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1
1. INTRODUCTION
A separation process is a method that results in conversion of a mixture or solution of
chemical substances into two or more distinct product mixtures. The resulting distinct products
may contain more of the original mixture’s certain component.
One method of separation is by filtration. Filtration is any of various mechanical,
physical or biological operations that separate solids from fluids (liquids or gases) by adding a
medium through which only the fluid can pass. The fluid that passes through is called
the filtrate. For filtration, the resistance is equal to the resistance through the cake plus the
resistance through the filter medium.
Filtration is different from sieving. In sieving, particles that are too big to pass through
the holes of the sieve are retained. In filtration, a multilayer lattice retains those particles that
are unable to follow the porous channels of the filter. Particles that cannot pass are called cake
and usually blocks the surface of the filter and hinders the filtration. Commercially, the term
filter is applied to membranes where the separation lattice is so thin that the surface becomes
the main zone of particle separation, even though these products might be described as sieves.
Filtration is also important and widely used as one of the unit operations of chemical
engineering. It may be simultaneously combined with other unit operations to process the feed
stream, as in the biofilter, which is a combined filter and biological digestion device.
An industrial filter press is a tool used in separation processes, specifically to separate
solids and liquids. The process uses the principle of pressure drive thus, the presence of a pump
is required. Among other uses, filter presses are utilized in marble factories in order to separate
water from mud in order to reuse the water during the marble cutting process.
2
This experiment, entitled “Plate and Frame Filter Press”, is to determine how concentration is
related to the weight and volume of cake that it obtains and the length of time a certain volume
of filtrate is obtained. This also shows the plot between the volume of filtrate versus time per
volume of filtrate.
3
2 THEORITICAL BACKGROUND
A filter press is a piece of batch operation, fixed volume equipment that separates
liquids and solids using pressure filtration. A slurry is pumped into the filter press and
dewatered under pressure. It is used for water and wastewater treatment in a variety of different
applications ranging from industrial to municipal.
A plate and frame filter is also referred as membrane filter plate. This type of filter press
consists of many plates and frames assembled alternately with the supports of a pair of rails.
Figure 2.1 shows a simple mechanism on how a filter press works. This filter uses a centrifugal
pump to drive the slurry to the plate and frame and to avoid the solids from settling. For each
of the individual separating chambers, there is one hollow filter frame separated from two filter
plates by filter cloths. The introduced slurry flows through a port in each individual frame, and
the filter cakes are accumulated in each hollow frame. As the filter cake becomes thicker, the
filter resistance increases as well. So when the separating chamber is full, the filtration process
is stopped as the optimum pressure difference is reached. The filtrate that passes through filter
cloth is collected through collection pipes and stored in the filter tank. The cake accumulation
occurs at the hollow plate frame, then being separated at the filter plates by pulling the plate
and frame filter press apart. The cakes then fall off from those plates and are discharged to the
final collection point. Figure 2.2 shows the parts of a simple filter press.
Figure 2.1 Mechanism of filter press
4
Figure 2.2 Filter press
Variable that affects the filtration process includes the following: volume of slurry,
density of slurry, weight of slurry, solid in cake, volume of water, etc.
𝑉𝑠𝑙𝑢𝑟𝑟𝑦 = 𝑉 𝑤𝑎𝑡𝑒𝑟 + 𝑉𝐶𝑎𝐶𝑂3
𝜌 𝑆𝑙𝑢𝑟𝑟𝑦 =
𝑀𝑠𝑙𝑢𝑟𝑟𝑦
(
𝑀
𝜌
)
𝑤𝑎𝑡𝑒𝑟
+ (
𝑀
𝜌
)
𝐶𝑎𝐶𝑂3
𝑊𝑡 𝑠𝑙𝑢𝑟𝑟𝑦 = 𝑉𝑠𝑙𝑢𝑟𝑟𝑦 × 𝜌𝑠𝑙𝑢𝑟𝑟𝑦
𝑆𝑜𝑙𝑖𝑑 𝑐𝑎𝑘𝑒 = 𝑤𝑡% 𝐶𝑎𝐶𝑂3 × 𝑤𝑡% 𝑠𝑙𝑢𝑟𝑟𝑦
𝑊𝑡 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 𝑖𝑛 𝑠𝑙𝑢𝑟𝑟𝑦 = 𝑤𝑡. 𝑜𝑓 𝑠𝑙𝑢𝑟𝑟𝑦 − 𝑤𝑡. 𝑜𝑓 𝑠𝑜𝑙𝑖𝑑
𝑉 𝑤𝑎𝑡𝑒𝑟 =
𝑀 𝑤𝑎𝑡𝑒𝑟
𝜌 𝑤𝑎𝑡𝑒𝑟
5
3. EXPERIMENTAL SECTION
3.1. Materials and Apparatus
Plate and Frame Filter Press Equipment
Water
Calcium Carbonate
3.2 Procedure
• 18 liters of slurry containing 10% by weight of calcium carbonate and 90% by
weight water was prepared. The feed tank was fed with the predetermined amount in
slurry. To be secured, the movable head was tightened to lock. The experiment was
started by opening the necessary valves. The agitator and the pump was switched on
simultaneously The switch of both the agitator and the pump was switched off when
the slurry from the head tank was already contained. The procedure was repeated using
20% by weight calcium carbonate.
