Understanding water application efficiency is crucial in irrigation management. It helps farmers and engineers determine how effectively the water diverted to a field is stored in the crop's root zone, minimizing waste and ensuring optimal water use for agricultural productivity. Let's break down the calculation for the given scenario.

Water Application Efficiency Explained

Water application efficiency ($E_a$) is a measure of how efficiently irrigation water is applied and stored in the crop root zone. It is expressed as a percentage and calculated using the formula:

$$E_a = \frac{\text{Water stored in the root zone}}{\text{Water delivered to the field}} \times 100$$

To calculate this efficiency, we first need to determine the total volume of water delivered to the field and the actual volume of water stored in the root zone.

Volume of Water Delivered to the Field

The question provides the flow rate of water diverted and the duration of irrigation. We need to ensure that the units are consistent for calculation.

• Flow Rate (Q): 12 m³/sec
• Irrigation Duration (t): 5 hours

First, convert the irrigation duration from hours to seconds to match the units of the flow rate:

Time in seconds = 5 hours $\times$ 3600 seconds/hour = 18000 seconds

Now, calculate the total volume of water delivered to the field:

Volume Delivered ($V_{delivered}$) = Flow Rate $\times$ Time

$$V_{delivered} = 12 \text{ m}^3/\text{sec} \times 18000 \text{ sec}$$

$$V_{delivered} = 216000 \text{ m}^3$$

Volume of Water Stored in the Root Zone

The question states the area of the field and the depth of water stored in the root zone after irrigation. We need to convert the field area from hectares to square meters.

• Field Area (A): 30 hectare
• Water Stored in Root Zone (d_stored): 0.4 m

Since 1 hectare = 10,000 m², the field area in m² is:

Field Area (A) = 30 hectare $\times$ 10,000 m²/hectare = 300,000 m²

Now, calculate the volume of water stored in the root zone:

Volume Stored ($V_{stored}$) = Field Area $\times$ Water Stored Depth

$$V_{stored} = 300,000 \text{ m}^2 \times 0.4 \text{ m}$$

$$V_{stored} = 120,000 \text{ m}^3$$

Calculating Water Application Efficiency

Now that we have both the volume of water delivered and the volume of water stored, we can calculate the water application efficiency.

• Volume Delivered ($V_{delivered}$): 216,000 m³
• Volume Stored ($V_{stored}$): 120,000 m³

Using the formula:

$$E_a = \frac{V_{stored}}{V_{delivered}} \times 100$$

$$E_a = \frac{120,000 \text{ m}^3}{216,000 \text{ m}^3} \times 100$$

$$E_a = \frac{120}{216} \times 100$$

Simplify the fraction:

$$E_a = \frac{5}{9} \times 100$$

$$E_a \approx 0.55555 \times 100$$

$$E_a \approx 55.55\%$$

Therefore, the water application efficiency in this case is approximately 55.55%.

Summary of Calculations

This efficiency value indicates that 55.55% of the water diverted to the field was effectively stored within the crop's root zone, available for plant use. The remaining percentage might be lost due to factors such as deep percolation, surface runoff, or evaporation.