ABSTRACT

The compressor was switched on and the air flow rate was set using the rotameter. The air flowed through the column and exited at the top. The pressure drop across the column, the plate alone in this case, was measured with the manometer. The air flow rate was increased to a maximum value in 1cm steps and then decreased again. The temperature of the air was measured using a thermometer for each change in flow rate. The compressor was switched off and the sand was added via the top of the column. The compressor was then turned back on and the same procedure followed except: started with 0.5cm steps until 10cm was reached then 1cm steps until the maximum value was reached and decreased the same way. Additionally, the depth of the bed was measured.

i

TABLE OF CONTENTS

ABSTRACT....................................................................................................................II

AIM..............................................................................................................................1

APPARATUS / PROCEDURE...........................................................................................1

RESULTS.......................................................................................................................2

1. RAW RESULTS.......................................................................................................................2

2. OBSERVATIONS.....................................................................................................................2

CALCULATIONS.............................................................................................................3

1. CARMAN-KOZENY EQUATION..............................................................................................3

2. GENERALIZED ANALYSIS......................................................................................................3

3. USING ERGUN EQUATION.....................................................................................................4

4. MINIMUM THEORETICAL FLUIDIZING VELOCITY.................................................................4

5. CALCULATION OF THEORETICAL PRESSURE DROP ACROSS BED:..........................................4

GRAPHS........................................................................................................................7

DISCUSSION...............................................................................................................12

SOURCES OF ERRORS..................................................................................................................12

COMPARISONS.............................................................................................................................12

A. BED HEIGHT........................................................................................................................12

B. PRESSURE DROP – ASCENDING AND DESCENDING.............................................................13

C. PRESSURE DROP – EXPERIMENTAL AND CALCULATED......................................................13

D. PRESSURE DROP – FLUIDIZED BED.....................................................................................13

E. MINIMUM FLUIDIZING VELOCITY.......................................................................................13

RECOMMENDATIONS.................................................................................................14

CONCLUSION..............................................................................................................15

APPENDIX...................................................................................................................16

i

List of Figures, Diagrams & Graphs

Figure 1 Schematic Diagram of Equipment Used...................................................1

Table 1 Observations Of Particle Behavouir..........................................................2

Table 2 Raw Results For Pressure Drop Across Empty Column............................16

Table 3 Raw Results For Pressure Drop Across Column With Sand.....................17

Graph 1 Changes In Pressure Drop Across Distributor Plate With Changing Velocity..................................................................................................................7

ii

AIM

The purpose of this experiment was basically to compare the different theoretical relationships available for packed/fluidized beds with actual experimental results obtained. Specifically, the following were examined:

- Determining the pressure drop across packed beds.

- Comparing the measured value of the minimum fluidizing velocity with that predicted.

- Comparing the measured value of pressure drop across a fluidized bed with that predicted.

APPARATUS / PROCEDURE

1. The fan was switched on and the air flow rate was set to a value of 1 on the rotameter. The pressure drop across the plate was measured.

2. Using steps of 1 on the rotameter, the air flow rate was increased to 23 and the pressure drops and air temperatures were recorded.

3. The air velocity was then decreased in increments of 1. The pressure drop and air temperature were measured.

4. The fan was switched off and the sand was charged to the column. 5. The fan was then turned on and the air flow was set to 0.5 on the rotameter. The pressure drop, depth of

bed, temperature and observations were recorded.6. The flow rate was increased in steps of 0.5 up to a value of 10 and readings were taken.7. Increments of 1 were used for flow rates between 10-23 (on the rotameter)8. Next, the air flow rate was decreased using the same step changes, and taking the same measurements

as above.9. The fan was switched off.

FIGURE 1 SCHEMATIC DIAGRAM OF EQUIPMENT USED

1

RESULTS

1. Raw Results

See Appendix, Tables 1 and 2, for experimental results.

2. Observations

Rotameter Reading Observations

Ascending

1 – 14cm

15cm

Nothing noticeable happened

On one side of the column, bubbles, about fist sized, were seen rising to the top of the bed.

16 – 17cm Powder fine particles were seen escaping at top of bed. Bubbles were now rising through entire cross section of column not just on one side.

18cm Bubble sizes start to increase. Finer particles still released at top of column.

