Stokes' law is applicable to soil particles of size between

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BPSC AE Paper 5 (Civil) 11 Nov 2022 Official Paper
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  1. 0.2 mm to 0.2 m
  2. 0.3 mm to 3 m
  3. 0.2 mm to 2 m
  4. 0.3 mm to 0.2 m

Answer (Detailed Solution Below)

Option 1 : 0.2 mm to 0.2 m
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Explanation:

Stokes Law

Assumptions

  • It is assumed that particles show discrete settling (i.e. grains of different sizes fall through a liquid at different velocities).
  • Particles assumed spherical in shape.
  • Medium is assumed infinite.
  • Particles size range 0.2 mm to 0.0002 mm.

Settling velocity,

\({V_s} = {\frac{{(G - 1){γ _w}d}}{{18μ }}^2}\)

where,

G = specific gravity, γ= unit weight of water, d = diameter of particle, μ = dynamic viscosity

Additional Information 

Limitations in the use of Stoke's Law in Sedimentation analysis:

  • Stoke's law is applicable for spherical particles only. The fine clay particles are not spherical in shape. While applying Stoke's law, the concept of equivalent diameter is used. The equivalent diameter of a soil particle is defined as the diameter of an imaginary sphere that has the same specific gravity as the soil particle and settles with the same terminal velocity as that of the soil particle.
  •  It is assumed that every particle settles independently without interference from other particles as well as from the sides of the jar. To minimize error due to this assumption, it is recommended that not more than 50 gms of soil particles be taken in 1000 ml of soil suspension.
  • The soil particles in the soil suspension may have different values of specific gravity. But in the computations, an average value of G is used.
  • The lower limit of particle size for the validity of Stoke's Law is 0.0002 mm. However, the upper limit for the same is 0.2 mm. For particles of size less than 0.0002 mm, Brownian movement affects their settlement and in the case of particles larger than 0.2 mm, turbulence affects the settlement.
  • Stokes's law is valid upto a maximum Reynolds number of 1.
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