Question

An 8-hour storm with incremental rainfall during each successive hour is tabulated herewith. What will be the correction to total runoff when, the actual $\varphi -index$ was 0.5 cm/hour but a wrong magnitude of 0.6 cm/hour was adopted in computing the total runoff?

$\begin{array}{cc}\text{Time from}& \text{Incremental rainfall}\\ \text{start (hour)}& \text{in each hour (cm)}\\ 1& 0.4\\ 2& 0.8\\ 3& 1.2\\ 4& 0.9\\ 5& 1.8\\ 6& 1.0\\ 7& 0.3\\ 8& 0.8\end{array}$

• A. +1.0 cm
• B. +0.9 cm
• C. +0.8 cm
• D. +0.6 cm

Answer 1

The correct option is D +0.6 cm

Total runoff
$=(0.8+1.2+0.9+1.8+1.0+0.8)-\varphi index\times T\varphi$
$=(0.8+1.2+0.9+1.8+1.0+0.8)-0.6\times 6$
$=2.9$

Now, total runoff as per correct value of $\varphi index$, is

$=(0.8+1.2+0.9+1.8+1.0+0.8)-0.5\times 6$
= 6.5 - 3.0 = 3.5 cm

Correction = 3.5 - 2.9 = 0.6 cm