Separation Process Principles- 2n - Seader & Henley - Solutions Manual

Assumptions attainment of equilibrium solids have an

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Unformatted text preview: are obtained from Table 17.4. Exercise 17.5 (continued) Differential Analysis Average Particle Size, mm Dp Mass Fraction, xi 2.855 2.030 1.440 1.015 0.725 0.513 0.363 0.256 0.181 0.128 0.098 0.077 0.0120 0.0290 0.1880 0.2879 0.2200 0.1110 0.0600 0.0390 0.0180 0.0131 0.0120 0.0101 1.0000 x/Dp x/Dp^2 x/Dp^3 0.0042 0.0143 0.1306 0.2836 0.3034 0.2166 0.1655 0.1525 0.0992 0.1020 0.1222 0.1316 Sums Surface-mean diameter = D S = Mass-mean diameter = xDp 0.0342 0.0588 0.2708 0.2922 0.1595 0.0569 0.0218 0.0100 0.0033 0.0017 0.0012 0.0008 0.0015 0.0070 0.0907 0.2794 0.4185 0.4227 0.4566 0.5958 0.5482 0.7972 1.2466 1.7204 0.0005 0.0035 0.0630 0.2753 0.5773 0.8247 1.2596 2.3274 3.0287 6.2281 12.7209 22.4885 1.7258 0.9110 6.5847 49.7974 1 = 0.579 mm 1.7258 DW = 0.911 mm Arithmetic-mean diameter = D N = Volume-mean diameter = DV = 6.5847 = 0.132 mm 49.7974 1 = 0.272 mm 49.79741/ 3 Exercise 17.6 Subject: Particle size analysis from data in terms of numbers of particles of each size range Given: Table of particle-size distribution for perfect spheres of silica of size from 1 to almost 100 microns. Find: (a) Differential and cumulative plots (b): (1) Surface mean diameter (same as surface-mean diameter) (2) Arithmetic-mean diameter (3) Mass-mean diameter (4) Volume-mean diameter Analysis: Use a spreadsheet to do the calculations and prepare the plots. The equations for Part (b) are as follows by calculations using the spreadsheet values on the next page for the sums: (1) Surface mean diameter from solution to Exercise 17.4: n DS = 3 i =1 n i =1 N i D pi = 2 N i D pi 5, 680,872 = 25.6 microns 222, 058 (2) Arithmetic-mean diameter from (17-9): n DN = i =1 N i D pi n i =1 Ni = 12, 256 = 12.2 microns 1, 000 (3) Mass-mean diameter from solution to Exercise 17.4: n DW = i =1 n i =1 4 N i D pi 3 = N i D pi 190, 270, 428 = 33.5 microns 5, 680,872 (4) Volume-mean diameter for (17-14): n DV = i =1 Ni D n i =1 Ni 3 pi 1/ 3 5, 680,872 = 1, 000 1/ 3 = 17.8 microns Exercise 17.6 (continued) Exercise 17.6 Differential and Cumulative Undersize Screen Analyses Cumulative Undersize Analysis Differential Analysis Average Particle size, microns No. of Particles, Ni NDp NDp^2 NDp^3 NDp^4 1.2 1.7 2.4 3.4 4.8 6.8 10.0 14.0 19.0 26.0 36.0 51.0 67.0 2 5 14 60 100 190 250 160 110 70 28 10 1 2.4 8.5 33.6 204.0 480.0 1292.0 2500.0 2240.0 2090.0 1820.0 1008.0 510.0 67.0 2.9 14.5 80.6 693.6 2304.0 8785.6 25000.0 31360.0 39710.0 47320.0 36288.0 26010.0 4489.0 3.5 24.6 193.5 2358.2 11059.2 59742.1 250000.0 439040.0 754490.0 1230320.0 1306368.0 1326510.0 300763.0 4.1 41.8 464.5 8018.0 53084.2 406246.1 2500000.0 6146560.0 14335310.0 31988320.0 47029248.0 67652010.0 20151121.0 Sums: 1000 12256 222058 5680872 Cumulative Oversize Analysis Average Size, Dp microns Cumulative number Undersize Cumulative number Oversize 1.2 1.7 2.4 3.4 4.8 6.8 10.0 14.0 19.0 26.0 36.0 51.0 67.0 998 993 979 919 819 629 379 219 109 39 11 1 0 2 7 21 81 181 371 621 781 891 961 989 999 1000 190270428 Differential and cumulative plots of the a...
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This document was uploaded on 02/24/2014 for the course CBE 2124 at NYU Poly.

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