Question

Two closed thin vessels, one cylindrical and other spherical with an equal internal diameter and wall thickness are subjected to equal internal pressure. The ratio of hoop stress in the cylindrical vessel to that of the spherical vessel is

1. 4
2. 2
3. 1
4. 0.5

Answer 1

Correct Answer - Option 2 : 2

Concept:

For cylindrical pressure vessel:

Hoop stress is given by:

\({σ _{hoop}} = \frac{{Pd}}{{2t}}\)

Longitudinal stress is given by:

\({σ _{long}} = \frac{{Pd}}{{4t}}\)

For spherical pressure vessel, hoop stress and longitudinal stress is equal:

σhoop = σlong =  \(\frac{{{{Pd}}}}{{4{{t}}}}\)

Calculation:

Given:

d_c = d_s, t_c = t_s, P_c = P_s

\(\frac{{{{\left( {{{\rm{\sigma }}_{\rm{h}}}} \right)}_{{\rm{Cylindrical\;}}}}}}{{{{\left( {{{\rm{\sigma }}_{\rm{h}}}} \right)}_{{\rm{spherical}}}}}} = \frac{{{{\left( {\frac{{{\rm{Pd}}}}{{2{\rm{t}}}}} \right)}_{{\rm{cyl}}}}}}{{{{\left( {\frac{{{\rm{Pd}}}}{{4{\rm{t}}}}} \right)}_{{\rm{sph}}}}}} = \frac{{{{\rm{P}}_{\rm{c}}}{{\rm{d}}_{\rm{c}}}}}{{2{{\rm{t}}_{\rm{c}}}}} \times \frac{{4{{\rm{t}}_{\rm{s}}}}}{{{{\rm{P}}_{\rm{s}}}{{\rm{d}}_{\rm{s}}}}} = 2\)

∴ the ratio of hoop stress in the cylindrical vessel to that of the spherical vessel is 2.