Fine-grained soil. The hydrometer test
uses Stokes equation (for the velocity of a free falling sphere in
suspension) to determine grain size distribution smaller than #200
sieve.
The grain size distributions of soils are commonly determined by
sieve (smallest being #200) and hydrometer procedures. In the hydrometer
analysis the soil smaller than #200 sieve is placed in suspension and by
use of Stokes' equation for the velocity of a free falling sphere the
equivalent particle size and percent of soil in suspension are computed.
For soils with both fine and coarse grained materials a combined
analysis is made using both the sieve and hydrometer procedures.
Stokes Law:
A sphere falling freely through a liquid of infinite extent will
accelerate rapidly to a certain maximum velocity and will continue at
that velocity as long as conditions remain the same. The relationship of
the terminal velocity to the physical properties of the sphere and the
liquid are expressed by Stokes' Equation as follows:
Equation Set 1.1: Stokes Equation
Stokes' Law is applicable to spheres varying from 0.02 mm to 0.0002
mm in diameter. As applied to soil particles falling through water,
inaccuracies occur due to the following:
- Soil particles are not spheres
- The fluid is not of infinite extent
- The specific gravity of individual particles may vary
- Turbulence caused by larger particles falling
- Brownian movement of smaller particles
- Disturbance due to insertion and removal of hydrometer
- The test is actually used for diameters as large as 0.07 mm
By proper sample and laboratory technique all except item 1 can be
controlled or minimized so that the resulting inaccuracies can be
ignored in normal testing. The shape of soil particles will vary from
cubes to flakes with each of the shapes between these limits having
different influence. The results of the hydrometer analysis are valid if
they are considered equivalent grain diameter rather than actual grain
diameter.