This question was previously asked in

CGPSC Civil Official Paper 2 (Held on April 2014 - Shift 2)

Option 4 : 7.50

ST 1: Building Material and Concrete Technology

18752

20 Questions
20 Marks
12 Mins

**Concept:**

The ϕ – index is a rate of infiltration in which, the rate of infiltration exceeds the value at which volume of runoff become equals to the volume of rainfall.

\( {ϕ_{\left( {index} \right)}} = \frac{{{Total\; Infiltration}}}{{Total\;time\;of\;the\;storm}}\)

\( {ϕ_{\left( {index} \right)}} = \frac{{{P_{total}} - Q}}{{Total\;time}}\)

where

PTotal = Total precipitation

Q = Runoff

**Calculation:**

ϕ - index = 75 cm/hr

ϕ - index is the average rate of rainfall such that the volume of rainfall in excess of that rate is equal to the volume of surface runoff

So runoff (R) in cm is,

R \(=(12.5-7.5) \dfrac{15}{60}+ (17.5 - 7.5) \dfrac{15}{60}+ (22.5 - 7.5) \dfrac{15}{60}\)

R \(=\dfrac{5\times 15}{60}+\dfrac{10 \times 15}{60}+ \dfrac{15 \times 15}{60}\)

\(R=\dfrac{15}{60}(5+10+15)\)

R \(=\dfrac{15}{60}\times 30\)

∴ R = 7.5 cm