Solution Fpn
Assuming the galena and quartz particles are of similar shapes, then from equation 1.42, the required density of fluid when Stokes' law applies is given by:
The required density of fluid when Newton's law applies is given by:
Thus, the required density of the fluid is between 1196 and 2377 kg/m3.
1.5.2. Gravity settling The settling tank
Material is introduced in suspension into a tank containing a relatively large volume of water moving at a low velocity, as shown in Figure 1.25. The particles soon enter the slowly moving water and, because the small particles settle at a lower rate, they are carried further forward before they reach the bottom of the tank. The very fine particles are carried away in the liquid overflow. Receptacles at various distances from the inlet collect different grades of particles according to their terminal falling velocities, with the particles of high terminal falling velocity collecting near the inlet. The positions at which the particles are collected may be calculated on the assumption that they rapidly reach their terminal falling velocities, and attain the same horizontal velocity as the fluid.
- Figure 1.25. Gravity settling tank
If the material is introduced in solid form down a chute, the position at which the particles are deposited will be determined by the rate at which they lose the horizontal component of their velocities. The larger particles will therefore be carried further forward and the smaller particles will be deposited near the inlet. The position at which the particles are deposited may be calculated using the relations given in Chapter 3.
The elutriator
Material may be separated by means of an elutriator, which consists of a vertical tube up which fluid is passed at a controlled velocity. The particles are introduced, often through a side tube, and the smaller particles are carried over in the fluid stream while the large particles settle against the upward current. Further size fractions may be collected if the overflow from the first tube is passed vertically upwards through a second tube of greater cross-section, and any number of such tubes can be arranged in series.
The Spitzkasten
This plant consists of a series of vessels of conical shape arranged in series. A suspension of the material is fed into the top of the first vessel and the larger particles settle, while the smaller ones are carried over in the liquid overflow and enter the top of a second conical vessel of greater cross-sectional area. The bases of the vessels are fitted with wide diameter outlets, and a stream of water can be introduced near the outlet so that the particles have to settle against a slowly rising stream of liquid. The size of the smallest particle which is collected in each of the vessels is influenced by the upward velocity at the bottom outlet of each of the vessels. The size of each successive vessel is increased, partly because the amount of liquid to be handled includes all the water used for classifying in the previous vessels, and partly because it is desired to reduce, in stages, the surface velocity of the fluid flowing from one vessel to the next. The Spitzkasten thus combines the principles used in the settling tank and in the elutriator.
The size of the material collected in each of the units is determined by the rate of feeding of suspension, the upward velocity of the liquid in the vessel and the diameter of the vessel. The equipment can also be used for separating a mixture of materials into its constituents, provided that the size range is not large. The individual units can be made of wood or sheet metal.
The Hydrosizer, illustrated in Figure 1.26, works on the same principle although it has a number of compartments trapezoidal in section. It is suitable for use with materials finer
- Figure 1.26. Hydrosizer
than about 4-mesh (ca. 5 mm) and it works at high concentrations in order to obtain the advantages of hindered settling. Altogether eight sharply classified fractions are produced, ranging from coarse nearest to the feed inlet to fine from the eighth compartment, at feed rates in the range 2-15 kg/s.
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