Sedimentation (hydrometer) analysis assumptions: Stokes-law based grain-size analysis assumes which of the following about particles and the settling environment?

Introduction / Context:
Hydrometer and pipette analyses estimate fine-grained soil size distribution from sedimentation velocity. The interpretation relies on Stokes’ law, which links particle diameter to terminal settling velocity under laminar flow. Understanding the idealizing assumptions behind Stokes’ law is essential for correct test application and limitations.

Given Data / Assumptions:

• Spherical, smooth particles.
• Laminar flow with negligible inertia (low Reynolds number).
• Independent settling without particle interaction.
• Infinite or sufficiently large fluid domain with negligible wall effects.

Concept / Approach:

Stokes’ law expresses v = (g (ρ_s − ρ_f) d^2) / (18 μ) for a single rigid sphere settling in a viscous fluid. Wall proximity, particle concentration, shape irregularity, and flocculation violate the assumptions and bias diameter estimates. Laboratory procedures attempt to mitigate these effects by dilution, dispersants, and selecting appropriate cylinder sizes.

Step-by-Step Solution:

Verification / Alternative check:

Corrections exist for wall effects and non-sphericity, confirming that these are indeed simplifying assumptions, not always realities.

Why Other Options Are Wrong:

(e) omits the important wall-effect assumption; (a)–(c) alone are incomplete; therefore the aggregate is correct.

Common Pitfalls:

Applying Stokes’ law at high concentrations or with flocculated clays; ignoring temperature-viscosity corrections.

Final Answer:

All the above