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4. Appendices
4.1 Sample calculations
4.1.1. Power requirement calculations
For an impeller speed reading of 55 RPM operated in an Baffled tank with size
4flat blade impeller
Actual Impeller Speed:
Actual RPM = (1.26*RPM reading) – 40.84
= (1.26*55 RPM) – 40.84 = 28.46 RPM
RPM to RPS:
N = RPM/60 = 28.46 RPM/60s = 0.4743 RPS
Angular velocity:
ω= 2πN = 2Π(0.4743 RPS) = 2.9803 rad/s
Force reading conversion from g to N:
Fg = 9g
= 0.0882 N
Average Force:
Fave = (FN + Fg)/2 = (0.09N + 0.0882N)/2 = 0.0891N
Torque:
τ = Fave * Moment Arm = 0.0891N * 0.11m = 0.0098 J
Experimental Power Requirement:
Reynolds Number:
Power Number, NPo:
from plot of NPo vs NRe shown in appendix 4.2 using curve no. 10 for
baffled tank and curve no.29 for unbaffled tank
14
Power from graph:
Correction factor:
Theoretical Power requirement:
Percent Difference:
4.1.2. Conductivity measurements
For baffled tank with size 4 flat blade impeller
Average initial conductivity:
Time of mixing:
Time at which conductivity is stable within 1 percent of the reading
4.1.3. Scale-up calculations (V2= 15m3)
For size 4 flat blade impelle
Scale-up ratio:
Scaling -up dimensions:
Tank Diameter:
Tank Height:
Liquid Height:
15
Impeller Diameter:
Impeller Elevation:
Impeller speed:
Where n=2/3, for equal power per unit volume, n=1, for equal liquid
motion and n=0.5, for equal Froude number
Scaling up power requirement:
Scaling up time of mixing:
16
4.2. Processed Data Tables
Table 4.2-1 Baffled Tank with Size 4 flat blade impeller experimental power requirement
Table 4.2-2 Unbaffled Tank with Size 4 flat blade impeller experimental power requirement
Impeller
Speed (RPM)
Actual Impeller
Speed
(RPM)
Actual Impeller
Speed
(RPS)
Angular
Speed (rad/s)
Force Balance Reading
Average
Force (N)
Torque
(J)
Experimental
Power (W)
Initial N Reading
Final N Reading
Actual
N
Reading
Initial g Reading
Final g Reading
Actual g Reading
Actual
N (from g
reading)
50.00 22.16 0.3693 2.3206
1.21
1.25 0.04
122.00
129.00 7.00 0.07 0.0543 0.0060 0.0139
80.00 59.96 0.9993 6.2790 1.29 0.08 132.00 10.00 0.10 0.0890 0.0098 0.0615
120.00 110.36 1.8393 11.5569 1.32 0.11 134.00 12.00 0.12 0.1138 0.0125 0.1447
150.00 148.16 2.4693 15.5153 1.35 0.14 140.00 18.00 0.18 0.1582 0.0174 0.2700
180.00 185.96 3.0993 19.4737 1.45 0.24 150.00 28.00 0.27 0.2572 0.0283 0.5509
215.00 230.06 3.8343 24.0918 2.00 0.79 205.00 83.00 0.81 0.8017 0.0882 2.1246
Impeller
Speed (RPM)
Actual Impeller
Speed
(RPM)
Actual Impeller
Speed
(RPS)
Angular
Speed (rad/s)
Force Balance Reading Average
Force (N)
Torque
(J)
Experimental
Power (W)
Initial N Reading
Final N Reading
Actual N Reading
Initial g Reading
Final g Reading
Actual g Reading
Actual N
(from g
reading)
55.00 28.46 0.4743 2.9803
1.21
1.30 0.09
122.00
131.00 9.00 0.0882 0.0891 0.0098 0.0292
