On Ground Water Flow to an Imperfect Gallery: Case of Evaporation from a Free Surface

Modeling the Movement of Groundwater VOD in a Rectangular Jumper with a Screen

“…at a 1 →1 (arcth a 1 = ∞) the coff erdam degenerates into a semi-infi nite left-handed unconfi ned formation. Thus, the exact solution of groundwater fl ow to the imperfect gallery, studied earlier [9], is obtained.…”

“…From [9] where the fl ow area to the left was limited by the equipotential shows that the relative error of the calculations is rather small and amounts to only 0.5 and 1.3% respectively. A technique for constructing an exact analytical solution of the problem of fl uid motion in a rectangular coff erdam with a screen in the presence of evaporation from the free surface of groundwater has been developed.…”

“…We introduce an auxiliary canonical variable  and functions: z() conformally mapping the upper half-plane >0 to the fl ow region z under the correspondence of points D = 0 , E = e , A = 1 , A 1 = a 1 , B = b , (a 1 , b are unknown affi xes of points A 1 and B in the plane ), C = ∞, and functions d / d and dz / d. We emphasize that, compared to [9], an additional boundary angular singular point A 1 appears here in the fl ow region z, which complicates the solution considerably.…”

“…The presented work gives an exact solution of the fi ltration problem in a rectangular coff erdam with a screen in the presence of evaporation from the free surface of groundwater. In this case, as well as in [9] (unlike in [7,8]) in the area of the fl ow velocity hodograph appear not rectilinear, but circular polygons, which does not allow using the classical Christoff el-Schwarz formula. The eff ect of evaporation from the free surface is studied using the method of Polubarinova-Kochina PY [1][2][3][4][5][6].…”

“…Therefore, as a fi rst approximation to the solution of this problem, its fl at analogues-problems about fl uid fl ow to a rectangular coff erdam with a screen and to an imperfect rectilinear gallerywere considered [1,[5][6][7][8], which give a certain qualitative insight into the possible dependence of fi ltration characteristics on the degree of well imperfection. Exact analytical solution of the problem of groundwater movement in unconfi ned reservoir to imperfect gallery in presence of evaporation from free surface is given in work [9]. As well as an approximate solution of the problem in the case when the fl ow area on the left is limited by some equipotential defi ned from the solution.…”