# How to Determine Runoff Coefficient – Mathematical Problem & Solution

## How to Determine Runoff Coefficient

When the nature of the surface of different areas and the impermeability factors of the areas are known or given, then the value of the runoff coefficient(K) may be determined by the following expression:

$K= \frac{a_{1}p_{1}+a_{2}p_{2}+\cdot \cdot \cdot \cdot \cdot }{A}$

Where,

a1, a2 = Area of different surfaces.
p1, p2 = Impermeability factors of those surfaces.
A = Total surface area.

### Mathematical Problem

A catchment area consists of the following surfaces:

1. Cultivated area = 50 hectares (p = 0.20)
2. Forest area = 30 hectares (p = 0.10)
3. Garden = 5 hectares (p = 0.05)
4. Residential = 15 hectares (p = 0.50).

Find the runoff coefficient of that catchment area.

Solution

Here, the total area will be = 50 + 30 + 5 + 15 = 100 hectares.

From the expression,

$K= \frac{a_{1}p_{1}+a_{2}p_{2}+\cdot \cdot \cdot \cdot \cdot }{A}$

Here,

$a_{1}$ = 50 and $p_{1}$ = 0.20

$a_{2}$ = 30 and $p_{2}$ = 0.10

$a_{3}$ = 5 and $p_{3}$ = 0.05

$a_{4}$ = 15 and $p_{4}$ = 0.50

We get the runoff coefficient,