Question

Which of the following is/are limitations of Stoke’s law?

• A. The effect of different particles depends on the settling velocity of particles
• B. Constant temperature during mechanical analysis
• C. Both A & B
• D. None of these

Hint:

Stoke's law assumes soil particles are smooth spheres settling independently in a fluid at a constant temperature.
Deviations in particle shape (platy clay) and temperature fluctuations (changing viscosity) are key limitations of the law.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Stoke's law describes the settling velocity of spherical particles in a viscous liquid.
It forms the physical basis for soil mechanical analysis methods (such as the hydrometer and pipette methods) used to determine soil texture.

Step 2: Detailed Explanation:
Stoke's law is mathematically expressed as:
\[ v = \frac{g (\rho_p - \rho_f) d^2}{18 \eta} \]
where $v$ is the settling velocity, $g$ is gravity, $\rho_p$ is particle density, $\rho_f$ is fluid density, $d$ is particle diameter, and $\eta$ is fluid viscosity.
The law is based on several simplifying assumptions that introduce limitations when applied to real soil particles:
1. Requirement for Constant Temperature (B): Fluid viscosity ($\eta$) is highly temperature-dependent.
A change in temperature during sedimentation alters water viscosity, changing the settling velocity of particles.
Therefore, maintaining a constant temperature during mechanical analysis is a critical requirement and limitation.
2. Particle Shape and Settling Behavior (A): Stoke's law assumes particles are smooth, rigid spheres.
However, real soil particles are irregular, with clay particles being platy or disc-shaped.
These non-spherical shapes experience more drag, meaning their actual settling velocity is lower than that predicted by Stoke's law for an equivalent sphere.
The different settling velocities of irregular particles complicate the direct application of the law.
Since both statements represent practical limitations and assumptions of Stoke's law, Option (C) is the correct choice.

Step 3: Final Answer:
The limitations of Stoke's law include both the dependency of settling behavior on irregular shapes and the requirement for a constant temperature, corresponding to Option (C).