Rational method peak flow, Melamchi storm

Rational formula: $Q_p = 0.278\,C\,i\,A$ (Q in m³/s, i in mm/h, A in km²), where $i$ is the intensity for a duration equal to the time of concentration.

Step 1: Time of concentration (Kirpich)

$$\begin{aligned} t_c &= 0.0195\,L^{0.77}S^{-0.385} \\ &= 0.0195\,(6000)^{0.77}(0.013)^{-0.385} = 84.2 \text{ min} \end{aligned}$$

Step 2: Rainfall intensity for duration $t_c$

Cumulative rainfall from the start of the storm:

The depth in the first 84.2 min, by linear interpolation between 50 and 84 min (this is also the most intense 84.2-min window of the storm):

$$P = 40 + \frac{84.2-50}{84-50}(70-40) = 70.2 \text{ mm}$$ $$i = \frac{70.2}{84.2}\times 60 = 50.0 \text{ mm/h}$$

Step 3: Peak flow

$$\begin{aligned} Q_p &= 0.278\times 0.6\times 50.0 \times 100 \\ &= 834 \text{ m}^3/\text{s} \end{aligned}$$

Answer: peak flow ≈ 834 m³/s (note: a 100 km² catchment is large for the rational method, so this is a rough estimate).