Discussion
A 10 ha watershed received a 4-hour rainfall storm with rainfall intensity of 2, 1, 1.5, and 1 cm.h-1 in each subsequent hour, respectively. Assuming phi-index (φ) of 1 cm.h-1, the volume of direct runoff, in m3, is __________. (Rounded off to 2 decimal places)
Answer: A
The direct runoff volume is 1500 m3.
The φ-index is the constant loss rate; rainfall above it becomes direct runoff, hour by hour:
\[ \begin{aligned} \text{excess} &= (2-1) + 0 + (1.5-1) + 0 \\ &= 1.5\ \text{cm} = 0.015\ \text{m} \\ V &= 0.015 \times 10 \times 10^{4}\ \text{m}^{2} = 1500\ \text{m}^{3} \end{aligned} \]
Hours in which the intensity equals φ (1 cm/h) contribute nothing. 15000 m3 misplaces the hectare conversion by a factor of 10, and 4500 or 5500 m3 subtract the loss from the total rainfall (5.5 cm) carelessly or not at all.
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