## Size Separation

### GATE-CH-1992-4-a-mo-2mark

1992-4-a-mo

A particle $$A$$ of diameter 10 microns settles in an oil of specific gravity 0.9 and viscosity 10 poise under Stokes law. A particle $$B$$ with diameter 20 microns settling in the same oil will have a settling velocity

• same as that of $$A$$

• one-fourth as that of $$A$$

• twice as that of $$A$$

• four-times as that of $$A$$

### GATE-CH-1993-10-b-mo-2mark

1993-10-b-mo

For separating particles of different densities, the differential settling method uses a liquid sorting medium of density

• intermediate between those of the light and heavy ones

• less than that of either one

• greater than that of either one

• of any arbitrary value

### GATE-CH-1995-1-d-mo-1mark

1995-1-d-mo

Jigging is a technique by which different particles can be separated by

• particle size

• particle density

• particle shape

• mixed

### GATE-CH-1996-1-7-mo-1mark

1996-1-7-mo

Stokes equation is valid in the Reynolds number range

• 0.01 to 0.1

• 0.1 to 2

• 2 to 10

• 10 to 100

### GATE-CH-1999-2-6-mo-2mark

1999-2-6-mo

Velocity of a small particle of diameter $$D_p$$ at a distance $$r$$ from the rotational axis of a cyclone rotating at an angular speed $$\omega$$ is given by (the other symbols are as per standard notation)

• $$\displaystyle \left (\frac {D_p}{18}\frac {\rho _s-\rho }{\mu }\right )\omega ^2r$$

• $$\displaystyle \left (\frac {D_p^2}{18}\frac {\rho _s-\rho }{\mu }\right )\omega r^2$$

• $$\displaystyle \left (\frac {D_p}{18}\frac {\rho _s-\rho }{\mu }\right )\omega ^2r^2$$

• $$\displaystyle \left (\frac {D_p^2}{18}\frac {\rho _s-\rho }{\mu }\right )\omega ^2r$$

[Index]

### GATE-CH-2000-1-8-mo-1mark

2000-1-8-mo

For a sphere falling in a constant drag coefficient regime, its terminal velocity depends on its diameter $$d$$ as

• $$d$$

• $$d^{0.5}$$

• $$d^{2}$$

• $$1/d$$

### GATE-CH-2004-15-mo-1mark

2004-15-mo

For a particle settling in water at its terminal settling velocity, which of the following is true?

• buoyancy = weight + drag

• weight = buoyancy + drag

• drag = buoyancy + weight

• drag = weight

### GATE-CH-2013-33-mo-2mark

2013-33-mo

In the elutriation leg of a commercial crystallizer containing a mixture of coarse and very fine crystals of the same material, a liquid is pumped vertically upward. The liquid velocity is adjusted such that it is slightly lower than the terminal velocity of the coarse crystals only. Hence

• the very fine and coarse crystals will both be carried upward by the liquid

• the very fine and coarse crystals will both settle at the bottom of the tube

• the very fine crystals will be carried upward and the coarse crystals will settle

• the coarse crystals will be carried upward and the very fine crystals will settle

### GATE-CH-2016-7-mo-1mark

2016-7-mo

In a cyclone separator used for separation of solid particles from a dust laden gas, the separation factor is defined as the ratio of the centrifugal force to the gravitational force acting on the particle. $$S_r$$ denotes the separation factor at a location (near the wall) that is at a radial distance $$r$$ from the centre of the cyclone. Which one of the following statements is INCORRECT?

• $$S_r$$ depends on mass of the particle

• $$S_r$$ depends on the acceleration due to gravity

• $$S_r$$ depends on tangential velocity of the particle

• $$S_r$$ depends on the radial location ($$r$$) of the particle

### GATE-CH-1990-3-iii-mo-2mark

1990-3-iii-mo

Two very small silica particles are settling at their respective terminal velocities through a highly viscous oil column. If one particle is twice as large as the other, the larger particle will take ––––- times the time than by the smaller particle to fall through the same height.

[Index]

### GATE-CH-2013-15-mo-1mark

2013-15-mo

Separation factor of a cyclone 0.5 m in diameter and having a tangential velocity of 20 m/s near the wall is ____________(Take $$g= 10$$ m/s2)

### GATE-CH-1990-13-i-mo-6mark

1990-13-i-mo

A mixture of coal and sand particles having sizes smaller than $$1 \times 10^{-4}$$ m in diameter is to be separated by screening and subsequent elutriation with water.
(i) Recommend a screen aperture ($$\mu$$m) such that the oversize from the screen can be separated completely into sand and coal particles by elutriation.
(ii) Calculate also the required water velocity (mm/s).
Assume that Stokes’ law is applicable. Density of sand = 2650 kg/m$$^3$$; density of coal = 1350 kg/m$$^3$$; density of water = 1000 kg/m$$^3$$; viscosity of water = $$1 \times 10^{-3}$$ kg/m.s; g = 9.812 m/s$$^2$$.
(i) ____________
{#1}

(ii) ____________
{#2}

### GATE-CH-1995-16-mo-5mark

1995-16-mo

A binary mixture of 100 $$\mu$$m size having densities of 2 g/cm$$^3$$ and 4 g/cm$$^3$$ is to be classified by elutriation technique using water. Estimate the range [(i) minimum; (ii) maximum] of velocities (in mm/s) that can do the job and recommend a suitable value.
(i) ____________
{#1}

(ii) ____________
{#2}

### GATE-CH-1995-2-k-mo-2mark

1995-2-k-mo

A suspension of uniform particles in water at a concentration of 500 kg of solids per cubic meter of slurry is settling in a tank. Density of the particles is 2500 kg/m$$^3$$ and terminal velocity of a single particle is 20 cm/s. What will be the settling velocity of suspension? Richardson-Zaki index is 4.6

