6 pages project ( determine the salt concentrations using a 2nd order or higher Runge-Kutta method in Excel VBA)
>Salt Concentration Data
(g/L)
(g/L)
0 0 5 8
. 3
0 0 5
1
. 3
9
4 79
7 8.0 7
. 2
7 7
8.9 8
7 6 1 9
9 8 8 8 . 89
4
7
.6 3
872
9
128
12
014
7 467
.3987
0 .54 761
7
31
328
1
195
2 467
8
3 .2428
391
2
.05 713
042
783
979
9
427
2
86
013
302
1.7833
125
7 5 87
414
087
032
929
425
438
.3047
. 04
074
7
334
438
047
.5732
277
823
863
8 21
.3716
2
826
3
552
3 489
953
43
891
818
68
1 643
879
2
883
381
225
834
016
762
796
155
881
064
511
977
8 517
904
817
004
585
811
348
67
566
652
373
567
363
53
56
365
566
308
253
325
326
867
96
37
8
157
355
495
851
513
793
195
642
616
873
04
887
996
052
689
472
948
8
19
267
514
979
346
683
324
423
65
193
24
475
674
478
046
621
143
626
172
515
113
488
847
47
973
286
5
703
786
559
4
319
308
99
21
81
386
954
997
479
472
027
085
231
787
632
756
955
439
976
149
083
451
752
55
921
025
09
536
093
27
921
575
54
095
838
591
59
198
287
336
948
331
815
387
156
231
843
215
953
502
864
665
593
825
862
624
252
005
965
219
034
291
442
768
725
165
788
265
781
028
484
362
103
594
778
293
927
993
863
281
611
646
585
124
536
945
155
733
198
543
939
076
67
223
358
885
824
294
514
337
238
173
399
127
972
569
348
16
646
671
774
1
298
745
112
143
089
063
099
725
554
638
669
164
71
902
67
273
563
773
009
43
681
073
376
384
869
544
966
832
153
662
875
765
746
777
444
992
382
98
973
.5959
573
248
721
512
934
868
711
458
301
683
222
764
285
188
534
142
76
827
561
52
326
706
243
912
75
921
01
611
072
52
865
959
078
66
289
499
415
968
421
401
906
154
646
99
487
31
788
667
726
775
102
043
809
974
205
524
61
389
38
302
632
839
858
102
791
627
7
694
97
082
315
465
852
545
249
216
476
343
206
241
229
286
653
941
073
876
175
757
432
512
864
721
527
878
876
829
41
985
941
735
251
062
312
362
757
032
136
399
516
257
663
909
251
447
675
722
999
541
044
684
449
672
574
532
831
053
348
749
78
147
58
26
019
469
678
065
9
405
847
921
382
9
984
472
163
687
082
746
459
653
992
944
671
244
347
98
362
808
902
535
681
702
553
22
246
246
641
932
322
346
997
846
779
804
579
372
747
996
96
032
94
303
533
704
58
181
078
299
811
4
471
836
6
412
223
773
095
43
113
507
942
65
681
16
869
113
856
751
299
963
355
949
519
142
109
45
75
139
237
018
378
357
562
91
788
105
69.3578 687
8
629
3
591
012
275
932
158
619
02
416
897
094
612
972
9
471
425
401
205
426
809
4
208
309
2
941
284
387
963
415
8.0566 51.8471 9.884 4.5293 2.8 4.8199 3
3.787 1
43
6
2.678 2.2081 1.729 1.778 1.91 1.6444 1.3844 1.435 1.17 0.9195 3
8
0.921 0.7845 0.8707 0.8694 0.719 64
8.9928 8.9095 0.735 11.2473 0.63 10.93 6
2
0.5267 0.558 0.4516 0.5187 0.41 6.54 7
0.3348 0.3741 0.327 0.3548 0.2979 0.3329 0.291 0.2796 0.3287 0.2652 0.266 6.487 0.2445 0.2364 5.8714 0.2207 Cs1 0 0.1 0.2 0.30000000000000004 0.4 0.5 0.6 0.7 0.79999999999999993 0.89999999999999991 0.99999999999999989 1.0999999999999999 1.2 1.3 1.4000000000000001 1.5000000000000002 1.6000000000000003 1.7000000000000004 1.8000000000000005 1.9000000000000006 2.0000000000000004 2.1000000000000005 2.2000000000000006 2.3000000000000007 2.4000000000000008 2.5000000000000009 2.600000000000001 2.7000000000000011 2.8000000000000012 2.9000000000000012 3.0000000000000013 3.1000000000000014 3.2000000000000015 3.3000000000000016 3.4000000000000017 3.5000000000000018 3.6000000000000019 3.700000000000002 3.800000000000002 3.9000000000000021 4.0000000000000018 4.1000000000000014 4.2000000000000011 4.3000000000000007 4.4000000000000004 4.5 4.5999999999999996 4.6999999999999993 4.7999999999999989 4.8999999999999986 4.9999999999999982 5.0999999999999979 5.1999999999999975 5.2999999999999972 5.3999999999999968 5.4999999999999964 5.5999999999999961 5.6999999999999957 5.7999999999999954 5.899999999999995 5.9999999999999947 6.0999999999999943 6.199999999999994 6.2999999999999936 6.3999999999999932 6.4999999999999929 6.5999999999999925 6.6999999999999922 6.7999999999999918 6.8999999999999915 6.9999999999999911 7.0999999999999908 7.1999999999999904 7.2999999999999901 7.3999999999999897 7.4999999999999893 7.599999999999989 7.6999999999999886 7.7999999999999883 7.8999999999999879 7.9999999999999876 8.0999999999999872 8.1999999999999869 8.2999999999999865 8.3999999999999861 8.4999999999999858 8.5999999999999854 8.6999999999999851 8.7999999999999847 8.8999999999999844 8.999999999999984 9.0999999999999837 9.1999999999999833 9.2999999999999829 9.3999999999999826 9.4999999999999822 9.5999999999999819 9.6999999999999815 9.7999999999999812 9.8999999999999808 9.9999999999999805 10.09999999999998 10.19999999999998 10.299999999999979 10.399999999999979 10.499999999999979 10.599999999999978 10.699999999999978 10.799999999999978 10.899999999999977 10.999999999999977 11.099999999999977 11.199999999999976 11.299999999999976 11.399999999999975 11.499999999999975 11.599999999999975 11.699999999999974 11.799999999999974 11.899999999999974 11.999999999999973 12.099999999999973 12.199999999999973 12.299999999999972 12.399999999999972 12.499999999999972 12.599999999999971 12.699999999999971 12.799999999999971 12.89999999999997 12.99999999999997 13.099999999999969 13.199999999999969 13.299999999999969 13.399999999999968 13.499999999999968 13.599999999999968 13.699999999999967 13.799999999999967 13.899999999999967 13.999999999999966 14.099999999999966 14.199999999999966 14.299999999999965 14.399999999999965 14.499999999999964 14.599999999999964 14.699999999999964 14.799999999999963 14.899999999999963 14.999999999999963 15.099999999999962 15.199999999999962 15.299999999999962 15.399999999999961 15.499999999999961 15.599999999999961 15.69999999999996 15.79999999999996 15.899999999999959 15.999999999999959 16.099999999999959 16.19999999999996 16.299999999999962 16.399999999999963 16.499999999999964 16.599999999999966 16.699999999999967 16.799999999999969 16.89999999999997 16.999999999999972 17.099999999999973 17.199999999999974 17.299999999999976 17.399999999999977 17.499999999999979 17.59999999999998 17.699999999999982 17.799999999999983 17.899999999999984 17.999999999999986 18.099999999999987 18.199999999999989 18.29999999999999 18.399999999999991 18.499999999999993 18.599999999999994 18.699999999999996 18.799999999999997 18.899999999999999 19 19.100000000000001 19.200000000000003 19.300000000000004 19.400000000000006 19.500000000000007 19.600000000000009 19.70000000000001 19.800000000000011 19.900000000000013 20.000000000000014 20.100000000000016 20.200000000000017 20.300000000000018 20.40000000000002 20.500000000000021 20.600000000000023 20.700000000000024 20.800000000000026 20.900000000000027 21.000000000000028 21.10000000000003 21.200000000000031 21.300000000000033 21.400000000000034 21.500000000000036 21.600000000000037 21.700000000000038 21.80000000000004 21.900000000000041 22.000000000000043 22.100000000000044 22.200000000000045 22.300000000000047 22.400000000000048 22.50000000000005 22.600000000000051 22.700000000000053 22.800000000000054 22.900000000000055 23.000000000000057 23.100000000000058 23.20000000000006 23.300000000000061 23.400000000000063 23.500000000000064 23.600000000000065 23.700000000000067 23.800000000000068 23.90000000000007 24.000000000000071 24.100000000000072 24.200000000000074 24.300000000000075 24.400000000000077 24.500000000000078 24.60000000000008 24.700000000000081 24.800000000000082 24.900000000000084 25.000000000000085 25.100000000000087 25.200000000000088 25.30000000000009 25.400000000000091 25.500000000000092 25.600000000000094 25.700000000000095 25.800000000000097 25.900000000000098 26.000000000000099 26.100000000000101 26.200000000000102 26.300000000000104 26.400000000000105 26.500000000000107 26.600000000000108 26.700000000000109 26.800000000000111 26.900000000000112 27.000000000000114 27.100000000000115 27.200000000000117 27.300000000000118 27.400000000000119 27.500000000000121 27.600000000000122 27.700000000000124 27.800000000000125 27.900000000000126 28.000000000000128 28.100000000000129 28.200000000000131 28.300000000000132 28.400000000000134 28.500000000000135 28.600000000000136 28.700000000000138 28.800000000000139 28.900000000000141 29.000000000000142 29.100000000000144 29.200000000000145 29.300000000000146 29.400000000000148 29.500000000000149 29.600000000000151 29.700000000000152 29.800000000000153 29.900000000000155 30.000000000000156 30.100000000000158 30.200000000000159 30.300000000000161 30.400000000000162 30.500000000000163 30.600000000000165 30.700000000000166 30.800000000000168 30.900000000000169 31.000000000000171 31.100000000000172 31.200000000000173 