85.00 66.26 1.1043 6.9387 1.45 0.24 146.00 24.00 0.2352 0.2376 0.0261 0.1814
110.00 97.76 1.6293 10.2374 2.29 1.08 231.00 109.00 1.0682 1.0741 0.1182 1.2096
17
Table 4.2-3. Baffled Tank with Size 4 flat blade impeller theoretical power requirement
and percent difference
NRe NPo N3D'
5ρ
Power from
graph (W)
Theoretical
Power (W) % Difference
23089.7862 1.80 0.0340 0.0612 0.0286 2.14
53757.1763 1.80 0.4292 0.7726 0.3609 49.75
79313.3346 1.80 1.3785 2.4814 1.1591 4.36
Table 4.2-4. Unbaffled Tank with Size 4 flat blade impeller theoretical power requirement
and percent difference
NRe NPo N3D'
5ρ
Power from graph (W)
Theoretical Power (W)
% Difference
17978.5546 0.18 0.0161 0.0029 0.0057 142.01
48645.9446 0.17 0.3181 0.0541 0.1072 42.63
89535.7980 0.15 1.9832 0.2975 0.5895 75.46
120203.1880 0.14 4.7988 0.6718 1.3314 79.72
150870.5780 0.14 9.4885 1.3284 2.6325 79.07
186649.1997 0.14 17.9664 2.5153 4.9847 57.38
Table 4.2-5. Baffled Tank with Size 5 flat blade impeller theoretical power requirement
and percent difference
NRe NPo N3D'
5ρ
Power from graph (W)
Theoretical Power (W)
% Difference
22338.0263 1.80 0.0620 0.1115 0.0585 42.48
42581.0593 1.80 0.4292 0.7726 0.4055 54.34
54726.8792 1.80 0.9113 1.6403 0.8609 54.89
62824.0924 1.80 1.3785 2.4814 1.3023 38.38
Table 4.2-6. Unbaffled Tank with Size 5 flat blade impeller theoretical power requirement
and percent difference
NRe NPo N3D'
5ρ
Power from
graph (W)
Theoretical
Power (W) % Difference
14240.8131 0.20 0.0161 0.0032 0.0072 93.49
30435.2395 0.18 0.1567 0.0282 0.0628 35.74
79018.5188 0.16 2.7430 0.4389 0.9772 85.67
95212.9452 0.16 4.7988 0.7678 1.7096 88.15
135699.0113 0.15 13.8923 2.0838 4.6400 90.66
151893.4377 0.15 19.4832 2.9225 6.5074 90.89
168087.8641 0.15 26.4029 3.9604 8.8186 91.21
18
Table 4.2-7 Baffled Tank with Size 5 flat blade impeller experimental power requirement
Impeller Speed
(RPM)
Actual
Impeller
Speed (RPM)
Actual
Impeller
Speed (RPS)
Angular Speed
(rad/s)
Force Balance Reading
Average Force
(N)
Torque
(J)
Experimental Power
(W) Initial N
Reading
Final N
Reading
Actual
N Reading
Initial g
Reading
Final g
Reading
Actual g
Reading
Actual
N (from
g
reading)
60.00 34.76 0.5793 3.6401
1.24
1.32 0.08
126.00
135.00 9.00 0.09 0.0841 0.0093 0.0337
85.00 66.26 1.1043 6.9387 1.49 0.25 150.00 24.00 0.24 0.2426 0.0267 0.1852
100.00 85.16 1.4193 8.9179 1.63 0.39 167.00 41.00 0.40 0.3959 0.0435 0.3884
110.00 97.76 1.6293 10.2374 1.94 0.70 200.00 74.00 0.73 0.7126 0.0784 0.8025
Table 4.2-7 Unbaffled Tank with Size 5 flat blade impeller experimental power requirement
Impeller
Speed
(RPM)
Actual Impeller
Speed
(RPM)
Actual Impeller
Speed
(RPS)
Angular
Speed
(rad/s)
Force Balance Reading
Average
Force
(N)
Torque
(J)
Experimental
Power
(W) Initial N Reading
Final N Reading
Actual
N
Reading
Initial g Reading
