Question

An average rainfall of 16 cm occurs over a catchment during a period of 12 h with a uniform intensity. The unit hydrograph (unit depth = 1 cm, duration = 6 h) of the catchment rises linearly from 0 to 30 cumec in 6 h and then falls linearly from 30 to 0 cumec in the next 12 h. $\varphi -index$ of the catchment is known to be 0.5 cm/h. Base flow in the river is known to be 5 cumec.

Peak discharge of the resulting direct runoff hydrograph shall be

• A. 150 cumec
• B. 225 cumec
• C. 230 cumec
• D. 360 cumec

Answer 1

The correct option is B 225 cumec

$\begin{array}{ccccc}\text{Time}& \text{6h UH}& \text{Lagged by 6h}& \text{Addition}& \text{12h UH}\\ 0& 0& -& 0& 0\\ 6& 30& 0& 30& 15\\ 12& 15& 30& 45& 22.5\\ 18& 0& 15& 15& 7.5\\ & & 0& 0& 0\end{array}$

Peak discharge of 12 h UH
$=22.5m^3/s$

Average rainfall = 16 cm

Infilteration = 12 x 0.5 = 6 cm

Rainfall excess = 16 - 6 = 10 cm

Hence peak discharge of DRH
$=10\times \text{peak discharge of 12h UH}$
$=10\times 22.5=225m^3/s$