Problem 1: Sizing a Storm Sewer Pipe (Full Flow) A concrete storm sewer pipe ($n = 0.013$) must be designed to carry a peak discharge ($Q$) of $1.5 \text{ m}^3/\text{s}$ during a 10-year design storm. The available slope ($S$) along the street is 0.005 m/m. Assuming the pipe flows completely full under gravity (not pressurized), determine the minimum required commercial pipe diameter in millimeters.

Problem 2: Flow Velocity Check Using the 1000 mm ($1.0 \text{ m}$) concrete pipe selected in Problem 1 ($n=0.013$, $S=0.005$), calculate the actual flow velocity ($V$) when the pipe is flowing exactly full. Verify if it meets standard municipal guidelines which often require $V > 0.6 \text{ m/s}$ (to prevent sediment deposition) and $V < 3.0 \text{ m/s}$ (to prevent concrete scour).

Problem 3: Calculating Full Pipe Capacity A 600 mm (0.6 m) diameter corrugated high-density polyethylene (HDPE) storm sewer pipe ($n=0.012$) is laid at a slope of 1.5% ($0.015 \text{ m/m}$). Calculate the maximum flow capacity ($Q_{full}$) of this pipe in cubic meters per second.

Case Study 1: The "First Flush" Phenomenon in Urban Hydrology A significant concern in urban hydrology is the water quality of stormwater runoff. Discuss the "First Flush" phenomenon and how modern Low Impact Development (LID) strategies are designed to mitigate its devastating effects on receiving water bodies.

Case Study 2: Combined Sewer Overflows (CSOs) - A Legacy Problem Many older cities (e.g., London, New York, Chicago) operate "Combined Sewer Systems." Discuss what these systems are, why they fail during large storm events, and the enormous engineering challenges involved in solving the resulting Combined Sewer Overflows (CSOs).