برنامه تحت اکسل هیدرومتری با استفاده از معادله استوکس

( Hydrometer Calibration )

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اکسل (xls)

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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

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:

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:

1. Soil particles are not spheres
2. The fluid is not of infinite extent
3. The specific gravity of individual particles may vary
4. Turbulence caused by larger particles falling
5. Brownian movement of smaller particles
6. Disturbance due to insertion and removal of hydrometer
7. 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

Factors ignored in test
(see above)

Testing errors

� Variance in temp over the course of the test
� Loss of sample during agitation
� Disturbance of suspension when hydrometer inserted
� Accumulation of soil on the hydrometer bulb
� Evaporation
� Misreading meniscus

Type 151H hydrometer
Thermometer
A 1000 ml hydrometer jar


Mixing bowl
Spatula
Dispersion apparatus - milkshake mixer
Drying pan
Rubber membrane (parafilm)
Clock with seconds
Small graduated cylinder
deflocculating agent - 4% sodium hexa-metaphosphate (NaPO3)
40g/1000ml

Holtz, Kovaks and Sheahan (2011), page 34.

Holtz and Kovaks (1981), pages 28-29.

Das (1998), sections 1.6 and 1.7, starting on page 18.

Gorrill (1998), pages 9-12, 13, 53.

Bowles (1986), pages 47-57.

ASTM D421, D422

AASHTO T87, T88