The outer radius of the vessel will expand slightly as the PTV is pressurized. Roark (page 638, Case no. 1b) shows that the change in outer radius, , is proportional to the pressure, :
The quantity is the inner radius of the PTV while Poisson's ratio () and the elastic modulus () are material properties. Evaluating (3) using parameter values from Table 2 yields, Hence, over the range kpsi the maximum radial flexure is only in. Consequently, no visible distortion of the PTV is predicted.