Abstract
The Poiseuille and Darcy laws describe the velocity of groundwater flow under laminar conditions. These laws were deducted empirically in conduit and porous systems, respectively, and are widely used to model the groundwater flow. The analytical relationship between these hydraulic laws has been found by draining a tank-reservoir. Based on equations found, the discharge in a conduit under the Poiseuille law can be transformed in the same amount flowing inside a darcian system, and vice versa. This transformation occurs, for example, in karst aquifers, from the matrix to karst conduits during discharge phases, and from conduits to matrix during recharge phases.
Highlights
IntroductionUnder laminar condition of the flow, the most common hydraulic law used to model groundwater flow in saturated media are the Darcy and Poiseuille laws
In theIn porous medium, the turbulent flow occurs from the laminar condition when the velocity of the flow increases, and it is strictly connected to the structure dition when the velocity of the flow increases, and it is strictly connected to the structure the medium
The Darcy law has a wide use in groundwater hydrology in the porous medium, and in fractured/conduit systems, where the hydraulic conductivity, K, is considered as a mean value of a wide portion of rock masses
Summary
Under laminar condition of the flow, the most common hydraulic law used to model groundwater flow in saturated media are the Darcy and Poiseuille laws. Both hydraulic laws describe the velocity of groundwater flow in saturated zones, refer to different physical approaches (conduits and porous systems) To investigate their but refer to different physical approaches (conduits and porous systems). Poiseuille system system (conduit discharge (conduit medium) medium) in in the the same sameamount amountflowing flowinginside insidea darcian system (porous medium), and vice versa; scaling processes of the hydraulic seca darcian system (porous medium), and vice versa; scaling processes of the hydraulic tions have been considered These changing of the flow conditions occur, for example, sections have been considered. If the tank-tube, with section area AD (and diameter dD ) and length L, is filled by sand with hydraulic conductivity K, the Darcy law can be used to simulate the drainage from the tank-reservoir. The recession coefficient depends on the geometric and hydraulic characteristics of the reservoir (Equations (4) and (8)); it is the constant linking the discharge, Q(t), to the water volume stored V(t) in a linear reservoir:
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