Settling, Filtration and Mixing - Fluid Mechanics and Mechanical Operations - Chemical Engineering Previous Year Questions

1

2007 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Settling, Filtration and Mixing

Chemical Engineering (CH) 2007

In constant pressure filtration, the rate of filtration follows the relation
(\(v\) : filtrate volume, \(t\) : time, \(k\) and \(c\) : constants ).

A

\(\frac{dv}{dt} = kv + c\)

B

\(\frac{dv}{dt} = \frac{1}{kv + c}\)

C

\(\frac{dv}{dt} = kv\)

D

\(\frac{dv}{dt} = kv^2\)

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2

2007 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Settling, Filtration and Mixing

Chemical Engineering (CH) 2007

In the Stokes regime, the terminal velocity of particles for centrifugal sedimentation is given by
\[ U_t = \omega^2 r (\rho_p - \rho) d_p^2 / 18\mu \]
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.s ), 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

A

4.8

B

5.8

C

6.8

D

7.8

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3

2008 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Settling, Filtration and Mixing

Chemical Engineering (CH) 2008

Q.13 For laminar flow conditions, the relationship between the pressure drop (\( \Delta P_c \)) across an incompressible filter cake and the specific surface area (\( S_o \)) of the particles being filtered is given by ONE of the following

A

\(\Delta P_c \) is proportional to \(S_o \)

B

\(\Delta P_c \) is proportional to \(1/S_o \)

C

\(\Delta P_c \) is proportional to \(S_o^2 \)

D

\(\Delta P_c \) is proportional to \(1/S_o^2 \)

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4

2008 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Settling, Filtration and Mixing

Chemical Engineering (CH) 2008

Two identically sized spherical particles A and B having densities ρ_A and ρ_B, respectively, are settling in a fluid of density ρ. 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

A

\(\sqrt{\frac{\rho_A - \rho}{\rho_B - \rho}}\)

B

\(\sqrt{\frac{\rho_B - \rho}{\rho_A - \rho}}\)

C

\(\frac{\rho_A - \rho}{\rho_B - \rho}\)

D

\(\frac{\rho_B - \rho}{\rho_A - \rho}\)

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5

2008 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Settling, Filtration and Mixing

Chemical Engineering (CH) 2008

Consider the scale-up of a cylindrical baffled vessel configured to have the standard geometry (i.e. Height = Diameter). In order to maintain an equal rate of mass transfer under turbulent conditions for a Newtonian fluid, the ratio of the agitator speeds should be (Given N₁, D₁ are agitator speed and vessel diameter before scale-up; N₂, D₂ are agitator speed and vessel diameter after scale-up)

A

\(\frac{N_1}{N_2} = \frac{D_1}{D_2}\)

B

\(\frac{N_1}{N_2} = \frac{D_2}{D_1}\)

C

\(\frac{N_1}{N_2} = \left(\frac{D_1}{D_2}\right)^{2/3}\)

D

\(\frac{N_1}{N_2} = \left(\frac{D_2}{D_1}\right)^{2/3}\)

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6

2009 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Settling, Filtration and Mixing

Chemical Engineering (CH) 2009

The terminal settling velocity of a 6 mm diameter glass sphere (density: 2500 kg/m³) in a viscous Newtonian liquid (density: 1500 kg/m³) is 100 μm/s. If the particle Reynolds number is small and the value of acceleration due to gravity is 9.81 m/s², then the viscosity of the liquid (in Pa.s) is

A

100

B

196.2

C

245.3

D

490.5

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7

2011 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Settling, Filtration and Mixing

Chemical Engineering (CH) 2011

Consider the following two cases of movement of particles. In Case I, the particle moves along the positive y-direction and in Case II, the particle moves along negative y-direction. Gravity acts along the positive y-direction. Which ONE of the following options corresponds to the CORRECT directions of buoyancy acting on the particles?

A

Positive y-direction for both the cases

B

Negative y-direction for Case I, positive y-direction for Case II

C

Negative y-direction for both the cases

D

Positive y-direction for Case I, negative y-direction for Case II

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8

2011 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Settling, Filtration and Mixing

Chemical Engineering (CH) 2011

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

Size range (µm)	1–5	5–10	10–15	15–20	20–25	25–30
Weight of feed in the size range (g)	2.0	3.0	5.0	6.0	3.0	1.0
Weight of collected solids in the size range (g)	0.1	0.7	3.6	5.5	2.9	1.0

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

A

31

B

60

C

65

D

69

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9

2011 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Settling, Filtration and Mixing

Chemical Engineering (CH) 2011

On further increasing \(\overline{V_0}\), incipient fluidisation is achieved. Assuming that the porosity of the bed remains unaltered, the pressure drop per unit length (in Pa/m) under incipient fluidisation condition is

A

3675

B

7350

C

14700

D

73501

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10

2012 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Settling, Filtration and Mixing

Chemical Engineering (CH) 2012

A bed of spherical glass beads (density 3000 kg/m³, diameter 1 mm, bed porosity 0.5) is to be fluidized by a liquid of density 1000 kg/m³ and viscosity 0.1 Pa.s. Assume that the Reynolds number based on particle diameter is very small compared to one. If \( g = 10 \) m/s², then the minimum velocity (in m/s) required to fluidize the bed is

