Lab 6 Pressure Vessel
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Pressure Vessel Lab Nick Leach Group 3a MAE 244, Sec. 2, Dr. Feng December 1, 2005
Schematic:
Analysis of Results: •
Data Reduction:
The equations mainly used in this lab are: σz = PD , σh = PD , εz = 1 (σz – υ*σHh) , εh = 1 (σh – υ*σz) , 4t 2t E E where σz is the longitudinal stress, σh is the hoop stress, εz is the longitudinal strain, εh is the hoop strain, P is the load, D is the diameter of the vessel, t is the thickness of the vessel walls, E is the modulus of elasticity for the material of the vessel, and υ is the value of Poisson’s Ratio for the material. •
Pressure 0
Comparisons: Gage 90
Gage 0
Gage -45
1 (με)
2 (με)
3 (με)
0
0
Gage -45 4
Gage 67.5 5
Gage -22.5 6
Gage 45 7
Gage 90 8
(με)
(με)
(με)
(με)
(με)
0
0
0
0
0
0
30
12
22
35
20
38
8
21
21
40
77
18
46
44
66
25
44
72
60
110
27
68
66
96
37
65
105
80
148
35
90
87
126
49
88
140
Table 1: Tabulated Experimental Data for Strain Gages Strain Gage Sg R Kt Material E G υ Vessel Diameter Thickness
2.110+-0.5% 120+-0.3% Ω 0.2+-0.2% 10.0 (10^6) psi 3.8 (10^6) psi 0.33 3.5" 0.0675"
Table 2: Equipment Properties
Strain v. Pressure 160 140
Strain (με)
120 100 80 60 40 20 0 0
20
40
60
80
Pressure (psi) Gage 90
Gage 0
Gage -45
Gage -45
Gage 67.5
Gage -22.5
Gage 45
Gage 90
Graph 1: Strain v. Pressure
100
Discussion: •
Conclusions: As you can see by the graph, the data is perfectly linear for each loading, as
was expected. Notice that the slopes are different from each other except for the gage at 90 degrees and the one at 45 degrees. This is simply because of the 45o turn of the elements and the layout of the rosette. The theory of thin-walled pressure vessels is very accurate in that it can give a strain measurement to a very specific value at any pressure within the boundaries of the material, and do it at any arbitrary angle. I think that if the walls of the vessel aren’t t<
Longitudinal Experimental Value (με) 35 Analytical Value (με) 35 Percent Diff. (%) 0
Hoop 148 173 14.45
Table 3: Experimental v. Analytical Values and Percent Diff. •
Limitations and Experimental Error: Some assumptions are made that control the accuracy of the experiment. First of all, we have to assume that the vessel is homogenously manufactured: that the material is exactly the same throughout. This is important because if the material is made wrong, then it could give faulty results at one or more of the gages. Second, we have to assume that the laboratory is controlled- that the temperature is a constant 24o Celsius and that there are no large magnetic fields passing through the equipment.
Schematic:
Analysis of Results: •
Data Reduction:
The equations mainly used in this lab are: σz = PD , σh = PD , εz = 1 (σz – υ*σHh) , εh = 1 (σh – υ*σz) , 4t 2t E E where σz is the longitudinal stress, σh is the hoop stress, εz is the longitudinal strain, εh is the hoop strain, P is the load, D is the diameter of the vessel, t is the thickness of the vessel walls, E is the modulus of elasticity for the material of the vessel, and υ is the value of Poisson’s Ratio for the material. •
Pressure 0
Comparisons: Gage 90
Gage 0
Gage -45
1 (με)
2 (με)
3 (με)
0
0
Gage -45 4
Gage 67.5 5
Gage -22.5 6
Gage 45 7
Gage 90 8
(με)
(με)
(με)
(με)
(με)
0
0
0
0
0
0
30
12
22
35
20
38
8
21
21
40
77
18
46
44
66
25
44
72
60
110
27
68
66
96
37
65
105
80
148
35
90
87
126
49
88
140
Table 1: Tabulated Experimental Data for Strain Gages Strain Gage Sg R Kt Material E G υ Vessel Diameter Thickness
2.110+-0.5% 120+-0.3% Ω 0.2+-0.2% 10.0 (10^6) psi 3.8 (10^6) psi 0.33 3.5" 0.0675"
Table 2: Equipment Properties
Strain v. Pressure 160 140
Strain (με)
120 100 80 60 40 20 0 0
20
40
60
80
Pressure (psi) Gage 90
Gage 0
Gage -45
Gage -45
Gage 67.5
Gage -22.5
Gage 45
Gage 90
Graph 1: Strain v. Pressure
100
Discussion: •
Conclusions: As you can see by the graph, the data is perfectly linear for each loading, as
was expected. Notice that the slopes are different from each other except for the gage at 90 degrees and the one at 45 degrees. This is simply because of the 45o turn of the elements and the layout of the rosette. The theory of thin-walled pressure vessels is very accurate in that it can give a strain measurement to a very specific value at any pressure within the boundaries of the material, and do it at any arbitrary angle. I think that if the walls of the vessel aren’t t<
Longitudinal Experimental Value (με) 35 Analytical Value (με) 35 Percent Diff. (%) 0
Hoop 148 173 14.45
Table 3: Experimental v. Analytical Values and Percent Diff. •
Limitations and Experimental Error: Some assumptions are made that control the accuracy of the experiment. First of all, we have to assume that the vessel is homogenously manufactured: that the material is exactly the same throughout. This is important because if the material is made wrong, then it could give faulty results at one or more of the gages. Second, we have to assume that the laboratory is controlled- that the temperature is a constant 24o Celsius and that there are no large magnetic fields passing through the equipment.
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