A cylindrical pressure vessel has internal diameter 1.2 m and plate thickness of 12 mm. Find out the maximum internal pressure it can sustain so that neither circumferential nor longitudinal nor radial stress exceed 140 MPa. Also find out the maximum internal pressure that a spherical pressure

Question

A cylindrical pressure vessel has internal diameter 1.2 m and plate thickness of 12 mm. Find out the maximum internal pressure it can sustain so that neither circumferential nor longitudinal nor radial stress exceed 140 MPa. Also find out the maximum internal pressure that a spherical pressure vessel with same external diameter and thickness can withstand.

Accepted Answer

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

[latex] \sigma_1=140=\frac{p(600)}{12} [/latex]

or p = 2.8 MPa

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

[latex] \sigma_2=\frac{p r}{2 t}=\frac{2.8 imes 600}{2 imes 12}=70 MPa [/latex]

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, [latex] \sigma_3=p=2.8 MPa [/latex].

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

[latex] 140=\frac{p(600)}{2(12)} [/latex]

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.

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

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