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The equations for stresses in thin- and thick-wall cylinders can be found in many mechanics of materials references, and are summarized here, with a = inner radius, b = outer radius, r = radial position where stress is to be found, and t = wall thickness.

Notice that in thick-wall theory, the hoop stress varies with the radial position, while the stress is assumed to be constant in thin-wall theory. Comparing the substitution of a and b for r in the hoop stress thick-wall equation will convince you that stress is greater on the inner surface. The hoop stress variation in thick-walled vessels can be depicted as follows (the view shown corresponds to looking from above the pressure vessel):

By using the parameters given in the problem statement and the above formulae for hoop stress, we find that the maximum hoop stresses using the thin-wall and thick-wall approximations yield 3000 psi and 3571 psi, respectively. This corresponds to a 16% difference which tells us that the thin wall theory might not be adequate for this geometry. Thin-wall theory actually gives good results when b/a ratio is less than 1.10, and that is not the case here.

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