How do theoretical concepts from fluid mechanics inform the design and analysis of hydraulic structures such as dams and spillways? Explore the principles governing fluid flow, including continuity, momentum, and energy equations, and demonstrate how these principles are applied to predict the behavior of water under varying hydraulic conditions. Explain the theoretical considerations involved in optimizing the shape, dimensions, and operating parameters of hydraulic structures to ensure efficient water management, flood control, and energy generation. Discuss theoretical approaches to assessing the stability and safety of dams and spillways, considering factors such as hydrostatic pressure, uplift forces, and hydraulic transients in your analysis.