Sedimentation Appendix
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Calculations Part I. Same concentration, different volume
Height vs. Time 1000 800 600
800 cm
400
600 cm 400 cm
200 0 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 Concentration: 2.5% a.
Initial height (zo) = 800 mm Time, θ (min)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
0
800
26
249
52
137
78
122.5
2
750
28
233
54
136
80
122
4
690
30
219
56
134
82
121
6
635
32
205
58
133
84
120
8
579
34
193
60
131
86
119
10
520
36
181
62
130.5
88
118.5
12
473
38
169
64
129
90
117.5
14
422
40
159
66
128
92
117
16
377
42
150
68
128
94
116.5
18
338
44
146
70
126
96
115.5
20
309
46
143
72
125
98
115
22
284
48
141
74
124
24
265
50
139
76
123
20110.01
Height, z (mm)
20110.01
Time, θ (min)
Velocity, v
Concentration, c
zi (mm)
dθ
10
789
29.774
26.49963
20
580.3
42.985
13.50006
34.65451
30
429
61.286
6.999967
46.87648
40
349.3
73.537
4.74999
57.57232
50
189
189
1
106.4022
25.48797
60
178.8
238.4
0.75
112.4721
70
169
270.4
0.625
118.9941
80 90
151.8 151.4
404.8 403.73
0.375 0.375003
132.477 132.827
98
139.5
558
0.25
144.1578
Sample 1: height vs. time 900 800 700 y = -27.36x + 800.1 R² = 0.999
600
Height = 800 cm
500
constant - 1
400 300 y = -0.438x + 157.1 R² = 0.994
200 100 0 0
20
40
60
80
100
120
Critical point: θc=28min zc=250 mm
Sample 1: Determination of Velocity
Height = 800 cm
900
y = -26.5x + 789
10
y = -13.5x + 580.3
20
800
700
y = -7x + 429
30
y = -4.75x + 349.3
40
600
500
y = -x + 189
50
400
y = -0.75x + 178.8
60
y = -0.625x + 169
70
300
200
y = -0.375x + 151.8
80
100
y = -0.375x + 151.4
90
0
-20
0 -100
-200
20
40
60
80
100
120
140 y = -0.25x + 139.5
98
b.
Initial height (zo) = 600 mm
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
0
600
26
167
52
104
78
92.5
2
555
28
154
54
103
80
92
4
503
30
143
56
102
82
91
6
455
32
132
58
101
84
91
8
400
34
122
60
100
86
90
10
354
36
117
62
99
88
89
12
312
38
115
64
98
90
88
14
276
40
113
66
97.5
92
88
16
248
42
111
68
97.5
94
87
18
228
44
109
70
96
96
87
20
209
46
108.5
72
95
98
86
22
194
48
106
74
94
24
180
50
105
76
93.5
14835.5
14835.5
Velocity, v
Concentration, c
Time, θ (min)
zi (mm)
dθ
10 20 30 40 50 60 70 80 90
575.3 380.3 308 153 130 130 135 139.9 121.8
12656.6 3232.55 1694 153 65 65 67.5 87.4375 45.675
22 8.5 5.5 1 0.5 0.5 0.5 0.625 0.375
25.78742 39.00999 48.16721 96.96405 114.1192 114.1192 109.8926 106.0436 121.8021
98
110.8
27.7
0.25
133.8944
Sample 2: height vs. time
700 600 500
Height = 600 cm 400
constant-1
300
y = -24.41x + 600.6 R² = 0.999
200
constant-2 Linear (constant-1)
y = -0.401x + 124.4 R² = 0.994
100
Linear (constant-2)
0 0
20
40
60
80
100
120
Critical point: θc=23.5 min zc=175 mm
Sample 2: Determination of Velocity y = -22x + 575.3
Height = 600 cm 10
y = -8.5x + 380.3
20
y = -5.5x + 308 y = -x + 153
30
y = -0.5x + 130
50
700 600 500 400 300
y = -0.5x + 130
200
y = -0.625x + 139.9
70
y = -0.375x + 121.8 y = -0.25x + 110.8
80
100
y = -0.5x + 135
98
0 -20
c.