31.300000000000175 31.400000000000176 31.500000000000178 31.600000000000179 31.70000000000018 31.800000000000182 31.900000000000183 32.000000000000185 32.100000000000186 32.200000000000188 32.300000000000189 32.40000000000019 32.500000000000192 32.600000000000193 32.700000000000195 32.800000000000196 32.900000000000198 33.000000000000199 33.1000000000002 33.200000000000202 33.300000000000203 33.400000000000205 33.500000000000206 33.600000000000207 33.700000000000209 33.80000000000021 33.900000000000212 34.000000000000213 34.100000000000215 34.200000000000216 34.300000000000217 34.400000000000219 34.50000000000022 34.600000000000222 34.700000000000223 34.800000000000225 34.900000000000226 35.000000000000227 35.100000000000229 35.20000000000023 35.300000000000232 35.400000000000233 35.500000000000234 35.600000000000236 35.700000000000237 35.800000000000239 35.90000000000024 36.000000000000242 36.100000000000243 36.200000000000244 36.300000000000246 36.400000000000247 36.500000000000249 36.60000000000025 36.700000000000252 36.800000000000253 36.900000000000254 37.000000000000256 37.100000000000257 37.200000000000259 37.30000000000026 37.400000000000261 37.500000000000263 37.600000000000264 37.700000000000266 37.800000000000267 37.900000000000269 38.00000000000027 38.100000000000271 38.200000000000273 38.300000000000274 38.400000000000276 38.500000000000277 38.600000000000279 38.70000000000028 38.800000000000281 38.900000000000283 39.000000000000284 39.100000000000286 39.200000000000287 39.300000000000288 39.40000000000029 39.500000000000291 39.600000000000293 39.700000000000294 39.800000000000296 39.900000000000297 40.000000000000298 40.1000000000003 40.200000000000301 40.300000000000303 40.400000000000304 40.500000000000306 40.600000000000307 40.700000000000308 40.80000000000031 40.900000000000311 41.000000000000313 41.100000000000314 41.200000000000315 41.300000000000317 41.400000000000318 41.50000000000032 41.600000000000321 41.700000000000323 41.800000000000324 41.900000000000325 42.000000000000327 42.100000000000328 42.20000000000033 42.300000000000331 42.400000000000333 42.500000000000334 42.600000000000335 42.700000000000337 42.800000000000338 42.90000000000034 43.000000000000341 43.100000000000342 43.200000000000344 43.300000000000345 43.400000000000347 43.500000000000348 43.60000000000035 43.700000000000351 43.800000000000352 43.900000000000354 44.000000000000355 44.100000000000357 44.200000000000358 44.30000000000036 44.400000000000361 44.500000000000362 44.600000000000364 44.700000000000365 44.800000000000367 44.900000000000368 45.000000000000369 45.100000000000371 45.200000000000372 45.300000000000374 45.400000000000375 45.500000000000377 45.600000000000378 45.700000000000379 45.800000000000381 45.900000000000382 46.000000000000384 46.100000000000385 46.200000000000387 46.300000000000388 46.400000000000389 46.500000000000391 46.600000000000392 46.700000000000394 46.800000000000395 46.900000000000396 47.000000000000398 47.100000000000399 47.200000000000401 47.300000000000402 47.400000000000404 47.500000000000405 47.600000000000406 47.700000000000408 47.800000000000409 47.900000000000411 48.000000000000412 48.100000000000414 48.200000000000415 48.300000000000416 48.400000000000418 48.500000000000419 48.600000000000421 48.700000000000422 48.800000000000423 48.900000000000425 49.000000000000426 49.100000000000428 49.200000000000429 49.300000000000431 49.400000000000432 49.500000000000433 49.600000000000435 49.700000000000436 49.800000000000438 49.900000000000439 50.000000000000441 50.100000000000442 50.200000000000443 50.300000000000445 50.400000000000446 50.500000000000448 50.600000000000449 50.70000000000045 50.800000000000452 50.900000000000453 51.000000000000455 51.100000000000456 51.200000000000458 51.300000000000459 51.40000000000046 51.500000000000462 51.600000000000463 51.700000000000465 51.800000000000466 51.900000000000468 52.000000000000469 52.10000000000047 52.200000000000472 52.300000000000473 52.400000000000475 52.500000000000476 52.600000000000477 52.700000000000479 52.80000000000048 52.900000000000482 53.000000000000483 53.100000000000485 53.200000000000486 53.300000000000487 53.400000000000489 53.50000000000049 53.600000000000492 53.700000000000493 53.800000000000495 53.900000000000496 54.000000000000497 54.100000000000499 54.2000000000005 54.300000000000502 54.400000000000503 54.500000000000504 54.600000000000506 54.700000000000507 54.800000000000509 54.90000000000051 55.000000000000512 55.100000000000513 55.200000000000514 55.300000000000516 55.400000000000517 55.500000000000519 55.60000000000052 55.700000000000522 55.800000000000523 55.900000000000524 56.000000000000526 56.100000000000527 56.200000000000529 56.30000000000053 56.400000000000531 56.500000000000533 56.600000000000534 56.700000000000536 56.800000000000537 56.900000000000539 57.00000000000054 57.100000000000541 57.200000000000543 57.300000000000544 57.400000000000546 57.500000000000547 57.600000000000549 57.70000000000055 57.800000000000551 57.900000000000553 58.000000000000554 58.100000000000556 58.200000000000557 58.300000000000558 58.40000000000056 58.500000000000561 58.600000000000563 58.700000000000564 58.800000000000566 58.900000000000567 59.000000000000568 59.10000000000057 59.200000000000571 59.300000000000573 59.400000000000574 59.500000000000576 59.600000000000577 59.700000000000578 59.80000000000058 59.900000000000581 60.000000000000583 60.100000000000584 60.200000000000585 60.300000000000587 60.400000000000588 60.50000000000059 60.600000000000591 60.700000000000593 60.800000000000594 60.900000000000595 61.000000000000597 61.100000000000598 61.2000000000006 61.300000000000601 61.400000000000603 61.500000000000604 61.600000000000605 61.700000000000607 61.800000000000608 61.90000000000061 62.000000000000611 62.100000000000612 62.200000000000614 62.300000000000615 62.400000000000617 62.500000000000618 62.60000000000062 62.700000000000621 62.800000000000622 62.900000000000624 63.000000000000625 63.100000000000627 63.200000000000628 63.30000000000063 63.400000000000631 63.500000000000632 63.600000000000634 63.700000000000635 63.800000000000637 63.900000000000638 64.000000000000639 64.100000000000634 64.200000000000628 64.300000000000622 64.400000000000617 64.500000000000611 64.600000000000605 64.7000000000006 64.800000000000594 64.900000000000588 65.000000000000583 65.100000000000577 65.200000000000571 65.300000000000566 65.40000000000056 65.500000000000554 65.600000000000549 65.700000000000543 65.800000000000537 65.900000000000531 66.000000000000526 66.10000000000052 66.200000000000514 66.300000000000509 66.400000000000503 66.500000000000497 66.600000000000492 66.700000000000486 66.80000000000048 66.900000000000475 67.000000000000469 67.100000000000463 67.200000000000458 67.300000000000452 67.400000000000446 67.500000000000441 67.600000000000435 67.700000000000429 67.800000000000423 67.900000000000418 68.000000000000412 68.100000000000406 68.200000000000401 68.300000000000395 68.400000000000389 68.500000000000384 68.600000000000378 68.700000000000372 68.800000000000367 68.900000000000361 69.000000000000355 69.10000000000035 69.200000000000344 69.300000000000338 69.400000000000333 69.500000000000327 69.600000000000321 69.700000000000315 69.80000000000031 69.900000000000304 70.000000000000298 70.100000000000293 70.200000000000287 70.300000000000281 70.400000000000276 70.50000000000027 70.600000000000264 70.700000000000259 70.800000000000253 70.900000000000247 71.000000000000242 71.100000000000236 71.20000000000023 71.300000000000225 71.400000000000219 71.500000000000213 71.600000000000207 71.700000000000202 71.800000000000196 71.90000000000019 72.000000000000185 72.100000000000179 72.200000000000173 72.300000000000168 72.400000000000162 72.500000000000156 72.600000000000151 72.700000000000145 72.800000000000139 72.900000000000134 73.000000000000128 73.100000000000122 73.200000000000117 73.300000000000111 73.400000000000105 73.500000000000099 73.600000000000094 73.700000000000088 73.800000000000082 73.900000000000077 74.000000000000071 74.100000000000065 74.20000000000006 74.300000000000054 74.400000000000048 74.500000000000043 74.600000000000037 74.700000000000031 74.800000000000026 74.90000000000002 75.000000000000014 75.100000000000009 75.2 75.3 75.399999999999991 75.499999999999986 75.59999999999998 75.699999999999974 75.799999999999969 75.899999999999963 75.999999999999957 76.099999999999952 76.199999999999946 76.29999999999994 76.399999999999935 76.499999999999929 