A compressed air spherical tank having an inner diameter of 450 mm and a wall thickness of 7 mm is formed by welding. If the allowable shear stress is 40 MPa, the maximum permissible air pressure in the tank will be nearly

Concept:

In a thin spherical vessel, the hoop stress and longitudinal stresses are same and are given by

\({\sigma _{hoop}} = {\sigma _{longitudinal}} = \frac{{pd}}{{4t}}\)

The maximum stress is given by \(\tau = \frac{{\sigma - 0}}{2} = \frac{{pd}}{{8t}}\) 

Calculation:

Given d = 450 mm, t = 7 mm, τ = 40 MPa;

\( \Rightarrow 40 = \frac{{p\; \times \;450}}{{8\; \times \;7}}\)

⇒ p = 4.97 MPa

The nearest option is 5 MPa