The estimated catchment area for a 5-year return period is 101520 m². Actual time of concentration is 5.05 min, yielding a peak runoff of 2036504 m³/s. Assuming te = 10 min introduces a 49.5% error in peak runoff.
(a) Estimate Catchment Area:
Given:
te = 10 min
T = 5 yr
S = 0.002
Calculate i from the IDF curve:
i = 7836 * (48.67 * 0.11 + (0.5895 + 5^-0.67))
i ≈ 25.23 mm/h
Now, substitute into the catchment area formula:
A = (10 * 25.23) / (0.0125 * 0.002)
A ≈ 101520 m²
(b) Actual Time of Concentration (tc) and Peak Runoff:
Use the catchment area obtained in part (a) and the calculated i to find tc:
tc = (0.0125 * 0.002 * 101520) / 25.23
tc ≈ 5.05 min
Now, calculate the peak runoff:
Q = 0.8 * 101520 * 25.23
Q ≈ 2036504 m³/s
(c) Percentage Error in Peak Runoff:
Assuming te = 10 min, find the estimated tc and Q:
tc_assumed = 10 min
Q_assumed = 0.8 * 101520 * 25.23
Calculate the percentage error:
Percentage Error = |(5.05 - 10) / 10| * 100
Percentage Error ≈ 49.5%
Considering a 49.5% error, it may be significant depending on the project's sensitivity to runoff variations. Further evaluation is needed based on project requirements.