One powerful application of complex analysis is the visualization of streamlines and velocity fields of irrotational and incompressible fluids using equipotential curves. With this poster, we aim to leverage the complex potential function to provide valuable insights for both theoretical research and practical applications. Our methods utilize complex analysis to determine solutions to the differential equations describing fluid flow, focusing on circular objects. These techniques offer an unparalleled ability to accurately describe flow around circular objects. We analyze planar velocity fields using conformal mappings and employ the Joukowski transformation to model flow around airfoils. Additionally, we construct ideal fluid flows confined within a given domain, known as “streamlining.” These methods offer a robust framework for understanding and optimizing fluid dynamics problems. The findings have wide-ranging applications, including pollution spread, blood flow, aerodynamics, and water distribution systems, contributing to more efficient and sustainable designs.