Assignment #2

[William A. Anderson]

ChE 572

Problem Set #2

1)

The following particle size data were collected from a sampling device:

Size Range (:m) 0-4 4-8 8-16 16-30 30-50 >50
Mass (mg) 25 125 100 75 30 5

Is the distribution log-normal? If so, estimate Fg and d50. [.2.0 &
10.8 :m, respectively].

A certain cyclone separator has the following theoretical efficiency
versus particle size relationship:

Size (:m) 0-2 2-4 4-7 7-10 10-15 15-25 25-40
40-60 >60
Eff. (%) 10 25 45 70 85 95 97
98 100

Calculate the overall efficiency of this cyclone for the particle
distribution described above.
[ans. .74%]

2) Calculate the Cunningham correction factor for a particle with a
0.03 :m diameter in air at 1 atm pressure and 150EC. [12.1]

3) Assuming Stokes behaviour, calculate the terminal settling
velocity in standard air for the following particles: (a) diameter = 5
:m, specific gravity = 0.8; (b) diameter = 40 :m, specific gravity =
2.5. Check the result for part (b) using text equation 3.21 (Theodore
and Buonicore), and explain any differences in the results. Which
result is likely correct? [(a) 6.16 x 10-4 m/s].

4) For a gravitational settling chamber, determine the length
required to collect 50 :m diameter particles if the flow rate is 30,000
cfm (ft3/min), and the chamber depth is 15 ft, the chamber height is 5
ft, and the particle specific gravity is 2.5. Assume the air
temperature is 80EF. Good design practice calls for a bulk velocity of
less than 10 ft/s. Why, and does this design meet that requirement?
[about 110 ft ?].

5) An air stream contains particulates with density 1200 kg/m3,
with the following size distribution:

Size (:m) 0-4 4-10 10-20 20-40 40-80 >80
Mass (%) 3 10 30 40 15 2

Design a single cyclone to handle 20,000 cfm (at 250EF and 1
atm) of this air. The required efficiency must be between 75% and 80%,
and the maximum allowable pressure drop is 8 in. H2O. Estimate the cost
of this equipment. [no single "correct" solution; simply must meet
design criteria]
??

Bill Anderson

Prof. W.A. Anderson
Dept. of Chemical Engineering
University of Waterloo
Waterloo, ON N2L 3G1
Canada
(519)888-4567 Extension 5011
Fax: (519)746-4979
Email: wanderson@.uwaterloo.ca