Rational Method for a Composite Catchment:  Example

Calculate the peak discharge by the rational method for a 1-km2 composite catchment with the following characteristics:

 Subarea A Subarea B Area (km2) 0.4 0.6 Runoff coefficient 0.6 0.3 Time of concentration (min) 20 60

Assume a return period T = 10 y and the following IDF function:

1000T 0.2
 I  =   ________________            (tr  +  20) 0.7

in which I = rainfall intensity, in millimeters per hour; T = return period, in years; and tr = rainfall duration, in minutes. To compute the contribution of subarea B, assume that the flow concentrates linearly at the outlet, i.e., each equal increment of time causes an equal increment of area contributing to the flow at the outlet.

First, choose rainfall durations between 20 min and 60 min at 10-min intervals. For each rainfall duration, rainfall intensity is calculated by the IDF equation. The assumption of linear concentration for subarea B leads to the following:

 Rainfall duration(min) Rainfall intensity(mm/h) Contributing area of B(km2) 20 119.83 0.2 30 102.50 0.3 40 90.22 0.4 50 80.99 0.5 60 73.76 0.6

For tr = 20 min, the peak flow is:

 Qp = 0.2778 I  ∑ (C A) Qp = 0.2778 (119.83) [(0.6 × 0.4) + (0.3 × 0.2)] = 9.986 m3/s

Successive trials for rainfall durations of 30, 40, 50, and 60 min result in lower peak flows. Therefore, the peak flow is 9.986 m3/s ≅ 10 m3/s and the design rainfall duration is 20 min.