# A thin cylinder of inner radius 500 mm and thickness 10 mm is subjected to an internal pressure of 5 MPa. The average hoop stress in MPa is

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A thin cylinder of inner radius 500 mm and thickness 10 mm is subjected to an internal pressure of 5 MPa. The average hoop stress in MPa is

1. 125
2. 250
3. 500
4. 1000

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Correct Answer - Option 2 : 250

Concept:

For thin cylindrical vessel:

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

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

Calculation:

Given:

r = 500 mm, d = 1000 mm, p =  5 MPa = 5 N/mm2, t = 10 mm

$\sigma_h=\frac{{pd}}{{2t}} = \frac{{5 \times 1000}}{{2 \times 10}} = 250\;N/m{m^2}$

For thin spherical vessel:

Hoop stress/Longitudinal stress:

${\sigma _h} = {\sigma _L} = \frac{{pd}}{{4t}}$