![Spherecity of cube
率 = As / Ap Where: As is the surface area of the equivalent
sphere and Ap is the measured surface area.
The sphericity can have a value ranging from 0-1, where 率 = 1
for an ideal sphere.
The volume of a spherical particle is:
Vp= (1/6) dp
3
Where: dp is the diameter of the particle.
The surface area of a sphere is:
As = dp
2
= [ (6 Vp / )(1/3)
]2
Thus, for a particle, 率 can be
calculated by measuring its volume and surface area:
率 = As / Ap = (6 Vp / )(2/3)
/ Ap An example: A cube measuring
1 1 1 cm has a volume of 1 cm3
, and a surface area of 6
(1 1) = 6 cm2
. Its sphericity is:
率 = (6 1 / )(2/3)
/ 6 = 0.806](https://image.slidesharecdn.com/momodule1-240812110231-353ce302/85/Mechanical-Operations-slides-for-chemical-engineers-6-320.jpg)
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Mechanical Operations slides for chemical engineers
- 1. MECHANICAL OPERATIONS (CHE1022) Dr. Aabid Hussain Shaik Associate Professor Chemical Engineering Department, SCHEME Contact information: Room no. SMV 221 Email: aabidhussain.s@vit.ac.in
- 2. Module 1 Introduction to particulate solids Particle shape, size Mixed particle sizes Size analysis cumulative and differential Various mean diameters Screen analysis Standard screens Various Industrial screens LOs Will be able to use different size analysis methods to determine particle size. Will be able to calculate the particle size distribution using screen analysis.
- 3. Particulate Assembly of small particles They are characterized by *Size *Shape *Density Regular specified by size, shape Irregular-arbitrarily defined
- 4. Equivalent diameter (irregular shaped particles)
- 5. Volume: V Sp Sphericity (陸s) = 6 倹 where Vp is the volume of the particle, Ap is its surface area, and Dp is the diameter of a sphere with the same volume Answer: 0.806
- 6. Spherecity of cube 率 = As / Ap Where: As is the surface area of the equivalent sphere and Ap is the measured surface area. The sphericity can have a value ranging from 0-1, where 率 = 1 for an ideal sphere. The volume of a spherical particle is: Vp= (1/6) dp 3 Where: dp is the diameter of the particle. The surface area of a sphere is: As = dp 2 = [ (6 Vp / )(1/3) ]2 Thus, for a particle, 率 can be calculated by measuring its volume and surface area: 率 = As / Ap = (6 Vp / )(2/3) / Ap An example: A cube measuring 1 1 1 cm has a volume of 1 cm3 , and a surface area of 6 (1 1) = 6 cm2 . Its sphericity is: 率 = (6 1 / )(2/3) / 6 = 0.806
- 7. Calculate the sphericity of a cylinder of dia 1 cm and height 3 cm. Spherecity = surface area of the sphere of same volume as the particle/surface area of the particle Volume of particle = rc 2 h = p x 0.52 x 3 = 2.356 cm3 Radius of sphere of volume 2.356 cm3 : 4 rs 3 / 3 = 2.356 rs = 0.8255 cm Surface area of sphere of same volume as the particle = 4 rs 2 = 4 x p x 0.82552 = 8.563 cm2 Surface area of particle = 2 rc (h + rc) = 2 x p x 0.5 x (3 + 0.5) = 10.996 cm2 Sphericity (f s) = 8.563/10.996 = 0.779
- 8. Calculate shperecity of a cylinder having diameter 1 cm and height 5 cm
- 9. Particle size- specified by diameter. Size expressed in different units according to size range *coarse inch (or) mm *Fine - screen size (mesh) *Very fine - 袖m (or) nm *Ultra fine m2 /gm (specific surface area)
- 10. Mixture of particles (same size) No. of particles in the sample Total surface area
- 11. Specific surface of mixture(different size) ++ xi is the mass fraction
- 12. Number of particles in Mixture (Different sizes) = 1 =1 ヰ 倹 3 = 1 倹ｂ 3 ｐ= 倹 3 Volume shape factor: Volume is proportional of cube of diameter, the constant of proportionality is knows as volume shape factor (a). a=/6 for spheres
- 13. Average particle size Volume Surface mean diameter
- 14. Arithmetic mean diameter = =1 ( 倹 ) =1 = =1 ( 倹 )
- 15. Mass mean diameter 倹 = =1 (ヰ 倹)
- 17. Determining Particle Size: Various methods are used for measurement of particle size. These depends on size range, the physical properties and the condition of dryness or wetness. The following methods are used in laboratory. 1. Microscope 2. Screening 3. Sedimentation 4. Elutriation 5. Centrifuging
- 18. Screening (Sieving) Importance of screening: Removes the fine from the feed material before a reduction equipment. Prevents oversized material to enter into unit operations. Produce a process grade material to meet specific feed size. Removes fines from finished product before packing.
