Pick up the correct statement from the following: A. Hoop strain of the walls of a cylinder due to liquid is $$\frac{{{\text{pd}}}}{{2{\text{tE}}}}\left[ {1 – \frac{1}{{2{\text{m}}}}} \right]$$ B. Longitudinal strain in the walls of a cylinder due to liquid is $$\frac{{{\text{pd}}}}{{2{\text{tE}}}}\left[ {\frac{1}{2} – \frac{1}{{\text{m}}}} \right]$$ C. Volumetric change in the cylinder due to liquid is $$\frac{{{\text{pd}}}}{{2{\text{tE}}}}\left[ {\frac{5}{2} – \frac{2}{{\text{m}}}} \right]$$ D. All the above

”Hoop
$$” option2=”Longitudinal strain in the walls of a cylinder due to liquid is $$\frac{{{\text{pd}}}}{{2{\text{tE}}}}\left[ {\frac{1}{2} – \frac{1}{{\text{m}}}} \right]$$” option3=”Volumetric change in the cylinder due to liquid is $$\frac{{{\text{pd}}}}{{2{\text{tE}}}}\left[ {\frac{5}{2} – \frac{2}{{\text{m}}}} \right]$$” option4=”All the above” correct=”option4″]

The correct answer is D. All the above.

The hoop strain of the walls of a cylinder due to liquid is given by:

$$\varepsilon_h = \frac{p d}{2 t E} \left[ 1 – \frac{1}{2 m} \right]$$

where:

  • $p$ is the pressure of the liquid
  • $d$ is the diameter of the cylinder
  • $t$ is the thickness of the cylinder
  • $E$ is the Young’s modulus of the material of the cylinder
  • $m$ is the Poisson’s ratio of the material of the cylinder

The longitudinal strain in the walls of a cylinder due to liquid is given by:

$$\varepsilon_l = \frac{p d}{2 t E} \left[ \frac{1}{2} – \frac{1}{m} \right]$$

The volumetric change in the cylinder due to liquid is given by:

$$\Delta V = \frac{p d^2}{2 t E} \left[ \frac{5}{2} – \frac{2}{m} \right]$$

Therefore, all the statements in the question are correct.

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