Determine the particle-size distribution of soil particles finer than 75 µm (0.075 mm) by sedimentation using the principles of Stokes’ law.
Hydrometer analysis is based on the sedimentation principle that larger soil particles settle faster than smaller particles in a soil-water suspension.
According to Stokes’ law, the settling velocity of approximately spherical particles is related to the square of their diameter. Therefore, when the settling time and effective depth are known, the corresponding particle diameter can be determined.
The hydrometer measures the density of the soil suspension at a particular depth and time. From the corrected hydrometer reading, the percentage of soil particles finer than the corresponding particle diameter is calculated.
| S. No. | Apparatus | Typical Requirement |
|---|---|---|
| 1 | Density Hydrometer | IS 3104, approximately 0.995–1.030 range |
| 2 | Measuring Cylinder | 1000 mL capacity |
| 3 | Thermometer | 0–50°C range, approximately 0.5°C accuracy |
| 4 | Water Bath / Constant Temperature Room | For temperature control |
| 5 | Mechanical Stirring Apparatus | Suitable for soil dispersion |
| 6 | 75 µm IS Sieve | For separation of fine fraction |
| 7 | Balance | Accuracy 0.01 g |
| 8 | Stopwatch | For sedimentation timing |
| 9 | Wash Bottle | Distilled water |
| 10 | Glass Rod | Approximately 15–20 cm |
| 11 | Conical Flask | 1000 mL |
| 12 | Funnel and Filter Paper | For pretreatment |
| 13 | Measuring Cylinder | 100 mL |
| 14 | Blue Litmus Paper | For checking acidity |
Fill a 1000 mL measuring cylinder with approximately 800 mL distilled water and record the initial water level.
Carefully immerse the hydrometer and record the new water level. The difference between the two levels gives the approximate volume of the submerged hydrometer.
Determine the volume between two graduations and measure the vertical distance between those graduations.
where A is the cross-sectional area of the measuring cylinder in cm².
Measure the distance from the neck of the hydrometer to the bottom of the bulb and record it as h.
Measure the distance H between the neck of the hydrometer and each major calibration mark.
where:
Place the hydrometer in a measuring cylinder containing distilled water and determine the difference between the readings taken at the top and bottom of the meniscus.
Since the soil suspension is normally opaque, the hydrometer reading is taken at the top of the meniscus and the appropriate meniscus correction is applied.
where:
Take the required quantity of representative soil and prepare the sample in accordance with the adopted grain-size analysis procedure.
Where required, add approximately 150 mL hydrogen peroxide to the soil in a suitable wide-mouth conical flask. Stir gently and allow the mixture to stand.
Subsequently heat gently and stir periodically. Continue treatment until the required decomposition of organic matter has been achieved.
Where required, add hydrochloric acid to the cooled soil suspension and allow the reaction to proceed in accordance with the adopted laboratory procedure.
Filter the mixture and wash the soil with warm distilled water until the filtrate shows no acid reaction to litmus.
Transfer the washed soil to a suitable dish and oven-dry. Record the dry mass after pretreatment as Wb.
where:
The supplied procedure specifies a dispersing solution prepared using:
| Material | Quantity |
|---|---|
| Sodium Hexametaphosphate | 33 g |
| Sodium Carbonate | 7 g |
| Distilled Water | Make volume to 1 litre |
Transfer the dispersed suspension through the 75 µm IS sieve.
Wash the material retained on the sieve using distilled water. Dry the retained fraction and determine its dry mass for use in the overall particle-size distribution.
Collect the material passing the 75 µm sieve in a 1000 mL measuring cylinder and add distilled water until the total volume is exactly 1000 mL.
Close the 1000 mL cylinder with a suitable stopper and shake it vigorously by turning it end-over-end to obtain a uniform suspension.
Immediately after shaking is completed, start the stopwatch, remove the stopper and allow the suspension to settle.
Take hydrometer readings at approximately:
0.5, 1, 2 and 4 minutes.
After each reading, remove and rinse the hydrometer and place it in distilled water maintained at approximately the same temperature.
Continue observations at suitable later intervals such as:
8, 15, 30, 60, 120, 240, 540 and 1440 minutes
Additional readings may be taken where required by the adopted procedure.
Record the temperature of the soil suspension during the test. Temperature influences the viscosity of water and therefore affects the sedimentation velocity and calculated particle size.
Prepare a blank/reference cylinder containing the specified dispersing-agent solution and distilled water to a total volume of 1000 mL.
Maintain the blank at approximately the same temperature as the soil suspension and determine the hydrometer reading at the top of the meniscus.
The correction associated with the dispersing agent and blank effects is represented by the composite correction C.
where:
For each sedimentation observation, determine the effective depth corresponding to the corrected hydrometer reading and calculate the equivalent particle diameter.
where:
The percentage finer based on the dry mass of soil used for the hydrometer analysis is calculated using the adopted hydrometer equation.
where:
Where hydrometer results are combined with sieve-analysis results, convert the percentage finer to the basis of the total original dry sample.
where:
| Sample No. | |
|---|---|
| Total dry sample weight, W | |
| Weight passing 2 mm sieve, W′ | |
| Dry weight used for hydrometer analysis, Wd | |
| Specific gravity, G | |
| Meniscus correction, Cm | |
| Composite correction, C | |
| Pretreatment loss, P |
| Date / Time | Elapsed Time (min) | Observed Hydrometer Rh' | Temp. °C | Corrected Hydrometer Rh | Effective Depth He (cm) | Factor M | Particle Size D (mm) | Corrected Reading R | % Finer N′ | % Finer N |
|---|---|---|---|---|---|---|---|---|---|---|
| 0.5 | ||||||||||
| 1 | ||||||||||
| 2 | ||||||||||
| 4 | ||||||||||
| 8 | ||||||||||
| 15 | ||||||||||
| 30 | ||||||||||
| 60 | ||||||||||
| 120 | ||||||||||
| 240 | ||||||||||
| 540 | ||||||||||
| 1440 |
The hydrometer analysis results are used to determine the percentage of soil particles finer than the corresponding equivalent particle diameter.
The final grain-size distribution is obtained by combining the hydrometer results with the coarse-fraction sieve-analysis results.
The resulting curve represents the particle-size distribution of the soil over the applicable size range.
| Common Error | Possible Effect | Control Measure |
|---|---|---|
| Incomplete dispersion | Particles remain flocculated | Ensure adequate dispersing treatment |
| Delay in starting stopwatch | Incorrect sedimentation time | Start timing immediately after homogenization |
| Temperature variation | Incorrect viscosity correction | Monitor suspension temperature |
| Incorrect meniscus reading | Systematic hydrometer error | Determine and apply meniscus correction correctly |
| Incorrect composite correction sign | Incorrect percentage finer | Retain the sign determined from blank testing |
| Disturbing the suspension | Altered sedimentation conditions | Avoid movement of the cylinder during settling |
| Reading hydrometer inconsistently | Variable observations | Use a consistent reading procedure |
| Incorrect sample-mass basis | Incorrect combined PSD curve | Maintain consistent mass corrections |
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