A

3.33×10⁻⁴

B

3.33×10⁻¹

C

3

D

30

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11

2013 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Settling, Filtration and Mixing

Chemical Engineering (CH) 2013

Taking the acceleration due to gravity to be 10 m/s², the separation factor of a cyclone 0.5 m in diameter and having a tangential velocity of 20 m/s near the wall is __________

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12

2013 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Settling, Filtration and Mixing

Chemical Engineering (CH) 2013

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

A

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

B

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

C

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

D

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

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13

2018 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Settling, Filtration and Mixing

Chemical Engineering (CH) 2018

The terminal velocity of a spherical particle in gravitational settling under Stokes’ regime varies

A

linearly with the particle diameter

B

linearly with the viscosity of the liquid

C

directly with the square of particle diameter

D

inversely with the density of particle

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14

2019 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Settling, Filtration and Mixing

Chemical Engineering (CH) 2019

A disk turbine is used to stir a liquid in a baffled tank. To design the agitator, experiments are performed in a lab-scale model with a turbine diameter of 0.05 m and a turbine impeller speed of 600 rpm. The liquid viscosity is 0.001 Pa s while the liquid density is 1000 kg/m³. The actual application has a turbine diameter of 0.5 m, an impeller speed of 600 rpm, a liquid viscosity of 0.1 Pa s and a liquid density of 1000 kg/m³. The effect of gravity is negligible. If the power required in the lab-scale model is \(P_1\) and the estimated power for the actual application is \(P_2\), then the ratio \(P_2/P_1\) is

A

\(10^3\)

B

\(10^4\)

C

\(10^5\)

D

\(10^6\)

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15

2020 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Settling, Filtration and Mixing

Chemical Engineering (CH) 2020

In a constant-pressure cake filtration with an incompressible cake layer, volume of the filtrate (V) is measured as a function of time t. The plot of t/V versus V results in a straight line with an intercept of 10^4 s m^-3. Area of the filter is 0.05 m^2, viscosity of the filtrate is 10^-3 Pa s, and the overall pressure drop across the filter is 200 kPa. The value of the filter-medium resistance (in m^-1) is

A

1 \times 10^9

B

1 \times 10^{10}

C

1 \times 10^{11}

D

1 \times 10^{12}

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16

2020 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Settling, Filtration and Mixing

Chemical Engineering (CH) 2020

A rigid spherical particle undergoes free settling in a liquid of density 750 kg m^-3 and viscosity 9.81 × 10^-5 Pa·s. Density of the particle is 3000 kg m^-3 and the particle diameter is 2 × 10^-4 m. Acceleration due to gravity is 9.81 m s^-2. Assuming Stokes' law to be valid, the terminal settling velocity (in m s^-1) of the particle is

A

2 × 10^-3

B

3 × 10^-3

C

4 × 10^-3

D

5 × 10^-3

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17

2021 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Settling, Filtration and Mixing

Chemical Engineering (CH) 2021

A batch settling experiment is performed in a long column using a dilute dispersion containing equal number of particles of type A and type B in water (density 1000 kg m\(^{-3}\)) at room temperature.
Type A are spherical particles of diameter 30 μm and density 1100 kg m\(^{-3}\).
Type B are spherical particles of diameter 10 μm and density 1900 kg m\(^{-3}\).
Assuming that Stokes’ law is valid throughout the duration of the experiment, the settled bed would

A

consist of a homogeneous mixture of type A and type B particles

B

consist of type B particles only

C

be completely segregated with type B particles on top of type A particles

D

be completely segregated with type A particles on top of type B particles

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18

2021 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Settling, Filtration and Mixing

Chemical Engineering (CH) 2021

Seawater is passed through a column containing a bed of resin beads.
Density of seawater = 1025 kg m^-3
Density of resin beads = 1330 kg m^-3
Diameter of resin beads = 50 μm
Void fraction of the bed at the onset of fluidization = 0.4
Acceleration due to gravity = 9.81 m s^-2
The pressure drop per unit length of the bed at the onset of fluidization is __________ Pa m^-1 (round off to nearest integer).

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19

2022 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Settling, Filtration and Mixing

Chemical Engineering (CH) 2022

In a constant-rate cake filtration operation, the collected filtrate volumes are 120 m³ and 240 m³ at 1 min and 2 min, respectively. Assume the cake resistance to be constant and the filter medium resistance to be negligible. If the pressure-drop across the cake is 10 kPa at 1 min, its value at 2 min is ______ kPa (rounded off to the nearest integer).

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20

2023 · Chemical Engineering · Fluid Mechanics and Mechanical Operations · Settling, Filtration and Mixing

Chemical Engineering (CH) 2023

For a packed-bed comprising of uniform-sized spherical particles of diameter \(D_p\), the pressure drop across the bed is given by the Kozeny-Carman equation when the particle Reynolds number (\(Re_p\)) < 1. Under this condition, minimum fluidization velocity is proportional to \(D_p^n\). Which one of the following is the CORRECT value of exponent \(n\)?

A

2

B

\(-1\)

C

\(-2\)

D

1

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