Question:
The use of Stokes' law for measurement of the size of soil particle depends on certain simplifying assumptions. These are:
A. Particles must be spherical, smooth and rigid
B. Fall must be unhindered
C. Particles must be of uniform density
D. Size of particles must be small compared to the size of molecules of liquid
Choose the correct answer from the options given below:
The use of Stokes' law for measurement of the size of soil particle depends on certain simplifying assumptions. These are:
A. Particles must be spherical, smooth and rigid
B. Fall must be unhindered
C. Particles must be of uniform density
D. Size of particles must be small compared to the size of molecules of liquid
Choose the correct answer from the options given below:
A. Particles must be spherical, smooth and rigid
B. Fall must be unhindered
C. Particles must be of uniform density
D. Size of particles must be small compared to the size of molecules of liquid
Choose the correct answer from the options given below:
Show Hint
Remember that Stokes' Law is only valid for a specific range of soil particle sizes (\( 0.0002 \text{ mm} \text{ to } 0.05 \text{ mm} \)):
- Particles \( < 0.0002 \text{ mm} \) are kept in suspension by Brownian motion.
- Particles \( > 0.05 \text{ mm} \) cause excessive turbulence, violating laminar flow assumptions.
- Particles \( < 0.0002 \text{ mm} \) are kept in suspension by Brownian motion.
- Particles \( > 0.05 \text{ mm} \) cause excessive turbulence, violating laminar flow assumptions.
Updated On: Aug 5, 2026
- A, B and D only
- A, B and C only
- A, C and D only
- B, C and D only
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
Stokes' Law describes the settling velocity of a spherical particle falling through a viscous fluid.
In soil science, it is the governing principle behind particle size analysis (pipette and hydrometer methods) used to separate sand, silt, and clay fractions.
Because real soil particles are irregular, several simplifying assumptions are required to apply Stokes' Law.
Step 2: Detailed Explanation:
Let us evaluate each of the given assumptions:
- A. Particles must be spherical, smooth, and rigid: This is correct.
Stokes' Law is derived mathematically for perfect, smooth spheres.
Since clay particles are actually platy or tabular, the law calculates their "equivalent spherical diameter" (the diameter of a sphere that would settle at the same rate).
- B. Fall must be unhindered: This is correct.
The suspension must be sufficiently dilute (usually \( < 5\% \) solids by weight) so that individual settling particles do not collide or interact with each other or with the walls of the cylinder.
- C. Particles must be of uniform density: This is correct.
The average density of soil mineral solids is assumed to be a constant \( 65 \text{ g/cm}^3 \).
Large variations in density (due to organic matter or heavy minerals) would violate this assumption.
- D. Size of particles must be small compared to the size of molecules of liquid: This is incorrect.
For Stokes' Law to apply, the settling particles must be much larger than the liquid molecules, so that the fluid behaves as a continuous medium and Brownian motion does not affect their settling.
Particles smaller than \( 0.0002 \text{ mm} \) are kept in suspension by Brownian motion and do not settle according to Stokes' Law.
Therefore, the correct assumptions are A, B, and C.
Step 3: Final Answer:
The simplifying assumptions of Stokes' Law are A, B, and C only.
Stokes' Law describes the settling velocity of a spherical particle falling through a viscous fluid.
In soil science, it is the governing principle behind particle size analysis (pipette and hydrometer methods) used to separate sand, silt, and clay fractions.
Because real soil particles are irregular, several simplifying assumptions are required to apply Stokes' Law.
Step 2: Detailed Explanation:
Let us evaluate each of the given assumptions:
- A. Particles must be spherical, smooth, and rigid: This is correct.
Stokes' Law is derived mathematically for perfect, smooth spheres.
Since clay particles are actually platy or tabular, the law calculates their "equivalent spherical diameter" (the diameter of a sphere that would settle at the same rate).
- B. Fall must be unhindered: This is correct.
The suspension must be sufficiently dilute (usually \( < 5\% \) solids by weight) so that individual settling particles do not collide or interact with each other or with the walls of the cylinder.
- C. Particles must be of uniform density: This is correct.
The average density of soil mineral solids is assumed to be a constant \( 65 \text{ g/cm}^3 \).
Large variations in density (due to organic matter or heavy minerals) would violate this assumption.
- D. Size of particles must be small compared to the size of molecules of liquid: This is incorrect.
For Stokes' Law to apply, the settling particles must be much larger than the liquid molecules, so that the fluid behaves as a continuous medium and Brownian motion does not affect their settling.
Particles smaller than \( 0.0002 \text{ mm} \) are kept in suspension by Brownian motion and do not settle according to Stokes' Law.
Therefore, the correct assumptions are A, B, and C.
Step 3: Final Answer:
The simplifying assumptions of Stokes' Law are A, B, and C only.
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