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چکیده
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Wedge-shaped aquifers are sometimes cut by crossing streams so that the areal geometry can be delineated by an annular wedge of infinite radial extent. Despite their worldwide spread, the problem of groundwater flow in such geometrical entities has not received much attention in analytical studies. This paper presents a closed-form analytical solution for the aquifer head distribution in response to a system of multiwells superimposed on a background regional flow. The aquifer is isotropic, homogeneous and in prefect hydraulic connection with the surrounding streams. A steady-state Green’s function is constructed for this laterally bounded aquifer system. The formulation is general in the sense that the aquifer vertex angle as well as number of wells and their positions can be arbitrary chosen. Closed-form expression for the stream function is obtained by integration of the Cauchy-Riemann equations. Three types of hydrogeological boundary conditions are considered, combining streams of constant and linearly varying head and no-flow barrier. The results are applicable to both confined and unconfined flows. Extremely simple expressions are derived to quantify the amount of water exchange across stream-aquifer interfaces. Flow nets are given for a number of hypothetical test cases, demonstrating different aspects of the generated flow field. Sensitivity maps are prepared for the stream depletion rates due to a single pumping well and the role of aquifer vertex angle on the model response is investigated. Multiple stagnation points in the flow field are identified on a semi-analytical basis. This helps to assess how the position of a single stagnation point is affected by changes in the gradient of regional flow. For relatively high gradients, it is observed that the radial position of the stagnation point coincides with that of the well itself. Finally, the formulation is extended to account for rainfall recharge over an unconfined aquifer having the same areal extent.
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