If a soil has 10% less moisture than its field capacity, what will be depth of irrigation required to bring soil moisture level to field capacity for a soil having depth 0.4 m and bulk density 1.2 mega gram/\(\text{m}^3\)
Show Hint
Always keep track of units. Representing soil depth directly in centimeters (\(\text{cm}\)) and using bulk density in \(\text{g/cm}^3\) ensures the calculated irrigation water depth is directly in centimeters.
Step 1: Understanding the Concept:
To calculate the depth of irrigation required to replenish soil moisture to field capacity, we must relate the gravimetric moisture deficiency to equivalent water depth based on soil root-zone depth and bulk density. Key Formula or Approach:
The equivalent depth of water (\(d\)) required is calculated as:
\[ d = \Delta \theta_d \times \frac{\rho_b}{\rho_w} \times D \]
where: \(\Delta \theta_d\) = moisture deficit on a dry weight basis (expressed as a fraction)
\(\rho_b\) = bulk density of the soil (\(\text{g/cm}^3\) or \(\text{Mg/m}^3\))
\(\rho_w\) = density of water (\(\approx 1.0 \text{ g/cm}^3\) or \(1.0 \text{ Mg/m}^3\))
\(D\) = depth of the soil root zone Step 2: Detailed Explanation:
Let us identify the given values: Moisture deficit, \(\Delta \theta_d = 10\% = 0.10\)
Water density, \(\rho_w = 1.0 \text{ g/cm}^3\)
Now, substitute these values into the depth equation:
\[ d = 0.10 \times 1.2 \times 40 \text{ cm} \]
\[ d = 0.12 \times 40 \text{ cm} = 4.8 \text{ cm} \]
Thus, the depth of irrigation required to bring the soil moisture to field capacity is 4.8 cm. Step 2: Final Answer:
The correct option is (B), representing 4.8 cm.
