## 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/cm
^{3} - 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:

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

Where,

- W
_{s}= Unit Weight of soil or density of soil = 1.5 g/cm^{3} - W
_{w}= Density of water = 1g/cm^{3} - d = Depth of root zone = 65 cm
- F
_{c}= Field capacity = 45 % - M
_{0}= Optimum moisture content = 25.5 %

After putting the all value,

[latex]D_{w} = \frac{1.5\times 65}{1}\times\left [ 0.45 – 0.255 \right ][/latex]

[latex]Or, D_{w} = 97.5 \times 0.195 = 19.01 [/latex] cm

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

[latex]f_{w} = \frac{D_{w}}{C_{u}}[/latex]

Where,

- f
_{w}= Frequency of watering or frequency of irrigation - C
_{u}= Daily consumptive use of water = - D
_{w}= Depth of water to be applied in each watering

After putting all values, the frequency of irrigation

[latex]f_{w} = \frac{19.01}{1.8} = 10.56 = 11 days (say)[/latex]

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