Section 4: Soil and Water Conservation Engineering
Hydrology
Subtopic: Runoff estimation
Question Statement:
A 0.80 km² agricultural watershed has a slope of 0.30% and the maximum length of travel of water is 1 km. The 10-year maximum depth of rainfall is tabulated below:
Half of the watershed has row crops (runoff coefficient = 0.40), whilst the other half of the watershed has pasture (runoff coefficient = 0.35). The peak flow rate for the watershed (in m³·s⁻¹) for the 10-year return period is ________. (Rounded off to two decimal places)
Official Answer Key:
7.50 to 7.75
Step-by-Step Solution & Explanation
Step 1 — time of concentration (Kirpich’s formula).
tᶜ = 0.0195 L⁰·⁷⁷ S⁻⁰·³⁸⁵ (L in m, tᶜ in minutes)
L = 1000 m, S = 0.30% = 0.003
L⁰·⁷⁷ = 1000⁰·⁷⁷ = 204.2
S⁻⁰·³⁸⁵ = 0.003⁻⁰·³⁸⁵ = 9.362
tᶜ = 0.0195 × 204.2 × 9.362 = 37.27 minutes
Step 2 — design rainfall depth for a storm of duration equal to tᶜ. Interpolate the table between 30 min (50 mm) and 40 min (60 mm) — a gradient of 1 mm per minute:
P = 50 + (37.27 − 30) × 1.0 = 57.27 mm
Step 3 — design rainfall intensity:
i = P × 60/tᶜ = 57.27 × 60/37.27 = 92.2 mm·h⁻¹
Step 4 — weighted runoff coefficient:
C = (0.5 × 0.40) + (0.5 × 0.35) = 0.20 + 0.175 = 0.375
Step 5 — Rational formula (with A in hectares):
A = 0.80 km² = 80 ha
Q = C i A/360 = (0.375 × 92.2 × 80)/360 = 2766/360 = 7.68 m³·s⁻¹
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