Question

In a hydrometer analysis, the corrected hydrometer reading in a 1000 ml uniform soil suspension at the start of sedimentation was 28. After a lapse of 30 minutes, the corrected hydrometer reading was 12 and the corresponding effective depth 10.5 cm. the specific gravity of the solids was 2.68. Assuming the viscosity and unit weight of water at the temperature of the test as 0.001 Ns/m² and 9.81 kN/m³ respectively. Determine the weight of solids mixed in the suspension, the effective diameter corresponding to the 30 minutes reading and the percentage of particle finer than this size.

Answer 1

The weight of solids mixed in the suspension is 49,835.68 N, the effective diameter corresponding to the 30 minutes reading is 913.04 μm, and the percentage of particles finer than this size is 98.95%.

Step-by-step explanation:

In a hydrometer analysis, the weight of solids mixed in the suspension can be calculated using the equation:

Weight of Solids = (Initial hydrometer reading - Final hydrometer reading) x Specific Gravity of Solids x Unit Weight of Water x Volume of Suspension

Using the given information:

Weight of Solids = (28 - 12) x 2.68 x 9.81 x 1000 ml = 49,835.68 N

The effective diameter corresponding to the 30 minutes reading can be calculated using the equation:

Effective Diameter = (10.5 cm x 1000) / [(Final hydrometer reading - Initial hydrometer reading) x Specific Gravity of Solids]

Using the given information:

Effective Diameter = (10.5 cm x 1000) / [(12 - 28) x 2.68] = 913.04 μm

The percentage of particles finer than this size can be calculated using the equation:

Percentage of Particles Finer = 100 x [1 - (Cumulative Volume of Suspension / Total Volume of Suspension)]

Using the given information:

Percentage of Particles Finer = 100 x [1 - (10.5 cm / 1000 cm)] = 98.95%