Empirical flood formula, 100 sq km catchment

Method. Use the rational formula, with the time of concentration from Kirpich's empirical formula and the intensity from the maximum daily rainfall by the empirical reduction formula (IMD/Indian practice).

Data

A = 100 km², L = 60 km = 60 000 m, fall H = 20 m, C = 0.6, maximum daily (24 h) rainfall P = 200 mm.

Step 1: Slope and time of concentration

$$S=\frac{H}{L}=\frac{20}{60000}=3.333e-04$$ $$t_c=0.0195\,L^{0.77}S^{-0.385}=0.0195\,(60000)^{0.77}(3.333e-04)^{-0.385}=2032 \text{ min}=33.9 \text{ h}$$

Step 2: Rainfall intensity for duration $t_c$

$$i=\frac{P}{24}\left(\frac{24}{t_c}\right)^{2/3}=\frac{200}{24}\left(\frac{24}{33.9}\right)^{2/3}=6.62 \text{ mm/h}$$

Step 3: Peak flood

$$Q=0.278\,C\,i\,A=0.278\times0.6\times6.62\times100=110 \text{ m}^3/\text{s}$$

Answer: flood discharge ≈ 110 m³/s. (A 100 km² catchment is larger than the usual limit of the rational method, so the result is approximate.)