Question

A soil 80 cm deep has a volume water content = 0.12. Find out the quantity of water that must be added to bring the volume water content to 0.30.

• A. 9.6
• B. 24.0
• C. 14.4
• D. 18.4

Hint:

To solve this in one step: subtract the initial water content from the final content ($0.30 - 0.12 = 0.18$), and multiply this difference directly by the soil depth ($0.18 \times 80\text{ cm} = 14.4\text{ cm}$).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Volumetric water content ($\theta_v$) is defined as the volume of liquid water per unit volume of bulk soil.
To find the equivalent depth of water ($d$) held in a soil profile of total depth ($D$), we use the volumetric water content relationship.

Step 2: Key Formula or Approach:
The equivalent depth of water ($d$) is calculated as:
\[ d = \theta_v \times D \]
The quantity of water to be added ($\Delta d$) to raise the moisture level is:
\[ \Delta d = d_{\text{final}} - d_{\text{initial}} \]
\[ \Delta d = (\theta_{v, \text{final}} - \theta_{v, \text{initial}}) \times D \]

Step 3: Detailed Explanation:
Let us perform the calculations step-by-step:
-
Step 1: Identify the given values:
- Soil profile depth ($D$) = $80\text{ cm}$
- Initial volumetric water content ($\theta_{v, \text{initial}}$) = $0.12$
- Final volumetric water content ($\theta_{v, \text{final}}$) = $0.30$
-
Step 2: Calculate the initial equivalent water depth ($d_{\text{initial}}$):
\[ d_{\text{initial}} = 0.12 \times 80\text{ cm} = 9.6\text{ cm} \]
-
Step 3: Calculate the final equivalent water depth ($d_{\text{final}}$):
\[ d_{\text{final}} = 0.30 \times 80\text{ cm} = 24.0\text{ cm} \]
-
Step 4: Calculate the depth of water to be added ($\Delta d$):
\[ \Delta d = 24.0\text{ cm} - 9.6\text{ cm} = 14.4\text{ cm} \]
Therefore, the quantity of water that must be added is $14.4\text{ cm}$ (often expressed directly as depth units).
This matches Option (C).

Step 4: Final Answer:
The quantity of water that must be added is 14.4.