76.599999999999923 76.699999999999918 76.799999999999912 76.899999999999906 76.999999999999901 77.099999999999895 77.199999999999889 77.299999999999883 77.399999999999878 77.499999999999872 77.599999999999866 77.699999999999861 77.799999999999855 77.899999999999849 77.999999999999844 78.099999999999838 78.199999999999832 78.299999999999827 78.399999999999821 78.499999999999815 78.59999999999981 78.699999999999804 78.799999999999798 78.899999999999793 78.999999999999787 79.099999999999781 79.199999999999775 79.29999999999977 79.399999999999764 79.499999999999758 79.599999999999753 79.699999999999747 79.799999999999741 79.899999999999736 79.99999999999973 80.099999999999724 80.199999999999719 80.299999999999713 80.399999999999707 80.499999999999702 80.599999999999696 80.69999999999969 80.799999999999685 80.899999999999679 80.999999999999673 81.099999999999667 81.199999999999662 81.299999999999656 81.39999999999965 81.499999999999645 81.599999999999639 81.699999999999633 81.799999999999628 81.899999999999622 81.999999999999616 82.099999999999611 82.199999999999605 82.299999999999599 82.399999999999594 82.499999999999588 82.599999999999582 82.699999999999577 82.799999999999571 82.899999999999565 82.999999999999559 83.099999999999554 83.199999999999548 83.299999999999542 83.399999999999537 83.499999999999531 83.599999999999525 83.69999999999952 83.799999999999514 83.899999999999508 83.999999999999503 84.099999999999497 84.199999999999491 84.299999999999486 84.39999999999948 84.499999999999474 84.599999999999469 84.699999999999463 84.799999999999457 84.899999999999451 84.999999999999446 85.09999999999944 85.199999999999434 85.299999999999429 85.399999999999423 85.499999999999417 85.599999999999412 85.699999999999406 85.7999999999994 85.899999999999395 85.999999999999389 86.099999999999383 86.199999999999378 86.299999999999372 86.399999999999366 86.499999999999361 86.599999999999355 86.699999999999349 86.799999999999343 86.899999999999338 86.999999999999332 87.099999999999326 87.199999999999321 87.299999999999315 87.399999999999309 87.499999999999304 87.599999999999298 87.699999999999292 87.799999999999287 87.899999999999281 87.999999999999275 88.09999999999927 88.199999999999264 88.299999999999258 88.399999999999253 88.499999999999247 88.599999999999241 88.699999999999235 88.79999999999923 88.899999999999224 88.999999999999218 89.099999999999213 89.199999999999207 89.299999999999201 89.399999999999196 89.49999999999919 89.599999999999184 89.699999999999179 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6.1505000000000001 6.4816000000000003 6.2359999999999998 7.9901 8.0234000000000005 8.1267999999999994 7.8071000000000002 6.0902000000000003 7.6638999999999999 7.6276000000000002 7.6605999999999996 7.8304999999999998 7.7251000000000003 7.7565999999999997 7.5845000000000002 7.4138000000000002 7.5129000000000001 5.8750999999999998 5.7144000000000004 7.4067999999999996 5.9237000000000002 7.4678000000000004 7.4325000000000001 5.5155000000000003 5.4893999999999998 5.4634 7.2286999999999999 5.6026999999999996 5.5128000000000004 7.1894 5.4606000000000003 6.9965000000000002 5.4710999999999999 6.9302000000000001 5.3578000000000001 5.2710999999999997 5.3070000000000004 5.1604000000000001 6.8277999999999999 5.2919 5.2667999999999999 6.5522 5.1576000000000004 5.1920999999999999 5.2849000000000004 6.4870000000000001 5.1765999999999996 5.1520000000000001 5.7611999999999997 6.4218999999999999 6.3913000000000002 5.1113999999999997 4.9176000000000002 6.4130000000000003 4.9268000000000001 6.4077999999999999 6.2110000000000003 4.7464000000000004 4.7788000000000004 6.1227 4.8964999999999996 6.0103 4.7961 6.0603999999999996 5.8714000000000004 6.0559000000000003 4.5467000000000004 5.9983000000000004 5.9696999999999996 4.6383000000000001 Time (s) Salt Concentration (g/L) Université d’Ottawa Faculté de génie Département de University of Ottawa
Department of
Chemical and Biological Engineering
Fall 2019 1 CHG1371 1. Background To study the flow and mixing pattern in this system, salt was dissolved in the first tank to obtain a desired initial
salt concentration. Fresh water was then allowed to flow through the system, resulting in the dissolved salt to
flow through all three tanks and then eventually leaving the system. Each tank outlet stream is monitored with
an on-line thermal conductivity detector to provide instantaneous salt concentration measurements, ???. By
plotting this data over time (Figure 1), we can determine how long it takes for all the salt to leave the system,
and the maximum salt concentrations held by each tank throughout the run.
Figure 1. Salt concentration measurements from the experimental system
0
50
100
150
200
250
300
350
400
450
0 20 40 60 80 100
Sa C n n at n g/ Time (s)
Cs1
Cs2
Cs3
500 L
??1 (g/L)
250 L
??2 (g/L)
1000 L
??3 (g/L)
50 (L/s)
?? = 0
50 (L/s) ??1
50 (L/s) ??2
50 (L/s) CHG1371: Numerical Methods and Engineering Computation in Chemical Engineering
Winter 2020 2 It is also possible to numerically generate these salt concentration plots using differential equations. Assuming
that pure water is fed to the first tank and that each tank is perfectly mixed (i.e. the salt concentration in a tank
is uniform and equal to the concentration in the outlet stream from that tank), the following expressions for the
change in salt concentration over time can be determined for each tank:
???1
?? �̇�
?1 ???2
?? �̇� ?2 ???3
?? ?3 Here, ?? and ??? are the volume and salt concentration of each tank, and �̇� is the flowrate of water. The initial
salt concentration in tanks 1, 2 and 3 are 450 g/L, 0 g/L and 0 g/L, respectively. The tank volumes and water
flowrate are provided in the Block Flow Diagram.
2. Task ordinary differential equations using a 2nd order or higher Runge-Kutta method. You will then compare and
discuss the differences between the numerical data with the experimental findings in Figure 1. The experimental
plot data is available in the provided Excel sheet. Hint – what is the solubility of salt in water?
The numerical solution must be solved in Microsoft Excel using VBA. The solution should be flexible and robust
enough that different parameters (e.g. different �̇�, ?? and initial salt concentrations) could be easily changed
and a new solution would be automatically calculated.
3. Evaluation
A report will accompany the solution, a soft copy in format and must be submitted electronically prior to
the due date of Friday April 3rd, 2020 at 16:00. It is expected that the report should be about 6 pages, 1.5 spaced
and including figures, broken down as follows:
• 1 Page for Introduction/Background
• 2 Pages for VBA code design and Excel sheet set-up
• 2 Pages for Results/Discussion/Validation
• 1 Page for Improvements & Extensions/Conclusions
The VBA code should be included as text in an Appendix (not included in the number of pages). This project
should be done in groups of 2, and each member must share equal responsibility for the code and the report.
The deadline for joining a group on BrightSpace is March 20th, 2020 at 16:00. If you do not join a group by this
time, you will be randomly assigned. More information on the expectations of the report and the marking
scheme can be found in the Project Guidelines & Expectations document.
t (s)
Cs
1
Cs2 (g/L)
Cs
3
0
32
9
0.1
31
2.
5
8
7
6
0.2
37
5.6
97
1
3.1
15
0.0
30
0.3
31
4
57
14
1
8.9
92
0.0
89
0.4
30
5.3
47
2
4.9
72
0.
17
67
0.5
30
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12
11
0.
28
0.6
30
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4
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20
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36
0.7
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0.8
32
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5
4.3
51
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95
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63
5
2.9
62
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71
1
30
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16
5
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98
1.2
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34
3.7
27
7
1.6
78
1.9
54
1.2
29
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61
76
40
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19
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64
81
39
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1.4
32
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73
8
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3.
