Question

A soil is having a field capacity of \(42%\) and permanent wilting point of \(19%\). If irrigation has to be done at \(40%\) depletion of available moisture, at what soil moisture percentage the field is to be irrigated?

• A. \(23%\)
• B. \(28.2%\)
• C. \(30.5%\)
• D. \(32.8%\)

Hint:

Important irrigation formula: \[ \boxed{ AM = FC - PWP } \] and \[ \boxed{ \text{Irrigation Moisture} = FC - (\text{Allowable depletion}) } \] For this problem: \[ 42 - (0.4 \times 23) = 32.8% \] Memory Trick: \[ \boxed{ \text{“Subtract allowable depletion from field capacity”} } \]

Answer 1

The Correct Option is D

Concept: In irrigation engineering, soil moisture management is extremely important for maintaining proper plant growth and irrigation scheduling. The important moisture parameters involved are:
• Field Capacity (FC)
• Permanent Wilting Point (PWP)
• Available Moisture Content
• Allowable Moisture Depletion Field Capacity (FC): Field capacity is the amount of water retained in the soil after excess gravitational water has drained away. Permanent Wilting Point (PWP): Permanent wilting point is the moisture content below which plants cannot extract water and permanently wilt. Available Moisture (AM): Available moisture is the quantity of water available to plants between FC and PWP. Mathematically: \[ AM = FC - PWP \] Allowable Depletion: Plants are generally not allowed to consume all available moisture. Irrigation is scheduled when a certain percentage of available moisture is depleted.

Step 1: Writing the given data carefully. Given: \[ FC = 42% \] \[ PWP = 19% \] Allowable depletion: \[ 40% \] We need to determine the soil moisture percentage at which irrigation should be applied.

Step 2: Calculating available moisture content. Available moisture is: \[ AM = FC - PWP \] Substituting values: \[ AM = 42 - 19 \] \[ AM = 23% \] Thus total available moisture is: \[ \boxed{23%} \]

Step 3: Calculating allowable depletion amount. Allowable depletion is \(40%\) of available moisture. Therefore: \[ \text{Depletion} = 0.40 \times 23 \] \[ = 9.2% \] Hence allowable depletion is: \[ \boxed{9.2%} \]

Step 4: Determining irrigation moisture content. Initially, at field capacity: \[ \text{Soil moisture} = 42% \] After depletion of \(9.2%\): \[ \text{Moisture at irrigation} = 42 - 9.2 \] \[ = 32.8% \] Therefore irrigation should be applied when soil moisture falls to: \[ \boxed{32.8%} \]

Step 5: Comparing with the given options. Option (A): \[ 23% \] This represents available moisture only, not irrigation moisture level. Hence: \[ \boxed{\text{Option (A) is incorrect}} \] Option (B): \[ 28.2% \] Incorrect calculation. Hence: \[ \boxed{\text{Option (B) is incorrect}} \] Option (C): \[ 30.5% \] Incorrect result. Hence: \[ \boxed{\text{Option (C) is incorrect}} \] Option (D): \[ 32.8% \] This matches the calculated irrigation moisture percentage. Hence: \[ \boxed{\text{Option (D) is correct}} \] Final Conclusion: The soil should be irrigated when moisture content falls to: \[ \boxed{32.8%} \] Hence, the correct answer is: \[ \boxed{(D)\ 32.8%} \]