Question 30.1: A quartz mixture having the screen analysis shown in Table 3......
A quartz mixture having the screen analysis shown in Table 30.1 is screened through a standard 10-mesh screen. The cumulative screen analysis of overflow and underflow are given in Table 30.1. Calculate the mass ratios of the overflow and underflow to feed and the overall effectiveness of the screen.
| TABLE 30.1 Screen analyses for Example 30.1 |
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| Mesh | D_P,mm | Cumulative fraction smaller than D_p | ||
| Feed | Overflow | Underflow | ||
| 4 | 4.699 | 0 | 0 | |
| 6 | 3.327 | 0.025 | 0.071 | |
| 8 | 2.362 | 0.15 | 0.43 | 0 |
| 10 | 1.651 | 0.47 | 0.85 | 0.195 |
| 14 | 1.168 | 0.73 | 0.97 | 0.58 |
| 20 | 0.833 | 0.885 | 0.99 | 0.83 |
| 28 | 0.589 | 0.94 | 1.00 | 0.91 |
| 35 | 0.417 | 0.96 | 0.94 | |
| 65 | 0.208 | 0.98 | 0.975 | |
| Pan | 1.00 | 1.00 | ||
The cumulative analyses of feed, overflow, and product are plotted in Fig. 30.3. The cut-point diameter is the mesh size of the screen, which from Table 30.1 is 1.651 mm.
Also from Table 30.1, for this screen,
x_{F}=0.47\ \ \ \ \ x_{D}=0.85\ \ \ \ \ \ x_{B}=0.195
From Eq. (30.3), the ratio of overflow to feed is
{\frac{D}{F}}={\frac{x_{F}-x_{B}}{x_{D}-x_{B}}} (30.3)
{\frac{D}{F}}={\frac{0.47-0.195}{0.85-0.195}}=0.420
The ratio of underflow to feed is
{\frac{B}{F}}=1-{\frac{D}{F}}=1-0.42=0.58
The overall effectiveness, from Eq. (30.7), is
E={\frac{(x_{F}-x_{B})(x_{D}-x_{F})x_{D}(1-x_{B})}{(x_{D}-x_{B})^{2}(1-x_{F})x_{F}}} (30.7)
E={\frac{(0.47-0.195)(0.85-0.47)(1-0.195)(0.85)}{(0.85-0.195)^{2}(0.53)(0.47)}}=0.669