CivilHydrologymediumFE ExamCourseworkPE / Advanced

Peak Runoff by the Rational Method

A catchment of area $A = 10\ \text{hectares}$ has a runoff coefficient $C = 0.70$ .

The design rainfall intensity is $i = 50\ \text{mm/hr}$ .

Using the SI rational method, $Q = CiA/360$ with $Q$ in m³/s, $i$ in mm/hr and $A$ in hectares, find the peak runoff rate.

Given

C	0.7 -	Runoff coefficient
i	50 mm/hr	Rainfall intensity
A	10 ha	Catchment area

Hint 1

The 360 is purely a unit conversion for mm/hr and hectares into m³/s.

Hint 2

Substitute directly: no unit conversions are needed in this form.

Hint 3

Q = 0.7 × 50 × 10/360.

Worked solution — try the problem first

$Q = \frac{CiA}{360} = \frac{0.70 \times 50 \times 10}{360} = \frac{350}{360} = 0.972\ \text{m}^3/\text{s}$

$\boxed{Q = 0.972\ \text{m}^3/\text{s} \approx 972\ \text{L/s}}$

Where the 360 comes from. It is a unit-conversion constant, not physics:

$\frac{1\ \text{mm/hr} \times 1\ \text{ha}}{1} = \frac{0.001\ \text{m} \times 10{,}000\ \text{m}^2}{3600\ \text{s}} = \frac{10}{3600} = \frac{1}{360}\ \text{m}^3/\text{s}$

What C means. The runoff coefficient is the fraction of rainfall that becomes surface runoff — the rest infiltrates, evaporates, or is stored. $C = 0.70$ suggests substantial impervious cover; open parkland might be 0.2, dense pavement 0.9.

Assumptions worth remembering. The rational method assumes the storm duration equals the time of concentration and that rainfall is uniform over the catchment. It is a small-catchment tool — generally under about 80 hectares.

Concepts:Rational methodRunoff coefficientStorm drainage design

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