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P. Schmid, J. Luthin (1964)
The drainage of sloping landsJournal of Geophysical Research, 69
E. Youngs (1965)
Horizontal seepage through unconfined aquifers with hydraulic conductivity varying with depthJournal of Hydrology, 3
Boussinesq Boussinesq (1904)
Recherches théoriques sur l'écoulemeat des nappes d'eau infiltrées dans le sol et sur le débit des sourcesJ. Math. Pures Appl., 5
F. Henderson, R. Wooding (1964)
Overland flow and groundwater flow from a steady rainfall of finite durationJournal of Geophysical Research, 69
R. Wooding, T. Chapman (1966)
GROUNDWATER FLOW OVER A SLOPING IMPERMEABLE LAYER 1. APPLICATION OF THE DUPUIT-FORCHHEIMER ASSUMPTIONJournal of Geophysical Research, 71
Werner Werner (1957)
Some problems in non‐artesian ground‐water flowEos Trans. AGU, 38
P. Werner (1957)
Some problems in non‐artesian ground‐water flowEos, Transactions American Geophysical Union, 38
The Dupuit‐Forchheimer convention for horizontal impermeable beds is that the gradient of hydraulic potential is synonymous with the absolute slope of the water table. When the impermeable bed is sloping, however, the gradient is normally better approximated by dZ/dl, where l is the distance measured along the bed and Z is the height of the intersection with the water table of the perpendicular through l. Thus the solution of the resulting flow equation for drainage to a transverse ditch in the absence of surface recharge provides a family of branched curves for different slopes, instead of the single branched curve currently accepted. When there is surface recharge and a system of parallel equidistant drains, there is no simple analytic solution. However, numerical solutions show that the water table peak, as compared with a horizontal bed, is shifted downhill; its height is often not greatly affected.
Water Resources Research – Wiley
Published: Oct 1, 1971
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