Question

Assertion (A): Darc'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.

• 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:

Darc’s law is valid under steady-state, laminar flow in porous media.

Answer 1

The Correct Option is A

Darc’s law applies when flow is steady (unchanging over time) and stationary (flow at a point does not change), where potential gradient remains constant.

Answer 2

Alternate approach — Derivation from Darcy's equation:
Darcy's law for flow through a saturated porous medium is written as:
\[ q = -K \frac{dh}{dl} \]
where \( q \) is the flux, \( K \) is hydraulic conductivity, and \( \dfrac{dh}{dl} \) is the hydraulic gradient. This equation assumes \( K \) and \( \dfrac{dh}{dl} \) do not change with time, an assumption valid only under steady-state, non-turbulent, stationary flow. If flow were unsteady, the potential \( h \) at each point would vary with time, and the gradient \( \dfrac{dh}{dl} \) would not be constant along the flow path, invalidating the simple proportional relationship in the equation.
Since a constant potential gradient at every point is precisely the condition required for Darcy's law to hold, Reason (R) correctly explains why Assertion (A) is true, confirming option Both (A) and (R) are correct and (R) is the correct explanation of (A).