20-23cm Same as before, bubble sizes continue to increase.

Descending

22-16cm Similar to ascending expect bubble sizes decreasing. Fine particles still released at top of column.

15cm No more large bubbles seen, small air bubbles seen moving through one side of column, same side as when fluidization begun. Particles were seen ‘jumping’ at top of bed.

14cm Smaller air bubbles seen forming throughout the cross section of the bed about 2-3” from top of column and breaking at the surface.

13 – 1cm No more bubbles or any noticeable changes seen.

2

TABLE 1 OBSERVATIONS OF PARTICLE BEHAVOUIR

3

CALCULATIONS

1. Carman-Kozeny Equation

∆P =180 λ2 (1−ε )2

ε3

μuL

dm2

where: λ – shape factor - assumed to be 1

ε – voidage

μ – viscosity of air - 0.000018 kg/ms

u – superficial velocity of air, m/s

L – height of packing m

dm – average diameter of particle - 0.00090142m

∆P =180∗12 (1−0 .396)2 0 . 000018∗0 .13005∗0 .24

0 .3963∗0 .000901422

= 730.22 Pa

2. Generalized Analysis

∆P =

SL (1−ε ) ρU 2 [5 Re−1+0 . 4 Re−0.1 ]ε 3

Where S =

6 λdm

Re =

( ρU )(Sμ ) (1−ε ) ρ-density of air

∆P =

6230 .53∗0 . 255 (1−0 .418 )∗1. 17∗0 .1412 [5∗2 .5275−1+0 .4∗2 .5275−0.1 ]0. 4183

= 697.7 Pa

4

3. Using Ergun Equation

∆P =

150 (1−ε )2 μULε3dm

2+

1.75 (1−ε ) ρU 2L

ε3dm

=

150(1−0. 418)2∗0 . 000018∗0.142∗0 .255

0 . 4183∗0 . 0009632+

1. 75∗(1−0 . 418 )∗1 .17∗0 .1422∗0 .255

0. 4183∗0 . 000963

= 577.86 Pa

4. Minimum Theoretical Fluidizing Velocity

U0 =

( ρs−ρ ) gdm2 εo3

180 μλ2 (1−εo )

Where U0 – minimum fluidizing velocity

s – density of particles – 2640kg/m3

o – voidage when fluidization begins (approximated to 0.418)

=

(2817 . 43−1 .17 )×9 . 81×( 0. 000963 )2 ( 0. 418 )3

(180×0 .000018 ) (1−0 .418 )

= 0.9923 m/s.

5. Calculation of theoretical pressure drop across bed:

P = (1-) L (s - ) g

= (1-0.418) (0.27) (2817.43-1.17) (9.81)

= 4341.39 Pa

5

TABLE 2

6

Air Velocitym/s Experimental Carmen Kozeny Generalized Ergun

0.13005 48.90 730.22 844.27 698.100.14450 48.90 811.36 950.69 786.720.15895 48.90 892.49 1059.48 877.560.17368 48.90 975.21 1172.83 972.450.20263 48.90 1137.75 1402.61 1165.590.21710 48.90 1219.01 1520.98 1265.490.23157 48.90 1300.28 1641.64 1367.610.25411 48.90 1426.80 1834.02 1531.000.27633 48.90 1551.60 2029.16 1697.450.29088 48.90 1633.27 2159.71 1809.200.30592 48.90 1717.70 2297.05 1927.100.32048 48.90 1799.50 2432.38 2043.590.35018 48.90 1966.25 2715.21 2288.050.36536 48.90 2051.48 2863.31 2416.600.39459 48.90 2215.60 3155.26 2671.010.40986 48.90 2301.35 3311.31 2807.550.42518 48.90 2387.37 3470.26 2946.980.44055 48.90 2473.65 3632.11 3089.340.47067 48.90 2642.78 3956.35 3375.660.48615 48.90 2729.72 4126.61 3526.580.53119 48.90 2982.62 4635.64 3980.040.56160 48.90 3153.34 4990.74 4298.280.60690 97.81 3407.70 5536.89 4790.610.65234 97.81 3662.84 6105.12 5306.310.69792 146.71 3149.92 5465.36 4785.100.74482 146.71 3042.09 5455.69 4806.010.79200 195.61 2812.81 5233.66 4642.450.82318 195.61 2569.25 4917.47 4385.460.86808 195.61 2498.83 4934.40 4426.960.92940 195.61 2476.77 5085.77 4597.290.97437 244.51 1969.81 4273.63 3904.651.02094 244.51 1827.09 4122.42 3795.381.03757 293.42 1658.53 3833.92 3546.49

