Sedimentation (Stokes’ law): When other factors remain constant, the settling velocity of a grain in a fluid is primarily dependent upon which parameter?

Introduction / Context:

In soil mechanics and sedimentation analysis (e.g., hydrometer tests), Stokes’ law is used to relate the settling velocity of fine spherical particles to their size. This principle enables estimation of particle-size distributions for silts and clays beyond the practical limit of sieve analysis.

Given Data / Assumptions:

• Other factors—fluid properties, particle shape, and density difference—are held constant.
• Flow regime is laminar (low Reynolds number), and particles are effectively spherical.

Concept / Approach:

Under Stokesian conditions, the terminal settling velocity v is proportional to the square of the particle diameter: v ∝ d^2, with proportionality also involving the density difference and fluid viscosity. If those latter factors are fixed, the only remaining variable is particle size, which dictates the change in v.

Step-by-Step Solution:

Verification / Alternative check:

Hydrometer test calculations explicitly use v proportional to d^2 when converting measured rates to equivalent particle sizes.

Why Other Options Are Wrong:

• Options involving shape or weight vary factors that have been declared constant.
• Weight is not independent of size for identical material and is not the direct parameter in Stokes’ expression when others are fixed.

Common Pitfalls:

• Applying Stokes’ law at higher Reynolds numbers where turbulence or non-spherical drag dominates.

Final Answer:

size of grain