New Insights into Turbulent and Laminar Flow Relationships Using Darcy-Weisbach and Poiseuille Laws

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.