Question

Given below are two statements, one is labeled as Assertion (A), and the other one labeled as Reason (R).
Assertion (A): Darcy's law is valid for a steady and stationary flow process in the soil.
Reason (R): In a steady flow condition, potential and gradient at every point in the flow path remain constant.
In light of the above statements, choose the most appropriate answer from the options given below:

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A).
• B. Both (A) and (R) are correct but (R) is NOT the correct explanation of (A).
• C. (A) is correct but (R) is not correct.
• D. (A) is not correct but (R) is correct.

Hint:

For transient/unsteady flow, where water content changes over time, Darcy's law is combined with the mass conservation (continuity) equation to form the Richards' equation.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Darcy's law relates the rate of water flow through a porous medium to the hydraulic gradient.
Steady-state flow occurs when the moisture content and potential at any point in the system do not change with time.

Step 2: Detailed Explanation:
- Assertion (A) is correct: Darcy's law was originally formulated for steady, saturated water flow through sand filters.
It states that flux ($q$) is directly proportional to hydraulic gradient ($i$).
- Reason (R) is correct: Under steady and stationary conditions, the water potential and hydraulic gradient do not fluctuate over time at any point along the flow path.
This time-invariant gradient maintains a constant flow rate.
Thus, the time-independent nature of steady flow directly supports the application of Darcy's law without requiring a storage/continuity term (like Richards' equation).

Step 3: Final Answer:
Both statements are correct, and Reason (R) is the correct explanation of Assertion (A).