2. Flow forces in fluids give rise to velocities of particles relative to the fluid of:
vm = D2a(rp - rf)/18m
Where the particle is falling under gravity a = g, so giving Stokes' Law
vm = D2g(rp - rf)/18m
3. Continuous thickeners can be used to settle out solids, and the minimum area of a continuous thickener can be calculated from:
vm = (F - L)(dw/dt)/Ar
4. Gravitational and centrifugal forces can be combined in a cyclone separator.
5. In a centrifuge separating liquids and particles , the centrifugal force relative to the force of gravity is given by (0.011rN2)/g , and the steady state velocity vm , by D2N2r(rp - rf)/1640m
6. In centrifugal separation of liquids, the radius of the neutral zone is Ö[(rAr12 - rBr22) / (rA - rB)]
7. In a filter, the particles are retained and the fluid passes at a rate given by:
dV/dt = ADP/mr[w(V/A) + L]
8. Sieve analysis can be
used to estimate particle size distributions. In cumulative sieve analysis,
2. In the filter system of Problem 1, if the viscosity of the wine was 1.8 x 10-3 N s m-2, calculate the value of the specific cake resistance if the equivalent thickness of the filter cloth for the system is 1 mm with the pressure of 350 kPa in the test if the slurry concentration is 4 kg solid in 100 kg of water.
3. If in the system of Problem 1, the plant-scale operations produce a throughput in 1 hour of 2800 kg estimate the compressibility of the filter cake.
4. Calculate the settling velocity of sand particles 0.2 mm diameter in 22% salt solution of density 1240 kg m-3 at 20°C. Take the density of sand as 2010 kg m-3.
5. In a trough, 0.8 m long, there is a slowly (0.01 m s-1) flowing 22% salt solution. If it was desired to settle out sand particles, with which the solution had become contaminated, estimate the smallest diameter of sand particle that would be removed.
6. It is desired to establish a centrifugal force of 6000 g in a small centrifuge with an effective working radius of 9 cm. At what speed would the centrifuge have to rotate?
If the actual centrifuge bowl has a radius of 8 cm minimum and 9 cm maximum what is the difference in the centrifugal force between the minimum and the maximum radii?
7. In a centrifuge separating oil (of density 900 kg m-3) from brine (of density 1070 kg m-3), the discharge radius for the oil is 5 cm. Calculate a suitable radius for the brine discharge and for the feed intake so that the machine will work smoothly assuming that the volumes of oil and of brine are approximately equal.
8. If a centrifuge is regarded as similar to a gravity settler but with gravity replaced by the centrifugal field, calculate the area of a centrifuge of effective working radius r and speed of rotation N revolutions min -1 that would have the same throughput as a gravity settling tank of area 100 m2.
9. If an olive-oil/water emulsion of 50 mm droplets is to be separated in a centrifuge, from the water, what speed would be necessary if the effective working radius of the centrifuge is 5 cm? Assume that the necessary travel of the droplets is 3 cm and this must be done in 1 second to cope with the throughput in a continuous centrifuge.
10. A sieve analysis gives the following results:
Plot a cumulative size analysis and a size-distribution analysis, and estimate the weights, per 1000 kg of powder, which would lie in the size ranges 0.150 to 0.200 mm and 0.250 to 0.350 mm.
11. If a dust, whose particle size distribution is as in the table below, is passed through a cyclone with collection efficiency as shown in Fig. 10.2 estimate the size distribution of the dust passing out.