Question

The rainfall on 5 successive days in a catchment was 2, 7, 8, 4 and 3 cm. If the ϕ index for the storm is 3 cm / day, the total direct runoff volume generated from a 195 km² catchment is
1. 19.5 M m³
2. 23.4 M m³
3. 15.6 M m³
4. 32.5 M m³

Answer 1

Correct Answer - Option 1 : 19.5 M m³

Concept:

Runoff depth generated for a given period is given as

R = P - ϕ if P ≥ ϕ

R = 0 if P < ϕ

Where,

P is the rainfall and ϕ is the infiltration loss in that given period.

Calculation:

Rainfall, P- cm	Time period (hrs)	ϕ Index in cm/day	Runoff , R- cm	Remarks
2	1	3	0	P < ϕ
7	1	3	4	P > ϕ
8	1	3	5	P > ϕ
4	1	3	1	P > ϕ
3	1	3	0	P = ϕ

 

Total Runoff = 0 + 4 + 5 + 1 + 0 = 10 cm in a period of 5 hours.

Direct runoff Volume = Runoff × catchment area

V = 10 × 10^-2 × 195 × 10⁶ = 19.5 Mm³   ( 1 million m³ = 1 Mm³ = 10⁶)

∴ V = 19.5 Mm³