Size Reduction/FluidisationIf crushing rolls, 1 m in diameter, are set so that the crushing surfaces are 12.5 mm apart and the angle of nip is 31◦, what is the maximum size of particle which should be fed to the rolls? If the actual capacity of the machine is 12 per cent of the theoretical, calculate the throughput in kg/s when running at 2.0 Hz if the working face of the rolls is 0.4 m long and the bulk density of the feed is 2500 kg/m3. Power of 3 kW is supplied to a machine crushing material at the rate of 0.3 kg/s from 12.5 mm cubes to a product having the following sizes: 80 per cent 3.175 mm, 10 per cent 2.5 mm and 10 per cent 2.25 mm. What power should be supplied to this machine to crush 0.3 kg/s of the same material from 7.5 mm cube to 2.0 mm cube? The size distribution of a powder is measured by sedimentation in a vessel having the sampling point 180 mm below the liquid surface. If the viscosity of the liquid is 1.2 mNs/m2, and the densities of the powder and liquid are 2650 and 1000 kg/m3 respectively, determine the time which must elapse before any sample will exclude particles larger than 20 μm. If Stokes’ law applies when the Reynolds number is less than 0.2, what is the approximate maximum size of particle to which Stokes’ Law may be applied under these conditions? A column 0.6 m diameter and 4 m high is, packed with 25 mm ceramic Raschig rings and used in a gas absorption process carried out at 101.3 kN/m2 and 293 K. If the liquid and gas properties approximate to those of water and air respectively and their flowrates are 2.5 and 0.6 kg/m2s, what is the pressure drop across the column? In making calculations, Carman’s method should be used. By how much may the liquid flow rate be increased before the column floods? (b) the pressure gradient in the bed attributable to the presence of the particles. Calculate: (a) the density of the fluidised bed. The particles are 2 mm in diameter and have a density of 2500 kg/m3. The density and viscosity of water are 1000 kg/m3 and 1 mNs/m2 respectively. .Glass spheres are fluidised by water at a velocity equal to one half of their terminal falling velocities. It may be assumed that the cake is incompressible and that the cloth resistance is the same in the leaf as in the filter press.05 m2 filtering surface using a vacuum giving a pressure difference of 71. During the first 180 s the pressure difference for filtration is slowly raised to the final value of 400 kN/m2 and.4. What is the volume of filtrate collected per cycle and how much wash water is used? A sample of the slurry had previously been tested with a leaf filter of 0. The cakes are then washed with a pressure difference of 275 kN/m 2 for 600 s using thorough washing (See the plate and frame press in Section 7. during this period. filtration is carried out at constant pressure and the cakes are completely formed in a further 900 s. the rate of filtration is maintained constant. .3 kN/m2.Filtration A slurry is filtered in a plate and frame press containing 12 frames. After the initial period. The volume of filtrate collected in the first 300 s. was 250 cm3 and. each 0. after a further 300 s.4). an additional 150 cm3 was collected.3 m square and 25 mm thick. After a further 480 s the pressure was 600 m of liquid.0015 m2/s and the maximum head at zero flow 760 m of liquid.The relation between flow and head for a certain slurry pump may be represented approximately by a straight line.00015 m3/s through a leaf filter covered with a similar filter cloth but of one-tenth the area of the full-scale unit. Using this pump to feed a particular slurry to a pressure leaf filter: (a) How long will it take to produce 1 m3 of filtrate? (b) What will be the pressure across the filter after this time? A sample of the slurry was filtered at a constant rate of 0. . and after 625 s the pressure across the filter was 360 m of liquid. the maximum flow at zero head being 0. when the leaf was under an absolute pressure of 17 kN/m2. A laboratory test on a sample of the slurry using a leaf filter of area 200 cm2 and covered with a similar cloth to that on the drum produced 300 cm3 of filtrate in the first 60 s and 140 cm3 in the next 60 s. The bulk density of the dry cake was 1500 kg/m3 and the density of the filtrate was 1000 kg/m3.A slurry containing 40 per cent by mass solid is to be filtered on a rotary drum filter 2 m diameter and 2 m long which normally operates with 40 per cent of its surface immersed in the slurry and under a pressure of 17 kN/m 2. The minimum thickness of cake which could be readily removed from the cloth was 5 mm. At what speed should the drum rotate for maximum throughput and what is this throughout in terms of the mass of the slurry fed to the unit per unit time? . what is the