Question

Rainfall of magnitude 4.3 cm, followed by 3.7 cm, occurred on two consecutive 4h durations on a catchment area of $25k{m}^2$, 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)
$\begin{array}{ccccccccccccc}\text{Time(hours)}& 0& 4& 8& 12& 16& 20& 24& 28& 32& 36& 40& 44\\ \text{DRH}& 0& 9& 16& 20& 20& 17.8& 13.4& 9.4& 6.2& 3.7& 1.8& 0\\ \text{(ordinate}{m}^2/sec)& & & & & & & & & & & & \end{array}$

the $\varphi -index$ value will be _______cm/hr.

• A. 0.155

Answer 1

The correct option is A 0.155
$\text{Run-off,}Q=\frac{0.36\sum O.\Delta t}{A}=6.756cm$
$\varphi -index=w_{index}=\frac{P-Q}{t}=\frac{(4.3+3.7)-6.756}{8}$
$=0.155cm/hr$