6
4. RESULTS AND DISCUSSION
The data included the following: initial weight of plate, weight of plate + wet cake,
weight of plate + dry cake, filtering time, presence of cake cracks, and percentage moisture and
the summary can be found in the Appendix. The calculations of form filtration rate of both the
Ca(OCl)2 and CaCO3 were made and the results was plotted against time.
Figure 4.1 Form filtration rate vs. time in seconds of Ca(OCl)2
Figure 4.1 shows the filtration rate of Ca(OCl)2 against time of filtration in minutes.
the form filtration rate of Ca(OCl)2 is seen to be inversely proportional with the filtering time.
0
5
10
15
20
0 5 10 15 20 25
FIltrationrate
time (sec)
Filtration of Ca(OCl)2
7
Figure 4.1 Form filtration rate vs. time in seconds of CaCO3
Figure 4.2 shows the filtration rate of CaCO3 against time of filtration in minutes. the
form filtration CaCO3 rate of is seen to be inversely proportional with the filtering time.
Figure 4.3 Comparison of the form filtration rate vs. time in seconds of Ca(OCl)2 and
CaCO3
0
5
10
15
20
25
30
35
40
45
0 10 20 30 40 50 60 70
Filtrationrate(kg/hft^2)
Filtering time (s)
Filtration of CaCO3
0
5
10
15
20
25
30
35
40
45
0 20 40 60 80
FiltrationRate
time, s
CaCO3
Ca(OCl)2
8
It is observed in Figure 4.3 that CaCO3 has a longer filtering time interval compared
to Ca(OCl)2. This is because of the factors affecting the filtration rate. One factor is the weight
of the solid that is to be filtered. the heavier the substance or compound, the longer is filtering
time. CaCO3 has a molar mass of 100 g/mol and Ca(OCl)2 has a molar mass of 142.9 g/mol.
Since weight is a factor that affects filtration, CaCO3 must have a longer time interval compared
to Ca(OCl)2
9
5. CONCLUSION
A higher concentration of solids provide longer filtration rate since more solids are
needed to be filtered to obtain a certain volume of the filtrate. The cake obtained during the
filtration increases in longer filtration time. This is due to the accumulation of the cake in
overtime. Thus, with higher concentration of solute in the feed, longer time is needed to obtain
a certain volume of filtrate and this leads to increase of cake weight. Filtration also takes longer
time in dealing with heavy solids just like the CaCO3 than in lighter ones such as Ca(OCl)2.
Other factors affect the rate of filtration such as properties of the fluid (density, viscosity, etc.)
and solid properties (size, density, suspension, etc.)
The rate of filtration also decreases with an increase of time since the cake are
accumulating the top of the filter thus the fluid cannot pass through the filter anymore. It is
crucial to know the importance of the time of filtration. This can estimate whether the filtration
is sufficient and save time and resources by less inspection.
6. RECOMMENDATION
For the students to be able to fully grasp the knowledge behind the equipment used
in filtration, the laboratory should both have a rotary drum filter and filter press.