10
1.5
28
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46
7
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2.7
44
1.6
33
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3.96
58
1.7
33
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25
90
24
3.4
1.8
286.00
65
92.
56
4.
99
1.9
27
4.7
9
3.2
66
5.7
2
32
6.5
52
101.13
88
4.6
2.1
29
7.2
42
102.5191
6.6
49
2.2
2
77
104.7865
5.7892
2.3
3
13.1
106.8712
7.8
23
2.4
2
70
83
132.0019
8.6
2.5
30
8.3
1
34.3
7.1
2.6
303.0
55
1
17.2
9.6
43
2.7
28
3.6
1
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8.4
2.8
26
12
4.2
11.1
75
2.9
25
9.7
45
12
8.2
9.5446
3
25
7.7
1
29.5
12.7
3.1
29
6.9
15
3.5
10.3
3.2
2
48
1
60
74
11.1673
3.3
2
92.4
13
5.2
82
14.9
3.4
24
9.8
13
7.5
12.0866
3.5
2
50
1
61.1
16.1
3.6
24
5.9
165.0602
12.9
21
3.7
244.0799
173.
68
18
3.8
2
86.4
59
1
74.3
18.3
53
3.9
2
81.6
1
73.3
22
20.0116
4
2
38.4
1
75.3
20.8
4.1
2
41.6
15
7.4
16.9
4.2
2
29.7
85
1
52.4
19.5
4.3
2
70.5
154.0093
17.8
4.4
2
65.9
1
62.3
24.0223
4.5
2
34.2
1
56.9
2
4.8
4.6
2
22.6
1
87.8
1
9.1
4.7
2
42.8
1
92.8
20.9
4.8
2
57.7
94
166.0688
20.959
4.9
21
5.1
1
92.1
2
8.5
5
2
20.6
1
61.2
2
8.1
5.1
2
47.1
1
96.5
22.9
5.2
2
21.8
1
81.4
27.1
5.3
2
45.6
1
95.2
24.8
5.4
22
9.9
1
72.4
2
5.8
5.5
2
44.1
202.8333
2
6.2
5.6
203.7476
1
94.5
34.7
5.7
247.0949
1
95.3
34.4
5.8
2
45.1
198.074
35.6
5.9
241.0682
206.3411
37.1
6
21
9.4
203.3148
36.6
6.1
1
98.1
1
71.8
38.2
6.2
2
26.8
206.5068
30.3
6.3
203.6674
1
99.4
32.1
6.4
2
25.4
1
99.9
31.7
6.5
1
89.9
1
75.6
42.7
6.6
230.3
84
206.6299
42.9
6.7
1
97.4
1
76.3
43.3
6.8
1
93.8
1
78.5
34.7713
6.9
223.0237
1
78.8
35.4
7
21
9.2
202.1661
45.1389
7.1
1
83.3
208.1688
35.5
7.2
217.8785
1
81.3
37.8
7.3
208.2563
1
79.5
36.8
7.4
1
86.9
1
77.7
3
8.7
7.5
206.9936
202.9025
50.6
7.6
203.4518
1
79.7
51.9
7.7
1
82.6
208.7541
41.1
7.8
171.
69
2
12.5
40.4
7.9
1
74.1
181.6271
53.4
8
1
74.6
2
12.4
41.6831
8.1
201.2
80
1
73.7
56.079
8.2
1
73.8
17
9.3
44.4
8.3
194.5028
18
1.17
43.5
8.4
1
92.9
173.3019
45.6898
8.5
1
91.4
1
92.3
57.2
8.6
195.3934
1
72.9
58.0189
8.7
160.0836
1
76.5
60.9
8.8
162.3728
206.9035
48.1
8.9
1
59.3
1
91.2
62.4
9
1
91.1
171.8573
49.3
9.1
181.0415
205.8576
48.3
9.2
1
59.1
1
90.2
48.3244
9.3
1
57.8
1
99.3
51.1
9.4
1
83.6
200.8274
50.6174
9.5
1
57.1
207.9434
52.9
9.6
1
79.1
175.3993
66.6
9.7
1
51.3
1
76.8
69.1
9.8
1
79.6
1
70.7
67.4
9.9
173.357
19
6.54
70.6
10
1
75.2
205.3515
55.8
10.1
170.6804
1
74.9
71.4
10.2
1
48.7
202.3386
70.2
10.3
1
69.6
201.7423
56.2
10.4
1
46.4
175.2978
54.8
10.5
1
46.8
1
83.9
58.5
10.6
138.0855
1
99.8
72.2
10.7
1
41.5
1
97.3
57.6
10.8
143.5064
1
71.2
57.5
10.9
1
39.3
167.01
57.3
11
1
39.8
189.9447
77.5
11.1
1
37.2
1
94.6
68.5
11.2
1
55.2
1
90.3
61.5
11.3
1
36.5
1
68.2
77.3
11.4
1
32.6
1
94.3
79.3
11.5
1
30.1
1
66.9
63.6
11.6
1
53.2
176.8938
81.2
11.7
1
54.9
1
63.8
62.4936
11.8
1
32.7
1
64.9
80.3
11.9
131.7357
159.0435
64.8
12
1
37.5
1
89.7
64.5
12.1
1
44.7
1
85.4
66.4
12.2
1
46.3
1
84.6
84.0486
12.3
1
22.3
1
80.4
64.3
12.4
1
45.3
1
60.8
85.1
12.5
1
20.4
1
61.8
83.4
12.6
1
23.4
179.7558
67.9
12.7
136.8164
1
85.6
65.2
12.8
1
39.6
181.489
88.0456
12.9
139.8355
1
52.2
68.3
13
140.0247
154.8363
89.0739
13.1
1
17.4
1
82.2
7
0.719
13.2
1
25.3
1
53.3
71.1
13.3
134.3071
1
47.7
69.9
13.4
129.5644
178.0315
90.2479
13.5
110.1945
1
54.4
71.4516
13.6
109.3405
1
50.4
91.1842
13.7
132.6027
1
68.9
90.0201
13.8
108.8485
17
4.5293
92.0931
13.9
1
30.5
1
46.5
73.7023
14
1
17.7
1
45.8
92.9747
14.1
1
27.3
1
43.4
73.5
14.2
108.9916
141.1785
92.9988
14.3
125.4044
145.1234
71.7
14.4
121.0078
1
41.2
72.8
14.5
1
24.6
168.3018
96.7
14.6
118.0155
167.4051
93.7
14.7
111.5246
1
66.5
72.9463
14.8
105.1273
1
44.3
73.2
14.9
1
18.5
137.509
75.2355
15
9
8.0566
1
35.2
73.8077
15.1
97.2
1
41.9
74.0849
15.2
97.6
1
33.7
75.2217
15.3
98.9
134.4997
74.6244
15.4
99.2
1
46.9
99.2686
15.5
104.7948
1
56.3
75.1
15.6
109.1818
1
58.3
96.4
15.7
109.3674
1
57.4
76.5246
15.8
108.5198
1
56.5
100
15.9
107.6788
1
28.5
97.371
16
91.7
153.3776
75.4
16.1
109.0167
152.4872
80.1
16.2
92.2
1
47.3
101.822
16.3
98.4
1
39.5
98.5
16.4
90.8
1
49.8
103.2961
16.5
105.6762
144.7992
103.5772
16.6
103.8952
1
23.3
100.24
16.7
102.1355
1
26.7
102.3105
16.8
100.3968
124.6149
100.7534
16.9
99.6
1
46.7
77.3434
17
83.9264
1
40.5
104.8921
17.1
83.2
1
44.9
80.4527
17.2
100.0749
1
41.4
81.5
17.3
100.2103
119.5687
81.7
17.4
84.9
138.4236
79.1477
17.5
80.7
116.806
78.3
17.6
83.6586
135.4317
79.4
17.7
83.0103
1
34.5
83.336
17.8
92.8819
127.3854
103.9063
17.9
93.9
113.9312
106.8886
18
94.0359
1
35.8
104.2886
18.1
77.0426
1
32.5
81.1
18.2
89.1
116.7656
84.0932
18.3
76.6
1
33.3
103.8857
18.4
90.3183
115.2911
84.3
18.5
87.1
110.9014
107.9672
18.6
75.7
113.8264
82.7
18.7
76.7
1
29.9
108.2838
18.8
86.7
126.7171
94.2
18.9
76.4
1
29.4
106.691
19
86.1
1
27.4
105.8833
19.1
85.5
1
24.2
80.4576
19.2
70.7234
1
26.9
106.1412
19.3
77.9
105.3099
94.8
19.4
69.6314
106.9222
80.7345
19.5
82.9
103.9385
105.5407
19.6
83.0293
107.7956
82.8
19.7
68.7
101.4509
106.7011
19.8
82.4
119.819
85.8
19.9
81.1138
1
21.2
82.0777
20
79.7468
103.874
84.056
20.1
66.6733
109.771
85.0779
20.2
77.7885
109.0409
82.2711
20.3
75.7429
118.0623
83.2859
20.4
67.9982
117.2737
105.3732
20.5
66.7
112.2138
82.4334
20.6
65.5
95.5
110.2941
20.7
65.7
97.0045
86.3
20.8
69.3
95.3037
84.4
20.9
72.9769
96.7409
