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

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

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

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

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

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

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%

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).

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)