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Explanation of paradoxes in Dupuit‐Forchheimer Seepage Theory
Author(s) -
Kirkham Don
Publication year - 1967
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr003i002p00609
Subject(s) - infinitesimal , geotechnical engineering , soil water , drainage , groundwater , geology , mathematics , streamlines, streaklines, and pathlines , boundary (topology) , geometry , rotational symmetry , mechanics , mathematical analysis , soil science , physics , ecology , biology
Cutting into a porous medium of a large number of vertical, parallel, infinitely permeable, equally spaced, infinitesimally thin slots produces a fictitious soil that follows, exactly and without paradoxes Dupuit's assumptions and hence Dupuit‐Forchheimer (D.F.) drainage theory in two dimensions. A soil having these infinitesimally thin slots is designated a D.F. soil. For this fictitious soil, a formula for the proper depth and spacing of ditches and drain tiles is derived. The formula is the same one found in conventional D.F. literature. The formula, valid for both tiles and ditches and known to hold approximately for actual soils, is exact for a D.F. soil. Dupuit's two‐dimensional ‘parabolic seepage problem’ and others may now be considered as exactly solvable for D.F. soils. For three‐dimensional axially symmetric seepage flow, as into wells, the fictitious slots of a DF. soil become concentric coaxial rings. DF. streamlines are not horizontal; they converge in a special way. (Key words: Drainage; groundwater; seepage; hydraulics)