Document Type : Research Paper


1 Department of Mathematics, College of Computer Science and Mathematics, Tikrit University, Tikrit, Iraq

2 Department of Environmental Engineering, College of Engineering, University of Mustansiriyah, Baghdad, Iraq



This article delves into the intricate dynamics of groundwater flow within duct systems, ‎examining both critical and sub-critical flow conditions. Employing mathematical models, ‎sophisticated potential methodologies, numerical simulations, and flow net analysis, the ‎research investigates the behaviour of the phreatic surface under varying flow coefficients ‎ and slope angles . Noteworthy discoveries include the significant influence of the flow ‎coefficient on the curvature and deflection of the phreatic surface, with higher m values ‎resulting in steeper slopes. Additionally, the study emphasizes that changes in slope angle θ ‎impact the interface's shape, leading to variations in flow depth‏.‏‎ Innovative visualizations ‎incorporating streamlines and velocity potential contours offer insights into flow patterns, ‎recirculation zones, and potential turbulence areas. These critical finding supply essential insights for enhancing environmental strategies, optimizing water resource management, and improving the efficiency of fluid systems. The study emphasises how important it is to use flow net analysis and thoroughly investigate critical and sub-critical flow scenarios in order to handle issues related to groundwater management and sustainability. Stakeholder can enhance their capacity for fluid system optimization by applying these analytical tools, leading to improved environmental outcomes and informed decision-making.