96.0501
21
72.4113
98.153
107.6208
21.1
63.0383
108.7759
108.6226
21.2
71.2933
109.0566
107.6977
21.3
73.4
101.2288
109.6537
21.4
72.1
95.512
84.6671
21.5
70.9
106.8423
82.7615
21.6
7
1.064
108.0949
107.8027
21.7
58.8
108.3392
109.7443
21.8
59.6
89.0109
110.7198
21.9
60.5
105.8845
84.7
22
66.9912
104.1906
81.8
22.1
57.6927
100.5977
108.8088
22.2
57.2456
88.4
84.7339
22.3
66.6805
103.9356
86.6
22.4
5
6.3617
103.2152
107.8267
22.5
55.9
88.5
83.7
22.6
54.8883
86.0555
82.7717
22.7
65.8
98.3
83.7181
22.8
65.3
82.1
105.8265
22.9
64.2
98.7
109.6465
23
64.3155
82.7786
105.7686
23.1
52.7
94.7
109.5796
23.2
54.6
95.8
110.5018
23.3
59.9
80.1681
86.4465
23.4
53.8
91.8
85.4506
23.5
50.614
80.781
85.4126
23.6
60.8241
78.4
85.3
23.7
60.3
81.3579
86.2
23.8
57.6874
92.6
83.367
23.9
58.8758
78.5223
106.3049
24
48.6
90.5
108.1563
24.1
48.3056
89.8
109.0457
24.2
50.5
76.8627
109.9309
24.3
49.6
86.9839
106.9906
24.4
55.0564
86.3645
106.9152
24.5
47.3457
76.0414
107.7908
24.6
51.6
72.286
109.6152
24.7
54.8107
86.1234
108.5766
24.8
53.8776
83.9239
106.5849
24.9
45.895
86.4673
84.6258
25
53.0458
83.5
81.7024
25.1
53.1
72.0593
109.1557
25.2
44.8
84.6193
85.3477
25.3
53.2887
71.0273
81.4775
25.4
52.8
71.2744
85.1845
25.5
51.5
71.5
104.9564
25.6
43.9
68.0085
84.0684
25.7
42.6
81.6147
106.6271
25.8
51.7
67.7
83.8
25.9
49.9
79.7077
84.7408
26
43.0565
78.4048
107.2185
26.1
41.3
68.4
106.1568
26.2
42.8476
77.2
106.9715
26.3
49.2
66.057
83.4137
26.4
42.6348
76.1
80.5
26.5
40.9
76.3004
84.1
26.6
39.7
76.4401
105.5158
26.7
46.0355
75.1935
93.2
26.8
39.1
65.0579
102.4496
26.9
47.4
73.4211
102.314
27
39.4
74.2
92.8876
27.1
38.6
73.0224
102.0367
27.2
44.7008
63.1
104.6739
27.3
38.9
71.9
78.6
27.4
39.4435
71.4311
8
2.2081
27.5
37.9
61.8002
104.225
27.6
38.4257
61.3
81.9
27.7
43.8
68.5889
102.9963
27.8
38.2349
69.3578
7
9.884
27.9
36.7
67.5
103.5992
28
43.1
57.6828
91.5
28.1
42.071
66.5939
101.4473
28.2
41.3548
58.6
80.2
28.3
40.6
65.6
80.1687
28.4
41.8
57.2191
104.5947
28.5
36.2
54.9842
90.8015
28.6
34.7931
63.5
79.7717
28.7
33.7729
64.8908
99.5
28.8
40.5857
54.3
100.279
28.9
35.0988
53.3765
78.4611
29
36.6597
52.3
90.0276
29.1
38.1
52.0111
79.0843
29.2
33.5
62.5
78.0461
29.3
39.0372
52.9509
102.9784
29.4
38.7
51.9929
77.7635
29.5
33.4
58.8992
75.8
29.6
37.087
52.3371
101.5209
29.7
32.9
50.2
75.5
29.8
37.2033
51.0133
100.2518
29.9
36.2314
57.1672
78.8087
30
36.9
58.3628
99.8678
30.1
31.9
50.9
77.6
30.2
31.7224
50.0432
98.5981
30.3
30.1512
58.1
97.5
30.4
36.1
55.5
74.5
30.5
35.8838
52.055
76.1326
30.6
34.6
55.7
98.6
30.7
29.8697
54.87
74.0802
30.8
29.9569
55.4
98.2
30.9
29.7247
54.5
75.5103
31
34.5147
45.1248
99.6038
31.1
33.0019
53.2469
74.3295
31.2
32.4
46.9213
75.8968
31.3
29.1205
52.4524
94.6682
31.4
28.2865
44.2
97.8
31.5
32.8
50.7
73.6
31.6
31.4432
45.5
76.9
31.7
27.3368
42.8103
75.0779
31.8
27.1249
49.5
72.3
31.9
26.9147
43.5755
73.8956
32
26.1255
42.3
72.035
32.1
27.3632
50.3
97.2392
32.2
26.2937
50.3876
97.0184
32.3
26.09
41.8254
93.4
32.4
26.1692
49.1
74.7
32.5
25.6871
47.4675
71.2158
32.6
25.211
41.3324
91.9
32.7
24.7407
47.1963
70.8
32.8
24.549
41.5875
71.5486
32.9
28.6892
4
6.487
72.2091
33
25.2442
47.4306
91.0813
33.1
29.3121
44.9331
93.3
33.2
29.085
39.9
70.8672
33.3
24.1371
37.9349
92.0686
33.4
23.6897
45.5965
91.0242
33.5
27.8973
39.0247
89.9833
33.6
23.5802
37.0818
70.1
33.7
22.8888
43.344
93.6
33.8
22.7115
42.6104
70.6414
33.9
23.2866
43.0936
93.1
34
23.6031
43.9667
72.7
34.1
26.1319
42.8406
89.4
34.2
26.9079
35.4303
92.4389
34.3
25.9712
41.8037
88.1
34.4
2
1.91
41.487
87.9
34.5
21.9856
42.3271
68.5979
34.6
22.5266
40.4788
69.2
34.7
24.7048
41.6878
87.2
34.8
21.2449
34.2257
87.0589
34.9
21.3119
40.3
67.8
35
20.9169
33.7083
88.1762
35.1
2
0.5267
34.1877
70.6683
35.2
20.8202
39.7653
89.2
35.3
23.5781
38.0151
68.7301
35.4
20.276
35.9
68.5457
35.5
24.3195
37.7
89.3
35.6
23.0341
32.9089
85.9
35.7
23.291
32.6588
88.8
35.8
20.0866
31.365
67.8055
35.9
23.1457
36.3
69.1567
36
21.2651
37.4
85.825
36.1
20.0453
36.4
84.0597
36.2
22.1929
31.0974
86.8
36.3
19.3203
35.8923
83.5935
36.4
18.7583
36.6177
83.3601
36.5
21.4764
35.6782
84.6377
36.6
18.2657
31.1445
66.3
36.7
18.5269
35.1366
64.6
36.8
21.3806
30.6717
65.9391
36.9
21.6114
29.7971
84.4309
37
18.4929
34.3393
85.6798
37.1
20.6921
29.029
63.1471
37.2
20.9191
33.5045
83.707
37.3
17.2975
28.2771
84.9426
37.4
17.5449
28.6781
62.6
37.5
19.8688
30.6013
82.2474
37.6
17.6495
33.4045
62.2
37.7
20.3073
28.6291
81.0375
37.8
2
0.3348
32.8964
64.0573
37.9
16.692
27.3032
79.8
38
18.2007
31.2178
62.9
38.1
19.3239
27.7644
63.4
38.2
16.4861
31.9026
81.2857
38.3
18.8477
26.1905
61.6
38.4
18.7016
26.8471
63.6394
38.5
18.5567
26.9253
80.5579
38.6
18.5866
25.3131
8
0.3152
38.7
15.8571
30.7016
61.6488
38.8
18.4706
29.0819
70.6459
38.9
18.1578
24.7367
60.5708
39
18.5222
29.7296
80.7489
39.1
15.5383
29.7728
78.402
39.2
15.5837
29.0077
62.1
39.3
17.6014
24.2546
79.3126
39.4
17.9547
24.3334
39.5
14.7383
27.5591
76.7491
39.6
15.2669
28.3899
78.5788
39.7
17.0621
23.2616
60.4
39.8
17.2463
27.7001
60.2
39.9
14.4437
23.6701
77.1
40
16.98
22.731
57.8609
40.1
16.8484
23.058
57.6789
40.2
13.9571
23.13
75.0844
40.3
13.6967
25.9143
60.0124
40.4
16.6107
23.2665
74.6097
40.5
16.1823
26.2475
67.0023
40.6
13.3807
26.2874
57.4384
40.7
15.9325
22.7353
74.5645
40.8
15.6626