- 19. Types of standard screens: 1. Tyler standard screen series 2. Indian standard test sieves Types of Screen/sieve analysis 3. Differential Analysis 4. Cumulative Analysis The mesh number system is a measure of how many openings there are per linear inch in a screen. Sizes vary by a factor of 2. This can easily be determined as screens are made from wires of standard diameters, however, opening sizes can vary slightly due to wear and distortion.
- 20. Particle size distribution (a) Differential (b) Cumulative
- 21. Mesh Screen Openings, 亮m Avg. Particle size, 亮m Weight fraction retained, mg 6/8 2362 2845 0.017 8/10 1651 2006 0.235 10/14 1168 1410 0.298 14/20 833 1000 0.217 20/28 589 711 0.105 28/35 417 503 0.062 35/48 295 356 0.028 48/65 208 252 0.017 65/100 147 178 0.010 100/150 104 126 0.005 150/200 74 89 0.002 Pan 0.004 1.0 Differential Find: diameters Surface mean Mass mean Volume mean No. of particles Specific surface area a=2 Spherecity=0.571 Density=2650 kg/m3
- 22. Surface mean diameter Mass mean diameter Volume mean diameter Number of particles Specific surface area 倹 = =1 (ヰ 倹) = 1 =1 ヰ 倹 3 = 1 倹ｂ 3 ++
- 23. Mesh Screen Openings, 亮m Weight fraction retained, mg 6 3327 0.00 8 2362 0.017 10 1651 0.252 14 1168 0.55 20 833 0.767 28 589 0.872 35 417 0.934 48 295 0.962 65 208 0.979 100 147 0.989 150 104 0.994 200 74 0.996 Pan 1.0 Cumulative
- 24. Storage of solids 1. Bulk storage 2. Bin storage Bin - not so tall but usually wider Silo tall and relatively small in diameter Hopper - vessel with sloping at the bottom
- 25. Flow out of Bins Massflow-All thematerialmoveswheneverany iswithdrawn Funnel flow- Onlyaportionofthematerial flowswhenanyiswithdrawn
- 26. Best flow depends on the following physical characteristics of materials. 1. Particle size 2. Moisture content 3. Temperature 4. Age 5. Oil content.
- 27. Problems A large welded steel silo 4 m in diameter and 20 m high is to be built. The silo has a central discharge on a flat bottom. Estimate the pressure on the wall, at the bottom of of the silo if the silo is filled with (a) coal particles and (b) water. The coal particles have the following characteristics: Density = 560 kg/m3 = 20 degrees Jannesen coefficient = 0.4
- 28. Problem A large welded steel silo 12 ft in diamter and 60 ft high is to be built. The silo has a central discharge on a flat bottom. Estimate the pressure on the wall at the bottom of the silo filled with (a) plastic pellets and (b) water. The plastic pellet have the following characteristics: Density = 35 lb/cu ft = 20 degrees Jannesen coefficient = 0.4