# How to Determine Runoff by using Rational Method – Mathematical Problem & Solution

## How to Determine Runoff by using Rational Method

First of all, we need to understand which formula or expression is used for the determination of runoff. In the rational method, the runoff is given by the following expression:

$Q = \frac{KiA}{36}$

Where,

Q = Runoff in cumec
K = Coefficient of runoff
i = Intensity of rainfall in cm/hr
A = Catchment area in hectares

The above formula may also be expressed as follows,

$Q = \frac{KiA}{360}$

This formula applies when the intensity of rainfall is given in mm/hr. Otherwise, all units are the same as above.

### Mathematical Problem

A catchment area of 35 sq km consists of two-thirds rural area and one-third urban area. The rainfall in the whole catchment area is recorded as 30 mm/hr. Find the total runoff from the catchment area.

Solution:

We know the total are = 35 sq km = 3500 hectares ( 1 sq km = 100 hectares)

Now,

Rural area = $3500 \times \frac{2}{3}$ = 2333.33 hectares

Urban area = $3500 \times \frac{1}{3}$ = 1166.66 hectares.

Rainfall intensity i = 30 mm/hr.

Assuming, runoff coefficient for urban area = 0.50 and for rural area = 0.30

In rational method, the runoff is given by,

$Q = \frac{KiA}{360}$

Or, $\large Q = \frac{(0.30\times 25\times 2333.33) + (0.50\times 25\times 1166.66)}{ 360 }$

Or, $\large Q = \frac{17499.97+14583.25}{360}$

Or, Q = 89.12 cumec.