Pressure Drop, Pa

TABLE 3

7

Air Velocitym/s Experimental Carmen Kozeny Generalized Ergun

1.02254 293.42 2067.19 4592.19 4215.070.97743 293.42 2255.22 4820.80 4391.890.93231 293.42 2484.54 5109.09 4619.660.87080 244.51 2608.87 5138.00 4607.260.82576 244.51 2687.79 5130.76 4573.360.79573 244.51 2957.17 5491.15 4868.980.75069 244.51 3066.09 5515.98 4861.960.70455 195.61 3179.83 5537.21 4851.230.65854 195.61 3304.12 5567.67 4848.720.61364 195.61 3078.84 5058.17 4385.010.56785 146.71 2849.08 4557.21 3932.140.53796 146.71 2699.12 4240.50 3647.500.49235 146.71 2470.31 3772.91 3229.800.47743 146.71 2395.45 3624.08 3097.510.44760 146.71 2245.73 3332.57 2839.390.43199 97.81 2167.46 3183.45 2707.860.41710 97.81 2092.72 3043.18 2584.460.40220 97.81 2017.98 2904.98 2463.210.37241 97.81 1868.50 2634.84 2227.150.35695 97.81 1790.93 2497.95 2108.030.32720 97.81 1641.68 2240.97 1885.340.31184 97.81 1564.59 2111.53 1773.640.29699 97.81 1490.08 1988.61 1667.880.28214 97.81 1415.58 1867.81 1564.240.25986 97.81 1303.82 1690.63 1412.780.23721 97.81 1190.18 1515.45 1263.680.22204 97.81 1114.03 1400.90 1166.540.20723 97.81 1039.76 1291.38 1073.950.17735 97.81 889.81 1076.98 893.460.16257 97.81 815.66 974.31 807.400.14755 97.81 740.33 872.30 722.130.13280 97.81 666.29 774.32 640.45

Pressure Drop, Pa

GRAPHS

0

50

100

150

200

250

300

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000

ascending decending 2 per. Mov. Avg. (ascending) 2 per. Mov. Avg. (decending)

GRAPH 1 CHANGES IN PRESSURE DROP ACROSS DISTRIBUTOR PLATE WITH CHANGING VELOCITY

8

GRAPHS

GRAPH 2

9

0.2000

0.2250

0.2500

0.2750

0.3000

0.3250

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Decending Ascending

GRAPHS

GRAPH 3

10

0

500

1000

1500

2000

2500

3000

3500

4000

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

ascending Decending 2 per. Mov. Avg. (ascending) 2 per. Mov. Avg. (Decending)

GRAPHS

GRAPH 4

11

0

1000

2000

3000

4000

5000

6000

7000

0.00 0.20 0.40 0.60 0.80 1.00 1.20

as

ck gen ergun expt

GRAPHS

GRAPH 5

12

0

1000

2000

3000

4000

5000

6000

0.00 0.20 0.40 0.60 0.80 1.00 1.20

de

ck gen ergun expt

DISCUSSION

Sources of Errors

When the rotameter was set to a required value and the necessary measurements were being recorded, it was noticed that the rotameter value fluctuated. This indicates that the air flow to the column was not constant. The air velocity through the column is a major part of the calculations and since it was not possible to measure and record correct, corresponding values, the calculations made using air velocity for this experiment would not be accurate.

Initially, the top of the bed is supposed to be smooth and flat. This was difficult to achieve as the sand had to be poured from a reasonable height using a beaker. This means there was an error in measuring the bed height from the beginning. As bed movement begun, from the size and placement of bubbles seen in the column, it is certain that proper fluidization did not occur: initially there was channeling and then slugging! This is an indication that the distributor plate either does not have evenly placed orifices or that the plate is clogged. In slugging, the size of the bubbles causes the bed height to rise and fall significantly. This makes measuring the bed height extremely difficult to measure. Additionally, the column started to vibrate at higher velocities, even though there the final bed height was higher than the initial as it should be, the vibrations did caused the sand to settle (the top of the bed was level at the end of the experiment), thereby affecting the bed height. Therefore all calculations made using bed height would be inaccurate.

