Group case study on Pressure Vessel Safety.Basis of the presentation was The Great Molasses Flood of 1919.Includes solution of three mathematical problems,causes of pressure vessel failure,recommended shapes of vessels and conclusion of case study.

Published on: **Mar 4, 2016**

Published in:
Engineering

- 1. Pressure Vessel Safety Case study regarding pressure vessel safety covering causes of failure, safety factors , design consideration, types of stresses & their impacts.
- 2. Group Members Aamin Fahad Aziz Ali Hamza Muhammad Mubtasim Bin Tariq Syed Usama Mutahir Hadia Madni Muhammad Bilal Anjum
- 3. Contents Introduction to case study The Great Molasses Flood of 1919 Volume of Molasses (CSP 2.1) Why vessels are spherical & cylindrical? Mating of spherical and cylindrical parts Pressure to Elasticity ratio (CSP 2.7, CSP 2.8) Causes of Failure Methods of manufacturing pressure vessels Results and recommendations.
- 4. Introduction of Case Study Numerable accidents occurred in past because of pressure vessels failure. i. Rupture of Apollo oxygen tank in 1970 ii. Implosion of USS thresher in 1963 iii. Explosion of Russian submarine Kursk in 2001.
- 5. The Great Molasses Flood of 1919 The great molasses flood of 1919 15 January 1919, 6 story tall molasses tank exploded in Boston. Streets swamped with 12000 tons of molasses. 21 causalities and 150 injuries Boston’s North End
- 6. Volume of Molasses(CSP-1) Molasses is 44 % heavier than water Density of molasses in 1441 kg/m3 12000 tons of molasses are given. We have to calculate the volume of In Customary Units. 1 ton=2204.62 pounds Total mass = 12000 x 2204.62 = 2.64 x 107lbm 1441푘푔/푚3 = 90 lb/푓푡3 Volume = mass/density. V=2204.62 x 12000/90 = 293949 푓푡3 In metric units. Now 1 metric ton = 1000 kg Density = 1441 푘푔/푚3 Volume = Mass/Density = (12000 x 1000)/1441 Volume = 8327.55 m3 molasses .
- 7. Analysis Pressure Vessels Pressure Vessels are structures that are designed to contain or preclude a significant pressure. Types Generally Used Spherical Cylindrical
- 8. Why Spherical/Cylindrical? Other than spherical/Cylindrical flat vessels are possible. Lets compare them SPHERICAL/CYLINDRICAL Less crack propagation. Presence of membrane stresses. a.Axial Stress b.Hoop Stresses c.Radial Stresses. FLAT/SQUARE More Crack Propagation. Re-entrant corners are present. Cracks propagate from Stress concentrations which are present at these corners. Absence of membrane stresses.
- 9. Radial deformation in spheres is given by 푤 푡 = 푃 퐸 푅 푡 2 2 types of deformations in flat vessels I. Deformation due to stretching of sides II. Bending deflection of tube face 푤 푡 = 5푃 32퐸 퐻 푡 4 Where H~R The deflections due to the bending of the sides of rectangular tube are two orders of magnitude larger than the radial motion due to the extension of the walls of a circular cylinder. 푊푏푒푎푚 푊푐푦푙 ~ 퐻 푡 2 ≫ 1
- 10. Mating Analysis CYLINDERS Radial expansion per unit thickness 푊푐푦푙 푡 = 2−푣 푃 2퐸 푅 푡 SPHERES Radial expansion per unit thickness 푊푠푝ℎ 푡 = 1−푣 푃 2퐸 푅 푡 Membrane Stresses: 휎ℎ = 푃 푅 푡 휎푎 = 푃 푅 2푡 Two dimensional strain: ∈ℎ= 휎ℎ − 푣휎푎 퐸
- 11. Mating Analysis (Contd) If both Pressure and Radius are same then, comparing both equations (퐸푡)푐푦푙 (퐸푡)푠푝ℎ = 2 − 푣푐푦푙 1 − 푣푐푦푙 If materials are same then 푡푐푦푙 푡푠푝ℎ = 2 − 푣 1 − 푣 For a particular value of 푣, the cylinder should be thicker than sphere by a factor of almost 2.5. In order to overcome the bending effects of caused by mismatching of mates between cylinder and sphere, cylinders are tapered near the joints with locally increased thickness. Overcome Edge effects
- 12. 0.06 0.05 0.04 0.03 0.02 0.01 0 Pressure to Modulus Ratio VS. Hoop Strain 0.005 0.006 0.007 0.008 0.009 0.01 0.011 0.012 0.013 0.014 0.015 Pressure to Modulus Ratio VS. Hoop Strain Hoop Strain P/E
- 13. CS2.8 – Radial Deflection per Thickness VS. Pressure to Modulus Ratio Now if we were to determine the relationship between radial deflections per unit thickness ◦ and = Internal Radius = = 108.55 mm Thickness = t = 3mm So = (1309.23) With 1309.23 as a constant value for this case, we plot radial deflections per thickness against varying pressure to modulus ratio.
- 14. 70 60 50 40 30 20 10 0 Pressure to Modulus Ratio VS. Radial Deflection per unit thickness 0.01625 0.0195 0.02275 0.026 0.02925 0.0325 0.03575 0.039 0.04225 0.0455 0.04875 Pressure to Modulus Ratio VS. Radial Deflection per unit thickness P/E 흎/풕
- 15. Thank you