This question was previously asked in

Gujarat Engineering Service 2019 Official Paper (Civil Part 2)

Option 2 : 6.0 cm

ISRO Scientist Civil 2020 Paper

1948

80 Questions
240 Marks
90 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.

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

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

where

PTotal = Total precipitation, Q = Runoff

__Calculations:__

Given:

First set of data:

time (t) = 4 hr, Total precipitation (P) = 4 cm, Runoff (Q) = 2 cm

Second set of data:

time (t) = 8 hr, Total precipitation (P) = 10 cm, Runoff (Q) = ? cm

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

\({\phi _{index_1}} = \frac{{4 - 2}}{4} = 0.5\) cm/hr

\({\phi _{index_1}} = {\phi _{index_2}} = 0.5\)

\({\phi _{index_2}} = 0.5= \frac{{10 - Q}}{8} \)

\(\Rightarrow 8\times 0.5= {{10 - Q}}{} \)

Actual runoff (Q)= 10 – 4 = 6 cm