22.3234
57.0716
40.9
13.3625
22.3878
74.0871
41
15.1325
21.5144
57.3646
41.1
15.0152
21.5814
74.2676
41.2
12.7705
21.646
72.062
41.3
15.065
24.9075
7
3.787
41.4
1
5.3674
21.315
58.5777
41.5
12.8917
2
0.7013
72.6
41.6
14.855
20.5423
73.0685
41.7
14.8764
23.7081
73.4738
41.8
14.3548
20.8876
55.8881
41.9
12.0936
19.8544
7
1.071
42
12.3998
23.3825
72.1131
42.1
12.5683
23.6325
54.7
42.2
12.2084
19.8267
54.5201
42.3
14.0676
22.2129
56.2347
42.4
13.7001
19.3132
69.2724
42.5
13.5939
22.9143
69.0415
42.6
11.4526
22.5315
70.062
42.7
11.3638
21.7429
69.8
42.8
11.7769
18.319
69.5
42.9
11.437
18.3801
55.1
43
13.4453
21.2451
55.5473
43.1
12.9739
21.2806
67.6
43.2
10.93
21.5117
55.1724
43.3
12.8941
18.2128
52.5
43.4
12.555
20.7933
54.1
43.5
10.9154
21.019
69.1753
43.6
10.9485
17.987
68.9393
43.7
10.9804
17.8486
53.0344
43.8
10.6635
20.349
69.069
43.9
12.5361
17.014
52.0729
44
10.8412
19.8515
66.2
44.1
10.644
20.251
68.359
44.2
11.7974
19.7297
65.1
44.3
10.3682
17.0399
67.2
44.4
10.3984
16.9087
52.357
44.5
11.7448
18.742
49.8303
44.6
1
1.435
16.6493
52.578
44.7
9.7263
16.6968
64.6203
44.8
10.187
18.8355
49.3113
44.9
10.0017
18.8634
65.9039
45
11.1911
18.3747
51.8
45.1
11.3139
18.4035
65.4
45.2
11.2262
15.5563
57.2039
45.3
11.2423
17.9532
49.5921
45.4
9.2107
15.6504
63.0494
45.5
9.6471
18.1732
50.3745
45.6
9.0685
16.3938
47.9
45.7
10.9978
17.4061
47.7701
45.8
10.5158
15.3349
62.7
45.9
9.253
14.7362
55.8012
46
9.7674
16.8478
63.9
46.1
8.7225
16.5602
48.7553
46.2
8.7511
16.902
48.5
46.3
8.7787
14.4423
61.6087
46.4
8.7106
14.3309
6
0.291
46.5
8.831
14.0675
60.6
46.6
8.6694
13.959
48.4
46.7
10.1746
14.303
48.7985
46.8
10.004
15.9855
61.5882
46.9
8.1962
13.6385
60.2888
47
9.8495
13.3862
46.1255
47.1
8.3386
13.5749
6
0.921
47.2
9.4305
13.4701
59.1024
47.3
9.4457
15.8095
46.1549
47.4
9.4601
12.8352
47.0438
47.5
7.8223
13.3023
46.8721
47.6
9.0553
15.0251
59.2
47.7
8.1294
12.5404
58.5542
47.8
7.6419
14.9324
44.2755
47.9
7.8354
12.4848
45.6698
48
9.1123
14.5666
44.4677
48.1
8.7928
12.8332
58.7
48.2
7.7369
14.6107
51.3261
48.3
8.657
13.9659
58.8069
48.4
8.833
12.0103
56.042
48.5
8.0409
12.1795
43.1448
48.6
7.4999
11.9556
56.6
48.7
7.2834
14.0554
56.9321
48.8
7.4626
12.1555
42.6657
48.9
8.574
1
1.9347
56.5089
49
8.1982
13.2284
56.7
49.1
8.1346
11.6261
56.0878
49.2
7.9954
11.6603
44.0101
49.3
6.9512
11.3241
49.2643
49.4
6.9723
13.313
56.4
49.5
8.1829
11.2711
56.2295
49.6
6.7909
12.8676
42.866
49.7
12.8876
55.8071
49.8
6.5407
12.788
54.6298
49.9
6.8505
10.9268
41.4197
50
6.6543
12.4746
42.2227
50.1
7.4547
12.3782
54.0126
50.2
7.5379
12.3974
53.8079
50.3
6.2911
10.4792
41.2701
50.4
6.5892
12.4326
52.9275
50.5
7.2951
10.0936
41.4277
50.6
6.4874
10.4607
52.5253
50.7
7.318
10.2694
42.0469
50.8
6.2528
10.2997
40.9555
50.9
6.1376
10.0026
41.2626
51
6.9506
10.249
53.1128
51.1
7.0281
11.7755
51.0689
51.2
6.5174
11.6845
51.3313
51.3
6.7902
11.4888
50.221
51.4
6.7376
11.5046
51.5
6.6854
10.8968
50.7414
51.6
6.8231
11.0185
39.2632
51.7
6.6449
9.4006
44.956
51.8
5.5981
9.1252
38.9606
51.9
6.7892
10.0607
50.8544
52
6.1241
10.5819
50.2131
52.1
5.5905
8.9152
38.9524
52.2
6.4516
8.9445
39.2421
52.3
5.4444
9.0704
50.5091
52.4
6.4708
10.6455
49.8751
52.5 6.3617
10.2751
48.8093
52.6
5.3772
9.5287
49.0532
52.7
5.5095
8.6986
38.0516
52.8
5.7546
10.3201
48.6708
52.9 5.3674
9.961
4
8.9095
53
6.119
48.718
53.1
5.3407
8.7076
47.2501
53.2
5.9687
10.0046
36.8886
53.3
5.535
9.7467
36.7437
53.4
5.1077
8.3281
46.2749
53.5
5.722
8.2637
47.7688
53.6
5.7858
8.3761
47.998
53.7
5.741
9.1862
35.7526
53.8
5.803
9.2019
46.7918
53.9
5.758
7.8387
35.0583
54
5.5561
7.949
46.0117
54.1
5.6691
9.0749
36.8273
54.2
4.8511
8.9205
45.6479
54.3
4.7623
7.599
36.5358
54.4
5.3859
8.7831
44.4775
54.5
4.6887
7.6463
45.9116
54.6
4.6524
8.7293
35.2995
54.7
4.6163
8.9046
45.5468
54.8
5.2208
8.5144
34.2229
54.9
4.3984
8.7673
34.879
55
4.4613
8.4623
43.8194
55.1
4.5711
7.3766
34.994
55.2
5.1564
8.3318
34.4623
55.3
4.7374
7.0311
35.1043
55.4
4.7007
8.2801
33.4097
55.5
4.3844
8.216
43.3356
55.6
4.3967
7.0956
44.3177
55.7
4.133
8.0144
43.7557
55.8
4.7845
8.0267
32.4935
55.9
4.9735
6.8584
43.7848
56
4.8003
8.0494
42.4707
56.1
4.6741
6.6801
43.4323
56.2
4.8146
6.7725
42.1284
56.3
3.9883
6.7201
32.9671
56.4
4.0444
7.5903
42.5346
56.5
4.6172
7.7427
40.876
56.6
4.0248
6.2859
32.9383
56.7
3.9511
6.5145
32.8047
56.8
3.8783
6.3953
31.9374
56.9
4.5594
6.1411
40.5821
57
3.8185
7.1091
41.5094
57.1
4.4066
6.1136
32.2746
57.2
3.7595
6.1996
30.6984
57.3
3.852
7.1438
30.5733
57.4
3.621
6.2352
41.1951
57.5
4.2317
6.9034
31.0377
57.6
4.2385
6.9792
30.2002
57.7
4.3235
5.771
40.692
57.8
3.705
6.0444
31.0108
57.9
4.1407
5.8714
31.5856
58
3.5326
6.7029
39.4949
58.1
3.4291
5.9051
39.6809
58.2
4.1208
6.5996
30.1584
58.3
3.4511
6.5485
31.0701
58.4
3.4244
5.7691
38.8498
58.5
4.0626
6.6283
38.6898
58.6
3.2982
5.5007
39.2124
58.7
3.4545
5.4581
29.2031
58.8
3.2834
6.4755
29.4208
58.9
3.3295
6.4254
29.9728
59
3.8366
5.2744
37.8981
59.1
3.5249
5.4061
30.0595
59.2
3.1478
6.2773
29.9351
59.3
3.644
6.2287
36.767
59.4
3.7535
6.1243
28.3681
59.5
3.7585
5.9654
29.2359
59.6
3.6616
5.0341
37.6199
59.7
3.095
4.9951
32.577
59.8
3.1711
5.8823
35.6857
59.9
3.0472
5.8908
29.0759
60
3.4508
5.0945
36.9979
60.1
3.0328
5.5871
36.8438
60.2
3.4946
5.0159
27.7569
60.3
3.3712
4.8199
35.9016
