Question

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

Answer 1

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,

γ_w 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