Question

Given below are two statements, one is labelled as Assertion A and the other is labelled 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:

Darcy's Law is only valid for laminar flow (low Reynolds number). In very coarse sands or rocky media where flow is turbulent, Darcy's Law fails.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Darcy’s Law is the fundamental principle governing the flow of fluids through porous media like soil.
It states that the velocity of flow is directly proportional to the hydraulic gradient.
Mathematically, it is expressed as:
\[ v = K \times i \]
where \( v \) is the flux (velocity), \( K \) is the hydraulic conductivity, and \( i \) is the hydraulic gradient.

Step 2: Detailed Explanation:
Darcy's law is derived based on the assumption of laminar flow in a saturated medium under steady-state conditions.
Assertion A correctly points out that the law is valid for steady and stationary flow processes.
Steady-state flow implies that the conditions do not change with time at any given position in the soil.
Reason R provides the physiological basis for this validity.
In a steady flow condition, the water potential and the resulting potential gradient at every point along the flow path do not change over time.
If the potential gradient were to fluctuate, the flow would become transient, and the basic proportional relationship defined by Darcy might require more complex differential equations.
Furthermore, stationary flow implies that the soil matrix through which the water moves is not shifting or consolidating during the flow process.
Because the constant nature of the potential and gradient is exactly what defines a steady flow and makes the linear Darcy equation applicable, the Reason is a direct explanation of the Assertion.

Step 3: Final Answer:
Both statements are correct, and since the constant gradient is a prerequisite for the validity of the linear Darcy relationship in steady systems, R explains A.