60.4
3.3451
5.7183
28.4748
60.5
2.9714
4.7455
27.4106
60.6
3.3875
5.4253
31.3747
60.7
3.2679
5.4849
34.6802
60.8
2.8102
4.5353
26.7569
60.9
3.3094
4.6502
26.6447
61
3.2533
4.6638
27.4586
61.1
3.1678
33.7952
61.2
2.7541
4.4942
33.9592
61.3
3.208
5.3319
26.2002
61.4
5.1944
34.5845
61.5 3.1
4.3906
27.1887
61.6
3.134
5.1616
34.5948
61.7
3.1673
5.1216
29.9557
61.8
2.6285
5.1286
34.3038
61.9
3.005
4.3024
33.8621
62
2.5316
26.6204
62.1
2.7911
4.8737
25.3298
62.2
2.5202
4.158
32.5549
62.3
2.9953
4.7985
29.2047
62.4
2.5631
4.0939
33.4433
62.5
2.8679
4.1505
28.958
62.6
2.4967
4.6879
32.5838
62.7
2.4241
3.9125
31.8714
62.8
2.8282
4.0979
25.4461
62.9
2.3604
4.7082
32.1708
63
2.8366
4.5019
31.4672
63.1
2.3498
4.0034
25.1232
63.2
2.7671
3.8888
24.4542
63.3
2.3644
4.5225
24.63
63.4
2.6487
4.117
31.4924
63.5
2.678
3.84
24.6981
63.6
2.732
3.6886
24.5928
63.7
2.5876
4.4243
31.6416
63.8
2.2252
3.6317
30.6846
63.9
2.2323
3.7224
23.4607
64
2.6002
3.7329
23.6321
64.1
2.5561
3.587
27.0472
64.2
2.6074
4.1395
29.6246
64.3
2.4931
4.0307
30.8385
64.4
2.1237
3.9994
29.3713
64.5
2.5241
3.9685
22.8646
64.6
2.1829
3.3752
23.0313
64.7
2.1204
3.3863
30.0494
64.8
2.4206
3.3969
23.0964
64.9
2.0203
3.4073
23.5198
65
2.116
3.8171
28.8831
65.1
2.0554
3.7876
28.4998
65.2
2.193
3.2571
29.667
65.3
1.9801
3.8712
29.0255
65.4
2.375
3.1716
29.1562
65.5
2.2495
3.3219
22.4095
65.6
1.9557
3.8166
25.3555
65.7
1.9195
22.2165
65.8
1.9674
3.1086
28.6562
65.9
1.9313
3.7286
22.2753
66
2.1843
3.1279
22.4282
66.1
2.2491
3.6377
24.8125
66.2
2.2114
3.477
27.1756
66.3
2.0131
3.1215
27.3039
66.4
1.8577
3.0973
26.9407
66.5
1.8631
3.5586
27.3117
66.6
1.9666
2.9532
21.3661
66.7
2.049
2.8666
27.0752
66.8
2.0525
2.9393
27.6798
66.9
1.9213
3.2928
27.3199
67
1.792
2.8317
26.724
67.1
1.778
3.242
27.3205
67.2
1.7456
2.8186
20.8152
67.3
1.7134
2.736
21.1956
67.4
1.9404
2.8656
2
0.63
67.5
1.9987
2.8434
25.6805
67.6
1.7285
2.7323
19.7575
67.7
1.697
3.0942
25.6885
67.8 1.9347
3.1287
19.5855
67.9
1.6353
3.1335
20.6471
68
1.605
2.7061
25.5819
68.1
1.8375
2.9994
22.7412
68.2
1.5628
2.551
25.8116
68.3
1.5679
2.6437
25.4733
68.4
1.8122
2.5674
24.6885
68.5
1.6964
3.046
19.8878
68.6
1.6832
2.6102
19.8007
68.7
1.7871
2.8626
19.9354
68.8
1.5412
2.4347
24.4792
68.9
1.6444
2.4158
24.3718
69
1.729
2.9298
24.2648
69.1
1.5219
2.4842
19.5878
69.2
1.7029
2.4125
19.2851
69.3
1.4506
2.8622
24.1622
69.4
1.471
2.5819
24.4855
69.5
1.4282
2.3825
23.7363
69.6
1.4327
2.3641
18.9481
69.7
1.6224
2.6989
18.4407
69.8
1.4106
17.9374
69.9
1.3844
2.2847
23.3209
70
1.6001
2.612
23.6364
70.1
1.6027
2.6895
18.5342
70.2
1.4119
2.6687
23.6357
70.3
1.342
2.624
23.3249
70.4
1.3316
2.5559
23.0164
70.5
1.5391
2.1805
22.9147
70.6
1.5559
2.2107
22.8134
70.7
1.3295
2.4969
22.7125
70.8
1.3333
2.5239
20.1893
70.9
1.4919
2.4584
18.0899
71
1.2988
2.4165
17.8097
71.1
1.4827
2.443
17.3323
71.2
1.4575
2.3568
17.6522
71.3
1.5008
2.1158
17.179
71.4
1.259
2.4088
22.0174
71.5
1.4776
2.0612
22.3111
71.6
1.2662
2.3716
22.4069
71.7
1.2432
2.0078
16.4881
71.8
1.4173
2.2707
16.4148
71.9
1.3802
2.1256
22.1095
72
1.1628
2.2568
16.8433
72.1
1.3589
2.1974
21.5322
72.2
1.3611
2.2842
21.8157
72.3
1.136
2.1841
16.2417
72.4
1.3651
16.3574
72.5
1.3173
2.2113
16.846
72.6
1.3071
2.1941
18.6344
72.7
1.2969
2.1372
21.1484
72.8
1.1533
2.1801
20.6847
72.9
1.2046
2.1632
16.1797
73
1.0997
2.0488
15.5584
73.1
1.2691
2.033
15.4889
73.2
1.2357
15.6011
73.3
1.0743
2.0207
20.7686
73.4
1.2282
20.6757
73.5
1.0692
1.9895
15.7507
73.6
1.0495
1.9554
15.502
73.7 1.064
1.9772
19.5124
73.8
1.213
1.7235
19.7782
73.9
1.0587
1.9285
15.2946
74
1.2054
1.8053
20.1264
74.1
1.196
1.6838
19.165
74.2
1.0017
1.6885
19.5994
74.3
1.0047
1.9047
18.9934
74.4
1.1255
1.8549
15.2984
74.5
0.9785
19.3366
74.6
0.9815
1.5506
19.5904
74.7
1.1205
1.8463
15.2627
74.8
0.9768
1.5606
14.8565
74.9
1.1238
1.801
14.7896
75
1.1049
1.6701
18.9058
75.1
1.1166
1.5578
14.4903
75.2
0.9065
14.7566
75.3
0.9195
1.4848
18.4865
75.4 1.071
1.4895
14.2954
75.5
0.9053
1.5261
14.3945
75.6
0.8983
1.4824
14.3296
75.7
0.9204
1.5025
17.9933
75.8
0.9133
1.5694
17.7507
75.9
1.0206
1.5572
14.1365
76
1.0317
1.4524
17.5908
76.1
1.0143
1.6712
18.3073
76.2
1.0157
13.9458
76.3
1.0079
1.4189
14.0405
76.4
1.0092
1.4229
17.7461
76.5
0.8648
1.6051
17.6659
76.6
0.9846
1.3272
17.4303
76.7
0.8515
1.6096
13.4783
76.8
0.9427
1.3212
16.9644
76.9
0.9619
1.5703
17.6552
77
0.7968
1.2866
17.5752
77.1
0.9123
1.5461
17.4955
77.2
0.7845
1.4074
16.9619
77.3
0.8041
1.5362
17.3372
77.4
0.7639
1.2471
16.9584
77.5
0.8843
1.5125
16.4333
77.6
0.7856
1.5007
14.8715
77.7
0.8707
12.7314
77.8
0.757
1.4104
16.3578
77.9
0.8572
1.4528
12.9094
78
0.8911
1.2167
16.3554
78.1
0.7395
1.181
12.9376
78.2
0.8694
1.224
12.8788
78.3
0.7914
1.4083
15.9892
78.4
0.8245
1.4102
15.9164
78.5 0.7013
1.3865
16.1295
78.6
0.7268
1.1991
15.7718
78.7
0.8208
1.1898
12.5883
78.8
0.8145
1.1681
16.0508
78.9
0.8308
1.1344
15.5572
79
0.8169
1.2847
15.6257
79.1
0.6842
1.1169
12.0825
79.2
0.7748
1.301
11.7509
79.3
0.6809
1.1355
12.3853
79.4
0.6611
1.0793
15.6164
79.5
0.7929
1.2475
15.6815
79.6
0.7582
1.086
15.6098
79.7
0.7736
1.2514
12.0254
79.8
0.7535
1.0462
11.9705
79.9
0.7547
1.0609
13.3885
80
0.735
1.1885
11.9945
80.1
0.7224
1.1793
13.2662
80.2
0.7304
1.0253
11.885
80.3
0.7248
1.1943
14.591
80.4
0.7393
1.1741
13.0849
80.5
0.6269
