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.

The hydraulic phenomenon of upwelling groundwater flow affecting the karst area of the Grassano-Telese springs (southern Italy) has been investigated through piezometric measurements, discharge, and chemical–physical monitoring of springs, radon activity included. Locally, both large karst springs and sulfurous thermal springs are closely located, and raise several questions on their origin. In this study, the phenomenon of the upwelling flow is supported by different types of evidences: Amazing density of sinkholes connected to hypogenic speleogenesis processes, constancy of temperature, and hydraulic conductivity of spring water, change of radon activity during the hydrological year, increasing of the hydraulic head with depth. Numerical code provides an estimation of the upwelling phenomenon in an unconfined aquifer feeding the karst springs, using MODFLOW tools. Based on the results reached, the phenomenon of the upwelling flow is able to explain the hydrological processes observed in the Telese karst area.

Analytical solutions for turbulent and laminar water flow conditions are developed considering the drainage process of a simple tank reservoir, using the Darcy–Weisbach and the Poiseuille laws, respectively. Near the critical value of the Reynolds number, the Darcy–Weisbach and the Poiseuille laws do not match, and there is a gap regarding the possibility of describing the drainage analytically. This gap corresponds to the critical zone of the Moody diagram, where theoretically a constant discharge occurs under a decreasing hydraulic gradient. In the critical zone, this hydraulic behavior of the flow reflects the different energy losses occurring during the drainage, as the laminar flow is a more efficient flow condition than the turbulent one. In natural systems (e.g., springs and karst aquifers), a smooth transition from the turbulent to the laminar water flow occurs due to the heterogeneity in the medium.