A thick cylindrical pressure vessel of inner diameter $D_{i}$ and outer diameter $D_{o}$ is subjected to an internal fluid pressure of intensity $^{'} p^{'}$ . The variation of the circumferential tensile stress ' $p_{y}$ ' in the thickness of the shell will be

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Solution

The correct option is B
Variation of hoop stress $(f_{x})$ and radial pressure $(p_{x})$ can be obtained by using Lame's equation
i.e.,
$f_{r} - p_{r} = 2 A$ and $f_{r} + p_{r} + r \frac{d p_{r}}{d r} = 0$
$∴ f_{r} = \frac{B}{r^{2}} + A, p_{r} = \frac{B}{r^{2}} - A$
at $r = D_{i}$ we get $p_{r} = p$
$r = D_{o}$ we get $p_{r} = 0$
$∴ p_{r} = p (\frac{D_{o}^{2} - 4 r^{2}}{D_{o}^{2} - D_{1}^{2}}) (\frac{D_{1}^{2}}{4 r^{2}})$
Radial presssure distirbution is given by figure (b).

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