Rational Method Peak Runoff

The rational method is the oldest formula in urban drainage and still the one that sizes most storm sewers. Its logic is a single sentence: if rain of intensity $i$ falls long enough for the whole catchment to be contributing at once, and a fraction $C$ of it runs off, the peak flow is that fraction of the rainfall arriving on the area. In SI the arithmetic needs one bridging factor, because a millimetre an hour on a square metre is 2.778e-7 m³/s. Half of a 50 mm/h storm off ten hectares is $0.5 \times 50 \times 100000 / 3.6\times10^{6} = 0.694$ m³/s, which the familiar hectare shorthand gives as $0.00278 \times 0.5 \times 50 \times 10 = 0.695$.

The condition hidden in that sentence is the whole method. The storm duration must equal the time of concentration, and no shorter storm is allowed to win, because a shorter storm is more intense but only part of the catchment contributes. That is why you cannot pick an intensity without first computing a time of concentration and reading it off an IDF curve at that duration. It is also why the method is capped: most agencies stop at 80 hectares or so, and Ontario practice is often stricter, because on a large catchment the assumption of uniform rainfall over the whole area for the full travel time stops being remotely true.

The coefficient is where the judgement lives, and the classic mistake is treating it as a property of the surface. It is not. $C$ rises with return period, because a 100-year storm saturates soil that a 2-year storm never wets, and most manuals publish a frequency adjustment of 1.1 to 1.25 for the rarer events. Use an area-weighted composite for mixed land use, remember that 0.95 pavement is not the ceiling once you add frozen ground, and treat any answer with a coefficient above about 0.9 as a statement that the catchment is effectively a parking lot.