Question

The equation governing flow of water in saturated soil is

• A. Poiseuille's equation
• B. Bernoulli equation
• C. Darcy's equation
• D. Navier-Stokes equation

Hint:

Darcy's Law is only valid for laminar flow conditions (where Reynolds number is small, typically $<1$).
This is true for almost all natural groundwater and saturated soil water flow processes.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Water movement through soil pores is a physical transport process driven by hydraulic gradients.
Saturated water flow occurs when all soil pores are completely filled with water, and the flow is governed by a fundamental empirical law of hydrogeology and soil physics.

Step 2: Key Formula or Approach:
The flow of water in saturated porous media is defined by Darcy's Law:
\[ q = -K \cdot \frac{dH}{dL} \]
where $q$ is the flux (volume of water flowing per unit area per unit time), $K$ is the saturated hydraulic conductivity, and $\frac{dH}{dL}$ is the hydraulic gradient.

Step 3: Detailed Explanation:
Let us evaluate the physical equations listed:
1. Poiseuille's Equation:
This equation defines the laminar flow of a viscous fluid through a uniform cylindrical tube.
While it can model flow through individual soil capillaries, it is not used to describe bulk water flow through a complex, irregular soil pore network.
Thus, Option (A) is incorrect.
2. Bernoulli's Equation:
This is a statement of the conservation of energy for flowing fluids, relating pressure, velocity, and elevation.
It does not define flow through porous media where viscous resistance dominates.
Thus, Option (B) is incorrect.
3. Darcy's Equation:
Formulated by Henry Darcy in 1856, this empirical law states that the rate of water flow through a saturated soil column is directly proportional to the hydraulic gradient.
This is the standard equation used to model saturated hydraulic conductivity in soils.
4. Navier-Stokes Equation:
This is a complex partial differential equation that describes the motion of viscous fluid substances, which is too detailed for bulk agricultural soil water modeling.
Thus, Option (D) is incorrect.

Step 4: Final Answer:
The equation governing the flow of water in saturated soil is Darcy's equation.
Therefore, the correct option is (C).