Rational method peak flow from storm depths

The rational method gives $Q_p = 0.278\,C\,i\,A$ ($Q_p$ in m³/s, $i$ in mm/h, $A$ in km²), where $i$ is the average intensity of a storm whose duration equals the time of concentration $t_c$ of the catchment.

Step 1: Time of concentration (Kirpich's formula)

$$\begin{aligned} t_c &= 0.0195\,L^{0.77}\,S^{-0.385}\ \text{(min; }L\text{ in m)}\\ &= 0.0195\,(1100)^{0.77}\,(0.01)^{-0.385} = 25.23\ \text{min} \end{aligned}$$

Step 2: Intensity for each storm duration

Step 3: Intensity at $t_c$

$t_c = 25.23$ min lies between 20 and 40 min. Interpolating the storm depth linearly:

$$P = 40 + \frac{25.23 - 20}{40 - 20}(70 - 40) = 47.84\ \text{mm}$$ $$i = \frac{P}{t_c} = \frac{47.84}{0.4205} = 113.8\ \text{mm/h}$$

Step 4: Peak flow

$$Q_p = 0.278 \times 0.7 \times 113.8 \times 3 = 66.4\ \text{m}^3/\text{s}$$

Answer: Peak flow $\approx$ 66 m³/s (with $t_c$ = 25.2 min, $i$ = 114 mm/h). Kirpich's formula was used because no other method for $t_c$ was specified.