Pressure Vessel

Lab 5 Pressure Vessel and Strain Transformation

Melissa Hitt Group 3 MAE 244 Chuanyu Feng November 30, 2005

Pressure Gage

I. Simple Schematic Strain Gage

Pressure Vessel Schematic

Ruler

Pressure Tube

II. Analysis of Results •

Table for Strain Reading

Strain Gage: R = 120 +/- .3 Strain Gage: Sg = 2.110 +/- .5% Internal Diameter of Vessel = 3.5 in Thickness = .0675 in

Gage 90

Gage 0

Gage -45

1

2

3

(με)

(με)

Channel No. Pressure (PSI) 0 20 40 60 80

0 38 77 110 148

0 8 18 27 35

Gage -45

Gage 67.5

Gage -22.5

Gage 45

Gage 90

4

5

6

7

8

(με)

(με)

(με)

(με)

(με)

(με)

0 21 46 68 90

-1 20 43 65 86

0 30 66 96 126

0 12 25 37 49

-1 21 43 64 87

0 35 72 105 140

Linearity Between Strain and Pressure 160 140

Strain (με)

120 100 80 60 40 20 0 -20 0

20

40

60

80

Pressure (PSI) Gage 90 Gage 67.5

Gage 0 Gage -22.5

Gage -45 Gage 45

Gage -45 Gage 90

100

Stresses and Strains •

Theoretical Data

σz = PD , σH = PD , εz = 1 (σz - υσH) , εH = 1 (σH - υσz) 4t 2t E E υ E Diameter Thickness

0.33 10*106 psi 3.5 in 0.0675in

Pressure (PSI) 0 20 40 60 80

Longitudinal Stress Strain (PSI) (in/in) 0 259.2593 518.5185 777.7778 1037.037 35.2593*10-6

•

Pressure (PSI) 0 20 40 60 80

Hoop Stress (PSI) 0 518.5185 1037.037 1555.556 2074.074

Strain (in/in)

0.0001732

Experimental Data with Comparison

Longitudinal

Experimental* 35*10-6

Analytical 35*10-6

Percent Difference 0

Hoop

148*10-6

173*10-6

14.45086705

*The experimental data is taken directly from the chart in the above section. The 0 degree and 90 degree gages were used for the experimental data. This is because the longitudinal strain is the strain running in the horizontal or zero degree path on the vessel, and the hoop strain is the strain running in the vertical or 90 degree path on the vessel.

III. Discussion •

Is linearity expected between the strain and the pressure? Yes. It is logical to think that if the pressure is going to go up in say for example a closed pop container then the strain on the surface of the container is going to go up. Considering the equations: σz = PD , σH = PD 4t 2t it can be see that the pressure is directly related to stress. Stress and strain are also directly proportional therefore the pressure and the strain are directly proportional. When the pressure rises the strain rises and when the pressure decreases the strain will decrease also.

•

Are the data linear? Yes.

•

Discuss the accuracy of the theory.

The theory is very accurate for thin walled pressure vessels. In predicting the longitudinal stress in this experiment there was a zero percent difference. In predicting the hoop stress there was a 14 percent difference which is not quite so good but there could have been a number of factors off. The experimenters could have read the wrong data or not waited until the readings had stabilized. There were two 90 degree gages used. They did not result in the same strain at the same pressure. For example at the 80 psi reading the first 90 degree gage read 148 με and the second 90 degree gage read 140 με. This is a 5% difference, and could seriously mess up the results when comparing to the theoretical results. Therefore, the conclusion is that the accuracy of the Thin Walled Pressure Vessel Theory is excellent.