Section 4: Soil and Water Conservation Engineering
Hydrology
Subtopic: Runoff estimation
Question Statement:
A watershed has 1.8 km² of cultivated area, 2.2 km² of forest land and 1.4 km² of grassed area. The runoff coefficient of cultivated area, forest land and grassed area are 0.25, 0.15 and 0.30, respectively. The main drainage channel has a fall of 25 m in the total length of 2.5 km. The Intensity-Duration-Frequency relationship for the watershed is expressed as,
I = 70 T^0.25 / (t_c + 15)^0.4
where I - intensity in cm h⁻¹, T - recurrence interval in years and t_c - time of concentration in minutes. For a recurrence interval of 20 years, the peak rate of runoff for the watershed in m³s⁻¹ will be __________.
Official Answer Key:
85 to 95
Step-by-Step Solution & Explanation
Weighted runoff coefficient: C = (1.8×0.25 + 2.2×0.15 + 1.4×0.30)/(1.8+2.2+1.4) = (0.45+0.33+0.42)/5.4 = 1.20/5.4 = 0.2222.
Time of concentration (Kirpich formula, L in m, slope as fraction): t_c = 0.01947 L^0.77 S^−0.385, with L = 2500 m, S = 25/2500 = 0.01.
L^0.77 = 2500^0.77 = 413.3; S^−0.385 = 0.01^−0.385 = 5.888.
t_c = 0.01947 × 413.3 × 5.888 = 47.4 min.
Rainfall intensity (T = 20 yr): I = 70(20)^0.25 / (47.4+15)^0.4 = 70(2.1147)/(62.4)^0.4 = 148.03/5.223 = 28.34 cm/h.
Rational-method peak discharge (Q in m³/s, C dimensionless, I in cm/h, A in km²): Q = 2.778 × C × I × A = 2.778 × 0.2222 × 28.34 × 5.4 = 94.5 m³/s, within the accepted range 85–95 (which is generous enough to absorb the small sensitivity of t_c to the exact time-of-concentration formula used).
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