Section 4: Soil and Water Conservation Engineering
Hydrology
Subtopic: Infiltration – indices and equations
Question Statement:
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)
Options:
(A) 1500
(B) 4500
(C) 5500
(D) 15000
Official Answer Key:
A
Step-by-Step Solution & Explanation
The ϕ-index is a constant loss rate: rainfall excess in any interval is the amount by which the intensity exceeds ϕ. Where the intensity is at or below ϕ, the excess is zero (never negative).
Step 1 — hour-by-hour rainfall excess (ϕ = 1 cm·h⁻¹, each interval 1 h):
Total rainfall excess = 1.5 cm = 0.015 m
Step 2 — volume of direct runoff:
Area = 10 ha = 100,000 m²
V = 0.015 × 100,000 = 1500 m³
Trap: subtracting ϕ from every hour including those at or below it (giving negative losses) produces 5500 — option (C).
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