INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR
Date of Examination: 16.09.2016
Time: 2 hours
Full Marks: 30
Mid-Autumn Semester, 2016-2017
3rd Year B.Tech.(Hons.)/Integrated M.Tech.
Sub. Name: Mechanical Operations
Subject No. - CH31 007
No. of Students - 87 Chemical Engineering
Instructions: 1. Attempt ALL questions. 2. Assume, if necessary, clearly stating them.
3. Write the answers of each question in one place. 4) Credit will be given for stepwise
calculations and neatness. 5) No queries will be entertained during examination.
I. The screen analysis shown in the table bellow applies to a sample of crushed quartz.
The density of the particle is 2650 kg/rrr', and the geometric constants are a = 2 and b =
3.5. For the material in the size range between 4.699 mm to 0.417 mrn, calculate (a) Aw,
in sq. mm/g, b) Nw, in particles/g and volume surface mean diameter D, in mrn.
[5J
Screen Analysis
Mesh
Screen
opening, mm
Mass fraction
retained
Av. Particle
dia., mm
Cumulative
fraction
passing
4
4.699
0.0000
-
1.0000
6
3.327
0.0251
4.013
0.9749
8
2.362
0.1250
2.845
0.8499
10
1.651
0.3207
2.007
0.5292
14
1.168
0.2570
1.409
0.2722
20
0.833
0.1590
1.001
0.1132
28
0.589
0.0538
0.711
0.0594
35
0.417
0.0210
0.503
0.0384
48
0.295
0.0102
0.356
0.0282
65
0.208
0.0077
0.252
0.0205
100
0.147
0.0058
0.178
0.0147
150
0.104
0.0041
0.126
0.0106
200
0.074
0.0031
0.089
0.0075
pan
-
0.0075
0.037
0.0000
P.T.O.
2. A crusher is in closed circuit with a screen, crushing 1000 tons of dry ore per day.
Screen analysis of crusher discharge, screen over flow and screen under flow are as
follows:
Mesh
28
35
48
Crusher discharge
cumulative %
57.6
72.8
78.9
Screen
OfF
cumulative %
7.8
27.4
39.8
Screen
cumulative
73.9
87.7
91.8
Calculate the circulating load of the crusher
U/F
%
[3]
3. Assuming Stoke's law, calculate the time required by a spherical glass beads (Dp =
0.98 rrun) to reach half of its terminal velocity when settling in a pool of stagnant water at
20°C. The density of the particle is 1600kglm3.
[4]
4. If crushing rolls, 102 cm diameter, are set so that the crushing surfaces are 1.2 em
apart and the angle of nip is 31°, what is the maximum size of particle which should be
fed to the rolls? If the actual capacity of the machine is 12% of the theoretical, calculate
the throughput in tons per hour when running at 100 rpm, if the working face of the rolls
is 41 cm long and the feed weighs 2355 kg/rrr'.
[3]
5. 1.28 g of a powder of particle density 2500 kg.m" are charged into the cell of an
apparatus for measurement of particle size and specific surface area by permeametry
method. The cylindrical cell has a diameter of 1.14 ern and the powder forms a bed of
depth 1 ern. Dry air of density 1.2 kg.m" and viscosity 18.4 x 10-6Pa.s, flows at a rate of
36 cm3.min-'through the powder (in a direction parallel to the axis of the cylindrical cell)
and producing a pressure difference of 100 mm of water across the bed. Assuming
laminar flow condition in the cell, determine the surface-volume mean diameter,
Reynolds number, and the specific surface of the powder sample.
[5]
6. (a) Summarize three different models for predicting the energy requirement associated
with particle size reduction. Over what size ranges might each model be most
appropriately applied?
(b) Describe six material properties that would influence selection of a crusher/mill type.
[(3+3) = 6]
7. The resistance F of a sphere of diameter x, due to its motion with velocity u through a
fluid of density p and viscosity p, varies with Reynolds number (Re) as given below:
2.0
2.5
3.0
3.5
4.0
1.05
0.63
0.441
0.3R5
0.39
Find the mass ofa sphere of 0.013 m diameter which falls with a steady velocity of 0.6
m.s-J in a large deep tank of water of density 1000 kg.rn" and viscosity 0.0015 Pa.s.[4]