Chapter 8, Problem 8.2.1P

A spherical balloon is filled with a gas. The outer diameter of the balloon is 20 in. and the thickness is 0,012 in. Calculate the maximum permissible pressure in the balloon if the allowable tensile stress and the allowable shear stress in the balloon are 1 ksi and 0.3 ksi, respectively.

To determine

Maximum permissible pressure in the balloon.

Answer to Problem 8.2.1P

Maximum permissible pressure is $p_{\max }=1.442\text{ psi}$

Explanation of Solution

Given Information:

Outer diameter $D=20\text{ in}$

Thickness $t=0.012\text{ in}$

Tensile stress $\sigma =1\text{ ksi}$

Shear stress $\tau =0.3\text{ ksi}$

We know for inner diameter $d=D-2t=20-2\times 0.012=19.976\text{ in}$ ,

Tensile stress,

  $\begin{array}{l}\sigma =\frac{pr}{2t}\\ \sigma =\frac{p\times d/2}{2t}\\ 1000=\frac{p\times 19.976/2}{2\times 0.012}\\ p=2.403\text{ psi}\end{array}$

Shear stress,

  $\begin{array}{l}\tau =\frac{pr}{4t}\\ \tau =\frac{p\times d/2}{4t}\\ 0.3\times 1000=\frac{p\times 19.976/2}{4\times 0.012}\\ p=1.442\text{ psi}\end{array}$

From above we can see that the maximum permissible pressure is $p_{\max }=1.442\text{ psi}$

Conclusion:

Hence we get,

Maximum permissible pressure is $p_{\max }=1.442\text{ psi}$