Reduced cut size

A chart showing the reduced grade efficiency versus cell size starts in the origin, and the cell size corresponding to 50% reduced grade efficiency is known as the reduced cut size dso (Figure 11.6). 

Reduced grade efficiency curve and reduced cut size (c/50). 

If, in order to practically assess the performance of solid-fluid separators, a reduced grade efficiency curve is used, the particle size which gives 50% efficiency in such a curve is called the reduced cut size and is represented by x o-The maximum attainable efficiency related to particle size would be that minimum particle size with 100% probability of being reported to the underflow. Graphically, by extrapolating the end part of the curve to the horizontal axis, such size will be obtained. It has been proved that in practice, the maximum of the efficiency is around 98%, and the minimum size corresponding to this efficiency is represented by Xgg and known as the approximate limit of separation. 

A hydrocyclone, 44 mm in diameter, is used to separate a suspension of limestone in water. The density of the limestone is 2885 kg/m and the gravimetric separation efficiency was 28.34% while the partition coefficient was determined as 11.62%. Derive a grade efficiency curve to find out the reduced cut size, from the data given in Table 10.2. 

Finally, taking the reading from the above graph in the 50% point of the C (x) axis an approximate reduced cut size X50 = 40 pm is obtained. 

Stokes number including the reduced cut size Stokes number for power-law fluids... 

Stokes number for power-law fluids including the reduced cut size Temperature (0), tensile stress (M/LF), conveyor capacity (M/T)... 

This section describes a new and simple experimental method for obtaining the reduced cut size and the rest of the reduced grade efficiency curve of an operating separator. The method relies on feeding a known and fiiUy characterized slurry to the separator under test, and on measuring only two solids concentrations (in the feed and in the overflow), one static pressure differential (or some other flow rate-dependent variable) and the slurry temperature. These measurements are best done and logged by a personal computer, and, for hydrocyclones, have to be repeated at two different pressure settings. 

The selection chart in Figure 6.14 is very simple to use a hydrocyclone is selected on the basis of the required capacity and available pressure drop. If the reduced cut size is too high then the flow rate is divided by 2, 3,4 etc., and the procedure repeated with the lower value of Q until the cyclones (to be used in parallel) become small enough to give the required value of reduced cut size. The chart shows that reduced cut sizes down to almost 2 pm should be possible with 10 mm hydrocyclones. This has recently been confirmed in another investigation, but the units had to be run at high underflow dilutions. 

Geometric standard deviation of the reduced grade efficiency curve of the cyclone Performance criteria Total coarse recovery by mass, r Total reduced mass recovery, r Actual cut size, xso Reduced cut size,... 

The size corresponding to 50% on the reduced grade efficiency curve G (x) is referred to as the "reduced cut size" - see Fig.l. Most mathematical descriptions of the performance of hydrocyclones or sedimenting centrifuges are in terms of the reduced cut size. 

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