1.1541
11.0712
80.6
0.5956
0.9723
14.9101
80.7
0.6894
1.0076
14.8417
80.8
0.7036
14.5167
80.9
0.6917
1.1082
11.1253
81
0.5837
0.9739
14.2566
81.1
0.7001
0.956
11.1502
81.2
0.5684
1.1032
11.2251
81.3
0.6831
0.9208
14.4378
81.4
0.6715
0.9339
11.2473
81.5
0.5676
0.9166
10.9468
81.6
0.6673
13.7445
81.7
0.5771
0.9124
10.9697
81.8
0.5545
0.8856
10.5512
81.9
0.5383
1.0741
10.5026
82
0.635
1.056
10.6975
82.1
0.6359
1.0575
12.1003
82.2
0.6252
1.0111
13.7308
82.3
0.6319
0.8992
10.5504
82.4
0.604
1.0331
13.6047
82.5
0.5194
0.8573
13.3044
82.6
0.623
0.8507
13.4796
82.7
0.5226
0.9909
1
0.357
82.8
0.5855
0.8193
11.7154
82.9
0.498
0.9756
10.3787
83
0.5106
0.8963
13.1166
83.1
0.5121
0.9516
12.825
83.2
0.5838
0.8207
10.3507
83.3
0.5042
0.8056
12.8214
83.4
0.558
12.7622
83.5
0.565
9.7543
83.6
0.5502
0.9239
12.5316
83.7
0.4887
0.9082
12.8109
83.8
0.5417
0.7749
12.6398
83.9
0.4863
0.7689
9.6865
84
0.4571
12.5232
84.1
0.5544
0.8969
12.4652
84.2
0.5501
0.8654
12.2977
84.3
0.5409
0.8668
9.8364
84.4
0.453
0.8521
12.0754
84.5
0.5276
9.6372
84.6
0.5187
0.7439
12.1794
84.7
0.5243
0.7853
11.9084
84.8
0.4343
0.7091
9.0768
84.9
0.4452
11.9045
85
0.5075
0.8285
8.9928
85.1
0.4663
0.7003
9.0564
85.2
0.41
0.7176
12.0541
85.3
0.4866
0.6895
11.9982
85.4
0.4555
0.6767
8.8271
85.5
0.4249
0.8043
85.6
0.4888
0.7981
9.2597
85.7
0.4183
0.7774
85.8
0.4636
0.7785
8.7662
85.9
0.4776
0.6724
11.4649
86
0.4043
0.6672
8.5839
86.1
0.3925
0.7042
8.7451
86.2
0.3981
0.6289
11.4058
86.3
0.4629
11.2531
86.4
0.3793
0.6467
11.2999
86.5
0.4516
0.6144
86.6
0.3817
11.2932
86.7
0.4446
0.6116
8.6993
86.8
0.4493
0.6336
11.1883
86.9
0.4418
0.6022
11.1362
87
0.3781
0.6566
8.2891
87.1
0.3632
0.7102
8.3464
87.2
0.3683
0.6982
8.3075
87.3
0.4126
0.6864
87.4
0.3548
0.5919
10.5953
87.5
0.3482
0.6695
10.7342
87.6
0.3455
0.6705
10.4029
87.7
0.346
0.6653
10.3544
87.8
0.3515
0.5615
8.1706
87.9
0.4087
0.6122
7.8552
88 0.346
0.5589
8.1865
88.1
0.3434
0.5425
10.3455
88.2
0.403
0.5443
7.9279
88.3
0.327
0.5935
7.8002
88.4
0.3859
0.6183
10.1109
88.5
0.3901
0.5434
10.0637
88.6
0.3303
0.6088
7.7808
88.7
0.377
0.6213
8.0114
88.8
0.3147
0.6051
10.0118
88.9
0.3122
7.9367
89
0.3718
0.5957
9.9183
89.1
0.3074
0.5298
9.8719
89.2 0.3152 0.498
7.8258
89.3
0.3161
0.5985
7.616
89.4 0.357
0.5884
9.6477
89.5
0.3642
0.5784
9.8598
89.6
0.3285
0.4935
8.5335
89.7
0.3488
0.5801
9.6826
89.8
0.3558
0.5651
9.6373
89.9
0.2985
0.5607
7.5727
90
0.3471
0.5563
7.5372
90.1
0.3002
0.4746
7.0851
90.2
0.2979
9.1259
90.3
0.3329
0.5537
7.1013
90.4
0.2871
0.5494
9.3692
90.5
0.3339
0.4751
7.2802
90.6
0.2857
7.1647
90.7
0.3287
0.4579
9.2379
90.8
0.2693
0.4495
9.0332
90.9
0.2672
6.8234
91
0.2652
0.5099
9.0284
91.1
0.266
0.5155
8.9065
91.2
0.3191
0.521
8.8646
91.3
0.2706
0.4276
7.0899
91.4
0.3027
0.4943
7.0565
91.5
0.3004
0.4904
8.5841
91.6
0.2812
0.4224
8.9321
91.7
0.2539
6.6482
91.8
0.2547
0.4068
91.9
0.2555
0.4709
8.8066
92
0.248
0.405
6.631
92.1
0.2867
0.4195
6.5998
92.2
0.2925
0.4644
8.4563
92.3
0.2476
0.4348
8.4165
92.4
0.2774
0.4012
8.3768
92.5
0.2464
0.4024
6.4019
92.6
0.2445
0.3822
6.2976
92.7
0.2788
0.4467
6.5629
92.8
0.2792
0.3847
6.3118
92.9
0.2796
0.3776
8.1812
93
0.227
0.4405
6.2524
93.1
0.2302
0.433
6.1505
93.2
0.2681
0.3689
6.4816
93.3
0.2266
0.3741
6.236
93.4
0.2567
0.435
7.9901
93.5
0.2207
0.3643
8.0234
93.6
0.2551
0.4322
8.1268
93.7
0.2603
0.3509
7.8071
93.8
0.2156
0.3637
6.0902
93.9
0.218
0.3608
7.6639
94
0.2496
0.4152
7.6276
94.1
0.2153
0.4157
7.6606
94.2
0.2113
0.4088
7.8305
94.3
0.2279
0.4093
7.7251
94.4
0.2148
0.4061
7.7566
94.5
0.2379
0.3883
7.5845
94.6
0.2338
0.3962
7.4138
94.7
0.2364
0.3391
7.5129
94.8
0.2039
0.3293
5.8751
94.9
0.2045
0.3267
5.7144
95
0.1964
7.4068
95.1
0.2356
5.9237
95.2
0.1976
0.3816
7.4678
95.3
0.2003
7.4325
95.4
0.2281
0.3143
5.5155
95.5 0.218
0.366
5.4894
95.6
0.1895
0.3195
5.4634
95.7
0.2228
0.3037
7.2287
95.8
0.1866
0.3046
5.6027
95.9
0.1892
5.5128
96
0.1817
0.3521
7.1894
96.1
0.1882
0.3526
5.4606
96.2
0.1868
0.3531
6.9965
96.3
0.1756
0.3026
5.4711
96.4
0.2032
0.3476
6.9302
96.5
0.2017
5.3578
96.6
0.1791
5.2711
96.7
0.1985
0.3365
5.307
96.8
0.1707
5.1604
96.9
0.1694
6.8278
97
0.1755
5.2919
97.1
0.1686
0.3142
5.2668
97.2
0.1728
0.2673
6.5522
97.3
0.1805
5.1576
97.4
0.1612
5.1921
97.5
0.1777
0.2756
5.2849
97.6
0.1763
0.2878
97.7
0.1837
0.3085
5.1766
97.8 0.1892
0.3117
5.152
97.9
0.1843
0.2559
5.7612
98
0.1863
0.293
6.4219
98.1
0.1781
0.2935
6.3913
98.2
0.1582
0.2472
5.1114
98.3
0.1569
0.2508
4.9176
98.4
0.1789
0.2461
6.413
98.5
0.1742
0.2469
4.9268
98.6
0.155
0.2397
6.4078
98.7
0.1521
0.2484
6.211
98.8
0.1494
0.2622
4.7464
98.9
0.1673
4.7788
99
0.1423
0.2401
6.1227
99.1
0.1412
0.2382
4.8965
99.2
0.1557
6.0103
99.3
0.1699
0.2371
4.7961
99.4 0.1686
0.2677
6.0604
99.5
0.1642
0.2682
99.6
0.1418
0.2217
6.0559
99.7
0.1378
0.2689
4.5467
99.8
0.1605
5.9983
99.9
0.1607
0.2575
5.9697
100
0.1375
0.2173
4.6383
génie chimique et biologique
Faculty of Engineering
PROJECT 2 DESCRIPTION
Consider the following system of three continuous stirred tanks, connected in series and filled with water:
lt
o
ce
tr
io
(
L)
??3
= −
??1 (Eq 1)
=
(??1 − ??2) (Eq 2)
=
�̇�
(??2 − ??3) (Eq 3)
For this project, you will determine the salt concentrations for each tank over time, by solving the system of
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