Rainfall of magnitude 4.3 cm, followed by 3.7 cm, occurred on two consecutive 4h durations on a catchment area of $25 k m^{2}$ , and there resulted a DRH (after isolation of base flow in the flood flow hydrograph) with the following ordinates starting from the beginning of the rainfall, (Adopt trapezoidal formula)
$\begin{matrix} Time(hours) & 0 & 4 & 8 & 12 & 16 & 20 & 24 & 28 & 32 & 36 & 40 & 44 DRH & 0 & 9 & 16 & 20 & 20 & 17.8 & 13.4 & 9.4 & 6.2 & 3.7 & 1.8 & 0 (ordinate m^{2} / s e c) \end{matrix}$

the $ϕ - i n d e x$ value will be _______cm/hr.
0.155

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Solution

The correct option is A 0.155
$Run-off, Q = \frac{0.36 \sum O . Δ t}{A} = 6.756 c m$
$ϕ - i n d e x = w_{i n d e x} = \frac{P - Q}{t} = \frac{(4.3 + 3.7) - 6.756}{8}$
$= 0.155 c m / h r$

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