# 50 gm of oven dried soil of five sizes shown in the table is taken for hydrometer analysis and 1000 cc of suspension is prepared and filled in a jar u

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50 gm of oven dried soil of five sizes shown in the table is taken for hydrometer analysis and 1000 cc of suspension is prepared and filled in a jar up to 30 cm height.

 Particle size (mm) Weight (gm) 0·06 6 0·05 20 0·03 15 0·015 5 0·004 4

If the specific gravity of soil solids is 2.7 and viscosity of soil water suspension is 1× 10-6 kN-sec/m2, the time required for all the particles to settle to the bottom of the jar is

1. 2 hr 16 min
2. 5 hr 37 min
3. 11 hr 55 min
4. 23 hr 50 min

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Correct Answer - Option 2 : 5 hr 37 min

Concept

Given,

Height of jar = 30 cm

From stokes law

We know the velocity of settling particle is

${V_s} = \frac{{{\gamma _w} \times {d^2} \times \left( {G - 1} \right)}}{{18 \times \mu }}$

Where,

γw is the unit weight of water

d is the diameter of the particle

G is the specific gravity of the particle

μ is the viscosity of the fluid

Note: If the lighter particle from the group of particles settles at the bottom that means every particle is settled at the bottom.

 Particle size (mm) Weight (gm) 0·06 6 0·05 20 0·03 15 0·015 5 0·004 4

∴ Here diameter (d) = 0.004 mm is taken from the group

$Time\;required\;for\;settling\;of\;all\;particle = \frac{{Height\;of\;water\;level\;in\;jar}}{{Settling\;Velocity\;}}$

$t = \frac{{30 \times {{10}^{ - 2}}}}{{14.284 \times {{10}^{ - 6}}}}$

= 20215 sec

= 5.61 hr

= 5 hr 37 min

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