Radial Flexure of the PTV.

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, $r_o$, is proportional to the pressure, $p$:

$$\delta r_o = p \left[ \frac{(2-\sigma)r_i^2 r_o}{(r_o^2 - r_i^2)\kappa} \right] .$$ (3)

The quantity $r_i$ is the inner radius of the PTV while Poisson's ratio ($\sigma$) and the elastic modulus ($\kappa$) are material properties. Evaluating (3) using parameter values from Table 2 yields,

$$\delta r_o = p \left\{ \frac{1.7 \cdot (12 \mathrm{in})^2 \... ... \left(0.761 \mathrm{\mu in} \cdot \mathrm{psi}^{-1} \right) .$$ (4)

Hence, over the range $0 \longrightarrow 10$ kpsi the maximum radial flexure is only $\delta r_o \doteq 0.008$ in. Consequently, no visible distortion of the PTV is predicted.