40
-100
0
20
40
60
80
100
120
60
90
140
Initial height (zo) = 400 mm Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
s0
400
26
82
52
66
78
58.5
2
355
28
79.5
54
65
80
58
4
305
30
78
56
64.5
82
57.5
6
260
32
76
58
64
84
57
8
215
34
75
60
63.5
86
57
10
181
36
74
62
63
88
56
12
169
38
73
64
62
90
55.5
14
141
40
71.5
66
62
92
55
16
126
42
71
68
61.5
94
54.5
18
113
44
70
70
61
96
54
20
101
46
69
72
60
22
90
48
68
74
60
24
85
50
67
76
59.5
10397.58
54
98
10397.58 Time, θ (min)
zi (mm)
Velocity, v
dθ
Concentration, c
10
351
5967
17
20
216.3
1243.725
5.75
29.62274 48.07018
30
104
91
0.875
99.97673
40
92
46
0.5
113.0172
50
91.83
45.915
0.5
113.2264
60
87.08
32.655
0.375
119.4026
70 80 90
78.5 78 78
19.625 19.5 19.5
0.25 0.25 0.25
132.4532 133.3023 133.3023
98
54
0
0
192.5478
Sample 3: height vs. time
450 400 350
y = -23.25x + 400 R² = 0.999
300 250
Height=400 cm
200 150
constant-1
y = -0.262x + 79.25 R² = 0.997
100 50 0 0
Critical point: θc=18.5 min zc=112.5 mm
20
40
60
80
100
120
Sample 3: Determination of Velocity 450
Height=40 0 cm 10
y = -17x + 351
400
20
y = -5.75x + 216.3 350 y = -0.5x + 92
40
200
y = -0.5x + 91.83
50
150
y = -0.375x + 87.08
60
250
100 50 0 -50 0
20
40
60
80
100
y = -0.25x + 78.5
70
y = -0.25x + 78
80
y = -0.25x + 78
90
120
98
y = 54
Reynolds Number vs. Settling Time (Varying Initial Height) 0.0035000 0.0030000 Reynolds Number
-20
30
y = -0.875x + 104.0
300
Height: 80 cm
0.0025000
Height: 60 cm
0.0020000
Height: 40 cm 0.0015000 0.0010000 0.0005000 0.0000000 0.0000
0.2000
0.4000
0.6000
0.8000
1.0000
Settling Time, hours
1.2000
1.4000
1.6000
1.8000
Part II. Same volume, different concentration
height vs. time 1000 800 600 7.50% 400 5% 200
2.50%
0 -400-300-200-100 0 1002003004005006007008009001000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 4000
time (min)
Height = 900mm a.
Concentration = 7.5% Time, θ (min)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
0
900
32
760
64
618
96
472
2
893
34
750
66
609
98
463
4
880
36
743
68
599
100
454
6
877
38
733
70
589
102
445
8
868
40
725
72
580
104
436
10
858
42
716
74
571
106
427
12
849
44
708
76
561
108
419
14
840
46
698
78
552
110
411
16
832
48
690
80
543
112
402
18
823
50
681
82
534
114
395
20
813
52
670
84
525
116
390
22
804
54
661
86
516
118
386
24
795
56
654
88
507.5
120
383
26
787
58
646
90
499
122
380
28
778
60
637
92
489
3750
166
30
768
62
628
94
480
70576.57
Height, z (mm)
70576.57
Velocity, v
Concentration, c
Time, θ (min)
zi (mm)
dθ
20
908.3
4314.425
4.75
40
907
4081.5
4.5
77.8132
60
903
4063.5
4.5
78.15788
77.70183
80
895
4027.5
4.5
78.8565
100
894.6
3802.05
4.25
78.89176
120
563
2533.5
4.5
125.358
3750
387.2
22.8448
0.059
182.2742
Sample 1: height vs. time 1000 900 800
y = -4.427x + 901.6 R² = 0.999
700 7.50%
600 500
constant-1
y = -0.059x + 387.2 R² = 1
400 300
constant-2 Linear (constant-1)
200
Linear (constant-2)
100 0 -400-300-200-100 0 1002003004005006007008009001000110012001300140015001600170018001900200021002200230024002500260027002800290030003100320033003400350036003700380039004000
time (min)
Critical point: θc=90 min zc=385 mm
Sample 1: Determination of Velocity 1000
7.50%
y = -4.75x + 908.3
20
y = -4.5x + 907
40
800 600 400 200
y = -4.5x + 903
60
y = -4.5x + 895
80
y = -4.25x + 894.6
100
y = -1.5x + 563
120
y = -0.059x + 387.2 0 -400-300-200-100 0 100 200 300 400 500 600 700 800 9001000110012001300140015001600170018001900200021002200230024002500260027002800290030003100320033003400350036003700380039004000
-200
time (min)
3750
b.