optimum filtration time for minimum cost? . Estimate the optimum filtration time for maximum throughput. operating with a pressure difference of 70 kN/m2. In a test with a small leaf filter 0.2 m2 is operated with a pressure drop of 413 kN/m2 and with a downtime of 21. If the operating cost during filtration is £10/ks and the cost of a shutdown is £100.6 ks (6 h).A plate and frame press with a filtration area of 2.00025 m3 of filtrate was obtained in 300 s and a total of 0.05 m2 in area. 0.00040 m3 in 600 s. 3 m square. what is the minimum number of frames that needs to be used and what is the thickness of each? It may be assumed that the cakes are incompressible and that the resistance of the filter medium may be neglected. in addition.6 m long and 0. . The press takes 120 s to dismantle and 120 s to reassemble and. If filtration is to be carried out at the same overall rate as before.125 kg/s and the cake has a voidage of 0. If filtrate is produced at the rate of 0. is fed to a rotary drum filter 0.6 m diameter. what thickness of cake is produced when filtering with a pressure difference of 65 kN/m2? The density of the solids is 3000 kg/m3.5. containing 0. The rotary filter breaks down and the operation has to be carried out temporarily in a plate and frame press with frames 0. The drum rotates at one revolution in 360 s and 20 per cent of the filtering surface is in contact with the slurry at any instant. 120 s is required to remove the cake from each frame. with an operating pressure difference of 175 kN/m 2.A slurry.2 kg of solid per kilogram of water. For the first 600 s the slurry pump runs at maximum capacity. It is found that if the cloths are precoated with filter aid to a depth of 1.6 mm. What will be the increase in the overall throughput of the press if the precoat can be applied in 180 s? . the cloth resistance is reduced to 25 per cent of its former value. During this period the pressure rises to 415 kN/m2 and 25 per cent of the total filtrate is obtained. The filtration takes a further 3600 s to complete at constant pressure and 900 s is required for emptying and resetting the press.A sludge is filtered in a plate and frame press fitted with 25 mm frames. .3 m3 in 3600 s when filtration was stopped. Estimate the washing time if 3 m3 of wash water is used.A plate and frame press gave a total of 8 m3 of filtrate in 1800 s and 11. The resistance of the cloth may be neglected and a constant pressure is used throughout. In the filtration of a sludge. determine (a) the total filtration time and (b) the filtration cycle with the existing pump for a maximum daily capacity. Neglecting the resistance of the filter medium. until the pressure differences reaches 400 kN/m2. . if the time for removing the cake and reassembling the press is 1200 s. The constant rate operation requires 900 s and one-third of the total filtrate is obtained during this period. The cake is not washed. the initial period is effected at a constant rate with the feed pump at full capacity. The pressure is then maintained at this value for a remainder of the filtration. 2 m in diameter. with 20 frames 0. The filtration in the rotary filter is carried out at a constant pressure difference of 70 kN/m2. in place of the filter press.5 m long and 2. the pressure is raised to 350 kN/m2. The total volume of filtrate per cycle is 0. 1. calculate the speed of rotation of the drum which will result in the same overall rate of filtration as was obtained with the filter press. after which the frames are full. It is decided to use a rotary drum filter.Filtration is carried out in a plate and frame filter press. During this period. and one-quarter of the total filtrate per cycle is obtained. and the filter operates with 25 per cent of the drum submerged in the slurry at any instant.7 m3 and dismantling and refitting of the press takes 500 s. Assuming that the resistance of the cloth is the same in the two plants and that the filter cake is incompressible. At the end of the constant rate period. . and the rate of filtration is maintained constant for the first 300 s. filtration is continued at a constant pressure of 350 kN/m2 for a further 1800 s.3 m square and 50 mm thick. Using this pump to feed a slurry to a pressure leaf filter. the maximum flow at zero head being 0.The relation between flow and head for a slurry pump may be represented approximately by a straight line.0015 m3/s and the maximum head at zero flow 760 m of liquid. .00015 m3/s through a leaf filter covered with a similar filter cloth but of one-tenth the area of the full scale unit and after 625 s the pressure drop across the filter was 360 m of liquid. and (b) what will be the pressure drop across the filter after this time? A sample of the slurry was filtered at a constant rate of 0. (a) how long will it take to produce 1 m3 of filtrate. After a further 480 s the pressure drop was 600 m of liquid. 