What is the theoretical foundation of fluid mechanics in chemical engineering, and how do the Navier-Stokes equations play a pivotal role in this field? Discuss the significance of fluid dynamics understanding for designing processes such as reactors, separators, and pipelines. Highlight the applications of the Navier-Stokes equations in aerodynamics for optimizing aircraft and vehicle design, in hydraulic systems for efficient pump and pipeline design, and in chemical processing for modeling fluid behavior in reactors and mixers. Illustrate how these equations contribute to enhancing process efficiency, product quality, and overall engineering performance in various chemical engineering applications.