Concentration = 5% Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
0
900
32
559
64
332
96
246
2
880
34
542
66
321
98
244
4
856.5
36
524
68
311
100
243
6
834
38
508
70
300
102
242
8
811
40
492
72
290.5
104
241
10
788
42
477
74
281
106
240
12
764
44
461
76
272
108
239
14
742
46
446
78
265
110
238
16
719
48
433
80
261
112
237
18
697
50
418
82
258
114
236
20
676
52
404
84
256
116
235
22
655
54
391
86
254
118
234
24
635
56
378
88
252
120
233
26
615
58
367
90
250
122
232
28
596
60
355
92
248.5
3750
113
30
576.5
62
344
94
248
46390.55
46390.55
Velocity, v
Concentration, c
Time, θ (min)
zi (mm)
dθ
20
802.3
6217.825
7.75
57.82195
40
700.3
4026.725
5.75
66.24382
60
401.3
1504.875
3.75
115.6007
80
293
146.5
0.5
158.3295
100
293
146.5
0.5
158.3295
120
236
7.552
0.032
196.5701
3750
236
7.552
0.032
196.5701
Sample 2: height vs. time 1000 900 800 5%
700
constant-1
600 500 400 300
constant-2
y = -10.93x + 898.0 R² = 0.999
y = -0.032x + 236 R² = 1
200
Linear (constant-1) Linear (constant-2)
100 0 -400-300-200-100 0 100 200 300 400 500 600 700 800 9001000110012001300140015001600170018001900200021002200230024002500260027002800290030003100320033003400350036003700380039004000
time (min)
Critical point: θc=80 min zc=240 mm
Sample 2: Determination of Velocity 1200
5%
1000 800
y = -7.75x + 802.3
20
y = -5.75x + 700.3
40
y = -1.75x + 401.3
60
600 y = -0.5x + 293
80
400
y = -0.5x + 293
100
200
y = -0.032x + 236
120
y = -0.032x + 236
3750
0 -400-300-200-100 0 100 200 300 400 500 600 700 800 9001000110012001300140015001600170018001900200021002200230024002500260027002800290030003100320033003400350036003700380039004000
-200 time (min)
c.
Concentration = 2.5% Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
0
900
32
322
64
171.5
96
152
2
850
34
308
66
170
98
151
4
800
36
294
68
168
100
150
6
754
38
280
70
167
102
149
8
703
40
268
72
165
104
148
10
654
42
255
74
164
106
147
12
609
44
244
76
162
108
146
14
562
46
232
78
161
110
145.5
16
521
48
222
80
160
112
145
18
478
50
211
82
159
114
145
20
444
52
200
84
158
116
144.5
22
414
54
191
86
157
118
143
24
391
56
182
88
155.5
120
142
26
371
58
178.5
90
154
122
141.5
28
352
60
176
92
153
3750
73
30
336
62
173.5
94
153
22747.55
22747.55
Velocity, v
Concentration, c
Time, θ (min)
zi (mm)
dθ
20
765.3
12244.8
16
29.7237
40
517.6
3235
6.25
43.94813
60
251
313.75
1.25
90.62769
80
200
100
0.5
113.7378
100
200
100
0.5
113.7378
120
187.1
70.1625
0.375
121.5796
3750
187.1
70.1625
0.375
121.5796
Sample 3: height vs. time 1000 900 800
y = -24.32x + 898.7 R² = 0.999
2.50% constant-1
700 600
constant-2
500 400
Linear (constant-1)
300
y = -0.018x + 143.8 R² = 1
200 100 0
-400-300-200-100 0 100 200 300 400 500 600 700 800 9001000110012001300140015001600170018001900200021002200230024002500260027002800290030003100320033003400350036003700380039004000
time (min)
Linear (constant-2)
Critical point: θc=60 min zc=160 mm
Sample 3: height vs. time
1200 1000
2.50%
800
y = -16x + 765.3
20
y = -6.25x + 517.6
40
y = -1.25x + 251
60
y = -0.5x + 200
80
y = -0.5x + 200
100
600 400 200
120 y = -0.375x + 187.1
0
-400-300-200-100 0 1002003004005006007008009001000110012001300140015001600170018001900200021002200230024002500260027002800290030003100320033003400350036003700380039004000
-200
time (min)
3750
Height vs. Time 1000 800 600
800 cm
400
600 cm 400 cm
200 0 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 Concentration: 2.5% a.
