Assignment
Unit-2 Filtration
1. What is the difference between filtration and settling & sedimentation?
2. What is the difference between free settling and hindered settling?
3. If a rigid body moves in a fluid, how many forces act on them? Name them and represent their
direction of action in diagram.
4. Give the equation for drag force.
5. Period of accelerated fall vs period of constant fall. Which is important? Why?
6. Oil droplets having a diameter of 0.020 mm are to be settled from air at a velocity of 0.01 m/s. the
density and viscosity of air is 1.137 kg/m3 and 1.9x10-5 Pa.s. Assume the droplet to be a rigid
sphere. Calculate drag co-efficient.
7. Solid spherical particles of coffee extract from a dryer having a diameter of 400µm are falling
through air at a temperature of 422K. The density of particles is 1030 kg/m3. Calculate the
terminal settling velocity and the distance of fall in 5 s. The pressure is 101.32 kPa.
8. Give the equation for Reynolds number and terminal settling velocity for hindered settling.
9. Solid spherical particles having a diameter of 0.090 mm and a solid density of 2002 kg/m3 are
settling in a solution of water. The volume fraction of the solids in the water is 0.45. Calculate the
hindered settling velocity and the Reynolds number. The density and viscosity of water is 998
kg/m3 and 1.005x 10-3 Pa.s.
10. What are classifiers?
11. How will you select the medium for sink-and-float method?
12. A mixture of silica (B) and galena (A) solid particles having a size range of solid particles having
a size range of 5.21x10-6 m to 2.50 x 10-5 m is to be separated by hydraulic classification using
free settling conditions in water at 20°C. The specific gravity of silica is 2.65 and that of galena is
7.5. Calculate the size range of the various fractions obtained in the settling. The water viscosity
at 20°C is 1.005x10-3 Pa-s.
13. Draw sedimentation thickener and comment on the function of each of the parts.
14. A centrifuge having a radius of the bowl of 0.1016 m is rotating at N=1000 rev/min.
(a) Calculate the centrifugal force developed in terms of gravity
(b) Compare this force to that for a bowl with a radius of 0.2032 m rotating at the same rev/min
15. Equation for terminal settling velocity in centrifuge is------16. A viscous solution containing particles with density ρp=1461 kg/m3 is clarified by centrifugation.
Solution density ρ=801 Kg/m3; Viscosity μ=100 cp. Centrifuge bowl with r2=0.02225 m.;
r1=0.00716 m.; height=b=0.197 m.; Calculate critical particle diameter of the largest particles in
the exit stream if N=23000 rev/min, q=0.002832 m3/hr.
17. A viscous solution contains particles with a density ρp=1200 kg/m3 is to be clarified by
centrifugation. The solution density is ρ=850 kg/m3 and its viscosity is 80 cp. The centrifuge has
a bowl with r2 = 0.02m, r1 = 0.01m and height b=0.25 m. Calculate the critical particle diameter
of the largest particles in the exit stream if N=15000 rpm and flow rate q=0.002 m3/hr?
18. In the above problem, we would like to scale up the centrifuge. We have to design a centrifuge
such that it can handle 1.5 times q in Question (17). r1 and r2 remains same, find the length of the
centrifuge. Both the centrifuges have same rotational speed?
19. For the problem (16) calculate the sigma value of centrifuge.
20. What is the purpose of filter aid?
21. A batch settling test on slurry gave the following results, where the height in z meters between the
clear liquid and suspended solid is given at time t hours.
t(h)
0
0.5
1.0
1.75
3
5
12
20
z(m)
0.360
0.285
0.211
0.15
0.125
0.113
0.102
0.09
The original slurry concentration is 250 kg/m3 of slurry. Determine the velocities of settling and
concentrations and make a plot of velocity versus concentration.
22. Difference between compressible and incompressible cake.
23. Draw rotary drum filter and comment on the function of each of the parts.
24. Data for the laboratory filtration of CaCO3 slurry in water at 298.2 K (25°C) are reported as
follows at a constant pressure (–Δp) of 338 kN/m2 (7060 lbf/ft2); The filter area of the plate-andframe press was A = 0.0439 m2 (0.473 ft2) and the slurry concentration was cs = 23.47 kg/m3
(1.465 lbm/ft3). Calculate the constants α and Rm from the experimental data given, where t is time
in s and V is filtrate volume collected in m3.
t
V
t
4.4
0.498 × 10
–3
9.5
16.3
24.6
V
t
V
34.7
2.498 × 10
–3
73.6
4.004 × 10–3
1.000 × 10–3
46.1
3.002 × 10–3
89.4
4.502 × 10–3
1.501 × 10–3
2.000 × 10–3
59.0
3.506 × 10–3
107.3
5.009 × 10–3