002 m3/s of filtrate. What are suitable dimensions and operating conditions for the rotary filter.A continuous rotary filter is required for an industrial process for the filtration of a suspension to produce 0. at which time the cake thickness had reached 38 mm. and that the vacuum system is capable of maintaining a constant pressure difference of 70 kN/m2 across the filter? .023 m2 to which it was fed by means of a slurry pump to give filtrate at a constant rate of 0. assuming that the resistance of the cloth used is one-half that on the test filter. A sample was tested on a small laboratory filter of area 0.0125 m3/s. The pressure difference across the test filter increased from 14 kN/m2 after 300 s filtration to 28 kN/m2 after 900 s. 2 m long.0 kg/s of slurry containing 10 per cent of solids when rotated at 0. 1. handles 6. and what is the theoretical maximum quantity of slurry which can be handled? .005 Hz. By increasing the speed to 0.008 Hz it is found that it can then handle 7.2 m diameter and 1.2 kg/s. What will be the percentage change in the amount of wash water which may be applied to each kilogram of cake caused by the increased speed of rotation of the drum.A rotary drum filter. 0083 Hz. if the filter cake is incompressible and the filter cloth has a resistance equal to that of 1 mm of cake. the viscosity of filtrate = 10−3 N s/m2 and the slurry concentration = 20 per cent by mass solids. the specific resistance of cake = 2 × 1012 m−2 the density of solids = 2000 kg/m3. . If the thinnest cake that can be removed from the drum has a thickness of 5 mm. Calculate the rate of production of filtrate and the thickness of cake when it rotates at 0. the density of filtrate = 1000 kg/m3. It is desired to increase the rate of filtration by raising the speed of rotation of the drum.3 kN/m2 below atmospheric and with 30 per cent of its surface submerged in the slurry.A rotary drum with a filter area of 3 m3 operates with an internal pressure of 71. what is the maximum rate of filtration which can be achieved and what speed of rotation of the drum is required? The voidage of the cake = 0.4. produced 220 cm3 of filtrate in the first minute and 120 cm3 of filtrate in the next minute when the leaf was under a vacuum of 550 mm Hg. The bulk density of the wet cake was 1600 kg/m3 and the density of the filtrate was 1000 kg/m3. On the assumption that the cake is incompressible and that 5 mm of cake is left behind on the drum.A slurry containing 50 per cent by mass of solids of density 2600 kg/m 3 is to be filtered on a rotary drum filter. using a leaf filter with an area of 100 cm2 and covered with a cloth similar to that used on the drum. What drum speed will give a filtration rate of 80 per cent of the maximum? .25 m in diameter and 2. determine the theoretical maximum flowrate of filtrate obtainable.5 m long. A laboratory test on a sample of the slurry. which operates with 35 per cent of its surface immersed in the slurry and under a vacuum of 600 mm Hg. 2. what rotational speed is required? If the filter is now operated again at its original speed of 0.0167 Hz (1 rpm). by further treatment. by what factor will the filtration rate be increased? .033 Hz. its effective resistance is halved and the required filtration rate is now achieved at a rotational speed of 0. By suitable treatment of the filter cloth with a filter aid. If.033 Hz.A rotary filter which operates at a fixed vacuum gives a desired rate of filtration of a slurry when rotating at 0. it is possible to reduce the effective cloth resistance to a quarter of the original value. fitted with two 50 mm thick frames each 150 mm square. 300 mm diameter and 200 mm deep? The radius of the inner surface of the slurry is maintained constant at 75 mm and the speed of rotation is 65 Hz (3900 rpm). . It may be assumed that the filter cake is incompressible. and that the liquid in the slurry has the same density as water. How long will it take to produce the same volume of filtrate as is obtained from a single cycle when using a centrifuge with a perforated basket. that the resistance of the cloth is equivalent to 3 mm of cake in both cases.Centrifugation When an aqueous slurry is filtered in a plate and frame press. the frames are filled in 3600 s (1 h). operating with a pressure difference of 350 kN/m2. 6 MN/m2. .A centrifuge with a phosphor bronze basket. 380 mm in diameter. is to be run at 67 Hz with a 75 mm layer of liquid of density 1200 kg/m3 in the basket. What thickness of walls are required in the basket? The density of phosphor bronze is 8900 kg/m3 and the maximum safe stress for phosphor bronze is 87.