Pressure Loading of Thin-walled Spherical Vessel

Pressure Loading of thin-walled Spherical Vessel formulas
$\sigma_{sph} \;=\; \dfrac{ p \cdot r }{ 2 \cdot t }$ $R \;=\; \dfrac{ p \cdot r^2 \cdot \left( 1 - v \right) }{ 2 \cdot E \cdot t }$ $V \;=\; \dfrac{ 2 \cdot p \cdot \pi \cdot r^4 \cdot \left( 1 - v \right) }{ E \cdot t }$
Symbol	English	Metric
$\sigma_{sph}$ (Greek symbol sigma) = stress	$lbf\;/\;in^2$	$Pa$
$p$ = uniform internal pressure	$lbf\;/\;in^2$	$Pa$
$r$ = radius	$in$	$mm$
$t$ = thickness	$in$	$mm$
$\mu$ (Greek symbol mu) = Poisson's ratio	$dimensionless$	$dimensionless$
$E$ = modulus of elasticity	$lbf\;/\;in^2$	$Pa$
$R$ = increase in radius	$in$	$mm$
$V$ = increase in volume	$in^3$	$mm^3$