Question

A thick cylindrical pressure vessel of inner diameter $D_i$ and outer diameter $D_o$ is subjected to an internal fluid pressure of intensity ${}^{\prime }{p}^{\prime }$. The variation of the circumferential tensile stress '$p_y$' in the thickness of the shell will be

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Variation of hoop stress $\left(f_x\right)$ and radial pressure $\left(p_x\right)$ can be obtained by using Lame's equation
i.e.,
$f_r-p_r=2A$ and $f_r+p_r+r\frac{d{p}_r}{dr}=0$
$\therefore f_r=\frac{B}{r^2}+A,p_r=\frac{B}{r^2}-A$
at $r=D_i$ we get $p_r=p$
$r=D_o$ we get $p_r=0$
$\therefore p_r=p\left(\frac{D_o^2-4r^2}{D_o^2-D_1^2}\right)\left(\frac{D_1^2}{4r^2}\right)$
Radial presssure distirbution is given by figure (b).