1. Sedimentation Methods for Determining Particle Sizes
Rely on Stokes’ Law
Sphere of diameter D falling through viscous fluid reaches a terminal velocity, which depends on the bouyant weight of the sphere, the sphere diameter, and the fluid viscosity (for Re < 1)
Thus, a sphere of diameter D will fall distance h in time tD:
where  is the fluid viscosity, gs is the unit weight (= rg) of the sphere material, and gw is the unit weight of water
This is the basis of the “pipette” method of determining the sizes of fine soils – easy to explain, but requires high precision
Also the basis of the “hydrometer” method – more complex to explain, but simpler to do

2. Pipette Method
10 ml pipette
100 mm
Mix 50g of dry soil in 1 litre of water, and put into 1 litre graduated cylinder. Shake thoroughly so that soil is evenly dispersed in the water
Any 10 ml volume of the water will contain 0.5g of soil
Set on bench – allow to start settling
At pre-determined times, use pipette to take 10 ml sample from exactly 100 mm below the surface of the flask
Dry the sample, and weigh the dry soil
So how can this be used to work out particle size distribution?
1 litre flask

3. Coarse spheres (D1)
Fine spheres (D2) h
tD1
tD2

4. Coarse spheres (D1)
Fine spheres (D2) h
tD1
tD2

5. Spheres (D1 & D2)
Before tD1, particles D1 are at same concentration at height h as in original sample
After tD1, but before tD2, particles D1 are missing, but particles D2 are in their original concentration
After tD2, none of either D1 or D2 particles present
To find percentage of particles finer than D1, take sample just after tD1 h
tD1
tD2

6. Spheres (D1 & D2)
Before tD1, particles D1 are at same concentration at height h as in original sample
After tD1, but before tD2, particles D1 are missing, but particles D2 are in their original concentration
After tD2, none of either D1 or D2 particles present
To find percentage of particles finer than D1, take sample just after tD1 h
tD1
tD2

7. Continuous distribution
Choosing a time for taking a sample is like choosing a sieve size . Thus, to find percentage finer than 20 mm, take sample at depth 100 mm at time 4.57 minutes.
Dry the sample; weigh the dry soil.
Weight of soil in this 10 ml sample is same as weight of material finer than 20 mm in 10 ml of original sample.
Say 50 g of soil per litre – i.e. 0.5 g per 10 ml in original sample
Say 0.3 g of soil in sample taken at 4.57 minutes
Thus, % finer than 20 mm is 0.3/0.5 = 60%

8. Stoke's Law only valid for Reynold's Number < 1
Stoke's Law only valid for Reynold's Number < 1. From below, only valid for D < 100 mm if fluid is water).

9. Equipment for Hydrometer Test
Hydrometer measures the average density of the fluid (at about the depth to the centre of the bulb. This reduces as coarser material settles – hydrometer “samples” the density at different times (like the pipette in a sense)