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Hodograph Transformation for Flow Through a Dam With Sloping Walls and No Tail Water
Author(s) -
Boast C. W.
Publication year - 1986
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/wr022i010p01455
Subject(s) - hodograph , parabola , tailwater , plane (geometry) , geotechnical engineering , water table , transformation (genetics) , flow (mathematics) , geology , geometry , mathematics , mathematical analysis , groundwater , biochemistry , chemistry , gene
A method is presented to transform the hodograph plane (velocity plane) of an earthen dam with sloping walls to a plane where the unconfined saturated‐flow boundary value problem associated with such a dam can be solved using the Poisson integral. The solution would give, for example, the rate of flow of water through the dam, the extent of the surface of seepage on the downstream side of the dam, and the shape and position of the water table within the dam. The method, which is presented for the no‐tailwater case, applies to a dam with perpendicular upstream and downstream walls. It is based on the fact that the hodograph of such a dam consists simply of a triangle, plus an internal circular arc cut that represents the water table. A key step in the method is possible because, in the plane generated by the first Schwarz‐Christoffel transformation, the curve corresponding to the water table approaches a parabola near the point at infinity.