10
7. REFERENCES
1. Geankoplis, C.J. 2003. Transport Processes and Separation Process Principles 4th
Edition. Pearson Education, Inc. pages 800-814
2. McCabe, W.L. and Smith, J.L. 1993. Unit Operations of Chemical
Engineering.McGraw-Hill Inc. pages 1002-1003
3. http://www.mwwatermark.com/en_US/what-is-a-filter-press/
4. https://en.wikipedia.org/wiki/Filter_press
8. APPENDIX
Table 1. Cake Weight of Ca(OCl)2
Test No. Initial Plate Weight
(g)
Wt. of Plate + Wet
Cake (g)
Wt. of Plate + Dry
Cake (g)
1 34.90 119.80 66.4
2 34.80 158.80 81.6
3 32.90 181.7 89.2
4 32.60 202.8 98.0
Table 2. Initial Moisture Content of Ca(OCl)2
Test No. Filtering Time (s) Cake
Cracks
Cake Weight %Moisture
Form Wash Dry Wet Dry
1 5 30 60 Yes 84.9 31.5 62.8
2 10 30 60 Yes 123.9 46.7 62.3
3 15 30 60 Yes 148.8 56.3 62.16
11
4 20 30 60 Yes 170.2 65.4 61.57
Table 3. Filtration Rate of Ca(OCl)2
Test No. Form Filtration Rate (kg/ft2.h) Full Scale Filtration Rate (kg/ft2.h)
1 18.144 0.1265
2 13. 45 0.09396
3 10.81 0.07536
4 9.47 0.06564
Table 4. Cake weight of CaCO3
Test No. Initial Plate Weight
(g)
Wt. of Plate + Wet
Cake (g)
Wt. of Plate + Dry
Cake (g)
1 34.60 91.10 43.5
2 37.80 118.3 50.5
3 38.90 120.5 52.1
4 35.60 124.6 49.5
Table 5. Initial Moisture Content of CaCO3
Test No. Filtering Time (s) Cake
Cracks
Cake Weight %Moisture
Form Wash Dry Wet Dry
1 5 30 60 Yes 34.10 16.10 52.8
2 30 30 60 Yes 43.50 21.00 52.3
3 45 30 90 Yes 60.7 30.40 50.16
12
4 60 30 90 Yes 76.8 38.00 50.2
Table 6. Filtration Rate of CaCO3
Test No. Form Filtration Rate (kg/ft2.h) Full Scale Filtration Rate (kg/ft2.h)
1 38.64 0.06465
2 28.2 0.01405
3 18.31 0.01357
4 11.23 0.01271
Problem 2:
A calcium carbonate slurry is to be filtered in a press having a total area of 14.3 m2 and
operated at a constant pressure drop of 2 atm. The frames are 30mm thick. Assume that the
filter medium resistance is 1.15x10^10 per ft. Calculate the filtration time and the volume of
the filtrate obtained in one cycle. Cake density is 70lb/ft3 The specific cake resistance,
2.9x10^10 (in lb/ft2. Slurry concentration is 15.6lbft3.
Solution:
𝐶 =
𝑐 𝑠
1 − (
𝑚 𝑓
𝑚 𝑐
− 1)
𝐶𝑠
𝜌
=
15.6
1 − ( 2 − 1 )
15.6
62.3
= 20.81
𝑙𝑏
𝑓𝑡3
∆𝑝 = 2𝑎𝑡𝑚 × 14.69 = 29.29
𝑙𝑏𝑓
𝑖𝑛2
𝐴 = 𝑓𝑖𝑙𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑎𝑟𝑒𝑎 =
14.3
2
= 7.15 𝑚^2 = 76. 9 𝑓𝑡^2
𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 30𝑚𝑚 = 0.0984 𝑓𝑡
𝑚 𝑐 = 𝑡𝑜𝑡𝑎𝑙 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑎𝑘𝑒 𝑓𝑜𝑟𝑚𝑒𝑑 𝑖𝑛 𝑜𝑛𝑒 𝑐𝑦𝑐𝑙𝑒
13
= 𝐴 × 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 × 𝜌𝑐 = 76. 9 × 0.0984 × 70 = 529 𝑙𝑏
𝑉 =
𝑚 𝑐
𝐶
=
529
15.61
= 33.932 𝑓𝑡3
𝛼 = 2.9 × 1010
(∆𝑝)^0.36
𝑅𝑚 = 1.15x10^10
𝑡
𝑉
=
𝑘 𝑐
2
𝑉 +
1
𝑞 𝑜
𝑞 𝑜 =
(∆𝑝 𝐴)
𝜇𝑅𝑚
=
(76. 9 × 29.29)𝑥144𝑥32
6.6 × 10−4 𝑋 × 1.55 × 1010
= 1.0145
𝐾𝑐 =
𝜇 𝑐 𝛼
𝐴2 ∆𝑝 𝑔𝑐
=
6.6 × 10−4
× 10.81 × 2.9 × 1010
29.290.7
76. 92 × 29.29 × 32.174
= 1.24
𝑡
𝑉
=
𝑘 𝑐
2
𝑉 +
1
𝑞 𝑜
= 7.39 𝑚𝑖𝑛𝑠

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Press and frame filter- Ed Ryan M. Ruales

  • 1. 1 1. INTRODUCTION A separation process is a method that results in conversion of a mixture or solution of chemical substances into two or more distinct product mixtures. The resulting distinct products may contain more of the original mixture’s certain component. One method of separation is by filtration. Filtration is any of various mechanical, physical or biological operations that separate solids from fluids (liquids or gases) by adding a medium through which only the fluid can pass. The fluid that passes through is called the filtrate. For filtration, the resistance is equal to the resistance through the cake plus the resistance through the filter medium. Filtration is different from sieving. In sieving, particles that are too big to pass through the holes of the sieve are retained. In filtration, a multilayer lattice retains those particles that are unable to follow the porous channels of the filter. Particles that cannot pass are called cake and usually blocks the surface of