Question

If X is the stress on a spherical thin-walled pressure vessel and Y is the hoop stress on a cylindrical thin-walled pressure vessel; how are X and Y related?
1. X = Y
2. X = Y/2
3. X = 2Y
4. X = Y + constant

Answer 1

Correct Answer - Option 2 : X = Y/2

Explanation:

For thin cylinder:

Longitudinal stress: \({\sigma _L} = \frac{{pd}}{{4t}}\)

Hoop stress: \({\sigma _h} = \frac{{pd}}{{2t}} = 2{\sigma _L}\) = Y

For thin spherical vessel:

For a thin spherical pressure vessel, both longitudinal and hoop stress is the same and given as

\({\sigma _h} = \frac{{pd}}{{4t}} = {\sigma _L}\) = X

From the above expressions,

\(X =\frac{pd}{4t}\) and \(Y =\frac{pd}{2t}\)

Hence, X = Y/2