Reference no: EM132842204
UTS 49316 Material Handling - University of Technology Sydney
Question 1. it is necessary to design a mass-flow storage silo for a solid product of mean bulk density 835 + Q kg/m3. The average hold-up time in the silo is 48 hours and table 1 gives the relevant time-consolidated test results from Jenike Shear cell.
a) Sketch the family of yield loci for the results obtained from the experiment (Mohr's circles). And find the
b) Use the Mohr's circle to determine the internal angle of friction θ, the maximum principal plane stress σ1 and the unconfined yield stress σc for each yield loci.
c) Tabulate the maximum principal plane stress σ1 and the unconfined yield stress σc for each yield loci obtained. Use the data to sketch the flow function (FFM) plot (to determine the CAS).
d) The effective angle of internal friction δ can be found graphically by connecting the end=points of the individual locus by best straight line that passes through origin (check slide 111 lecture 2).
e) Using Jenike shear cell (Wall friction measurements) to measure the angle of wall friction δw.
f) Follow the steps in the design example (Lecture 3) to find the minimum hopper outlet:
1- for symmetrical outlet. And 2- for circular outlet.
Table 1. The time-consolidated test results from Jenike Shear cell
|
Test
|
1
|
2
|
3
|
|
|
Normal stress
(kN/m2)
|
Shear stress
(kN/m2)
|
Normal stress
(kN/m2)
|
Shear stress
(kN/m2)
|
Normal stress
(kN/m2)
|
Shear stress
(kN/m2)
|
|
3.11
|
4.66
|
1.74
|
2.61
|
1.37
|
1.8
|
|
6.22
|
6.84
|
2.98
|
3.36
|
1.99
|
2.11
|
|
8.08
|
8.08
|
4.35
|
4.23
|
2.49
|
2.43
|
|
10.57
|
9.64
|
6.72
|
5.47
|
3.11
|
2.74
|
|
13.37
|
11.19
|
|
|
3.86
|
3.11
|
|
Wall Friction Measurements
|
|
|
1
|
2
|
|
Normal
Force (kPa)
|
Shear Force
(kPa)
|
Normal
Force (kPa)
|
Shear Force
(kPa)
|
|
2
|
0.85
|
4
|
1.67
|
Question 2. Using the design data in table 2 to calculate the circular outlet minimum dimensions:
|
Material
|
Angle of internal
friction (δ)
|
Powder- friction
wall angle (δw)
|
Density, ρ
(kg/m3)
|
CAS
(kPa)
|
|
Spray-dried powder
|
30
|
25
|
976 + Q
|
0.92 + (P/16)
|
|
Quartz
|
40
|
23
|
834 + Q
|
1.6 + (P/16)
|
|
Zinc oxide
|
50
|
17
|
564 + Q
|
2.76 + (P/16)
|
Question 3. Consider the determination of a hopper geometry with the data obtained by Jenike shear testing has determined the following characteristics given below. The hopper to be designed is conical:
1- effective angle of internal friction (δ) = 60°,
2- kinematic angle of wall friction on mild steel, ((δw)) = 20°
|
Flow Property
|
Equation
|
|
Instantaneous Flow Function
|
σc = ((0.25 + Q/1000))σ1 + 1.4
|
|
Time Flow Function (2 Days)
|
σct = ((0.36 + (P/100))σ1 + 2.15
|
|
Bulk Density Variation
|
ρ = (619 + Q)(σ1/6.33)0.076 |
Determine the following:
a) The hopper half angle (θ) which will give mass flow,
b) The minimum diameter (Bmin) of the hopper outlet to ensure the flow of powder.
c) The discharge rate (consider dp > 500 μm).
Question 4. A large, welded steel silo 7.15+ (P/3) m in diameter and 11.75 + (Q/30) m high is to be built to store wheat. The silo has a central discharge on a flat bottom. Estimate the pressure of the wall at the bottom of the silo.
The angle of the wall friction is φ ' = 28º.