Question 3.7: A cylindrical pressure vessel has internal diameter 1.2 m an...

Before we try to solve, let us accept that the problem is too simple. Still, we have included the problem to give you some important practical feeling about pressure vessels. As we know that circumferential stress is the significant stress, we can straightway write

\sigma_1=140=\frac{p(600)}{12}

or         p = 2.8 MPa

This is the required pressure for cylindrical pressure vessel. The corresponding value of \sigma_2 , longitudinal stress is

\sigma_2=\frac{p r}{2 t}=\frac{2.8 \times 600}{2 \times 12}=70  MPa

As the pressure vessel is thin, radial stress as shown in Figure 3.13 is very small and equal to internal pressure, p. Therefore radial stress, \sigma_3=p=2.8  MPa .

For the general expression of radial stress in thick-walled cylinders, refer to Section 15.3. Now it is time to compare \sigma_1, \sigma_2 \text { and } \sigma_3 . It is clearly evident that for any value of pressure, \sigma_1 \text { or } \sigma_2 \gg \sigma_3 . So, we can reasonably neglect \sigma_3 from practical point of view. If we consider a spherical pressure vessel with similar diameter and thickness, requisite value of maximum pressure becomes

140=\frac{p(600)}{2(12)}

or      p = 5.6 MPa

So, you can easily see that the spherical vessel can withstand higher pressure than cylindrical pressure vessel. This generates a simple question: Why do we not go for spherical vessel always? The answer is simple. In case of spherical vessel, complicated fabrication methods are adopted, which often makes it too costly to choose.