• 20 cm/s

• 14.3 cm/s

• 7.16 cm/s

• 3.58 cm/s

### GATE-CH-1997-2-7-mo-2mark

1997-2-7-mo

A suspension of glass beads in ethylene glycol has a hindered settling velocity of 1.7 mm/s while the terminal settling velocity of the single glass bead in ethylene glycol is 17 mm/s. If the Richardson-Zaki hindered settling index is 4.5, the volume fraction of solids in the suspension is

• 0.1

• 0.4

• 0.6

• none of these

[Index]

### GATE-CH-2000-2-8-mo-2mark

2000-2-8-mo

A 30% (by volume) suspension of spherical sand particles in a viscous oil has a hindered settling velocity of 4.4 $$\mu$$m/s. If the Richardson-Zaki hindered settling index is 4.5, then the terminal settling velocity of sand grain is

• 0.9 $$\mu$$m/s

• 1 mm/s

• 22.1 $$\mu$$m/s

• 0.02 $$\mu$$m/s

### GATE-CH-2005-56-mo-2mark

2005-56-mo

What is the terminal velocity in m/s, calculated from Stokes’ law, for a particulate of $$0.1\times 10^{-3}$$ m, density 2800 kg/m3 settling in water of density 1000 kg/m3 and viscosity $$10^{-3}$$ kg/(m.s)? (Assume $$g=10$$ m/s2)

• $$2\times 10^{-2}$$

• $$4\times 10^{-3}$$

• $$10^{-2}$$

• $$8\times 10^{-3}$$

### GATE-CH-2007-40-mo-2mark

2007-40-mo

In the Stokes’ regime, the terminal velocity of particles for centrifugal sedimentation is given by $v_t = \frac {\omega ^2 r(\rho _p - \rho )d_p^2}{18\mu }$ where, $$\omega$$: angular velocity; $$r$$: distance of the particle from the axis of rotation, $$\rho _p$$: density of the particle; $$\rho$$: density of the fluid; $$d_p$$: diameter of the particle, and $$\mu$$: viscosity of the fluid.
In a Bowl centrifugal classifier operating at 60 rpm with water ($$\mu =0.001$$ kg.m-1.s-1), the time taken for a particle ($$d_p=0.0001$$ m, sp.gr = 2.5) in seconds to traverse a distance of 0.05 m from the liquid surface is

• 4.8

• 5.8

• 6.8

• 7.8

### GATE-CH-2008-41-mo-2mark

2008-41-mo

Two identically sized spherical particles $$A$$ and $$B$$ having densities $$\rho _A$$ and $$\rho _B$$, respectively, are settling in a fluid of density $$\rho$$. Assuming free settling under turbulent flow conditions, the ratio of the terminal settling velocity of particle $$A$$ to that of particle $$B$$ is given by

• $$\displaystyle \sqrt {\frac {\rho _A-\rho }{\rho _B-\rho }}$$

• $$\displaystyle \sqrt {\frac {\rho _B-\rho }{\rho _A-\rho }}$$

• $$\displaystyle \frac {\rho _A-\rho }{\rho _B-\rho }$$

• $$\displaystyle \frac {\rho _B-\rho }{\rho _A-\rho }$$

### GATE-CH-2011-35-mo-2mark

2011-35-mo

The particle size distribution of the feed and collected solids (sampled for same duration) for a gas cyclone are given below:

 Size range (µm) Weight of feed in the size range (g) Weight of collected solids    in the size range (g) 1–5 5–10 10–15 15–20 20–25 25–30 2 3 5 6 3 1 0.1 0.7 3.6 5.5 2.9 1

What is the collection efficiency (in percentage) of the gas cyclone?

• 31

• 60

• 65

• 69

[Index]

### GATE-CH-1991-3-i-a-mo-2mark

1991-3-i-a-mo

Spherical particles of limestone ($$d_p$$ = 0.16 mm, density = 2800 kg/m$$^3$$) take 5 minutes to settle under gravity through a 6 m column of a fluid of density 1200 kg/m$$^3$$. The drag coefficient is equal to ––––-

### GATE-CH-1991-14-ii-mo-6mark

1991-14-ii-mo

In a mixture of quartz (sp.gr = 2.65) and galena (sp.gr = 7.5), the size of the particles range from 0.0002 cm to 0.001 cm. On separation in a hydraulic classifier using water under free settling conditions, what are the size ranges of (i) quartz, and (ii) galena, in the pure products? (Viscosity of water = 0.001 kg/m.s; density = 1000 kg/m$$^3$$).
(i) pure quartz:

(a) minimum size ($$\mu$$m)
{#1}

(b) maximum size ($$\mu$$m)
{#2}

(ii) pure galena:

(a) minimum size ($$\mu$$m)
{#3}

(b) maximum size ($$\mu$$m)
{#4}

### GATE-CH-1998-15-mo-5mark

1998-15-mo

A concentrated suspension of spherical quartz particles in water settles under gravity. The particle diameter is $$D_p = 10^{-5}$$ m and the particle density is $$\rho _p$$ = 2650 kg/m$$^3$$. The initial voidage in the suspension is $$\epsilon = 0.8$$.
Obtain the expression for the terminal velocity ($$v_t$$) of a single particle assuming Stokes’ law to be valid.
(a) Find the initial settling velocity ($$v_s$$, in $$\mu$$m/s) of the particles in the suspension given $v_s = v_t \epsilon ^{4.6}$
{#1}

(b) Calculate the upward velocity of water (in $$\mu$$m/s) in the suspension resulting from the settling of the particles for $$\epsilon = 0.8$$.
{#2}

[Index]