Question

The rainfall of magnitudes 4.1 cm and 3.3 cm occurring on two consecutive 4 hours duration on a catchment of area $25k{m}^2$ produced the direct runoff hydrograph having area $1.75\times {10}^6{m}^3$. Then the value of $\varphi -index$ is_____cm/hr.

• A. $\frac{1}{10}$
• B. $\frac{1}{20}$
• C. $\frac{1}{30}$
• D. $\frac{1}{25}$

Answer 1

The correct option is B $\frac{1}{20}$

Area of hydrograph = Total volume of direct runoff
$=1.75\times {10}^6{m}^3$
$\text{Runoff depth}=\frac{\text{Runoff volume}}{\text{Catchment area}}=\frac{1.75\times {10}^6}{25\times {10}^6}$

$\Rightarrow \text{Runoff depth}=0.7m=7cm$

Total rainfall = 4.1 + 3.3 = 7.4 cm
Duration = 8 hours
$\therefore \varphi -index=\frac{7.4-7}{8}=0.05cm/hr=\frac{1}{20}cm/hr$