Solution to Problem 138 Pressure Vessel

$150 ~ \text{psi} = 150 ~ \dfrac{\text{lb}}{\text{in}^2} \cdot \left( \dfrac{12 ~ \text{in}}{1 ~ \text{ft}} \right)^2$

$150 ~ \text{psi} = 21,600 ~ \text{lb/ft}^2$
 

For longitudinal joint (tangential stress):
 

 

Consider 1 ft length
$F = 2T$

$pD = 2\sigma_t t$

$\sigma_t = \dfrac{pD}{2t}$

$\dfrac{33\,000}{t} = \dfrac{21\,600D}{2t}$

$D = 3.06 \, \text{ft} = 36.67 \, \text{in.}$
 

For girth joint (longitudinal stress):
 

 

$F = P$

$p (\frac{1}{4} \pi D^2) = \sigma_l (\pi Dt)$

$\sigma_l = \dfrac{pD}{4t}$

$\dfrac{16\,000}{t} = \dfrac{21\,600D}{4t}$

$D = 2.96 \, \text{ft} = 35.56 \, \text{in.}$
 

Use the smaller diameter, $D = 35.56 \, \text{in.}$           answer