**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:

[latex]Q = \frac{KiA}{36}[/latex]

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,

[latex]Q = \frac{KiA}{360}[/latex]

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 = [latex]3500 \times \frac{2}{3}[/latex] = 2333.33 hectares

Urban area = [latex]3500 \times \frac{1}{3}[/latex] = 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,

[latex]Q = \frac{KiA}{360}[/latex]

Or, [latex]\large Q = \frac{(0.30\times 25\times 2333.33) + (0.50\times 25\times 1166.66)}{ 360 }[/latex]

Or, [latex]\large Q = \frac{17499.97+14583.25}{360}[/latex]

Or, Q = 89.12 cumec.

Read Also:

Empirical Formula Used For Determination of Runoff

How to Calculate Annual Runoff