Question

According to Darcy's Law, the saturated flow of liquid through porous medium is proportional to

• A. Hydraulic head
• B. Hydraulic conductivity of soil
• C. Viscosity of water
• D. Both 1 and 2

Hint:

Darcy's Law: $Q = K \cdot A \cdot \frac{\Delta h}{L}$. Flow rate is directly proportional to Hydraulic Conductivity ($K$) and Hydraulic Head ($\Delta h$).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Darcy's law is the governing macroscopic constitutive equation for laminar fluid flow through saturated porous media.
Key Formula or Approach:
\[ Q = -K \cdot A \cdot \frac{\Delta h}{L} \implies v = K \cdot i \]
where \(K\) is hydraulic conductivity and \(i = \frac{\Delta h}{L}\) is hydraulic gradient (head loss per unit length).

Step 2: Detailed Explanation:
Henry Darcy's (1856) law states that the rate of fluid discharge \(Q\) through a saturated soil column is:
1. Directly proportional to the hydraulic head difference (hydraulic gradient \(\Delta h / L\)).
2. Directly proportional to the hydraulic conductivity of the soil (\(K\)).
3. Inversely proportional to fluid viscosity (which is incorporated inside the hydraulic conductivity term \(K = k \frac{\rho g}{\mu}\)).
Thus, flow is proportional to both hydraulic head and hydraulic conductivity.

Step 3: Final Answer:
Hence, saturated flow is proportional to Both 1 and 2, matching option (D).