Final g Reading
Actual g Reading
Actual
N (from g
reading)
50.00 22.16 0.3693 2.3206
1.21
1.24 0.03
122.00
130.00 8.00 0.08 0.0542 0.0060 0.0138
70.00 47.36 0.7893 4.9595 1.26 0.05 132.00 10.00 0.10 0.0740 0.0081 0.0404
130.00 122.96 2.0493 12.8763 1.30 0.09 133.00 11.00 0.11 0.0989 0.0109 0.1401
150.00 148.16 2.4693 15.5153 1.32 0.11 135.00 13.00 0.13 0.1187 0.0131 0.2026
200.00 211.16 3.5193 22.1126 1.39 0.18 140.00 18.00 0.18 0.1782 0.0196 0.4335
220.00 236.36 3.9393 24.7516 1.42 0.21 145.00 23.00 0.23 0.2177 0.0239 0.5927
240.00 261.56 4.3593 27.3905 1.45 0.24 150.00 28.00 0.27 0.2572 0.0283 0.7749
19
Table 4.2-8 Initial Conductivity
Time (s)
Size 4 flat blade impeller Size 5 flat blade impeller
Conductivity, K (mS/cm) Conductivity, K (mS/cm)
Baffled Unbaffled Baffled Unbaffled
0 1.58 1.51 1.53 1.53
5 1.54 1.54 1.56 1.58
10 1.56 1.56 1.54 1.54
15 1.57 1.54 1.54 1.58
20 1.54 1.53 1.53 1.54
25 1.58 1.54 1.56 1.51
30 1.54 1.56 1.57 1.54
35 1.54 1.55 1.53 1.58
40 1.58 1.57 1.54 1.5
45 1.57 1.54 1.54 1.54
50 1.53 1.55 1.55 1.57
Kave 1.56 1.54 1.54 1.55
20
Table 4.2-9 Conductivity as a function of time (time of mixing)
Time (s)
Size 4 flat blade impeller Size 5 flat blade impeller
Conductivity, K (mS/cm) Conductivity, K (mS/cm)
B ΔK % diff UnB ΔK % diff B ΔK % diff UnB ΔK % diff
0 1.56 - - 1.54 - - 1.54 - 1.55 - -
3 4.71 3.15 - 2.04 0.50 - 4.70 3.16 - 3.50 1.95 -
6 4.02 0.69 78.10 3.52 1.48 196.00 4.05 0.65 79.43 6.01 2.51 28.72
9 4.08 0.06 91.30 3.65 0.13 91.22 4.02 0.03 95.38 5.04 0.97 61.35
12 4.07 0.01 83.33 6.52 2.87 2107.69 4.01 0.01 66.67 4.51 0.53 45.36
15 4.08 0.01 0.00 3.51 3.01 4.88 4.02 0.01 0.00 4.16 0.35 33.96
18 4.07 0.01 0.00 3.50 0.01 99.67 4.01 0.01 0.00 4.08 0.08 77.14
21 4.08 0.01 0.00 3.56 0.06 500.00 4.02 0.01 0.00 4.00 0.08 0.00
24 4.04 0.04 300.00 3.53 0.03 50.00 4.00 0.02 100.00 3.59 0.41 412.50
27 4.07 0.03 25.00 3.54 0.01 66.67 4.01 0.01 50.00 3.58 0.01 97.56
30 4.05 0.02 33.33 3.53 0.01 0.00 4.02 0.01 0.00 3.57 0.01 0.00
33 4.07 0.02 0.00 3.55 0.02 100.00 4.02 0.00 100.00 3.56 0.01 0.00
36 4.05 0.02 0.00 3.54 0.01 50.00 4.01 0.01 0 3.57 0.01 0.00
39 4.04 0.01 50.00 3.51 0.03 200.00 4.02 0.01 0.00 3.54 0.03 200.00
42 4.06 0.02 100.00 3.56 0.05 66.67 4.00 0.02 100.00 3.56 0.02 33.33
45 4.08 0.02 0.00 3.53 0.03 40.00 4.02 0.02 0.00 3.57 0.01 50.00
48 4.05 0.03 50.00 3.52 0.01 66.67 4.02 0.00 100.00 3.58 0.01 0.00
51 4.06 0.01 66.67 3.55 0.03 200.00 4.00 0.02 0 3.55 0.03 200.00
54 4.06 0.00 100.00 3.54 0.01 66.67 4.01 0.01 50.00 3.56 0.01 66.67
57 4.05 0.01 0 3.53 0.01 0.00 4.01 0.00 100.00 3.56 0.00 100.00
60 4.05 0.00 100.00 3.56 0.03 200.00 4.01 0.00 0 3.56 0.00 0
63 4.04 0.01 0 3.54 0.02 33.33 4.02 0.01 0 3.55 0.01 0
66 4.05 0.01 0.00 3.56 0.02 0.00 4.03 0.01 0.00 3.54 0.01 0.00
69 4.06 0.01 0.00 3.55 0.01 50.00 4.02 0.01 0.00 3.55 0.01 0.00
