Thin-Walled Pressure Vessels

Abstract

A thin-walled pressure vessel is one in which the skin of the vessel has a thickness that is much smaller than the overall size of the vessel, and the vessel is subjected to internal pressure that is much greater than the exterior air pressure.

Appendix: Solutions

• 13.3.1 Show that Eq. (13.1) is correct.

Solution

• 13.3.2 Determine the strains in a thin-walled sphere under internal pressure p in terms of the other sphere properties.

Solution

$$\begin{aligned} \sigma_{1} & = \sigma_{2} = \frac{pr}{2t} \\ \varepsilon_{1} & = \frac{1}{E}\left( {\sigma_{1} - \nu \sigma_{2} } \right) = \frac{1}{E}\frac{pr}{2t}\left( {1 - \nu } \right) \\ \varepsilon_{2} & = \varepsilon_{1} \\ \end{aligned}$$

• 13.3.3 Show that Eq. (13.2) is correct

Solution

• 13.3.4 Show that Eq. (13.3) is correct

See the above-mentioned summation of forces.

• 13.3.5 Basketballs used by men are generally larger in diameter than those used by women. If the balls are made of the same material and have the same internal pressure, what is the ratio of the thickness of a men’s ball to that of the women’s ball if the stress is to be the same in both balls?

Solution

$$\sigma_{1} = \sigma_{2} = \frac{pr}{2t}\quad \Rightarrow \frac{p}{2\sigma } = \frac{{t_{M} }}{{r_{M} }} = \frac{{t_{W} }}{{r_{W} }}\quad \Rightarrow \frac{{t_{M} }}{{t_{W} }} = \frac{{r_{M} }}{{r_{W} }}$$