Initial height (zo) = 800 mm Time, θ (min)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
0
800
26
249
52
137
78
122.5
2
750
28
233
54
136
80
122
4
690
30
219
56
134
82
121
6
635
32
205
58
133
84
120
8
579
34
193
60
131
86
119
10
520
36
181
62
130.5
88
118.5
12
473
38
169
64
129
90
117.5
14
422
40
159
66
128
92
117
16
377
42
150
68
128
94
116.5
18
338
44
146
70
126
96
115.5
20
309
46
143
72
125
98
115
22
284
48
141
74
124
24
265
50
139
76
123
20110.01
Height, z (mm)
20110.01
Time, θ (min)
Velocity, v
Concentration, c
zi (mm)
dθ
10
789
29.774
26.49963
20
580.3
42.985
13.50006
34.65451
30
429
61.286
6.999967
46.87648
40
349.3
73.537
4.74999
57.57232
50
189
189
1
106.4022
25.48797
60
178.8
238.4
0.75
112.4721
70
169
270.4
0.625
118.9941
80 90
151.8 151.4
404.8 403.73
0.375 0.375003
132.477 132.827
98
139.5
558
0.25
144.1578
Sample 1: height vs. time 900 800 700 y = -27.36x + 800.1 R² = 0.999
600
Height = 800 cm
500
constant - 1
400 300 y = -0.438x + 157.1 R² = 0.994
200 100 0 0
20
40
60
80
100
120
Critical point: θc=28min zc=250 mm
Sample 1: Determination of Velocity
Height = 800 cm
900
y = -26.5x + 789
10
y = -13.5x + 580.3
20
800
700
y = -7x + 429
30
y = -4.75x + 349.3
40
600
500
y = -x + 189
50
400
y = -0.75x + 178.8
60
y = -0.625x + 169
70
300
200
y = -0.375x + 151.8
80
100
y = -0.375x + 151.4
90
0
-20
0 -100
-200
20
40
60
80
100
120
140 y = -0.25x + 139.5
98
b.
Initial height (zo) = 600 mm
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
0
600
26
167
52
104
78
92.5
2
555
28
154
54
103
80
92
4
503
30
143
56
102
82
91
6
455
32
132
58
101
84
91
8
400
34
122
60
100
86
90
10
354
36
117
62
99
88
89
12
312
38
115
64
98
90
88
14
276
40
113
66
97.5
92
88
16
248
42
111
68
97.5
94
87
18
228
44
109
70
96
96
87
20
209
46
108.5
72
95
98
86
22
194
48
106
74
94
24
180
50
105
76
93.5
14835.5
14835.5
Velocity, v
Concentration, c
Time, θ (min)
zi (mm)
dθ
10 20 30 40 50 60 70 80 90
575.3 380.3 308 153 130 130 135 139.9 121.8
12656.6 3232.55 1694 153 65 65 67.5 87.4375 45.675
22 8.5 5.5 1 0.5 0.5 0.5 0.625 0.375
25.78742 39.00999 48.16721 96.96405 114.1192 114.1192 109.8926 106.0436 121.8021
98
110.8
27.7
0.25
133.8944
Sample 2: height vs. time
700 600 500
Height = 600 cm 400
constant-1
300
y = -24.41x + 600.6 R² = 0.999
200
constant-2 Linear (constant-1)
y = -0.401x + 124.4 R² = 0.994
100
Linear (constant-2)
0 0
20
40
60
80
100
120
Critical point: θc=23.5 min zc=175 mm
Sample 2: Determination of Velocity y = -22x + 575.3
Height = 600 cm 10
y = -8.5x + 380.3
20
y = -5.5x + 308 y = -x + 153
30
y = -0.5x + 130
50
700 600 500 400 300
y = -0.5x + 130
200
y = -0.625x + 139.9
70
y = -0.375x + 121.8 y = -0.25x + 110.8
80
100
y = -0.5x + 135
98
0 -20
c.