72 4.04 0.02 100.00 3.55 0.00 100.00 4.01 0.01 0.00 3.55 0.00 100.00
75 4.05 0.01 50.00 3.53 0.02 0 4.01 0.00 100.00 3.59 0.04 0
78 4.04 0.01 0.00 3.55 0.02 0.00 4.00 0.01 0 3.57 0.02 50.00
81 4.06 0.02 100.00 3.54 0.01 50.00 4.02 0.02 100.00 3.56 0.01 50.00
84 4.05 0.01 50.00 3.55 0.01 0.00 4.03 0.01 50.00 3.56 0.00 100.00
87 4.05 0.00 100.00 3.56 0.01 0.00 4.02 0.01 0.00 3.55 0.01 0
90 4.03 0.02 0 3.53 0.03 200.00 4.02 0.00 100.00 3.59 0.04 300.00
93 4.04 0.01 50.00 3.53 0.00 100.00 4.02 0.00 0 3.59 0.00 100.00
96 4.03 0.01 0.00 3.56 0.03 0 4.02 0.00 0 3.55 0.04 0
21
Table 4.2-10 Scale up dimensions
Dimensions
Small Scale Large Scale
Size 4 flat blade
Size 5 flat blade
Size 4 flat blade
Size 5
flat blade
Impeller Diameter, D' (m) 0.200 0.178 1.6369 1.4568
Elevation, Zi(m) 0.110 0.105 0.9003 0.8594
Tank
Diameter,DT(m) 0.288 2.3571
Height, HT (m) 0.420 3.4375
Volume, V(m3) 0.027 15.0000
Liquid Height, Zl(m) 0.300 2.4553
Scale-up ratio, R 8.184441282
Time (s)
Size 4 flat blade impeller Size 5 flat blade impeller
Conductivity, K (mS/cm) Conductivity, K (mS/cm)
B ΔK % diff UnB ΔK % diff B ΔK % diff UnB ΔK % diff
99 4.03 0.00 100.00 3.54 0.02 33.33 4.01 0.01 0 3.59 0.04 0.00
102 4.03 0.00 0 3.52 0.02 0.00 4.00 0.01 0.00 3.56 0.03 25.00
105 4.04 0.01 0 3.54 0.02 0.00 4.01 0.01 0.00 3.56 0.00 100.00
108 4.05 0.01 0.00 3.55 0.01 50.00 4.01 0.00 100.00 3.55 0.01 0
111 4.03 0.02 100.00 3.54 0.01 0.00 4.02 0.01 0 3.56 0.01 0.00
114 4.04 0.01 50.00 3.54 0.00 100.00 4.00 0.02 100.00 3.56 0.00 100.00
117 4.02 0.02 100.00 3.53 0.01 0 4.03 0.03 50.00 3.55 0.01 0
120 4.04 0.02 0.00 3.54 0.01 0.00 4.00 0.03 0.00 3.56 0.01 0.00
130 4.05 0.01 50.00 3.53 0.01 0.00 4.01 0.01 66.67 3.56 0.00 100.00
140 4.02 0.03 200.00 3.54 0.01 0.00 4.03 0.02 100.00 3.54 0.02 0
150 4.02 0.00 100.00 3.56 0.02 100.00 4.03 0.00 100.00 3.54 0.00 100.00
160 4.04 0.02 0 3.54 0.02 0.00 4.01 0.02 0 3.54 0.00 0
170 4.03 0.01 50.00 3.53 0.01 50.00 4.00 0.01 50.00 3.59 0.05 0
180 4.02 0.01 0.00 3.53 0.00 100.00 4.01 0.01 0.00 3.53 0.06 20.00
190 4.05 0.03 200.00 3.52 0.01 0 4.02 0.01 0.00 3.56 0.03 50.00
200 4.01 0.04 33.33 3.54 0.02 100.00 4.02 0.00 100.00 3.54 0.02 33.33
210 4.03 0.02 50.00 3.53 0.01 50.00 4.02 0.00 0 3.54 0.00 100.00
220 4.04 0.01 50.00 3.54 0.01 0.00 4.01 0.01 0 3.59 0.05 0
230 4.02 0.02 100.00 3.52 0.02 100.00 4.00 0.01 0.00 3.54 0.05 0.00
240 4.03 0.01 50.00 3.54 0.02 0.00 4.00 0.00 100.00 3.55 0.01 80.00
250 4.02 0.01 0.00 3.53 0.01 50.00 4.00 0.00 0 3.54 0.01 0.00
22
Table 4.2-11 Scaled-up power requirement and mixing time of baffled tank with Size 4 flat
blade impeller
n N1(rps) N2
(rps) Nre Npo N
3D'
5ρ Pgraph (W) Pth (W) tm (s)
0.67
0.4743 0.1160 3.7818E+05 1.80 18.2591 32.8664 15.3519 69.47
1.1043 0.2700 8.8046E+05 1.80 230.4250 414.7650 193.7365 29.84
1.6293 0.3984 1.2990E+06 1.80 740.0464 1332.0834 622.2153 20.23
