1 Tutorial - Mechanical Separation

Tutorial for Mechanical – Physical Separation

1. Slurry of CaCO3 in water at 298.2 K is filtered at a constant pressure of 46.2 kN/m2. The area of the plate and frame press was 0.0439 m 2 and the slurry concentration was 23 .47 kg solid/m3 filtrate. The filtration data is given in the table below: V x 103 (m3) t (s) V x 103 (m3) 0.5 17.3 1.5 1.0 41.3 2.0 *V = volume of filtrate collected, t = filtration time

t (s) 72.0 108.3

V x 103 (m3) 2.5 3.0

t (s) 152.0 201.7

a. Calculate the constant α and Rm. b. If the same slurry is filtered in a plate and frame press having 30 frames and total area o f 0.873 m2 per frame, calculate the time required to recover 2.26 m3 of filtrate. Assume the same constant pressure filtration of 46.2 kN/m 2, same filter cake properties and the same filter cloth are used. c. Calculate the total filter-cycle time if 0.283 m3 of wash water is used for through-washing, given the time to clean the press takes 30 mins. Equation:

 =      =       −∆ −∆    −∆ −∆  =      2 1 ( ) =        = 4 + (for plate and frame filter press) Ans: (a) α = 1.106 x 1011 m/kg, Rm = 6.4 x 10 10 m-1 (b) 293.8 s (c) wash time = 240.9 s

2. a. Calculate the terminal settling velocity of dust particle having a diameter of 60 µm in air at 294.3 K and 101.32 kPa. The dust particle can be considered spherical with density of 1280 kg/m3. Take the air density as 1.202 kg/m 3 and viscosity as 0.01828 x 10 -3 Pa.s [Ans: 0.1372 m/s] b. Oil droplets with diameter of 200 µm are settling from still air at 294.3 K and 101.32 kPa. The density of the oil is 900 kg/m3. A settling chamber with a height of 0.457 m is used. Calculate the terminal settling velocity. How long will it take for t he particle to settle? [Ans: 0.86 s]

Equation:

For spherical particle:

 N Re





vt 

4    p







    gD p

3C  D  

2

For laminar flow:

vt 



 gD p

  

p



 p



18 

 D p vt     

3. A dilute slurry contains small solid food particles with diameter of 5 x 10 -2  mm, which are to be removed by centrifuging. The particle density is 1050 kg/m3 and the solution density is 1000 kg/m 3. The viscosity of the liquid is 1.2 x 10 -3  Pa.s. A centrifuge at 3000 rev/min is to be used. The bowl dimensions are b = 100.1 mm, r1 = 5.00 mm, and r2 = 30.0 mm. Calculate the expected flow rate in m3/s just to remove these particles. [Ans: 8.76 x 10-5 m3/s] Equation:  N  2    



60 2

q



 N 



     p





r 2 r 1

2  r 

2

    D p

18  ln

60v 

 br 

2

2



r 12 