Slugging usually occurs just before a column is blown off. The column did not actually blow off during the experiment but the finer particles from the bed were lost when the bubbles popped at the surface of the bed. Also when the column was beginning filled fine particles were lost. The mass of particles lost may not have greatly affected the results unless a smaller mass of particles were used or if the sand contained more particles that size the column could have been blown off.

Comparisons

a. Bed height

Graph 2 shows how the height of the bed changes as the air velocity through the bed was increased and then decreased. For increasing air velocity, the bed height was constant until fluidization occurred, the bed height then increased. Decreasing velocity gave similar movement expect when fluidization stopped the bed height was higher than before any movement occurred. This is expected as the particles would not have returned to the same packing/positions as before.

13

b. Pressure drop – Experimental Ascending and Descending

The experimental results for pressure drop for both ascending and descending velocities are as expected from theory. For ascending velocity, the pressure drop increases, peaks then drops of a bit and then it almost levels off to a constant. The peak and drop off in pressure drop happens because of bridging of the bed close to the surface, the interlocking forces must be initially overcome so the pressure increases and then decreases once the forces have been broken. The velocity at which the pressure drop becomes almost constant is the minimum fluidising velocity. The almost constant pressure drop occurs when the bed is fluidised, in this case slugging. For the decreasing velocity, when the bed is fluidised the pressure drop is almost constant. After passing the minimum fluidising velocity the pressure drop decreases in a linear way. There is no peak as with increasing velocity as there in no interlocking forces to break through.

c. Pressure drop – Experimental and Calculated

d. Pressure drop – Fluidized Bed

The pressure drop across a fluidized bed is suppose to be close to a constant value, hence we can use the equation, P = (1-) L (s - ) g. This gave a value of 4103.6 Pa. Experimental results gave an average value of 3569.9 Pa. The difference in values can be accounted for by the error in obtaining L and ε as stated previously.

e. Minimum Fluidizing velocity

The calculated minimum fluidizing velocity was 0.831m/s. The actual minimum fluidizing velocity

was 0.697m/s where as Graph 3 gave a value of approximately 0.75m/s. Once again differences in

values can be explain by the errors in obtaining data to calculate a value for ε.

Pressure drops were calculated using the Carman-Kozeny Equation, Generalized Analysis and Ergun

Equation. These were plotted against increasing air velocities and shown in graph 3. Off the three, the

generalized analysis gave the the highest pressure drop followed by the Ergun Equation and Carman-

Kozeny. The generalized analysis gave the closest representation of the actual results. In all, a peak

14

occurred at a velocity of 0.42 m/s and this represents the onset of fluidizing. The pressure dips slightly

and then increases again. Note that this was not observed on the actual experimental results.

For decreasing air velocity, the calculated results were plotted and shown in graph 4. The decrease

appears to be fairly linear and this expected. It must be noted that all the experimental pressure drops

were higher than the calculated values with the generalized analysis being the closed approximation. The

difference can be accounted for by errors present.

A further error was the use of the manometers. The scale should have been more sensitive, as for the

empty column the differences in the height of water was noticeable but the scale did not permit a

change in value.

Other errors include the assumptions that the shape factor was 1, and the assumption that the voidage

was a constant 0.418. It is known that the voidage varies.

