Question

A 3-hour rainfall occurred over a catchment area of $300k{m}^2$, with successive 30 minutes rainfall intensities as 5, 8, 13, 18, 2 and 3 mm/hour respectively. If the average storm loss $\varphi -index$ for the catchment is 0.6 cm/hour, then the observed runoff volume would be __________ ha-m. (Rounded off to the nearest integer).

• A. 315

Answer 1

The correct option is A 315
$\begin{array}{ccccccc}\text{Time(hr)}& 0-0.5& 0.5-1& 1.0-1.5& 1.5-2& 2-2.5& 2.5-3.0\\ \text{i, mm/hr}& 5& 8& 13& 18& 2& 3\\ \text{P, mm}& 2.5& 4& 6.5& 9& 1& 1.5\end{array}$


$\varphi -index=6mm/hr$
$t_e=1.5hours$
$P_e=4+6.5+9$
$=19.5mm$

$\varphi -index=\frac{P_e-R}{t_e}$

$6=\frac{19.5-R}{1.5}$

$R=10.5mm$

$\text{Runoff volume}=C\times A\times R$
$=300\times {10}^6\times 10.5\times {10}^{-3}$
$=3150000m^3$
$=315ha-m$