Question

The ratio of circumferential stress to the longitudinal stress in the walls of a cylindrical shell, due to flowing liquid, is

• A. $\frac{1}{2}$
• B. 1
• C. 1.5
• D. 2

Answer 1

The correct option is D 2

Circumferential stress/hoop-stress $\left({\sigma }_h\right)$:


${\sigma }_h=\frac{pd}{2t}$
Longitudinal stress $\left({\sigma }_l\right)$:

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

$\frac{{\sigma }_h}{{\sigma }_l}=\left(\frac{pd}{2t}\right)\times \left(\frac{4t}{pd}\right)=2$
Note : Hoop strain $\left({ϵ}_h\right):$

${ϵ}_h={\sigma }_h+\mu {\sigma }_l$

${ϵ}_h=\frac{pd}{4tE}(2-\mu )$

Longitudinal strain $\left({ϵ}_l\right):$

${ϵ}_l={\sigma }_l+\mu {\sigma }_h$

${ϵ}_l=\frac{pd}{4tE}(1-2\mu )$

where
$\mu =Poisso{n}^{\prime }sratio$

Volumetric strain $\left({ϵ}_v\right):$
${ϵ}_v={ϵ}_l+2{ϵ}_h$

$=\frac{pd}{4tE}(1-2\mu +4-2\mu )$

${ϵ}_v=\frac{pd}{4tE}(5-4\mu )$