40
-100
0
20
40
60
80
100
120
60
90
140
Initial height (zo) = 400 mm Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
s0
400
26
82
52
66
78
58.5
2
355
28
79.5
54
65
80
58
4
305
30
78
56
64.5
82
57.5
6
260
32
76
58
64
84
57
8
215
34
75
60
63.5
86
57
10
181
36
74
62
63
88
56
12
169
38
73
64
62
90
55.5
14
141
40
71.5
66
62
92
55
16
126
42
71
68
61.5
94
54.5
18
113
44
70
70
61
96
54
20
101
46
69
72
60
22
90
48
68
74
60
24
85
50
67
76
59.5
10397.58
54
98
10397.58 Time, θ (min)
zi (mm)
Velocity, v
dθ
Concentration, c
10
351
5967
17
20
216.3
1243.725
5.75
29.62274 48.07018
30
104
91
0.875
99.97673
40
92
46
0.5
113.0172
50
91.83
45.915
0.5
113.2264
60
87.08
32.655
0.375
119.4026
70 80 90
78.5 78 78
19.625 19.5 19.5
0.25 0.25 0.25
132.4532 133.3023 133.3023
98
54
0
0
192.5478
Sample 3: height vs. time
450 400 350
y = -23.25x + 400 R² = 0.999
300 250
Height=400 cm
200 150
constant-1
y = -0.262x + 79.25 R² = 0.997
100 50 0 0
Critical point: θc=18.5 min zc=112.5 mm
20
40
60
80
100
120
Sample 3: Determination of Velocity 450
Height=40 0 cm 10
y = -17x + 351
400
20
y = -5.75x + 216.3 350 y = -0.5x + 92
40
200
y = -0.5x + 91.83
50
150
y = -0.375x + 87.08
60
250
100 50 0 -50 0
20
40
60
80
100
y = -0.25x + 78.5
70
y = -0.25x + 78
80
y = -0.25x + 78
90
120
98
y = 54
Reynolds Number vs. Settling Time (Varying Initial Height) 0.0035000 0.0030000 Reynolds Number
-20
30
y = -0.875x + 104.0
300
Height: 80 cm
0.0025000
Height: 60 cm
0.0020000
Height: 40 cm 0.0015000 0.0010000 0.0005000 0.0000000 0.0000
0.2000
0.4000
0.6000
0.8000
1.0000
Settling Time, hours
1.2000
1.4000
1.6000
1.8000
Part II. Same volume, different concentration
height vs. time 1000 800 600 7.50% 400 5% 200
2.50%
0 -400-300-200-100 0 1002003004005006007008009001000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 4000
time (min)
Height = 900mm a.
Concentration = 7.5% Time, θ (min)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
0
900
32
760
64
618
96
472
2
893
34
750
66
609
98
463
4
880
36
743
68
599
100
454
6
877
38
733
70
589
102
445
8
868
40
725
72
580
104
436
10
858
42
716
74
571
106
427
12
849
44
708
76
561
108
419
14
840
46
698
78
552
110
411
16
832
48
690
80
543
112
402
18
823
50
681
82
534
114
395
20
813
52
670
84
525
116
390
22
804
54
661
86
516
118
386
24
795
56
654
88
507.5
120
383
26
787
58
646
90
499
122
380
28
778
60
637
92
489
3750
166
30
768
62
628
94
480
70576.57
Height, z (mm)
70576.57
Velocity, v
Concentration, c
Time, θ (min)
zi (mm)
dθ
20
908.3
4314.425
4.75
40
907
4081.5
4.5
77.8132
60
903
4063.5
4.5
78.15788
77.70183
80
895
4027.5
4.5
78.8565
100
894.6
3802.05
4.25
78.89176
120
563
2533.5
4.5
125.358
3750
387.2
22.8448
0.059
182.2742
Sample 1: height vs. time 1000 900 800
y = -4.427x + 901.6 R² = 0.999
700 7.50%
600 500
constant-1
y = -0.059x + 387.2 R² = 1
400 300
constant-2 Linear (constant-1)
200
Linear (constant-2)
100 0 -400-300-200-100 0 1002003004005006007008009001000110012001300140015001600170018001900200021002200230024002500260027002800290030003100320033003400350036003700380039004000
time (min)
Critical point: θc=90 min zc=385 mm
Sample 1: Determination of Velocity 1000
7.50%
y = -4.75x + 908.3
20
y = -4.5x + 907
40
800 600 400 200
y = -4.5x + 903
60
y = -4.5x + 895
80
y = -4.25x + 894.6
100
y = -1.5x + 563
120
y = -0.059x + 387.2 0 -400-300-200-100 0 100 200 300 400 500 600 700 800 9001000110012001300140015001600170018001900200021002200230024002500260027002800290030003100320033003400350036003700380039004000
-200
time (min)
3750
b.
