## Consider the process of designing a large$-$scale urban drainage system in a metropolitan area that experiences significant seasonal rainfall, leading to frequent flooding issues. In the context of hydraulic engineering and urban planning, detail the key theoretical principles and calculations that must be undertaken to ensure the system is capable of handling peak flow rates during extreme weather events. Discuss how principles of fluid dynamics, hydrology, and environmental impact assessments are integrated into the design process. Include considerations for the selection of appropriate materials, system layout, and the incorporation of green infrastructure to enhance sustainability. Additionally, elaborate on the methods used to model the drainage system's performance under various scenarios, the importance of maintaining regulatory compliance, and the potential challenges faced during the implementation phase. How does the interplay between theoretical knowledge and practical constraints influence the final design of such a critical infrastructure project?