Question

A sphrical pressure vessel of diameter 500 mm with 8 mm wall thickness is given a coating of lacquer which cracked when the strain reaches $1.5\times {10}^{-4}$ . Take $E=2.05\times {10}^{5}N/m{m}^2$. Poisson's ratio $\mu =\mathrm{0.30.}$ The integral pressure at which the lacquer cracked is MPa

• A. 2.81

Answer 1

The correct option is A 2.81
Let ${\sigma }_h$ be the hoop stress at which the maximum strain reaches the value, $\epsilon =1.5\times {10}^{-4}$

$\frac{{\sigma }_h}{E}(1-\mu )=\epsilon$

$\therefore {\sigma }_h=\frac{E\epsilon }{1-\mu }$

${\sigma }_h=\frac{2.05\times {10}^5\times 1.5\times {10}^{-4}}{1-0.30}=43.928N/m{m}^2$

Let p be the internal pressure to produce the above hoop stress

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

$\therefore p=\frac{4{\sigma }_{h}t}{d}=\frac{4\times 43.928\times 8}{500}=2.81N/m{m}^2$