What is the relationship between permeability and viscosity of water?

Question

Examoogle · Accepted Answer

The correct answer is Option B: Inversely proportional. Permeability ($k$) in soil is inversely proportional to the dynamic viscosity ($\mu$) of the permeating fluid. According to Darcy's Law and Kozeny-Carman equations, as the viscosity of water increases (usually due to a decrease in temperature), the resistance to flow increases, resulting in a lower coefficient of permeability.

Step-by-Step Solution & Concepts:
Permeability ($k$) in soil is inversely proportional to the dynamic viscosity ($\mu$) of the permeating fluid. According to Darcy's Law and Kozeny-Carman equations, as the viscosity of water increases (usually due to a decrease in temperature), the resistance to flow increases, resulting in a lower coefficient of permeability.

Working Principle: Permeability is defined as the ability of soil to allow fluid to flow through its pores. The intrinsic permeability ($K_i$) is a property of the soil structure, while the hydraulic conductivity ($k$) depends on both the medium and the fluid. The relationship is expressed as $k = K_i \cdot \frac{\gamma}{\mu}$, where $\gamma$ is the unit weight of fluid and $\mu$ is dynamic viscosity. Thus, for a fixed medium, $k \propto \frac{1}{\mu}$.

Key Formulas: $k = K_i \cdot \frac{\gamma}{\mu}$ — Darcy's hydraulic conductivity formula; $k \propto \frac{1}{\mu}$ — Inverse relationship between permeability and viscosity

Key Points: Permeability is highly sensitive to temperature because water viscosity decreases as temperature increases.; As temperature increases, water becomes less viscous, leading to higher permeability.; Intrinsic permeability ($K_i$) is purely a function of soil pore geometry (size and distribution of voids).; Darcy's Law assumes laminar flow, which is sensitive to fluid viscosity.

Advantages: Accurate prediction of seepage rates in dams and embankments.; Better understanding of ground water flow behavior under varying climate conditions.

Disadvantages: Does not account for non-laminar flow conditions.; Requires precise measurement of fluid temperature for accurate analysis.

Applications: Dewatering of construction sites.; Designing seepage control measures for earthen dams.; Groundwater hydrology studies.

Additional Info: The viscosity of water is approximately $0.001 	ext{ Pa}\cdot	ext{s}$ at $20^{\circ}	ext{C}$.. Option A is incorrect because permeability decreases as viscosity increases, confirming an inverse relationship rather than a direct one.

Answer: B is correct — Permeability is inversely proportional to the viscosity of water, meaning that as the fluid becomes more viscous, its flow through the soil pores is restricted.

Exam Tip: Always remember that in soil mechanics, an increase in temperature lowers water viscosity, which in turn causes an increase in the measured coefficient of permeability ($k$).

Examoogle · Answer

Option A: Directly proportional

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Option C: Both are equal

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Option D: None of the mentioned

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