Pumping events are often conducted in the alluvial fan due to its considerable amount of water; If pumping events occur in the nearby vicinity of the streams, it will inevitably influence the complex microbial ecosystems in both the river and the aquifer, induce the issue of water rights permits, and affect the development of the water resource management. Therefore, it becomes necessary to accurately predict groundwater flow as a result of pumping in the wedge-shaped aquifer. In this paper, we propose an analytical solution to describe the drawdown distribution and the stream depletion rate (SDR) due to pumping in a wedge-shaped aquifer, which represents the shape of the alluvial fan bounded by two streams. Moreover, we adopt the lagging theory into the model by introducing two lagging parameters in Darcy’s law to allow the water flow and the hydraulic gradient to occur at different times. This measure facilitates the reflection of the inertial force because of a higher pumping rate and the microstructural interaction resulting from the water transfer between the primary pores and secondary pores (e.g., dead-end pores and very-small pores). It leads to the predicted result being closer to reality when these effects are profound. We found that the drawdown and SDR curves will behave like waves when the flux lagging dominates. The SDR value can be over unit due to the additional recharge driven by inertial force; the drawdown and SDR acts more like an unconfined or dual-porosity flow if storage lagging governs the system. Moreover, lagging parameters have the largest effect on drawdown and SDR when the times are close to the corresponding values of lagging parameters. The case of wedge-shaped domain bounded by two impervious barriers is considered to further explore the boundary effects on aquifer response to pumping
