A dumbbell-shaped pressure vessel of uniform wall thickness t is subjected to an internal pressure p. the ends are made of spherical shaped vessels of radius d, connected by a cylindrical vessel of diameter d at the middle as shown. Find the longitudinal stress. σ 1 at the centre of the cylindrical portion of the dumbbell-shaped pressure vessel.
1
\({\sigma _1} = \frac{{2pd}}{t}\)
2
\({\sigma _1} = \frac{{pd}}{t}\)
3
\({\sigma _1} = \frac{{pd}}{{2t}}\)
4
\({\sigma _1} = \frac{{pd}}{{4t}}\)