Question

The settling rates of dispersed soil particles in hydrometer method of soil texture determination is governed by

• A. Darcy's law
• B. Stoke's law
• C. Bernoulli's principle
• D. Poiseuille's law

Hint:

Stokes' Law assumes that all soil particles are smooth, rigid spheres. Since clay particles are actually plate-like, the law calculates their "equivalent spherical diameter" (ESD).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Soil texture determination by mechanical analysis involves separating soil particles into sand, silt, and clay fractions.
The hydrometer and pipette methods are quantitative techniques based on the differential sedimentation velocities of these particles suspended in an aqueous column.
Key Formula or Approach:
The settling velocity of a spherical particle in a fluid medium is governed by Stokes' Law:
\[ v = \frac{2}{9} \frac{(\rho_s - \rho_f) g r^2}{\eta} \] where:
\( v \) = settling velocity (\(\text{m/s}\))
\( \rho_s \) = density of the solid particle (\(\approx 2.65\text{ g/cm}^3\))
\( \rho_f \) = density of the fluid (\(\approx 1.0\text{ g/cm}^3\))
\( g \) = acceleration due to gravity
\( r \) = radius of the particle
\( \eta \) = dynamic viscosity of the fluid

Step 2: Detailed Explanation:
Stokes' Law states that larger, heavier particles (such as sand) settle faster than smaller, lighter particles (such as silt and clay).
During hydrometer analysis, the soil is chemically dispersed (often using sodium hexametaphosphate) to break down aggregates into individual primary particles.
The soil suspension is then shaken and allowed to settle in a cylinder.
At specific time intervals calculated using Stokes' Law, hydrometer readings are taken to measure the density of the remaining suspension.
Since larger sand and silt particles settle out of the measuring zone first, the remaining density reflects the concentration of the smaller, suspended silt and clay fractions.

Step 3: Final Answer:
The settling rates of dispersed soil particles are governed by Stokes' Law.