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

Abstract

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.

Keywords

• groundwater
• Darcy–Weisbach law
• Poiseuille law
• turbulent
• laminar
• critical zone