Problem 1: Rational Method Calculation A 50-hectare urban catchment has a runoff coefficient of 0.7. The time of concentration is 30 mins. The rainfall intensity for a 30-min duration is 50 mm/hr. Find the peak discharge.

Problem 2: Time of Concentration (Kirpich's Formula) A small mountainous catchment has a main channel flow path length ($L$) of 1,200 meters. The elevation at the top of the catchment divide is 550 meters, and the elevation at the catchment outlet is 400 meters. Estimate the time of concentration ($t_c$) using Kirpich's formula for channel flow.

Problem 3: SCS Curve Number Method A rural watershed has an average Curve Number ($CN$) of 75. A storm occurs that drops a total of 4.5 inches of rainfall ($P$). Calculate the potential maximum retention ($S$) and the total runoff depth ($Q$) in inches.

Case Study 1: Urbanization and the Rational Method A 100-hectare agricultural watershed is slated for heavy commercial development. Discuss how this land-use change will affect the variables in the Rational Method ($Q_p = 0.278 CIA$) and predict the impact on peak discharge.

Case Study 2: Limitations of the SCS Curve Number Method The SCS Curve Number method is one of the most widely used hydrologic models worldwide for estimating runoff from ungauged catchments. Discuss its primary strengths and its critical limitations.