## Filtration

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

1992-4-d-mo

During washing of filter at the end of constant pressure filtration, the rate of washing equals the

• rate of filtration at time zero

• rate of filtration at the end of filtration

• rate of filtration when half the filtrate has been obtained

• rate of filtration at the end of filtration, but decreases with time subsequently

### GATE-CH-2004-16-mo-1mark

2004-16-mo

In constant pressure filtration,

• resistance decreases with time

• rate of filtration is constant

• rate of filtration increases with time

• rate of filtration decreases with time

### GATE-CH-2007-13-mo-1mark

2007-13-mo

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

• $$\displaystyle \frac {dV}{dt} = kV + c$$

• $$\displaystyle \frac {dV}{dt} = \frac {1}{kV + c}$$

• $$\displaystyle \frac {dV}{dt} = kV$$

• $$\displaystyle \frac {dV}{dt} = k V^2$$

### GATE-CH-2008-13-mo-1mark

2008-13-mo

For laminar flow conditions, the relationship between the pressure drop ($$\Delta P$$) across an incompressible filter cake and the surface area per unit volume of particles ($$S_0$$) of the particles being filtered is given by ONE of the following

• $$\Delta P$$ is proportional to $$S_0$$

• $$\Delta P$$ is proportional to $$1/S_0$$

• $$\Delta P$$ is proportional to $$S_0^2$$

• $$\Delta P$$ is proportional to $$1/S_0^2$$

### GATE-CH-1991-4-iv-mo-2mark

1991-4-iv-mo

For 100% increase in pressure the specific resistance of a filter cake increases by (i) 末末- %, if the compressibility coefficient is 0.5; and increases by (ii) 末末- %, if the compressibility coefficient is 0.8.
(i) ____________
{#1}

(ii) ____________
{#2}

[Index]

### GATE-CH-2003-55-mo-2mark

2003-55-mo

The basic filtration equation is given as $\frac {dt}{dV} = \frac {\mu }{A\Delta P} \left (\frac {\alpha CV}{A} + R_m\right )$ where $$V$$ is volume of the filtrate, $$A$$ is the filtration area, $$\alpha$$ is specific cake resistance, $$\mu$$ is viscosity of the filtrate, and $$C$$ is the concentration of solids in the feed slurry.

In a 20 min. constant rate filtration, 5 m3 of filtrate was obtained. If this is followed by a constant pressure filtration, how much more time in minutes will it take for another 5 m3 of filtrate to be produced? Neglect filter medium resistance, $$R_m$$; assume incompressible cake.

• 10

• 20

• 25

• 30

### GATE-CH-2004-54-mo-2mark

2004-54-mo

A centrifugal filtration unit operating at a rotational speed of $$\omega$$ has inner surface of the liquid (density $$\rho _L$$) located at a radial distance $$R$$ from the axis of rotation. The thickness of the liquid film is $$\delta$$ and no cake is formed. The initial pressure drop during filtration is

• $$\displaystyle \frac {1}{2}\omega ^2R^2\rho _L$$

• $$\displaystyle \frac {1}{2}\omega ^2\delta ^2\rho _L$$

• $$\displaystyle \frac {1}{2}\omega ^2\delta \rho _L(2R+\delta )$$

• $$\displaystyle \frac {1}{2}\omega ^2R \rho _L(R+2\delta )$$

### GATE-CH-2005-55-mo-2mark

2005-55-mo

A centrifuge of diameter 0.2 m in a pilot plant rotates at a speed of 50 Hz in order to achieve effective separation. If this centrifuge is scaled up to a diameter of 1 m in the chemical plant, and the same separation factor is to be achieved, what is the rotational speed of the scaled up centrifuge?

• 15 Hz

• 22.36 Hz

• 30 Hz

• 44.72 Hz

### GATE-CH-2006-41-mo-2mark

2006-41-mo

A filtration is conducted at constant pressure to recover solids from dilute slurry. To reduce the time of filtration, the solids concentration in the feed slurry is increased by evaporating half the solvent. If the resistance of the filter medium is negligible, the filtration time will be reduced by a factor of

• 1

• 2

• 4

• 8

### GATE-CH-1989-13-i-mo-4mark

1989-13-i-mo

A leaf filter filtering a slurry, gave a total of 8 m$$^3$$ filtrate in 30 minutes. Filtration was continued till 11.3 m$$^3$$ of filtrate was collected. Estimate the washing time in minutes, if 11.3 m$$^3$$ of wash water are used. The resistance of the cloth can be neglected and a constant pressure is used throughout.

[Index]

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

1990-13-ii-mo

A filtration is carried out for 10 min at a constant rate in a leaf filter and thereafter it is continued at constant pressure. This pressure is that attained at the end of the constant rate period. If one quarter of the total volume of the filtrate is collected during the constant rate period, what is the total filtration time (in minutes)? Assume that the cake is incompressible and the filter medium resistance is negligible.