the filter and hinders the filtration. Commercially, the term filter is applied to membranes where the separation lattice is so thin that the surface becomes the main zone of particle separation, even though these products might be described as sieves. Filtration is also important and widely used as one of the unit operations of chemical engineering. It may be simultaneously combined with other unit operations to process the feed stream, as in the biofilter, which is a combined filter and biological digestion device. An industrial filter press is a tool used in separation processes, specifically to separate solids and liquids. The process uses the principle of pressure drive thus, the presence of a pump is required. Among other uses, filter presses are utilized in marble factories in order to separate water from mud in order to reuse the water during the marble cutting process.
  • 2. 2 This experiment, entitled “Plate and Frame Filter Press”, is to determine how concentration is related to the weight and volume of cake that it obtains and the length of time a certain volume of filtrate is obtained. This also shows the plot between the volume of filtrate versus time per volume of filtrate.
  • 3. 3 2 THEORITICAL BACKGROUND A filter press is a piece of batch operation, fixed volume equipment that separates liquids and solids using pressure filtration. A slurry is pumped into the filter press and dewatered under pressure. It is used for water and wastewater treatment in a variety of different applications ranging from industrial to municipal. A plate and frame filter is also referred as membrane filter plate. This type of filter press consists of many plates and frames assembled alternately with the supports of a pair of rails. Figure 2.1 shows a simple mechanism on how a filter press works. This filter uses a centrifugal pump to drive the slurry to the plate and frame and to avoid the solids from settling. For each of the individual separating chambers, there is one hollow filter frame separated from two filter plates by filter cloths. The introduced slurry flows through a port in each individual frame, and the filter cakes are accumulated in each hollow frame. As the filter cake becomes thicker, the filter resistance increases as well. So when the separating chamber is full, the filtration process is stopped as the optimum pressure difference is reached. The filtrate that passes through filter cloth is collected through collection pipes and stored in the filter tank. The cake accumulation occurs at the hollow plate frame, then being separated at the filter plates by pulling the plate and frame filter press apart. The cakes then fall off from those plates and are discharged to the final collection point. Figure 2.2 shows the parts of a simple filter press. Figure 2.1 Mechanism of filter press
  • 4. 4 Figure 2.2 Filter press Variable that affects the filtration process includes the following: volume of slurry, density of slurry, weight of slurry, solid in cake, volume of water, etc. 𝑉𝑠𝑙𝑢𝑟𝑟𝑦 = 𝑉 𝑤𝑎𝑡𝑒𝑟 + 𝑉𝐶𝑎𝐶𝑂3 𝜌 𝑆𝑙𝑢𝑟𝑟𝑦 = 𝑀𝑠𝑙𝑢𝑟𝑟𝑦 ( 𝑀 𝜌 ) 𝑤𝑎𝑡𝑒𝑟 + ( 𝑀 𝜌 ) 𝐶𝑎𝐶𝑂3 𝑊𝑡 𝑠𝑙𝑢𝑟𝑟𝑦 = 𝑉𝑠𝑙𝑢𝑟𝑟𝑦 × 𝜌𝑠𝑙𝑢𝑟𝑟𝑦 𝑆𝑜𝑙𝑖𝑑 𝑐𝑎𝑘𝑒 = 𝑤𝑡% 𝐶𝑎𝐶𝑂3 × 𝑤𝑡% 𝑠𝑙𝑢𝑟𝑟𝑦 𝑊𝑡 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 𝑖𝑛 𝑠𝑙𝑢𝑟𝑟𝑦 = 𝑤𝑡. 𝑜𝑓 𝑠𝑙𝑢𝑟𝑟𝑦 − 𝑤𝑡. 𝑜𝑓 𝑠𝑜𝑙𝑖𝑑 𝑉 𝑤𝑎𝑡𝑒𝑟 = 𝑀 𝑤𝑎𝑡𝑒𝑟 𝜌 𝑤𝑎𝑡𝑒𝑟
  • 5. 5 3. EXPERIMENTAL SECTION 3.1. Materials and Apparatus Plate and Frame Filter Press Equipment Water Calcium Carbonate 3.2 Procedure • 18 liters of slurry containing 10% by weight of calcium carbonate and 90% by weight water was prepared. The feed tank was fed with the predetermined amount in slurry. To be secured, the movable head was tightened to lock. The experiment was started by opening the necessary valves. The agitator and the pump was switched on simultaneously The switch of both the agitator and the pump was switched off when the slurry from the head tank was already contained. The procedure was repeated using 20% by weight calcium carbonate.
