laminar flows of viscous Incompressible fluids

Abstract

This thesis deals with laminar flow of viscous incompressible fluids focusing on the fundamental principles, Mathematical modeling and practical applications. To understand the idea well some preliminary concepts were discussed. Types of fluids, some basic properties of fluids, shearing stress, skin friction and definitions were reviewed. The thesis employs the Navier Stoke sequations and continuity equation to model fluid behavior and analyzes the velocity profiles and flow rates between two parallel plates, in circular pipes and other geometries. Key parameters such as the Reynolds number, velocity, and pressure gradients are evaluated; results indicate that maintaining laminar flow is crucial for maximizing efficiency in various fluids dynamics application, as it reduces energy loss and turbulence. High viscosity leads to increase pressure drop, parabolic velocity profile and lower flow rates in laminar condition. The maximum velocity observed at the center of the pipe and gradually decreases to zero at the pipe walls due to viscous effect. This research contributes to better understanding of laminar flow dynamics and its implications for engineering and industrial applications.