Question

The rainfall figures for successive 30 – minute intervals are 35, 40, 120, 85, 45, 45 and 30 mm/hr. If the ϕ index is 35 mm/hour, determine W-index.
1. 24.3 mm/hour
2. 44.3 mm/hour
3. 34.3 mm/hour
4. 54.3 mm/hour

Answer 1

Correct Answer - Option 3 : 34.3 mm/hour

Concept:

ϕ_index = \(\frac{P_e-R}{t_e}\) and W_index = \(\frac{P-R}{t_r}\)

Where,

P_e = effective rainfall causing runoff, R = runoff, 

t_e = duration of effective rainfall, P = total rainfall and t_r = total duration of rainfall

Calculation:

Given,

ϕ_index = 35 mm/hr

∵  We know that,  runoff occurs when the intensity of rainfall (i) >  ϕ_index 

∴ From rainfall intensity data, the intensity of 30 mm/hr < 35 mm/hr, hence ignored in the calculation of ϕ_index. 

⇒ P_e = (35 + 40 + 120 + 85 + 45 + 45) × 0.5

⇒ Pe = 185 mm and t_e = 3 hr

∵ We know that, ϕindex = \(\frac{P_e-R}{t_e}\)

⇒ 35 = \(\frac{185-R}{3}\) 

⇒ R = 80 mm

Now, P = (35 + 40 + 120 + 85 + 45 + 45 + 30) × (30/60)

⇒ P = 200 mm and t_r = 3.5 hr

∵ We know that, Windex = \(\frac{P-R}{t_r}\)

⇒ Windex = \(\frac{200-80}{3.5}\)

⇒ W_index = 34.28 mm/hr