RECOMMENDATIONS

1. An air blower with a more constant output should be supplied.

2. The experiment could be repeated and the average values used.

3. The experiment could be repeated with different particle sizes and different gases.

4. Equipment for determining the sand voidage should be provided.

15

CONCLUSION

16

APPENDIX

Raw Results

TABLE 4 RAW RESULTS FOR PRESSURE DROP ACROSS EMPTY COLUMN

17

Temperature Temperaturecm L/min ⁰C LHS RHS cm L/min ⁰C LHS RHS1 125.0 27.0 26.00 26.50 23 862.5 42.5 24.75 27.752 150.0 28.0 26.00 26.50 22 850.0 43.0 24.75 27.753 187.5 28.5 26.00 26.50 21 812.5 43.5 24.75 27.754 218.8 28.5 26.00 26.50 20 775.0 43.5 24.75 27.755 250.0 29.0 26.00 26.50 19 725.0 43.5 25.00 27.506 275.0 30.0 26.00 26.50 18 687.5 44.0 25.00 27.507 312.5 30.5 26.00 26.50 17 662.5 44.0 25.00 27.508 350.0 31.0 26.00 26.50 16 625.0 44.0 25.00 27.509 375.0 31.0 26.00 26.50 15 587.5 44.0 25.25 27.2510 412.5 32.0 26.00 26.50 14 550.0 44.0 25.25 27.2511 450.0 32.5 26.00 26.50 13 512.5 44.0 25.25 27.2512 475.0 33.0 26.00 26.50 12 475.0 44.0 25.50 27.0013 512.5 34.0 25.75 26.75 11 450.0 44.0 25.50 27.0014 550.0 35.5 25.75 26.75 10 412.5 44.0 25.50 27.0015 587.5 37.0 25.50 27.00 9 375.0 43.5 25.50 27.0016 625.0 38.0 25.50 27.00 8 350.0 43.5 25.75 26.7517 662.5 39.0 25.25 27.25 7 312.5 43.5 25.75 26.7518 687.5 39.5 25.25 27.25 6 275.0 43.0 25.75 26.7519 725.0 40.0 25.25 27.25 5 250.0 43.0 25.75 26.7520 775.0 40.0 25.25 27.25 4 218.8 43.0 25.75 26.7521 812.5 41.0 25.00 27.50 3 187.5 42.5 25.75 26.7522 850.0 42.0 25.00 27.50 2 150.0 42.5 25.75 26.7523 862.5 42.5 24.75 27.75 1 125.0 42.0 25.75 26.75

AscendingRotameter Pressure Drop, cm

DecendingRotameter Pressure Drop, cm

APPENDIX

Temperature Bed Depth Temperature Bed Depthcm L/min ⁰C LHS RHS m cm L/min ⁰C LHS RHS m0.5 112.5 34.5 24.00 29.00 0.2400 23.0 862.5 47.0 6.25 46.75 0.32001.0 125.0 34.5 23.75 29.25 0.2400 22.0 850.0 47.0 6.50 46.50 0.30001.5 137.5 34.5 23.25 29.75 0.2400 21.0 812.5 47.0 6.75 46.25 0.29002.0 150.0 35.0 22.50 30.25 0.2400 20.0 775.0 47.0 7.00 46.00 0.28002.5 175.0 35.0 21.75 31.00 0.2400 19.0 725.0 46.5 7.25 45.75 0.27253.0 187.5 35.0 21.25 31.50 0.2400 18.0 687.5 46.5 7.50 45.50 0.26753.5 187.5 35.0 20.50 32.00 0.2400 17.0 662.5 46.5 7.75 45.25 0.26004.0 218.8 36.0 20.00 32.50 0.2400 16.0 625.0 46.5 8.00 45.00 0.25504.5 237.5 36.5 19.75 33.00 0.2400 15.0 587.5 46.0 9.00 44.00 0.25005.0 250.0 36.5 19.00 33.75 0.2400 14.0 550.0 45.5 9.75 43.75 0.24505.5 262.5 37.0 18.25 34.75 0.2400 13.0 512.5 45.5 10.25 42.50 0.24506.0 275.0 37.0 17.75 35.25 0.2400 12.0 475.0 45.0 11.75 41.25 0.24506.5 300.0 37.5 17.00 36.00 0.2400 11.0 450.0 45.0 13.00 39.75 0.24507.0 312.5 38.0 16.50 36.50 0.2400 10.0 412.5 44.5 14.25 38.50 0.24507.5 337.5 38.0 15.75 37.25 0.2400 9.5 400.0 44.5 15.25 37.75 0.24508.0 350.0 38.5 15.00 37.75 0.2400 9.0 375.0 44.5 15.75 37.25 0.24508.5 362.5 39.0 14.25 38.50 0.2400 8.5 362.5 44.0 16.25 36.75 0.24509.0 375.0 39.5 13.75 39.25 0.2400 8.0 350.0 44.0 16.75 36.25 0.24509.5 400.0 40.0 12.50 40.25 0.2400 7.5 337.5 44.0 17.50 35.50 0.245010.0 412.5 40.5 12.00 40.75 0.2400 7.0 312.5 44.0 18.00 35.00 0.245011.0 450.0 41.0 10.50 42.50 0.2400 6.5 300.0 43.5 18.50 34.50 0.245012.0 475.0 41.5 9.00 44.00 0.2400 6.0 275.0 43.5 19.25 33.75 0.245013.0 512.5 42.0 7.50 45.25 0.2400 5.5 262.5 43.0 19.75 33.25 0.245014.0 550.0 42.5 6.00 46.75 0.2400 5.0 250.0 43.0 20.50 32.75 0.245015.0 587.5 43.0 8.00 45.00 0.2500 4.5 237.5 43.0 20.75 32.25 0.245016.0 625.0 44.0 7.75 45.25 0.2550 4.0 218.8 43.0 21.25 31.75 0.245017.0 662.5 45.0 7.75 45.25 0.2625 3.5 187.5 42.5 21.50 31.50 0.245018.0 687.5 45.5 7.50 45.50 0.2700 3.0 187.5 42.0 22.25 30.75 0.245019.0 725.0 45.5 7.25 45.75 0.2750 2.5 175.0 42.0 22.50 30.50 0.245020.0 775.0 46.0 7.00 46.00 0.2800 2.0 150.0 41.5 23.00 30.00 0.245021.0 812.5 46.0 6.75 46.25 0.3000 1.5 137.5 41.5 23.50 29.50 0.245022.0 850.0 46.5 6.50 46.50 0.3100 1.0 125.0 41.0 23.75 29.25 0.245023.0 862.5 47.0 6.25 46.75 0.3200 0.5 112.5 41.0 24.25 28.75 0.2450

