Question

The drainage area of a watershed is $50k{m}^2$. The $\varphi -index$ is 0.5 cm/hour and the base flow at the outlet is $10m^3/s$. One hour unit hydrograph (unit depth = 1 cm) of the watershed is triangular in shape with a time base of 15 hours. The peak ordinate occurs at 5 hours.
The peak ordinate (in $m^3/s$) of the unit hydrograph is

• A. 10.00
• B. 18.52
• C. 37.03
• D. 185.20

Answer 1

The correct option is B 18.52

Unit hydrograph is a hydrograph of direct runoff resulting from 1 cm of effective rainfall. So volume of water contained inside the unit hydrograph (i.e., area of unit hydrograph) = 1 cm x catchment area


$\frac{1}{2}\times a\times 15hrs=1cm\times A$

$\frac{1}{2}\times a\times 15\times 3600=0.01\times 50\times {10}^6$

$a=18.52m^3/s/cm\text{of effective rainfall}$