For an urban catchment, if the time of concentration is 30 minutes, what duration of rainfall intensity must be used with the Rational Method to estimate the peak flow?

For an urban catchment with a Time of Concentration of 30 minutes, the duration of rainfall intensity that must be used with the Rational Method to estimate the peak flow is 30 minutes. The Time of Concentration, abbreviated as Tc, is the time it takes for runoff from the hydraulically most distant point in a catchment to reach the outlet. In the context of the Rational Method, which is a common hydrological formula used to estimate peak discharge (Q) from a drainage basin (Q = C I A, where C is the runoff coefficient, I is the average rainfall intensity, and A is the drainage area), the selection of rainfall intensity is critical. To estimate the true peak flow, it is assumed that the entire catchment is contributing runoff simultaneously to the outlet. This condition is met when the duration of the rainfall event is equal to or greater than the Time of Concentration. If the rainfall duration were shorter than Tc, not all parts of the catchment would be contributing flow to the outlet at the same time, meaning the actual peak flow would not be captured. If the rainfall duration were longer than Tc, the average rainfall intensity for that longer period would typically be lower than the average intensity for a duration equal to Tc, according to Intensity-Duration-Frequency (IDF) curves. Therefore, to ensure that the highest average rainfall intensity corresponding to the full contribution of the catchment is used, the rainfall duration (for which the intensity 'I' is selected from IDF curves) must be set equal to the Time of Concentration. This ensures that the Rational Method calculates the maximum possible peak flow for the given catchment and design storm frequency.