### GATE-CH-1992-14-b-mo-6mark

1992-14-b-mo

A filter press contains 20 frames, each of 0.6 m by 0.6 m inside dimensions. The frames are 0.025 m thick. The press is equipped with 1 and 3 button plates for washing. The volume of wash water used is 10% of the filtrate per cycle. The time required for filtering at constant pressure is 2 hours by which time the frames are full. Washing is done at the same pressure as filtering and the viscosity of wash water is nearly the same as that of the filtrate. What is the time (in hour) for washing? There is 0.05 m$$^3$$ of final cake per m$$^3$$ of filtrate. Neglect the resistance of the filter medium.

### GATE-CH-1993-20-mo-5mark

1993-20-mo

A constant pressure filtration test gave data that can fit an expression, $$dt/dV = 9.3V + 8.5$$; ($$t$$ in seconds; $$V$$ in litres). If the resistance of the filter medium is assumed unaffected with pressure drop and the compressibility coefficient of the filter cake is 0.3, what will be the time (in seconds) taken for the collection of 3.5 litres of filtrate at a filtration pressure twice that used in the test?

### GATE-CH-2015-36-mo-2mark

2015-36-mo

A typical batch filtration cycle consists of filtration followed by washing. One such filtration unit operating at constant pressure difference first filters a slurry during which 5 liters of filtrate is collected in 100 s. This is followed by washing, which is done for $$t_W$$ seconds and uses 1 liter of wash water. Assume the following relation to be applicable between the applied pressure drop $$\Delta P$$, cake thickness $$L$$ at time $$t$$, and volume of liquid $$V$$ collected in time $$t$$

$\frac{\Delta P}{L} = k_1\frac {dV}{dt}; \qquad L=k_2V, \text{if L is changing.}$

$$k_1$$ and $$k_2$$ can be taken to be constant during filtration and washing. The wash time $$t_W$$, in seconds (up to one decimal place), is ____________

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

1992-4-c-mo

Match the following:

• I. Cut diameter

• II. Specific cake resistance

• III. Size reduction ratio

• IV. Angle of internal friction

[Index]

### GATE-CH-1988-13-ii-mo-4mark

1988-13-ii-mo

Show that for a nonwashing plate and frame filter press, operating at constant pressure with negligible filter medium resistance, the optimum cycle occurs when the time for filtering equals the time lost in opening, dumping, cleaning and reassembling the press.

### GATE-CH-1989-3-iii-b-mo-1mark

1989-3-iii-b-mo

In through washing type plate-and-frame filter press, during the washing, the wash water passes through 末末- the thickness of cake and the washing area is 末末- the filtration area.

### GATE-CH-2001-9-mo-5mark

2001-9-mo

The volumetric flow rate during constant pressure filtration is $\frac{dV}{dt} = \frac{1}{K_cV+1/q_0}$ where $$V$$ is the total volume of filtrate collected in time $$t$$, and $$K_c$$ and $$q_0$$ are constants.

1. Integrate the above equation to obtain a relation between $$V$$ and $$t$$.

2. Make a sketch of $$t/V$$ versus $$V$$ from your results.

3. Given $$V=1.0$$ litre at $$t=41.3$$ s and $$V=2.0$$ litre at $$t=108.3$$ s, find $$K_c$$.

### GATE-CH-2002-22-mo-5mark

2002-22-mo

In a filtration process, if $$V$$ is the volume of filtrate collected in time $$t$$, a general relationship can be given as $\frac{dt}{dV} = \frac{\mu}{A (\Delta P)}\left(\frac{\alpha c V}{A} + R_m\right)$ where $$\alpha$$ is the specific cake resistance, $$R_m$$ is the filter medium resistance, $$A$$ is the filter area, $$c$$ is the concentration of solids in the slurry, $$\mu$$ is the viscosity of the filtrate and $$\Delta P$$ is the overall pressure drop.

1. Filtration experiments were carried out at a constant pressure drop on a slurry containing 20 kg/m$$^3$$ of in water. The data obtained from the plots of $$t/V$$ vs. $$V$$ at two different pressure drops are given in the table below:

Pressure drop (N/m$$^2$$) Slope (s/litre$$^2$$) Intercept (s/litre)
$$5\times10^4$$ 12.5 26.5
$$35\times10^4$$ 3.5 6.9

If the filter area is 0.09 m$$^2$$ and the viscosity of the filtrate is 0.001 kg/m.s, determine the specific cake resistance and the filter medium resistance corresponding to each pressure drop.

2. Determine from the above data whether the cake is compressible.

[Index]