Delve into the fundamentals of fluid mechanics in chemical engineering, examining the behavior of fluids under different flow regimes and boundary conditions. Analyze the principles of fluid statics, fluid dynamics, and rheology, including the Navier$-$Stokes equations and their applications in engineering analysis. Explore the design and operation of fluid handling equipment, such as pumps, compressors, and pipelines, considering factors such as pressure drop, flow regime transitions, and turbulent flow phenomena.