1.00
0.4743 0.0580 1.8898E+05 1.80 2.2784 4.1010 1.9156 139.03
1.1043 0.1349 4.3997E+05 1.80 28.7522 51.7539 24.1742 59.72
1.6293 0.1991 6.4914E+05 1.80 92.3421 166.2158 77.6393 40.47
0.50
0.4743 0.1658 5.4063E+05 1.80 53.3463 96.0234 44.8525 48.60
1.1043 0.3860 1.2587E+06 1.80 673.2154 1211.7877 566.0253 20.87
1.6293 0.5695 1.8571E+06 1.80 2162.1376 3891.8477 1817.8796 14.15
Table 4.2-12 Scaled-up power requirement and mixing time of unbaffled tank with Size 4
flat blade impeller
n N1(rps) N2
(rps) Nre Npo N
3D'
5ρ Pgraph (W) Pth (W) tm(s)
0.67
0.3693 0.0903 2.9446E+05 0.15 8.6196 1.2929 0.6465 202.59
0.9993 0.2443 7.9675E+05 0.13 170.7498 22.1975 11.0987 78.49
1.8393 0.4497 1.4665E+06 0.12 1064.6587 127.7590 63.8795 43.79
1.00
0.3693 0.0451 1.4714E+05 0.16 1.0755 0.1721 0.0860 396.88
0.9993 0.1221 3.9814E+05 0.13 21.3060 2.7698 1.3849 157.08
1.8393 0.2247 7.3280E+05 0.12 132.8469 15.9416 7.9708 87.63
0.50
0.3693 0.1291 4.2096E+05 0.15 25.1831 3.7775 1.8887 141.71
0.9993 0.3493 1.1390E+06 0.13 498.8668 64.8527 32.4263 54.91
1.8393 0.6429 2.0964E+06 0.12 3110.5331 373.2640 186.6320 30.63
23
Table 4.2-13 Scaled-up power requirement and mixing time of baffled tank with Size 5 flat
blade impeller
n N1(rps) N2
(rps) Nre Npo N
3D'
5ρ Pgraph (W) Pth(W) tm (s)
0.67
0.5793 0.1417 3.6586E+05 1.80 18.5765 33.4378 17.5492 73.93
1.1043 0.2700 6.9742E+05 1.80 128.6707 231.6073 121.5546 38.78
1.4193 0.3470 8.9635E+05 1.80 273.1696 491.7052 258.0620 30.18
1.00
0.5793 0.0708 1.8282E+05 1.80 2.3180 4.1723 2.1898 147.95
1.1043 0.1349 3.4850E+05 1.80 16.0554 28.8997 15.1674 77.61
1.4193 0.1734 4.4791E+05 1.80 34.0858 61.3544 32.2007 60.39
0.50
0.5793 0.2025 5.2303E+05 1.80 54.2737 97.6926 51.2721 51.71
1.1043 0.3860 9.9701E+05 1.80 375.9275 676.6695 355.1369 27.13
1.4193 0.4961 1.2814E+06 1.80 798.0990 1436.5781 753.9604 21.11
Table 4.2-14 Scaled-up power requirement and mixing time of unbaffled tank with Size 5
flat blade impeller
n N1(rps) N2
(rps) Nre Npo N
3D'
5ρ Pgraph (W) Pth (W) tm (s)
0.67
0.3693 0.0903 2.3324E+05 0.15 4.8132 0.7220 1.6076 263.31
0.7893 0.1930 4.9849E+05 0.13 46.9851 6.1081 13.6006 129.16
2.0493 0.5011 1.2942E+06 0.12 822.2747 98.6730 219.7120 51.08
1.00
0.3693 0.0451 1.1655E+05 0.16 0.6006 0.0961 0.2140 515.82
0.7893 0.0964 2.4910E+05 0.13 5.8627 0.7622 1.6971 258.47
2.0493 0.2504 6.4672E+05 0.12 102.6025 12.3123 27.4154 102.22
0.50
0.3693 0.1291 3.3344E+05 0.14 14.0624 1.9687 4.3837 188.43
0.7893 0.2759 7.1262E+05 0.13 137.2729 17.8455 39.7360 90.35
2.0493 0.7163 1.8502E+06 0.12 2402.3780 288.2854 641.9159 35.73
24
Figure 4.2-1 Power Consumption of various agitators expressed in terms of Po as a
function of Reynolds number, Re. For curves marked with ° surface effects become
important and the Froude number Fr = g/n2D’ is included as indicated for Re > 300.
