This article presents a novel algebraic model that predicts fluid behavior in both incompressible and compressible flows, avoiding traditional differential equations. The study investigates how viscosity and dynamic pressure influence fluid dynamics using quadratic functions. The model incorporates quadratic functions to account for viscous effects and compares its predictions with established theoretical models. Vertex analysis helps identify optimal conditions for minimizing these functions, shedding light on how viscosity and compressibility affect flow efficiency. This work highlights the importance of incorporating viscous effects in fluid dynamics analysis, offering a more reliable and efficient approach for modeling boundary layer flows in engineering and applied research.