FIG. 9.4.6 Radial unconfined flow with infiltration. (Reprinted from O.D.L. Strack, 1989, Groundwater mechanics, Vol. 3, Pt. 3, Prentice-Hall, Inc.)
FIG. 9.4.6 Radial unconfined flow with infiltration. (Reprinted from O.D.L. Strack, 1989, Groundwater mechanics, Vol. 3, Pt. 3, Prentice-Hall, Inc.)
The constant C in this equation can be determined from the boundary condition that r = R, $ = $o. The expression for $ then becomes
The location of the divide is obviously at the center of the island where d$/dr = 0 and rd = 0.
Figure 9.4.7 shows radial flow in an unconfined aquifer with infiltration in which water is pumped out of a well located at the center of a circular island.
The principle of superposition can be used to solve this problem. In the first case, the radial flow is from pump-
ing alone; in the second, the flow is from infiltration. Since the differential equations for both cases are linear (Laplace's equation and Poisson's equation), the solution for each can be superimposed to obtain a solution for the whole with the sum of both solutions meeting the boundary conditions.
The addition of the two solutions, Equations 9.4(15) and 9.4(31), with a new constant C gives
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