  • 6. 6 4. RESULTS AND DISCUSSION The data included the following: initial weight of plate, weight of plate + wet cake, weight of plate + dry cake, filtering time, presence of cake cracks, and percentage moisture and the summary can be found in the Appendix. The calculations of form filtration rate of both the Ca(OCl)2 and CaCO3 were made and the results was plotted against time. Figure 4.1 Form filtration rate vs. time in seconds of Ca(OCl)2 Figure 4.1 shows the filtration rate of Ca(OCl)2 against time of filtration in minutes. the form filtration rate of Ca(OCl)2 is seen to be inversely proportional with the filtering time. 0 5 10 15 20 0 5 10 15 20 25 FIltrationrate time (sec) Filtration of Ca(OCl)2
  • 7. 7 Figure 4.1 Form filtration rate vs. time in seconds of CaCO3 Figure 4.2 shows the filtration rate of CaCO3 against time of filtration in minutes. the form filtration CaCO3 rate of is seen to be inversely proportional with the filtering time. Figure 4.3 Comparison of the form filtration rate vs. time in seconds of Ca(OCl)2 and CaCO3 0 5 10 15 20 25 30 35 40 45 0 10 20 30 40 50 60 70 Filtrationrate(kg/hft^2) Filtering time (s) Filtration of CaCO3 0 5 10 15 20 25 30 35 40 45 0 20 40 60 80 FiltrationRate time, s CaCO3 Ca(OCl)2
  • 8. 8 It is observed in Figure 4.3 that CaCO3 has a longer filtering time interval compared to Ca(OCl)2. This is because of the factors affecting the filtration rate. One factor is the weight of the solid that is to be filtered. the heavier the substance or compound, the longer is filtering time. CaCO3 has a molar mass of 100 g/mol and Ca(OCl)2 has a molar mass of 142.9 g/mol. Since weight is a factor that affects filtration, CaCO3 must have a longer time interval compared to Ca(OCl)2
  • 9. 9 5. CONCLUSION A higher concentration of solids provide longer filtration rate since more solids are needed to be filtered to obtain a certain volume of the filtrate. The cake obtained during the filtration increases in longer filtration time. This is due to the accumulation of the cake in overtime. Thus, with higher concentration of solute in the feed, longer time is needed to obtain a certain volume of filtrate and this leads to increase of cake weight. Filtration also takes longer time in dealing with heavy solids just like the CaCO3 than in lighter ones such as Ca(OCl)2. Other factors affect the rate of filtration such as properties of the fluid (density, viscosity, etc.) and solid properties (size, density, suspension, etc.) The rate of filtration also decreases with an increase of time since the cake are accumulating the top of the filter thus the fluid cannot pass through the filter anymore. It is crucial to know the importance of the time of filtration. This can estimate whether the filtration is sufficient and save time and resources by less inspection. 6. RECOMMENDATION For the students to be able to fully grasp the knowledge behind the equipment used in filtration, the laboratory should both have a rotary drum filter and filter press.
