Practice Question: Rainfall Excess Based on a Hydrograph

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Solution

Answer: D) 4.0 in

Peak Flow Rate:
$$ Q\ =\ 40\ (ft^3)/s $$
Storm Peak Duration:
$$ T_{peak}=20\ hr-5\ hr=15\ hr $$
Storm Complete Duration:
$$ T_{storm}=25\ hr $$
Catchment area:
$$ A=200\ acre\ast\frac{43560\ ft^2}{1\ acre}=8.7\ast{10}^6\ ft^2 $$

1) Calculate volume of runoff based on the hydrograph:

$$ V_{runoff}=Q\ast\left(\frac{T_{storm}+T_{peak}}{2}\right)=40\frac{ft^3}{s}\ast\left(\frac{25\ hr+15\ hr}{2}\right)\ast\frac{3600\ s}{1\ hr}\ \ $$

$$ V_{runoff}\ =\ 2.88\ast{10}^6\frac{ft^3}{s} $$
2) Calculate the excess rainfall based on the catchment area:
$$ Excess=\frac{V_{runoff}}{A} =\frac{2.88\ast{10}^6\frac{ft^3}{s}}{8.7\ast{10}^6\ ft^2}\ast12= 4.0\ in $$

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