Hydraulic Engineering and Fluid Dynamics:

What theoretical principles and mathematical models underpin the field of hydraulic engineering, particularly in the analysis and design of fluid flow systems? Begin by examining the fundamental laws of fluid mechanics, including conservation of mass, momentum, and energy, and elucidate their application to hydraulic engineering problems. Explore theoretical concepts such as laminar and turbulent flow, boundary layer theory, and flow regime transitions, highlighting their significance in predicting flow behavior and hydraulic performance. Investigate advanced mathematical models such as the Navier$-$Stokes equations, computational fluid dynamics $($CFD$),$ and empirical flow equations, discussing their theoretical foundations and practical applications in hydraulic engineering design. Analyze the theoretical considerations involved in hydraulic infrastructure design, such as open channel flow, pipe network analysis, and sediment transport, and evaluate emerging theoretical frameworks for addressing complex hydraulic challenges, such as climate change adaptation and urban flood management.