AscendingRotameter Pressure Drop, cm

DecendingRotameter Pressure Drop, cm

TABLE 5 RAW RESULTS FOR PRESSURE DROP ACROSS COLUMN WITH SAND

18

APPENDIX

Sample Calculations

A. Rotameter Reading to Velocity

Rotameter Reading = 1 cm

From correlation chart,

1cm = 125 l/min at 15 oC

125 l/min = 125l/(60*1000)

Cross Sectional Area Of Bed = πd2/4

A = π*(0.14)2/4

= 0.01539 m2

= 125/(60*1000) = 0.002083 m3/s

Correcting To Actual Temperature (27 oC)

V 1

T 1

=V 2

T 2

Where 1 and 2 represent different conditions of volumetric flow and temperature

Therefore, V 2=T 2(V 1

T 1)

Corrected Volumetric Flow rate

19

Q =(273+27 )( 0 .002083

273+15 )= 0.002170 m3/s

Corrected Velocity

V = Q/A = 0.002170/0.01539

= 0.141 m/s

1. Calculating Pressure Drop Across Plate

For 1st reading of increasing air flow through empty column

∆P = ρgh

= 1000*9.81*(21.25-21.00)/100 = 24.525 Pa

graph of pressure drop across plate vs velocity was ploted and used to get further values (graph 1)

