To calculate the gross depth of irrigation required to bring the soil moisture content back to field capacity, we can follow these steps:

Step 1: Determine the available water content (AWC)

The available water content is the difference between the moisture content at field capacity and the moisture content at the wilting point.

$\text{AWC} = \text{Field Capacity} - \text{Wilting Point}$ $\text{AWC} = 32\% - 12\% = 20\%$

Step 2: Determine the moisture depletion at 60% available water

The crop is irrigated when the available soil water is reduced to 60%. So, the soil has only 60% of the available water and needs to be refilled to field capacity (100% available water).

$\text{Moisture depletion} = (100\% - 60\%) \times \text{AWC}$ $\text{Moisture depletion} = 40\% \times 20\% = 8\%$

Thus, the soil moisture deficit that needs to be refilled is 8%.

Step 3: Calculate the depth of irrigation water required

To calculate the required irrigation depth, we use the following formula:

$\text{Net Irrigation Depth (d)} = \frac{\text{Moisture Deficit} \times \text{Root Zone Depth} \times \text{Bulk Density}}{1}$

Given:

• Moisture Deficit = 8% = 0.08
• Root Zone Depth = 50 cm
• Bulk Density = 1.5 g/cm³ = 1.5 g/cm³ × 1 cm³/g = 1.5 cm

$\text{d} = 0.08 \times 50 \times 1.5 = 6 \, \text{cm}$

So, the net depth of irrigation is 6 cm.

Step 4: Calculate the gross irrigation depth

Since the water application efficiency is 75%, we need to account for water losses:

$\text{Gross Irrigation Depth} = \frac{\text{Net Irrigation Depth}}{\text{Application Efficiency}}$ $\text{Gross Irrigation Depth} = \frac{6}{0.75} = 8 \, \text{cm}$

Thus, the gross depth of irrigation required is 8 cm.

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Would you like more details on any of the steps or a further breakdown?

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Here are 5 related questions to expand on this topic:

1. How does soil bulk density affect irrigation calculations?
2. What factors can influence field water application efficiency?
3. How would the calculation change if the field water application