Runoff and Hydrographs MCQ with answer and solution

Concept

SCS-CN method gives direct runoff Q from rainfall P, using S from CN and Ia = 0.2S.

Formula

S = 25400/CN - 254 (mm); Ia = 0.2S; Q = (P - Ia)² / (P - Ia + S)

Step-by-step solution

1. CN = 50, so S = 25400/50 - 254 = 254 mm = 25.4 cm 2. Ia = 0.2 × 25.4 = 5.08 cm 3. P = 20 cm, so P - Ia = 14.92 cm 4. Q = 14.92² / (14.92 + 25.4) 5. Q = 222.61 / 40.32 = 5.52 cm

Explanation

First find the storage S from CN. Initial abstraction is 0.2S. Then use the SCS runoff equation. The standard method gives Q about 5.52 cm, which is not in the options.

Why the other options are wrong

15.70 cm, 151.70 mm and 17.51 cm do not result from the SCS equation with S = 10.

Shortcut

Net rainfall must always be less than the total rainfall (20 cm).

Common mistake

Using Ia = 0 gives 8.81 cm. Forgetting to convert S from mm to cm.