Question

If a thin cylinder is subjected to a fluid pressure of 0.2 N/mm² whose thickness is 5 mm and diameter is 20 mm. What is the magnitude of Hoop stress generated in it?
1. 0.2 N/mm²
2. 0.4 N/mm2
3. 1.4 N/mm2
4. 0.8 N/mm2

Answer 1

Correct Answer - Option 2 : 0.4 N/mm2

Concept

For thin cylindrical vessel:

Hoop stress, \({\sigma _h} = \frac{{pd}}{{2t}}\)

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

Volumetric strain, \({\epsilon_v} = \frac{{pd}}{{4tE}}\left( {5 - 4\mu } \right)\)

Calculation:

d = 20 mm, t = 5 mm, p = 0.2 N/mm²,

\({\sigma _h} = \frac{{pd}}{{2t}} = \frac{{0.2 \times 20}}{{2 \times 5}} = 0.4\ N/mm^2\)

 

For thin spherical vessel:

Hoop stress/Longitudinal stress:

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

Hoop strain/longitudinal strain:

\({\epsilon_L} = {\epsilon_h} = \frac{{pd}}{{4tE}}\left( {1 - \mu } \right)\)

Volumetric strain:

\({\epsilon_v} = 3{\epsilon_h} = \frac{{3pd}}{{4tE}}\left( {1 - \mu } \right)\)