Concentration = 5% Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
0
900
32
559
64
332
96
246
2
880
34
542
66
321
98
244
4
856.5
36
524
68
311
100
243
6
834
38
508
70
300
102
242
8
811
40
492
72
290.5
104
241
10
788
42
477
74
281
106
240
12
764
44
461
76
272
108
239
14
742
46
446
78
265
110
238
16
719
48
433
80
261
112
237
18
697
50
418
82
258
114
236
20
676
52
404
84
256
116
235
22
655
54
391
86
254
118
234
24
635
56
378
88
252
120
233
26
615
58
367
90
250
122
232
28
596
60
355
92
248.5
3750
113
30
576.5
62
344
94
248
46390.55
46390.55
Velocity, v
Concentration, c
Time, θ (min)
zi (mm)
dθ
20
802.3
6217.825
7.75
57.82195
40
700.3
4026.725
5.75
66.24382
60
401.3
1504.875
3.75
115.6007
80
293
146.5
0.5
158.3295
100
293
146.5
0.5
158.3295
120
236
7.552
0.032
196.5701
3750
236
7.552
0.032
196.5701
Sample 2: height vs. time 1000 900 800 5%
700
constant-1
600 500 400 300
constant-2
y = -10.93x + 898.0 R² = 0.999
y = -0.032x + 236 R² = 1
200
Linear (constant-1) Linear (constant-2)
100 0 -400-300-200-100 0 100 200 300 400 500 600 700 800 9001000110012001300140015001600170018001900200021002200230024002500260027002800290030003100320033003400350036003700380039004000
time (min)
Critical point: θc=80 min zc=240 mm
Sample 2: Determination of Velocity 1200
5%
1000 800
y = -7.75x + 802.3
20
y = -5.75x + 700.3
40
y = -1.75x + 401.3
60
600 y = -0.5x + 293
80
400
y = -0.5x + 293
100
200
y = -0.032x + 236
120
y = -0.032x + 236
3750
0 -400-300-200-100 0 100 200 300 400 500 600 700 800 9001000110012001300140015001600170018001900200021002200230024002500260027002800290030003100320033003400350036003700380039004000
-200 time (min)
c.
Concentration = 2.5% Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
Time, θ (min)
Height, z (mm)
0
900
32
322
64
171.5
96
152
2
850
34
308
66
170
98
151
4
800
36
294
68
168
100
150
6
754
38
280
70
167
102
149
8
703
40
268
72
165
104
148
10
654
42
255
74
164
106
147
12
609
44
244
76
162
108
146
14
562
46
232
78
161
110
145.5
16
521
48
222
80
160
112
145
18
478
50
211
82
159
114
145
20
444
52
200
84
158
116
144.5
22
414
54
191
86
157
118
143
24
391
56
182
88
155.5
120
142
26
371
58
178.5
90
154
122
141.5
28
352
60
176
92
153
3750
73
30
336
62
173.5
94
153
22747.55
22747.55
Velocity, v
Concentration, c
Time, θ (min)
zi (mm)
dθ
20
765.3
12244.8
16
29.7237
40
517.6
3235
6.25
43.94813
60
251
313.75
1.25
90.62769
80
200
100
0.5
113.7378
100
200
100
0.5
113.7378
120
187.1
70.1625
0.375
121.5796
3750
187.1
70.1625
0.375
121.5796
Sample 3: height vs. time 1000 900 800
y = -24.32x + 898.7 R² = 0.999
2.50% constant-1
700 600
constant-2
500 400
Linear (constant-1)
300
y = -0.018x + 143.8 R² = 1
200 100 0
-400-300-200-100 0 100 200 300 400 500 600 700 800 9001000110012001300140015001600170018001900200021002200230024002500260027002800290030003100320033003400350036003700380039004000
time (min)
Linear (constant-2)
Critical point: θc=60 min zc=160 mm
Sample 3: height vs. time
1200 1000
2.50%
800
y = -16x + 765.3
20
y = -6.25x + 517.6
40
y = -1.25x + 251
60
y = -0.5x + 200
80
y = -0.5x + 200
100
600 400 200
120 y = -0.375x + 187.1
0
-400-300-200-100 0 1002003004005006007008009001000110012001300140015001600170018001900200021002200230024002500260027002800290030003100320033003400350036003700380039004000
-200
time (min)
3750
Related Documents
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Appendix
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