  • 10. 10 7. REFERENCES 1. Geankoplis, C.J. 2003. Transport Processes and Separation Process Principles 4th Edition. Pearson Education, Inc. pages 800-814 2. McCabe, W.L. and Smith, J.L. 1993. Unit Operations of Chemical Engineering.McGraw-Hill Inc. pages 1002-1003 3. http://www.mwwatermark.com/en_US/what-is-a-filter-press/ 4. https://en.wikipedia.org/wiki/Filter_press 8. APPENDIX Table 1. Cake Weight of Ca(OCl)2 Test No. Initial Plate Weight (g) Wt. of Plate + Wet Cake (g) Wt. of Plate + Dry Cake (g) 1 34.90 119.80 66.4 2 34.80 158.80 81.6 3 32.90 181.7 89.2 4 32.60 202.8 98.0 Table 2. Initial Moisture Content of Ca(OCl)2 Test No. Filtering Time (s) Cake Cracks Cake Weight %Moisture Form Wash Dry Wet Dry 1 5 30 60 Yes 84.9 31.5 62.8 2 10 30 60 Yes 123.9 46.7 62.3 3 15 30 60 Yes 148.8 56.3 62.16
  • 11. 11 4 20 30 60 Yes 170.2 65.4 61.57 Table 3. Filtration Rate of Ca(OCl)2 Test No. Form Filtration Rate (kg/ft2.h) Full Scale Filtration Rate (kg/ft2.h) 1 18.144 0.1265 2 13. 45 0.09396 3 10.81 0.07536 4 9.47 0.06564 Table 4. Cake weight of CaCO3 Test No. Initial Plate Weight (g) Wt. of Plate + Wet Cake (g) Wt. of Plate + Dry Cake (g) 1 34.60 91.10 43.5 2 37.80 118.3 50.5 3 38.90 120.5 52.1 4 35.60 124.6 49.5 Table 5. Initial Moisture Content of CaCO3 Test No. Filtering Time (s) Cake Cracks Cake Weight %Moisture Form Wash Dry Wet Dry 1 5 30 60 Yes 34.10 16.10 52.8 2 30 30 60 Yes 43.50 21.00 52.3 3 45 30 90 Yes 60.7 30.40 50.16
  • 12. 12 4 60 30 90 Yes 76.8 38.00 50.2 Table 6. Filtration Rate of CaCO3 Test No. Form Filtration Rate (kg/ft2.h) Full Scale Filtration Rate (kg/ft2.h) 1 38.64 0.06465 2 28.2 0.01405 3 18.31 0.01357 4 11.23 0.01271 Problem 2: A calcium carbonate slurry is to be filtered in a press having a total area of 14.3 m2 and operated at a constant pressure drop of 2 atm. The frames are 30mm thick. Assume that the filter medium resistance is 1.15x10^10 per ft. Calculate the filtration time and the volume of the filtrate obtained in one cycle. Cake density is 70lb/ft3 The specific cake resistance, 2.9x10^10 (in lb/ft2. Slurry concentration is 15.6lbft3. Solution: 𝐶 = 𝑐 𝑠 1 − ( 𝑚 𝑓 𝑚 𝑐 − 1) 𝐶𝑠 𝜌 = 15.6 1 − ( 2 − 1 ) 15.6 62.3 = 20.81 𝑙𝑏 𝑓𝑡3 ∆𝑝 = 2𝑎𝑡𝑚 × 14.69 = 29.29 𝑙𝑏𝑓 𝑖𝑛2 𝐴 = 𝑓𝑖𝑙𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑎𝑟𝑒𝑎 = 14.3 2 = 7.15 𝑚^2 = 76. 9 𝑓𝑡^2 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 30𝑚𝑚 = 0.0984 𝑓𝑡 𝑚 𝑐 = 𝑡𝑜𝑡𝑎𝑙 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑎𝑘𝑒 𝑓𝑜𝑟𝑚𝑒𝑑 𝑖𝑛 𝑜𝑛𝑒 𝑐𝑦𝑐𝑙𝑒
  • 13. 13 = 𝐴 × 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 × 𝜌𝑐 = 76. 9 × 0.0984 × 70 = 529 𝑙𝑏 𝑉 = 𝑚 𝑐 𝐶 = 529 15.61 = 33.932 𝑓𝑡3 𝛼 = 2.9 × 1010 (∆𝑝)^0.36 𝑅𝑚 = 1.15x10^10 𝑡 𝑉 = 𝑘 𝑐 2 𝑉 + 1 𝑞 𝑜 𝑞 𝑜 = (∆𝑝 𝐴) 𝜇𝑅𝑚 = (76. 9 × 29.29)𝑥144𝑥32 6.6 × 10−4 𝑋 × 1.55 × 1010 = 1.0145 𝐾𝑐 = 𝜇 𝑐 𝛼 𝐴2 ∆𝑝 𝑔𝑐 = 6.6 × 10−4 × 10.81 × 2.9 × 1010 29.290.7 76. 92 × 29.29 × 32.174 = 1.24 𝑡 𝑉 = 𝑘 𝑐 2 𝑉 + 1 𝑞 𝑜 = 7.39 𝑚𝑖𝑛𝑠