$$z=\frac{L^2}{Dt}$$ $$For~z \leq 20$$ $$~~~~S_F = S_{flow}\frac {1-\frac{2}{3}(d/t)}{1-\frac{2}{3}(d/t)/M}$$ $$For~z > 20$$ $$~~~~S_F = S_{flow}(1-d/t)$$ $$\rm where: S_{flow}=1.1({SMYS})$$ $$M=\sqrt{1+0.8z}$$ $$ D =\rm outer~diameter$$ $$ d =\rm defect~depth$$ $$ t =\rm wall~thickness$$ $$ L =\rm defect~length$$

$$z=\frac{L^2}{Dt}$$ $$For~z \leq 50$$ $$~~~~M=\sqrt{1+0.6275z-0.003375z^2}$$ $$~~~~S_F = S_{flow}\frac {1-0.85(d/t)}{1-0.85(d/t)/M}$$ $$For~z > 50$$ $$~~~~M=0.032z+3.3$$ $$~~~~S_F = S_{flow}\frac {1-0.85(d/t)}{1-0.85(d/t)/M}$$ $$\rm where: S_{flow}={SMYS}+10ksi$$ $$ D =\rm outer~diameter$$ $$ d =\rm defect~depth$$ $$ t =\rm wall~thickness$$ $$ L =\rm defect~length$$

$$P_{sw} = ({MF})({SF})(P_f)$$ $$P_f = \frac{2tf_u\left(1-\frac {d}{t}\right)}{(D-t)\left(1-\left(\frac{d}{tQ}\right)\right)}$$ $$\rm where:$$ $$f_u=\rm {SMTS}$$ $$Q=\sqrt{1+0.31\left(\frac {l}{\sqrt{Dt}}\right)^2}$$ $$MF=\rm modeling~factor=0.9$$ $$SF = \rm safety~factor=0.72$$ $$ D =\rm outer~diameter$$ $$ d =\rm defect~depth$$ $$ t =\rm wall~thickness$$ $$ l =\rm defect~length$$

$$P_f = \frac{2tf_u\left(1-\frac {d}{t}\right)}{(D-t)\left(1-\left(\frac{d}{tM}\right)\right)}$$ $$\rm where:$$ $$f_u=\rm {SMTS}$$ $$M=\sqrt{1+0.805(z)}$$ $$z=\frac{L^2}{Dt}$$ $$MF=\rm modeling~factor=0.9$$ $$SF = \rm safety~factor=0.72$$ $$ D =\rm outer~diameter$$ $$ d =\rm defect~depth$$ $$ t =\rm wall~thickness$$ $$ l =\rm defect~length$$

$$\frac {\sigma_{AX}}{\sigma_{flow}} = \frac {\nu(\pi-\beta(1-\nu))}{\nu\pi+2(1-\nu)\sin(\beta)}$$ $$\rm where: \nu = 1 - \frac{d}{t}$$ $$\rm d = defect~depth$$ $$\rm t = wall~thickness$$ $$\rm \beta = \frac {c}{R} (in~radians)$$ $$\rm c = half~defect~(circumferential)~length$$ $$\rm R = pipe~radius$$ $$\rm \sigma_{AX} = flow~stress$$ $$\rm and~in~which~\sigma_{flow}~denotes~total~axis~stress$$

$$\frac {\sigma_{AX}}{\sigma_{flow}} = \frac {\nu}{1-(1-\nu)/f}$$ $$\rm where: \nu = 1 - \frac{d}{t}$$ $$\rm d = defect~depth$$ $$\rm t = wall~thickness$$ $$ f = \sqrt{1+\frac{(W/t)^2}{2}}$$ $$\rm W = circumferential~width~of~defect$$