2. Calculating Pressure Drop Across Bed And Plate

For 2nd reading of increasing air flow through packed bed

∆P = ρgh

= 1000*9.81*(24.75-17.5)/100 = 711.225 Pa

20

3. Calculating Pressure Drop Across Bed (experimental value)

∆P = ∆Pbed&plate - ∆Pplate

= 711.225 – 25 = 686.225 Pa

21

APPENDIX

Sample Calculations Results

TABLE 6

22

Temperature Air Velocity

cm L/min ⁰C LHS RHS @ 15 ⁰C Temp. Corrected m/s m N/m2

1 125.0 27.0 26.00 26.50 0.00208 0.00217 0.14097 0.005 48.902 150.0 28.0 26.00 26.50 0.00250 0.00261 0.16973 0.005 48.903 187.5 28.5 26.00 26.50 0.00313 0.00327 0.21252 0.005 48.904 218.8 28.5 26.00 26.50 0.00365 0.00382 0.24794 0.005 48.905 250.0 29.0 26.00 26.50 0.00417 0.00437 0.28383 0.005 48.906 275.0 30.0 26.00 26.50 0.00458 0.00482 0.31325 0.005 48.907 312.5 30.5 26.00 26.50 0.00521 0.00549 0.35655 0.005 48.908 350.0 31.0 26.00 26.50 0.00583 0.00616 0.39999 0.005 48.909 375.0 31.0 26.00 26.50 0.00625 0.00660 0.42856 0.005 48.9010 412.5 32.0 26.00 26.50 0.00688 0.00728 0.47297 0.005 48.9011 450.0 32.5 26.00 26.50 0.00750 0.00796 0.51681 0.005 48.9012 475.0 33.0 26.00 26.50 0.00792 0.00841 0.54642 0.005 48.9013 512.5 34.0 25.75 26.75 0.00854 0.00911 0.59148 0.010 97.8114 550.0 35.5 25.75 26.75 0.00917 0.00982 0.63786 0.010 97.8115 587.5 37.0 25.50 27.00 0.00979 0.01054 0.68467 0.015 146.7116 625.0 38.0 25.50 27.00 0.01042 0.01125 0.73072 0.015 146.7117 662.5 39.0 25.25 27.25 0.01104 0.01196 0.77705 0.020 195.6118 687.5 39.5 25.25 27.25 0.01146 0.01243 0.80767 0.020 195.6119 725.0 40.0 25.25 27.25 0.01208 0.01313 0.85309 0.020 195.6120 775.0 40.0 25.25 27.25 0.01292 0.01404 0.91192 0.020 195.6121 812.5 41.0 25.00 27.50 0.01354 0.01476 0.95910 0.025 244.5122 850.0 42.0 25.00 27.50 0.01417 0.01549 1.00656 0.025 244.5123 862.5 42.5 24.75 27.75 0.01438 0.01575 1.02298 0.030 293.42

Pressure DropRotameter Pressure Drop, cm Volumetric Flowrate, m3/s

Ascending

TABLE 7

23

Temperature Air Velocity

cm L/min ⁰C LHS RHS @ 15 ⁰C Temp. Corrected m/s m N/m2

22 850.0 43.0 24.75 27.75 0.01417 0.01554 1.00976 0.030 293.4221 812.5 43.5 24.75 27.75 0.01354 0.01488 0.96673 0.030 293.4220 775.0 43.5 24.75 27.75 0.01292 0.01419 0.92212 0.030 293.4219 725.0 43.5 25.00 27.50 0.01208 0.01328 0.86262 0.025 244.5118 687.5 44.0 25.00 27.50 0.01146 0.01261 0.81930 0.025 244.5117 662.5 44.0 25.00 27.50 0.01104 0.01215 0.78951 0.025 244.5116 625.0 44.0 25.00 27.50 0.01042 0.01147 0.74482 0.025 244.5115 587.5 44.0 25.25 27.25 0.00979 0.01078 0.70013 0.020 195.6114 550.0 44.0 25.25 27.25 0.00917 0.01009 0.65544 0.020 195.6113 512.5 44.0 25.25 27.25 0.00854 0.00940 0.61075 0.020 195.6112 475.0 44.0 25.50 27.00 0.00792 0.00871 0.56606 0.015 146.7111 450.0 44.0 25.50 27.00 0.00750 0.00826 0.53627 0.015 146.7110 412.5 44.0 25.50 27.00 0.00688 0.00757 0.49158 0.015 146.719 375.0 43.5 25.50 27.00 0.00625 0.00687 0.44619 0.015 146.718 350.0 43.5 25.75 26.75 0.00583 0.00641 0.41644 0.010 97.817 312.5 43.5 25.75 26.75 0.00521 0.00572 0.37182 0.010 97.816 275.0 43.0 25.75 26.75 0.00458 0.00503 0.32669 0.010 97.815 250.0 43.0 25.75 26.75 0.00417 0.00457 0.29699 0.010 97.814 218.8 43.0 25.75 26.75 0.00365 0.00400 0.25986 0.010 97.813 187.5 42.5 25.75 26.75 0.00313 0.00342 0.22239 0.010 97.812 150.0 42.5 25.75 26.75 0.00250 0.00274 0.17791 0.010 97.811 125.0 42.0 25.75 26.75 0.00208 0.00228 0.14802 0.010 97.81

