Calculate the arithmetic and volume mean diameter DN for the -4 to +200 mesh fractions of the material (quartz) analysed in Table below. Take a = 2, s = 0.571 and density = 2650 kg/m3 for crushed quartz particles. Mesh Screen opening Dpi mm Average particle diameter in increment Dpi , mm Mass fraction retained xi Cumulative fraction smaller than Dpi 4 4.699 6 3.327 8 2.362 10 1.651 14 1.168 20 0.833 28 0.589 35 0.417 48 0.295 65 0.208 100 0.147 150 0.104 200 0.074 Pan -------- ---- 0.000 4.013 0.0251 2.845 0.1250 2.007 0.3207 1.409 0.2570 1.001 0.1590 0.711 0.0538 0.503 0.0210 0.356 0.0102 0.252 0.0077 0.178 0.0058 0.126 0.0041 0.089 0.0031 0.037 0.0075 1.000 0.9749 0.8499 0.5292 0.2722 0.1132 0.0594 0.0384 0.0282 0.0205 0.0147 0.0106 0.0075 0.0000