On ground water seepage under hydraulic structures

A way to calculate the seepage attached to the flow around the Zhukovskii rabbet with more than one-sheeted area of complex velocity

“…In this case, the area of complex velocity is not one sheeted in contrast to the case described in [1], where the area of the complex velocity is one sheeted. The Polubarinova Kochina method [2,3] and also the procedures of conformal mapping [4][5][6] for special areas, which are typical for the problems of under ground hydromechanics [7][8][9] are used to solve the mixed multi parametric boundary problem.…”

“…The moving water flowing around the rabbet rises at a certain height GF and forms a free surface DF, to which the infiltrated water flows with intensity ε. In the examined case, the velocity of the flow at the rabbet's end is infinite, in contrast to [1], where the peak of this velocity is limited by value ε.…”

“…2 are changed dras tically. This area, belonging to the class of polygons in polar grids [8,10], becomes two sheeted (in con trast to the case examined in [1]), and if we travel along the boundary, at points C and G, we pass to the second Riemann sheet and back.…”

“…Under such assumptions, traditional for the examined class of flows, the process of seepage simulation is reduced to the problem of how to find the complex potential ω(z) under the following boundary conditions: (1) where is the seepage flow rate. The procedure for determining the water height GF behind the rabbet, i.e., S -d, is of great interest.…”

“…Figure 1 depicts schematically the flow pattern. As before [1], we examine a flat steady state motion of incompressible fluid according to Darcy's law in uniform and isotropic soil through a soil layer of power …”