Pressure DropVolumetric Flowrate, m3/s

DescendingRotameter Pressure Drop, cm

TABLE 8

24

Air Velocity Bed Depth Vol of bed ε Reynolds #m/s m 1-(Vcol/Vsand) (ρu)/[(Sμ)(1-ε)]

0.13005 0.2400 0.00369 0.396 2.1030.14450 0.2400 0.00369 0.396 2.3370.15895 0.2400 0.00369 0.396 2.5700.17368 0.2400 0.00369 0.396 2.8090.20263 0.2400 0.00369 0.396 3.2770.21710 0.2400 0.00369 0.396 3.5110.23157 0.2400 0.00369 0.396 3.7450.25411 0.2400 0.00369 0.396 4.1090.27633 0.2400 0.00369 0.396 4.4690.29088 0.2400 0.00369 0.396 4.7040.30592 0.2400 0.00369 0.396 4.9470.32048 0.2400 0.00369 0.396 5.1830.35018 0.2400 0.00369 0.396 5.6630.36536 0.2400 0.00369 0.396 5.9080.39459 0.2400 0.00369 0.396 6.3810.40986 0.2400 0.00369 0.396 6.6280.42518 0.2400 0.00369 0.396 6.8760.44055 0.2400 0.00369 0.396 7.1240.47067 0.2400 0.00369 0.396 7.6110.48615 0.2400 0.00369 0.396 7.8620.53119 0.2400 0.00369 0.396 8.5900.56160 0.2400 0.00369 0.396 9.0820.60690 0.2400 0.00369 0.396 9.8140.65234 0.2400 0.00369 0.396 10.5490.69792 0.2500 0.00385 0.420 11.7560.74482 0.2550 0.00393 0.432 12.7970.79200 0.2625 0.00404 0.448 14.0080.82318 0.2700 0.00416 0.463 14.9750.86808 0.2750 0.00423 0.473 16.0850.92940 0.2800 0.00431 0.482 17.5340.97437 0.3000 0.00462 0.517 19.6961.02094 0.3100 0.00477 0.532 21.3251.03757 0.3200 0.00493 0.547 22.371

Ascending

TABLE 9

25

Air Velocity Bed Depth Vol of bed ε Reynolds #m/s m 1-(Vcol/Vsand) (ρu)/[(Sμ)(1-ε)]

1.02254 0.3000 0.00462 0.51689 20.670.97743 0.2900 0.00446 0.50023 19.100.93231 0.2800 0.00431 0.48238 17.590.87080 0.2725 0.00419 0.46814 15.990.82576 0.2675 0.00412 0.45820 14.880.79573 0.2600 0.00400 0.44257 13.940.75069 0.2550 0.00393 0.43164 12.900.70455 0.2500 0.00385 0.42027 11.870.65854 0.2450 0.00377 0.40844 10.870.61364 0.2450 0.00377 0.40844 10.130.56785 0.2450 0.00377 0.40844 9.370.53796 0.2450 0.00377 0.40844 8.880.49235 0.2450 0.00377 0.40844 8.130.47743 0.2450 0.00377 0.40844 7.880.44760 0.2450 0.00377 0.40844 7.390.43199 0.2450 0.00377 0.40844 7.130.41710 0.2450 0.00377 0.40844 6.890.40220 0.2450 0.00377 0.40844 6.640.37241 0.2450 0.00377 0.40844 6.150.35695 0.2450 0.00377 0.40844 5.890.32720 0.2450 0.00377 0.40844 5.400.31184 0.2450 0.00377 0.40844 5.150.29699 0.2450 0.00377 0.40844 4.900.28214 0.2450 0.00377 0.40844 4.660.25986 0.2450 0.00377 0.40844 4.290.23721 0.2450 0.00377 0.40844 3.920.22204 0.2450 0.00377 0.40844 3.670.20723 0.2450 0.00377 0.40844 3.420.17735 0.2450 0.00377 0.40844 2.930.16257 0.2450 0.00377 0.40844 2.680.14755 0.2450 0.00377 0.40844 2.440.13280 0.2450 0.00377 0.40844 2.19

Decending