Discussion
The area of the watershed, in km2 is
Answer: A
The watershed area is about 7.56 km2.
Subtract the base flow of 1 m3 s−1 to get direct runoff: 0, 6, 25, 36, 26, 12, 0. The runoff volume is the sum of the ordinates times the 1-hour interval, and it must equal the total excess rainfall (2 + 3 = 5 cm) over the area:
\[ \begin{aligned} V &= (6 + 25 + 36 + 26 + 12)(3600) \\ &= 105 \times 3600 = 378000\ \text{m}^{3} \\ A &= \frac{378000}{0.05} = 7.56 \times 10^{6}\ \text{m}^{2} \end{aligned} \]
That is 7.56 km2. Forgetting to remove the base flow adds 7 m3 s−1-hours and gives about 8.06 km2; the other options do not follow from a 5 cm rainfall excess.
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