Question

The time area method is often used to estimate catchment runoff process. In this method, the catchment of concern is split into several sub-areas where runoff generated from each sub-area is thought to take the same amount of time to travel to the outlet of the catchment. Suppose a catchment can be split into M sub-areas. For the i-th sub-area (i=1,2,…, M), the size of the area is Ai km² and it takes i-th hours for the runoff generated to reach the outlet. If the catchment is subjected to a net rain process lasting over N hours (N≥1) with a constant intensity of r mm/hour. Using the time area method derive the peak runoff at the outlet of this catchment in m³/s

Answer 1

Hello, I have tried to answer the question based on the concepts of hydrograph.

Hydrograph is a graphical variation of discharge against time.It is the response of a given catchment to a rainfall input.

Initially I derived the expression for peak discharge considering the condition : duration of storm (N) is greater than or equal to the number of segments (M) the area is divided with the help of isochrones. This expression of discharge can be treated as a general expression for discharge.

Henceforth I took two cases where :

case i) in which I assumed N is greater than M , and hence derived the expression for peak discharge

case ii) wherein I explained that if N is less than M, then the peak discharge obtained will always be less than that obtained in case i

Refer photographs for detailed analysis. Thank you.