In soil mechanics, the concept of seepage velocity (also known as the superficial velocity) is crucial for understanding the flow of water through soils. Seepage velocity is related to the discharge velocity and the porosity of the soil. Let's break down the key concepts and see which statement correctly describes the relationship between these parameters.

Concepts:

• Discharge Velocity (v): The rate at which water flows across the total cross-sectional area of the soil, including both the solid and void parts. It is measured as the volume of water flowing per unit area per unit time. It is also sometimes referred to as the Darcy velocity, after Henry Darcy, who famously described this concept.
• Seepage Velocity (v_s): The velocity at which water actually moves through the interconnected void spaces in the soil. It accounts for the fact that water only flows through the voids, hence it's faster than discharge velocity.
• Porosity (n): The ratio of the volume of voids to the total volume of soil. It essentially describes how much of the soil volume is available as space for water flow.

Relation between Seepage Velocity, Discharge Velocity, and Porosity:

The seepage velocity can be calculated using the formula:

v_s = \frac{v}{n}

where v_s is the seepage velocity, v is the discharge velocity, and n is the porosity of the soil.

Explanation of Options:

1. The statement "Seepage velocity is independent of soil porosity" is incorrect. Seepage velocity directly depends on porosity, as it describes how voids influence the flow.
2. The statement "Seepage velocity is equal to discharge velocity divided by porosity" is correct as it aligns with the formula v_s = \frac{v}{n}.
3. The statement "Seepage velocity is equal to discharge velocity multiplied by porosity" is incorrect, as this would incorrectly account for how voids affect flow.
4. The statement "Seepage velocity is always less than discharge velocity" is incorrect. Seepage velocity is typically greater than discharge velocity because it only accounts for the pathways water can travel through, not the entire cross-section.

Conclusion: Given the formula and the logical reasoning, the correct answer is that the seepage velocity is equal to discharge velocity divided by porosity. Therefore, the correct statement is: "Seepage velocity is equal to discharge velocity divided by porosity."