Determine the mode and median sizes of the distribution

Assignment Help Mechanical Engineering

Reference no: EM131897209

Question 1:

For the following non-sperical particles, calculate the equivalent diameters, d_v, d_s, d_sv, and the sphericity, ψ:
a. A cylinder with diameter = 300 μm and aspect ratio (length/diameter) = 5.0.
b. A disk with diameter = 300 μm and aspect ratio = 0.1.
c. A rectangular block with dimensions (WxHxL) = 0.1 m x 0.5 m x 0.02 m.
d. A hollow cylinder with inner radius x outer radius x length = 7.5 x 10 x 20 mm.

Question 2:
A fine powder (SG = 2.5) consists of spherical particles with the following size distribution:

Diameter (μm)	Number	Diameter (μm)	Number
< 2.00	2738	5.04 - 6.35	5151
2.00 - 2.52	5108	6.35 - 8.00	3869
2.52 - 3.18	5396	8.00 - 10.1	1799
3.18 - 4.00	5510	10.1 - 12.7	329
4.00 - 5.04	5109	12.7 - 16.0	24

a. Graphically present the PSD data provided in the forms of (i) Relative frequency distribution diagram, and (ii) Cumulative distribution (undersize & oversize) plots.

b. Determine the mode and median sizes of the distribution.

c. Calculate the following average diameters of the powder:
i. Arithmetic mean diameter (d_an)
ii. Surface area mean diameter (d_Sn)
iii. Volume mean diameter (d_Vn)
iv. Surface area-volume mean diameter (d_SVn)

d. Show that the particle size data above follows the log-normal distribution. Determine the corresponding geometric mean (d_gn) and standard deviation (σg). Use these parameters to calculate d_An, d_Sn, d_Vn and d_SVn and compare the results with those calculated in (c).

Question 3:

Particle size analysis for a sample of solid material (SG = 2.6) by microsieving produced the following data:

Average Dia. (μm)	5.5	9.0	14.9	24.6	67
% Weight	16	13	25	30	16

a. Show that the PSD follows log-normal size distribution, and determine the geometric (mass) mean (d_gw) & geometric standard deviation (σ_w).
b. Calculate average particle diameters appropriate to processes where:
(i) the particles are used as a catalytic bed for a surface-controlled reaction;
(ii) the particles are widely dispersed and cause local mass-controlled reaction.

Question 4:

A powder has the size analysis given below

Size range (mm) < 1 1 - 3 3 - 5 5 - 7 7 - 9 9 - 11 11 - 13 >13

Mass in range (g) 0 5 8 12 8 6 4 0

a. Determine the median, mode and mean of the size distribution.

b. If the particles are spherical with density = 2150 kgm^-3, what number and surface area of particles were included in the above analysis?

Part B - Test Yourself Questions

a. Give three (3) definitions of equivalent sphere diameters that are used to describe sizes of non- spherical particles. Illustrate the application of each term with a practical example.

b. Define the surface-volume number mean diameter (d_SVn) for a powder containing spherical particles. Explain how d_SVn can be calculated from size distribution data based on (i) particle number measurement, and (ii) particle mass measurement.

c. How do you know if the particle sizes of a particulate solid follow log-normal size distribution? What are the key features of this size distribution function?

d. Explain the meaning of the following terms or concepts as applied to particulate systems:
- Sphericity
- Geometric mean diameter
- Porosity
- Mean, mode, median sizes

e. Name and define the most appropriate equivalent or mean particle size to describe the particles in the following situations:
- Gas bubbling through a column of liquid
- Printing ink used in bubble jet printers
- Formation of crystals from solution
- Coating of ceramic powder on machine parts
- Dust explosion

f. What is meant by log-normal particle size distribution? What characteristic of this distribution enable the easy inter-conversion of number and mass size distribution data?

g. Consider a ring-shaped particle having outside diameter D, thickness a and length L, derive expressions for the following quantities in terms of particle dimensions:
- Surface area diameter (dS)
- Volume diameter (dV)
- Surface-volume diameter (dSV)
- Sphericity (ψ)

h. Describe three techniques for particle size measurements. Explain why particle size values obtained from these different techniques may not necessarily be the same.

i. For each of the following particulate systems, name and define the most appropriate equivalent and mean diameters to describe the particle size.
(1) Paint; (2) Aerosol; (3) Bed of catalyst; (4) Finely ground coffee powder; (5) Breakfast cereals

j. What considerations should be made when selecting a particular technique for particle size measurement?

Reference no: EM131897209

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