# How to Determine the Frequency of Irrigation – Problem & Solution

## How to Determine the Frequency of Irrigation

Mathematical Problem

The following data are given to determine the frequency of irrigation

• Field capacity of soil = 45 %
• Permanent wilting point = 19 %
• Density of soil = 1.5 g/cm3
• Depth of root zone = 65 cm
• Daily consumptive use of water = 18 mm

Solution:

Available moisture = Field Capacity – Permanent wilting point = 45 – 19 = 26

Let readily available moisture = is 75 % of the available moisture,

So, readily available moisture is = 26 × 0.75 = 19.5 %

Optimum moisture content = 45 – 19.5 = 25.5 %

Now, by applying irrigation water the moisture content is to be raised from 25.5 % to 45 %.

Calculate the depth of water to be applied in each watering, by using the following equation:

$D_{w} = \frac{W_{s}\times d}{W_{w}}\times [F_{c}-M_{0}]$

Where,

• Ws = Unit Weight of soil or density of soil = 1.5 g/cm3
• Ww = Density of water = 1g/cm3
• d = Depth of root zone = 65 cm
• Fc = Field capacity = 45 %
• M0 = Optimum moisture content = 25.5 %

After putting the all value,

$D_{w} = \frac{1.5\times 65}{1}\times\left [ 0.45 - 0.255 \right ]$

$Or, D_{w} = 97.5 \times 0.195 = 19.01$ cm

Now, we can calculate the frequency of irrigation by using the following equation

$f_{w} = \frac{D_{w}}{C_{u}}$

Where,

• fw = Frequency of watering or frequency of irrigation
• Cu = Daily consumptive use of water =
• Dw = Depth of water to be applied in each watering

After putting all values, the frequency of irrigation

$f_{w} = \frac{19.01}{1.8} = 10.56 = 11 days (say)$