to obtain the solution to the practical problem—the seepage of ground water into drain tubes beneath a horizontal water table. The exact solution of the basic problem is not suitable for numerical work. Accordingly, approximate solutions of specified uncertainty are derived and are utilized for tabulation of numerical results. As an example, the analysis shows, in the case of 6 in. diameter drain tubes having 1 ft. long impermeable sections and buried 4 ft. deep in uniformly permeable soil, that increasing the openings from $\frac{1}{32}$ in. width to ¼ in. width will increase the flow 36 percent; while embedding the tubes in gravel, to make the $\frac{1}{32}$ in. openings of effectively infinite width, will increase the flow 180 percent.